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New Strong Line Abundance Diagnostics for H ii Regions: Effects of κ-Distributed Electron Energies and New Atomic Data Michael A. Dopita 123 , Ralph S. Sutherland 1 , David C. Nicholls 1 , Lisa J. Kewley 13 & Fr´ ed´ eric P. A. Vogt 1 [email protected] Abstract Recently, Nicholls et al. (2012), inspired by in situ observations of solar sys- tem astrophysical plasmas, suggested that the electrons in H ii regions are charac- terised by a κ-distribution of electron energies rather than by a simple Maxwell- Boltzmann distribution. Here we have collected together the new atomic data within a modified photoionisation code to explore the effects of both the new atomic data and the κ-distribution on the strong-line techniques used to de- termine chemical abundances in H ii regions. By comparing the recombination temperatures (T rec ) with the forbidden line temperatures (T FL ) we conclude that κ 20. While representing only a mild deviation from equilibrium, this is suffi- cient to strongly influence abundances determined using methods which depend on measurements of the electron temperature from forbidden lines. We present a number of new emission line ratio diagnostics which cleanly separate the two parameters determining the optical spectrum of H ii regions - the ionisation pa- rameter q or U and the chemical abundance; 12+log(O/H). An automated code to extract these parameters is presented. Using the homogeneous dataset from van Zee et al. (1998), we find self-consistent results between all these different diagnostics. The systematic errors between different line ratio diagnostics are much smaller than was found in the earlier strong line work. Overall the effect of the κ-distribution on the strong line abundances derived solely on the basis of theoretical models is rather small. Subject headings: physical data and processes: atomic processes, plasmas, atomic data – H ii regions —ISM: H ii regions, abundances 1 Research School of Astronomy and Astrophysics, Australian National University, Cotter Rd., Weston ACT 2611, Australia 2 Astronomy Department, King Abdulaziz University, P.O. Box 80203, Jeddah, Saudi Arabia 3 Institute for Astronomy, University of Hawaii, 2680, Woodlawn Drive, Honolulu, HI 96822 arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

Transcript of arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

Page 1: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

New Strong Line Abundance Diagnostics for H ii Regions: Effects

of κ-Distributed Electron Energies and New Atomic Data

Michael A. Dopita123, Ralph S. Sutherland1, David C. Nicholls1, Lisa J. Kewley13 &

Frederic P. A. Vogt1

[email protected]

Abstract

Recently, Nicholls et al. (2012), inspired by in situ observations of solar sys-

tem astrophysical plasmas, suggested that the electrons in H ii regions are charac-

terised by a κ-distribution of electron energies rather than by a simple Maxwell-

Boltzmann distribution. Here we have collected together the new atomic data

within a modified photoionisation code to explore the effects of both the new

atomic data and the κ-distribution on the strong-line techniques used to de-

termine chemical abundances in H ii regions. By comparing the recombination

temperatures (Trec) with the forbidden line temperatures (TFL) we conclude that

κ ∼ 20. While representing only a mild deviation from equilibrium, this is suffi-

cient to strongly influence abundances determined using methods which depend

on measurements of the electron temperature from forbidden lines. We present

a number of new emission line ratio diagnostics which cleanly separate the two

parameters determining the optical spectrum of H ii regions - the ionisation pa-

rameter q or U and the chemical abundance; 12+log(O/H). An automated code

to extract these parameters is presented. Using the homogeneous dataset from

van Zee et al. (1998), we find self-consistent results between all these different

diagnostics. The systematic errors between different line ratio diagnostics are

much smaller than was found in the earlier strong line work. Overall the effect

of the κ-distribution on the strong line abundances derived solely on the basis of

theoretical models is rather small.

Subject headings: physical data and processes: atomic processes, plasmas, atomic

data – H ii regions —ISM: H ii regions, abundances

1Research School of Astronomy and Astrophysics, Australian National University, Cotter Rd., Weston

ACT 2611, Australia

2Astronomy Department, King Abdulaziz University, P.O. Box 80203, Jeddah, Saudi Arabia

3Institute for Astronomy, University of Hawaii, 2680, Woodlawn Drive, Honolulu, HI 96822

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1. Introduction

Much of what we know - or believe we understand - about the chemical evolution history

of the Universe depends upon the interpretation of the strong emission lines originating

from H ii regions in distant galaxies. These emission lines enable us to investigate the

metallicity evolution of the Universe as a whole (Nagamine et al. 2001; De Lucia, Kauffmann,

& White 2004; Kobayashi, Springel, & White 2007; Yuan, Kewley, & Richard 2013). We

may also measure the mass-metallicity relationship of disk galaxies (see Kewley & Ellison

(2008) and references therein), understand how chemical abundance gradients are formed

and maintained (Bothun et al. 1984; Wyse & Silk 1985; Skillman, Kennicutt & Hodge 1989;

Vila-Costas & Edmunds 1992; Zaritsky, Kennicutt & Huchra 1994; van Zee et al. 1998) and

discover how abundance gradients can be removed in galaxy interactions (Kewley et al. 2010;

Rupke, Kewley & Chien 2010; Torrey et al. 2012; Rich et al. 2012). Chemical abundances

also encode information about the history of star formation, mass infall, and radial mixing

driven by viscous processes in galactic disks.

The “classical” technique to derive chemical abundances first uses the observed tempera-

ture, Te, derived from temperature sensitive line ratios such as [O III] λ4363/ [O III] λ5007in

combination with the ratio of a strong forbidden line of the element of interest to a Balmer

line of hydrogen to estimate the abundance of the observed ion of a given atomic species. For

those ions which do not produce an observable line in the optical, we estimate an ionisation

correction factor (ICF) based upon theory to account for the abundance of the unobserved

ions of the same atomic species. This Te+ ICF technique has been very extensively used over

the past 50 years since it was first devised by Aller & Liller (1959) and further developed by

Peimbert (1967) and Peimbert & Costero (1969).

Later on, strong line techniques were developed which simply rely on the ratio of for-

bidden lines to the hydrogen recombination lines, a natural enough approach if we believe

that such ratios encode information about the relative abundance of the ion considered

compared to hydrogen. The most commonly used ratios are often referred to by their short-

hand contractions; R2 =[O II] λλ3726,9/Hβ , R3 =[O III] λ5007/Hβ , R23 = R2 + R3

(Pagel et al. 1979), and similar ratios involving S, for example S23 = ([S II] λλ6717,31 +

[S III] λλ9069,9532)/Hβ (Diaz, & Perez-Montero 2000; Oey et al. 2002). The abundance

calibration for these ratios may either be based purely on photoionisation models, or on an

empirical calibration based upon alignment of the abundance scale to objects for which the

Te+ ICF technique has been used. Strong line techniques which depend on ratios involving

hydrogen recombination lines suffer from a fundamental ambiguity, in that these line ratios

decreases as both the low- and high- abundance ends, requiring some other technique to

resolve which “branch” the observed H ii region lies.

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Despite the best efforts of theoreticians, the degree of scatter among the different strong

emission line diagnostics remains alarming (e.g. Kewley & Dopita (2002); Kewley & Elli-

son (2008); Lopez-Sanchez et al. (2012)), and this scatter between the various strong line

techniques is strongly dependent on the approach used to estimate abundances from such ra-

tios. Some rely entirely upon the construction of theoretical H ii region models using stellar

model atmospheres and photoionisation codes (McGaugh 1991; Dopita et al. 2000). Others

seek to calibrate R23 or S23 in terms of abundances derived from objects for which there

are direct measurements of electron temperature Te from temperature sensitive line ratios

such as [O III] λ4363/[O III] λ5007. This method, was pioneered by Pagel et al. (1979) and

Alloin et al. (1979). This approach was used by Diaz, & Perez-Montero (2000), and has been

investigated in great detail in a series of papers by Pilyugin and his collaborators (Pilyugin

& Thuan 2005; Pilyugin & Mattsson 2011a) culminating in the “counterpart” method of

Pilyugin et al. (2012). A slightly different approach was used by van Zee et al. (1998), who

computed the oxygen abundances with the McGaugh (1991) method, using the N II line

to distinguish between the high- and low- abundance branches, and used this to propose a

calibration of N II/Hα. This is especially useful in the “turnover region” between the high-

and low- abundance branches.

In addition to the uncertainties depending on whether a given H ii region lies on the

high- or low- abundance branch, and those associated with the theoretical or observational

calibrations, considerable uncertainty is introduced into the derived strong line abundances

in those cases where the ionisation parameter is not explicitly solved for as a separate variable

(Pagel et al. 1979; Alloin et al. 1979; Zaritsky, Kennicutt & Huchra 1994; Pettini & Pagel

2004). The first to properly account for the effect of the ionisation parameter were Evans &

Dopita (1985, 1986), followed by McGaugh (1991). Although many bright H ii regions are

observed to have similar ionisation parameters, the observed scatter in U or q introduces

significant error into the abundance estimates.

Even when all of these effects are accounted for, there remains a significant offset between

those strong line techniques based purely upon photoionisation models (McGaugh 1991;

Kewley & Dopita 2002; Kobulnicky & Kewley 2004), and those based upon an empirical

alignment of the strong line intensities to abundances derived in objects for which Te has

been directly estimated (Pilyugin 2001a,b; Bresolin, Garnett & Kennicutt 2004; Pilyugin &

Thuan 2005; Pilyugin et al. 2012). The offset can be large, amounting to 0.3-0.5 dex, in

the sense that the strong-line abundances estimated from a Te abundance calibration are

systematically lower than those estimated from models. This is clearly highlighted in Lopez-

Sanchez et al. (2012). The cause of this offset is the same as the systematic difference seen

between abundances derived from model-based strong line techniques, and those obtained

by the traditional method of using the Te+ ICF technique.

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Three possibilities have been advanced to explain the offset in abundances between the

strong line and the Te+ ICF techniques:

• The models predicting the strong lines not deliver the correct electron temperature

either because they do not consider all the necessary physics, or because the physical

data they use is incorrect or incomplete.

• Fluctuations or gradients in the electron temperature systematically bias the estimate

of the temperature derived from line ratios such as [O III] λ4363/ [O III] λ5007 (Peim-

bert & Costero 1969).

• The measured electron temperature suffers from systematic errors relating to the choice

of the input atomic data used to derive it. The size of such errors was recently quantified

by Nicholls et al. (2013).

In order to eliminate the possibility that the strong line techniques have some systematic

error, Lopez-Sanchez et al. (2012) subjected a set of photoionisation models from the MAP-

PINGS code (Sutherland & Dopita 1993; Allen et al. 2008) to a double-blind derivation of

the abundances using the Te+ICF technique. This demonstrated that, for those species for

which the optical line emission arises principally in the low-ionisation zone of the H ii region,

N, S and Cl, the abundances input into the models could be recovered through the Te+ICF

analysis. However, for those species arising principally in the high-ionisation zone of the

H ii region - O, Ne and Ar - a systematic shift of 0.2-0.3 dex is found. This is in the same

sense as the offset observed for real H ii regions, the abundances estimated from a Te+ICF

calibration are systematically lower than those used in the photoionisation models. Thus,

at least part of the disagreement between the two techniques is due to real temperature

gradients which exist in the high-ionisation zones of the H ii regions.

These large-scale temperature gradients play a role analogous to the small-scale tem-

perature fluctuations proposed by Peimbert (1967) and used by very many others since then

e.g. Esteban (2002); Garcıa-Rojas & Esteban (2007); Pena-Guerrero et al. (2012). Kingdon

& Ferland (1995) attempted to reproduce temperature fluctuations in the context of detailed

phototionisation models, and the whole thorny issue of their existence and theoretical jus-

tification was discussed by Stasinska (2004). Both temperature gradients and temperature

fluctuations tend to increase the Te estimated from the [O III] λ4363/ [O III] λ5007 ratio,

because the emissivity of the [O III] λ4363 line is biased towards the regions of higher Te.

This results in a systematic underestimate of the total chemical abundances. There are

obvious physical causes for temperature gradients such as hardening of the radiation field

through radiative transfer effects and through the appearance or disappearance of important

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coolant ions, or through suppression of cooling by collisional de-excitation. Likewise, one

can imagine physical causes of small-scale temperature fluctuations (usually characterised

by a parameter, t2, the mean square fractional temperature fluctuation). These could result

from local turbulent heating, or else local shocks induced by colliding flows from ionisation

fronts. Such microphysics is not currently captured in photoionisation codes.

Recently, Nicholls et al. (2012), inspired by in situ observations of astrophysical plasmas

in and beyond the solar system, suggested that the electrons in H ii regions may be charac-

terised by a κ-distribution of electron energies rather than by a simple Maxwell-Boltzmann

distribution. Such distributions arise naturally in plasmas where there exist long-range en-

ergy transport processes (Livadiotis et al. 2011; Livadiotis & McComas 2011). These “hot

tail” electron distributions can arise from plasma waves, magnetic re-connection, shocks,

super-thermal atom or ion heating (as in a stellar wind H ii region interaction zone) or by

fast primary electrons produced by photoionisation with X-ray or EUV photons. In many

ways the physical processes which may drive a microscopic κ-distribution of electrons is sim-

ilar to that which may generate macroscopic temperature fluctuations, and neither can be

discounted a priori.

Nicholls et al. (2012) demonstrated that a κ-distribution enhances the emissivity of the

[O III] λ4363 line relative to [O III] λ5007, again resulting in a tendency for Te to be sys-

tematically overestimated compared to the Maxwell-Boltzmann distribution case. Similar

considerations apply to other temperature-sensitive line ratios, as demonstrated by Nicholls

et al. (2013). A cause for concern is that the newer fully-relativistic close-coupling calcu-

lations of atomic term energies and collision strengths such as those by Palay et a. (2012)

provide a different absolute calibration from that used hitherto for these same temperature-

sensitive ratios, as shown in Nicholls et al. (2013).

The three suggestions listed above suggest that there are grounds for supposing that

abundances derived from either strong line techniques or from the Te+ICF analysis may

be in error. Likewise, the solution to the abundance discrepancy problem is likely to be

found in a combination of one or more of these three effects, in addition to the temperature

gradient issue already discussed above. We need to systematically take into account the

newer atomic data and its effect on the photoionisation models before we can investigate the

effect of the κ-distribution of electron energies in these photoionisation models, or investigate

how temperatures derived from line sensitive line ratios are changed by use of either the new

atomic data or by the application of a κ-distribution.

The purpose of the current paper is to provide the first systematic and quantitative

study of the effect of the κ-distribution on the strong-line abundance diagnostics, not only

at optical wavelengths, but also insofar as the strong UV and IR lines are concerned. The

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rest of the paper is organised as follows. In Section 2 we discuss what changes we have made

to our photoionisation code to incorporate both the new atomic data and the κ-distribution

of electron energies. In Section 3 we explain the parameters of the photoionisation models

used in the grid of theoretical H ii regions. In section 4 we present a reference catalog of

H ii region models, varying the abundance set, the ionisation parameter, and the value of

κ. For each of the 324 models, we give the computed line intensities and a complete set

of ionic and recombination temperatures. In Section 5 we estimate the likely value of κ

using high-quality observations of galactic and extragalactic H ii regions. In Section 6 we

discuss the effect of the κ-distribution on the intensities of the strong emission lines in both

the UV and the far-IR regions of the spectrum. In Section 7 we present the results of

the line ratio diagnostics, and present a number of new line ratio diagrams which enable

us to cleanly separate the effects of both the chemical abundance, 12+log(O/H), and the

ionisation parameter, q, from strong-line spectra of H ii regions. In Section 8 we compare the

abundances derived for real data for H ii regions using these diagnostic line ratios, provide a

code to derive from observed strong line ratios the ionisation parameter and to provide the

abundance for a plausible range of κ values. Finally, we compare our derived abundances

with earlier work on these same H ii regions, and provide a preliminary estimate of the effect

that the κ-distribution has in producing a systematic offset between the strong-line and

Te+ICF techniques of deriving abundances.

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2. The MAPPINGS IV Code

We have modified the MAPPINGS code (Sutherland & Dopita 1993; Allen et al. 2008)

to incorporate new non-thermal (κ) electron energy excitation (Nicholls et al. 2012, 2013)

and to bring up to date the atomic data and the Maxwell averaged collision strengths. The

number of ionic species treated as full non-LTE multi-level ions has increased from 37 to 43.

The multi-level atoms are modelled using 3 to 9 levels depending on the ionic configuration.

In particular - of particular relevance to H ii region modelling - the species C I–C IV, N I–

N V, O I–O VI, Ne III–Ne V, S II–S IV are now uniformly handled. Ne II is still treated as a

two level atom for the purpose of computing its important 12.8µm transition.

2.1. Energy levels and fundamental constants

We have adopted the 2010 CODATA concordance on fundamental constants (Mohr et

al. 2012). All multi-level atom energy level data are converted from derived energies in ergs

to the more fundamental wavenumbers, in cm−1. The cm−1 values were taken uniformly

from the 2012 values in the NIST Atomic Spectroscopy Database v2 (Kramida et al. 2012),

and are now independent of constants such as h or the value of the electron volt. While

the effect of the change in the values of constants are small compared to the uncertainties

in the level energies, when comparing values to boundary thresholds in the computation,

more stable floating point representations lead to more stable execution of the code. The

real benefit of this change is to reduce (though not eliminate) systematic differences in the

treatment of different ionic species, by adopting a more uniform set of atomic values, not

readily possible in earlier decades.

2.2. Transition probabilities, Aji

In addition to a uniform source of energy level data, recent advances in atomic structure

calculations (Tachiev & Froese Fischer 1999, 2000, 2001, 2002) now suggest that the theoret-

ical transition probabilities have become very accurate, even for forbidden M2 quadrupole

transitions, such as [O III] λ5006.8. In a study of the O III transitions, Froese Fischer et

al. (2009) found excellent agreement at the level of 10% or better. With the advent of the

NIST MCHFD database based on these multi-configuration relativistic transition probability

calculations, we are now able to use MCHFD transition probabilities uniformly for all the

multi-level ions used in our models.

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2.3. Collision Strengths

For many of the multi-level atoms, the data used in MAPPINGS III (Sutherland &

Dopita 1993; Allen et al. 2008) were merely translated to the new code format. However for

the important species, new electron energy-averaged collision strengths (Υ) were calculated

from the original energy resolved collision strength data (Ω) (either published or supplied

as a private communication by the authors) The ions for which this treatment applies are

listed in Nicholls et al. (2013). This approach enables two key features:

1. We can convolve the original Ω data with a Maxwell-Boltzmann distribution to obtain

energy-averaged collision strengths Υ values for any temperature and at any resolu-

tion desired, removing interpolation errors that would arise if we depended only on

published tabular data, and

2. We are also able to convolve with κ non-thermal distributions and obtain directly the

Υκ values.

In order to be able to rapidly evaluate both the Maxwell-Boltzmann averaged collision

strength, Υ, and the equivalent κ -distribution averaged collision strength, Υκ, we fit cubic

spline functions in the following way:

1. High resolution integrals as a function, f(T ), of the Ω data convolved with the electron

distributions were computed, along with the local second derivative f ′′ at each point.

2. A fitting method akin to the one described in Press et al. (2007, p.120 et seq.) was

employed except that we used the actual second derivative from the high-resolution

integrals instead of a least squares fit to f at the subset of nodes.

3. By fixing the second derivative with the physical integral, the fitting procedure then

became one of choosing the location of the spline nodes that minimised the difference

between the spline fit and the high-resolution integral data, evaluating the spline at the

data points, usually 1000-3000 points. With optimal manual adjustment, the global

error between the spline with 17 points and the high-resolution data was less than 1e-3

and generally 5e-4 RMS, achieving approximately third order accuracy, and better

than that in some regions.

4. The temperature coordinates were normalised in a fashion similar to that used in

CHIANTI 7.1 (Dere et al. 1997; Landi et al. 2012) and originally proposed by Burgess

& Tully (1992), but here we use a more direct scaled temperature coordinate x =

T/(T +TC), where T is the temperature and TC is a characteristic temperature, chosen

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for each transition so that the main features of the Upsilon curve are well modelled. TCis not directly related to the threshold energy, as used by Burgess & Tully (1992) and

CHIANTI, but to structure in the Υ curve with energies characteristic of the major

resonances in the underlying Ω data.

This transform has the property of scaling the temperature to 0 ≤ x ≤ 1, and by includ-

ing spline nodes at or very near x = 0 and 1, ensures that the cubic spline interpolation is

very stable at extreme temperature values when transformed back to a physical temperature

scale, eliminating the well known instability of cubic spline extrapolation. In the atomic

data fitting procedure, every spline fit to every transition was plotted and evaluated.

2.4. Multi-Level Atoms

The high resolution Maxwell-averaged collision strength data used in (Nicholls et al.

2013) were adopted for O II (5 levels), O III (6 levels)), N II (6 levels), S II (5 levels) and

S III (6 levels). For Ne III, Ne IV and Ne V, the spline fits given in CHIANTI 7.1 were

transformed into the slightly different coordinate system used here. Lithium-like species,

C IV (3 levels), N V (3 levels) and O VI (3 levels) were fit from low resolution tabular data

given in the literature. Other important multi-level species include C I (5 levels), C II (5

levels), C III (5 levels), N I (5 levels), N III (5 levels), N IV (4 levels), O I (5 levels), O IV

(5 levels), O V, S I, and S IV where less detailed data were used, but include temperature

dependent data. Table 1 lists all the sources of data we have used in this work.

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Table 1: Literature sources used for collision strength data.

Ion Reference

C I Pequignot, D., & Aldrovandi, S. .M. .V., 1976, A&A, 50, 141

C II Tayal, S. S., 2008, A&A, 486, 629

C III Berrington, K. A. et al., 1985, Atomic Data & Nuclear Data Tables, 33, 195

C III Berrington, K. A. et al., 1989, J. Phys. B, 22, 665

C IV Liang, G. Y. & Badnell, N. R., 2011, A&A, 528, A69

N I Tayal, S. S., 2000, Atomic Data & Nuclear Data Tables, 76, 191

N I Tayal, S. S., 2006, ApJS, 163, 207

N II Tayal, S. S., 2011, ApJS, 195, 12

N III Stafford, R.P., Bell, K.L. & Hibbert, A., 1994, MNRAS, 266, 715

N IV Ramsbottom, C.A., Berrington, K.A., Hibbert, A. & Bell, K.L., Phys. Scr, 1994, 50, 246

N V Liang, G. Y. & Badnell, N. R., 2011, A&A, 528, A69

O I Bell, K.L., Berrington, K.A. & Thomas, M.R.J., 1998, MNRAS, 293, L83

O I Zatsarinny, O., & Tayal, S. S. 2003, ApJS, 148, 575

O II Tayal, S. S., 2007, ApJS, 171, 331

O III Palay, E. et al., 2012, MNRAS, 423, 35

O IV Blum, R. D. & Pradhan, A. K., 1992, ApJS, 80, 425

O V Berrington, K.A., 2003, private communication, 13-Mar-03

O V Bhatia, A. K. & Landi, E., 2012, Atomic Data & Nuclear Data Tables, in press

O VI Liang, G. Y. & Badnell, N. R., 2011, A&A, 528, A69

Ne III Landi, E. & Bhatia, A. K., 2005, Atomic Data & Nuclear Data Tables, 89, 139

Ne IV Ramsbottom, C. A., Bell, K. L. & Keenan, F. P., 1998, MNRAS, 293, 233

Ne V Badnell, N. R. & Griffin, D. C., 2000, J.Phys.B, 33, 4389

Si III Galavis, M. E., Mendoza, C.& Zeippen, C. J., 1995, A&AS, 111, 347

Si III Galavis, M. E., Mendoza, C.& Zeippen, C. J., 1998, A&AS,133, 245

Si III Mendoza C., & Zeippen C. J., 1982, MNRAS, 199, 1025

S II Tayal S. S. & Zatsarinny O., 2010, ApJS, 188, 32

S III Hudson, C. E., Ramsbottom, C. A. & Scott, M. P., 2012 ApJ, 750, 65

Ca V Galavis, M. E., Mendoza, C. & Zeippen, C. J., 1995, A&AS, 111, 347

Fe II Nussbaumer, H, & Storey, P. J., 1980, A&A, 89, 308

Fe II Nussbaumer, H. & Storey, P. J., 1988, A&A, 193, 327

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2.5. Collisional excitation rates

The collisional excitation rate from energy level 1 to 2, R12, depends on the collision

strength Ω12(E) and the energy E c.f. Nicholls et al. (2012);

R12 = neN1h2

8πmeg1

∞∫E12

Ω12(E)√E

f(E)dE (1)

where h is the Planck constant, me the mass of the electron g1 the statistical weight of the

lower level, f(E) the energy distribution function, N1 the number density of atoms in the

ground state and ne is the electron density.

The collisional excitation rate from level 1 to level 2 for a Maxwell-Boltzmann (M-B)

distribution is given by

R12(M− B) = neN1h2

4π3/2meg1(kBTU)−3/2

∞∫E12

Ω12(E) exp

[− E

kBTU

]dE , (2)

and for a κ-distribution, the corresponding rate is:

R12(κ) = neN1h2

4π3/2meg1

Γ(κ+ 1)

(κ− 32)3/2Γ(κ− 1

2)

(kBTU)−3/2∞∫

E12

Ω12(E)

(1 + E/[(κ− 32)kBTU)]κ+1

dE .

(3)

where E12 is the energy gap between levels 1 and 2, g1 is the statistical weight of the lower

state, and Γ is the gamma function.

If the detailed collision strengths, Ω(E), are known, equations 2 and 3 can be integrated

numerically, and the κ collisional excitation rate can be expressed in terms of the M-B

collisional excitation rate.

As a first order approximation, we can assume that the collision strength for excitations

from level 1 to 2, Ω12, is independent of energy. For this case the ratio of the rates of

collisional excitation from level 1 to level 2 for a κ distribution can be expressed analytically

(NDS12) as:

R12(κ)

R12(M− B)=

Γ(κ+ 1)

(κ− 32)3/2Γ(κ− 1

2)

(1− 3

)exp

[E12

kBTU

](1 +

E12

(κ− 32)kBTU)

)−κ. (4)

This equation can be evaluated analytically as a series of concave “banana curves” (see

(Nicholls et al. 2012), Figure 5).

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When collision strengths are computed, in some cases only the “effective collision

strengths”, ΥM−B(T ), computed assuming M-B equilibrium electron energies are published:

ΥM−B(T ) =

∞∫E=E12

Ω12(E) exp(−EkT

)d(EkT

)∞∫

E=E12

exp(−EkT

)d(EkT

) . (5)

Where data on the detailed energy dependence of Ω are not available, a reasonable

approximation for the effective collision strengths Υκ for a κ distribution can be calculated

in terms of the equilibrium effective collision strengths ΥM−B using equation 4:

Υκ =R12(κ)

R12(M− B)ΥM−B. (6)

Equation 6 allows us to compute the κ dependence of collisional excitation in terms of

that for an equilibrium energy distribution, even where complete data on Ω is not available.

In the revised MAPPINGS code, as described above, where detailed data for Ω are

available (see Nicholls et al. (2013)), we compute the effective collision strengths Υ for

temperatures between 103 and 107K, and express the effective κ collision strengths Υκ in

terms of the equilibrium ΥM−Bs. Where only M-B-averaged effective collision strengths are

available, we compute κ values using equation 6.

To demonstrate the accuracy of the procedures used, in Figure 1 we show the equilibrium

effective collision strengths for the lowest 10 or 15 transitions for the ions O III, O II, S II

and N II. The dots are the values as published in the literature (see Table 1); the thick red

lines represent the high temperature resolution computations using equation 6; and the thin

black lines are the spline fits to the high resolution data, calculated as described earlier.

In Figure 2 we show the effective collision strengths for the 3P2-1D2 and 3P2-

1S0 tran-

sitions in [O III]. M3 indicates the collision strengths used in the previous version of MAP-

PINGS. M4 indicates the latest versions. κ10 shows the effective collision strengths for

a non-equilibrium electron energy distribution with κ=10. While the 3P2-1D2 values are

reasonably similar between 103.5 and 104 K, at lower temperatures the divergence is consid-

erable between the older version and the new MAPPINGS data. Extrapolating the older

MAPPINGS data above 105K is likely to give severe errors. These differences are likely to

produce significant effects in models of X-ray ionized nebulae, or for models of the emission

spectrum of material entering shock fronts.

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– 13 –

Fig. 1.— The effective energy-averaged collision strengths, Υ, for a Maxwell-Boltzmann

electron energy distribution computed for the lowest transitions for O III, O II, S II and N II.

The dots are the values published in the literature; the thick red lines are our computations

made at high energy resolution using equation 6; and the thin black lines are our spline

fits to this high resolution data. Note that our interpolation scheme provides well-behaved

asymptotes as both the high- and low-temperature limits.

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– 14 –

Fig. 2.— Effective collision strengths for equilibrium (M3 and M4) and κ=10 electron energy

distributions (κ10), for the 3P2-1D2 and 3P2-

1S0 transitions in [O III]. M3 indicates the

effective collision strengths used in the previous version of MAPPINGS, M4 shows the new

values. The differences are greatest at low temperature in the 3P2-1D2 transition, producing

the greatest effect in high-abundance H ii regions.

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3. The Model Grid

3.1. Abundance Set and Dust Physics

The solar abundance set is taken from Grevesse et al. (2010), and the depletion factors

for each element are updated from Dopita et al. (2005) using the data from Kimura, Mann

& Jessberger (2003). These are listed in Table 2. The elemental depletion results from con-

densation of the heavy elements onto dust grains. The treatment of dust grain composition,

size distribution and absorption properties adopted here is essentially identical to that used

in MAPPINGS 3, and is described in detail by Dopita et al. (2005). Suffice it to say here

that within the ionised region, our dust model has silicate grains following a Mathis, Rumpl

& Nordsieck (1977) size distribution and a population of small carbonaceous grains. The

polycyclic aromatic hydrocarbon molecules are assumed to be destroyed within the ionised

H ii region (although they are present in the photodissociation regions around the periphery

of the H ii region). The effects of radiation pressure acting on dust (Dopita et al. 2002),

and photoelectric heating due to grain photoionisation (Dopita & Sutherland 2000) are fully

taken into account in the models.

A perennial problem with fitting the spectrum of H ii regions over a wide range of abun-

dances is the question of how to deal with the N and C abundances. Both of these elements

contain a primary nucleosynthetic contribution as well as a secondary nucleosynthetic source

which becomes important at higher abundance. In Dopita et al. (2000) the transition from

primary to secondary element was treated as more or less abrupt, but this does conform to

the extensive observationally derived data of van Zee et al. (1998) (for the N/O ratio) or to

the data of Garnett et al. (2004), and references therein, for both N/O and C/O. In this work,

we have adopted an empirical smooth function variation in both N/H and C/H as a function

of O/H. This is listed in Table 3, and the fit for the adopted N/O ratio as a function of O/H

is shown in figure 3, by comparison with the van Zee et al. (1998) dataset. Note the increased

scatter at the low abundance end, which may be of some importance to the accuracy of the

strong line abundance diagnostics developed in this paper for 12 + log(O/H) < 8.4.

For helium, we adopt a similar prescription as used by Dopita et al. (2002), which

provides a good fit to the He abundances observed in H ii regions. This has a primary

production of He added to the primordial He abundance. By number of atoms,

He

H= 0.0737 + 0.024

Z

Z.

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– 16 –

8.0 8.2 8.5 8.8 9.0 9.2

-1.8

-1.5

-1.2

-1.0

-0.8

-0.5

12+log(O/H)

log(N/O)

Fig. 3.— The relationship between the oxygen abundance; 12+log(O/H), and the N/O ratio

for the H ii regions observed by van Zee et al. (1998). The functional relationship adopted

in the models is indicated as a solid line, and is tabulated in Table 3. The accuracy of this

calibration is central to the accuracy of the new strong-line diagnostics developed in this

paper. Note that the increased scatter at the low abundnce end may pose an issue in the

determination of the chemical abundances of low-abundance H ii regions.

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– 17 –

3.2. Stellar model atmospheres

The stellar model atmospheres are based upon the STARBURST 99 code of Leitherer

et al. (1999). Here we have assumed a Salpeter initial mass function; dN/dm ∝ m−2.35, with

a lower mass cutoff of 0.1M and an upper mass cutoff of 120M, as described in Dopita

et al. (2000). We have used the Lejeune, Cuisinier, & Buser (1997) model atmospheres. For

stars with strong winds we switch to the Schmutz, Leitherer, & Gruenwald (1992) extended

model atmospheres using the prescription of Leitherer & Heckman (1995). We assume that

typical H ii regions are excited by a cluster with continuous star formation extending over

4 Myr. This approximation agrees with observed H ii regions since there is a strong bias

towards observing the younger H ii regions, which have in general higher densities, much

higher emissivities and larger absolute Hα fluxes (Dopita et al. 2006a). The models also

provide a good approximation to the typical age spread of the stars observed in luminous

clusters exciting bright H ii regions (Beccari et al. 2000; De Marchi et al. 2011).

We have elected to use the earlier STARBURST 99 models used by Dopita et al. (2000),

as they provide a harder radiation field than the models generated by more recent versions

of the code. These newer models incorporate fully self-consistent radiatively-driven atmo-

spheres, but they generate an EUV radiation field which is rather too soft to reproduce the

H ii region sequence (Dopita et al. 2006b). The most likely reason for this is that the stellar

winds of OB stars are clumpy rather than smooth, which assists the escape of EUV photons.

A small difficulty with the STARBURST 99 models is that the “solar” metallicity models

do not correspond to the Grevesse et al. (2010) abundance set. For oxygen in particular,

12 + log(O/H) default solar abundance has changed from 8.86 to 8.69 - nearly a factor

of two lower. Thus, for most of the abundance sets that we would like to compute, the

corresponding STARBURST 99 models are missing. To account for this, we generated stellar

model atmospheres by linear interpolation of the logarithmic fluxes at any given frequency

between the nearest adjacent STARBURST 99 models in metallicity, by assuming that the

logarithm of the flux varies in proportion to 12 + log(O/H). This allows us to construct a

more finely sampled grid of models in which the stellar and the nebular chemical abundances

are effectively identical, with the exception of the case 0.05Z, where the atmosphere used

is simply the lowest that can be obtained from the STARBURST 99 code, corresponding to

12 + log(O/H) ∼ 7.56 rather than 7.39.

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– 18 –

4. A reference catalog of H ii region models

We have run a grid of spherical isobaric H ii region models at 5.0, 3.0, 2.0, 1.0, 0.5,

0.3, 0.2, 0.1 and 0.05Z, where the solar abundance corresponds to 12 + log(O/H) = 8.69.

The full set of elemental abundances for solar abundance are listed in Table 2. The models

were terminated when more than 95% of the hydrogen has recombined, and the temperature

has fallen to less than 2000K. The pressure in the models was set at P/k = 105, typical of

bright H ii regions in external galaxies. The density of these models, n ∼ 10cm−3, is fixed by

the pressure, and is typical of giant extragalactic H ii regions. We do not need to consider

models of different densities since, at the densities typically encountered in these H ii regions,

collisional de-excitation is unimportant.

The ionisation parameter, log(q) 1 was fixed by its value at the inner boundary of

the H ii region. For each set of abundances log(q) ran from 8.5 down to 6.5 in steps of

0.25. Because these are spherical models, the radial divergence of the radiation field and

attenuation of the radiation field by absorption in the ionised plasma within the models

is important, especially at high ionisation parameter. By contrast, the low log(q) models

approximate to a thin shell of ionised gas. As an example, for the log(q) = 8.5 model at solar

abundance, the mean ionisation parameter in the ionised hydrogen is only log 〈q〉 = 7.95,

while for the log(q) = 6.5 model at solar abundance, the mean ionisation parameter in the

ionised hydrogen is log 〈q〉 = 6.42.

The full log(q);Z grid was run for several different values of κ = 10, 20, 50 and ∞(which corresponds to the standard Maxwell-Boltzmann case), giving a complete family of

324 models covering the three independent variables which control the strong-line emission

spectrum. The lines relevant to the abundance diagnostics, as well as those relevant for

measuring electron temperatures in the nebulae are tabulated in Tables 4 (the ‘blue’ lines)

and 5 (which lists the lines in the red and near-IR portions of the spectrum). In these Tables,

all line intensities are expressed as a fraction of the Hβ intensity, to four significant figures.

In the original models, the line fluxes are computed down to any intensity, but the spectral

line list for each model gives lines with F > 10−6 that of Hβ. This allows an accurate

computation of the effective forbidden line temperatures down to Te ∼ 3000K.

In order to compute the effective forbidden emission line temperatures, TFL, for the ions

1The dimensionless ionisation parameter U measures the ratio of the density per unit volume of ionising

photons to the particle (atom plus ion) number density. In this paper, we use the alternative definition, q,

which is defined as the ratio of the number of ionising photons impinging per unit area per second divided

by the gas particle number density. The transformation between the two definitions is simply U = q/c, c

being the speed of light.

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– 19 –

O III, Ar III, S III, O II, N II, and S IIwe have used the integrated line fluxes given by the

models along with the fitting formulae given by Nicholls et al. (2013), which were obtained

using the same atomic data. The temperature sensitive ratios used are as follows: [O III]

λ4363/λ5007, [Ar III] λ5192/λ7751, [S III] λ6312/λ9069, [O II] λ7318, 30/λ3727, 9, [N II]

λ5755/λ6584, and [S II] λ4068, 76/λ6731.

In addition to the forbidden line temperatures, we have computed the effective recombi-

nation temperatures from the average ionic kinetic (or internal energy) temperatures, TU in

the H+ and He+ zones. In a κ-distribution, the Maxwell-Boltzmann “core”, which determines

the energy distribution of the recombining electrons, and hence the recombinations occur at

a lower effective temperature, Trec, than the internal energy temperature; Trec = TU(1−3/2κ)

(Nicholls et al. 2012, 2013). We must therefore correct the average ionic kinetic temperatures

given by the code by this factor.

The complete list of nebular temperature estimates is given in Table 6. Figure 4 shows

the way in which both metallicity, ionisation parameter and κ affect the measured line

temperatures (T[OIII] and T[OII]), as well as the hydrogen recombination temperature (Trec).

Some general observations can be made about this. First, as is well-known, low-abundance

H ii regions have higher temperatures than high-abundance H ii regions. Second, the electron

temperature is usually positively correlated with log q. Third, T[OIII] is generally higher than

T[OII].

Figure 4 also brings out the way in which κ influences the effective (as measured)

forbidden emission line temperatures, TFL, and the hydrogen recombination temperature

Trec. In the presence of a κ distribution, Trec is always lowered, while the TFL is usually (but

not always) raised. The lower Trec will result in generally stronger recombination lines. This

may in turn lead to an overestimate of the chemical abundances derived from recombination

lines when temperatures derived from the forbidden lines are used to interpret these.

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– 20 –

6.5 7.0 7.5 8.0 8.54000

6000

8000

10000

12000

14000

16000

log q

T (K

)

6.5 7.0 7.5 8.0 8.54000

6000

8000

10000

12000

14000

16000

log q

T (K

)

12-log(O/H) = 7.69

12-log(O/H) = 8.69

12-log(O/H) = 9.1712-log(O/H) = 9.17

12-log(O/H) = 8.69

12-log(O/H) = 7.69

T[O III]

T[O II]

Trec

T[O III]

Trec

T[O II]

a) κ = inf. b) κ = 20.

Fig. 4.— The relationship between the forbidden line and recombination line temperatures

as a function of log q and chemical abundance. The left-hand panel is for the models with a

Maxwell-Boltzmann electron distribution, and the right hand panel is for the case κ = 20.

The red lines show the temperature in the high-ionisation zone of the H ii region, T[OIII], the

blue lines the temperature in the low-ionisation zone of the H ii region, T[OII], and the black

lines show the hydrogen recombination temperature Trec. For all models, the effect of κ is

to raise T[OIII], and lower Trec. However, T[OII] may either be higher (at high Z), or slightly

lowered (at low Z).

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5. What is the likely value of κ?

As Figure 4 shows, the most sensitive dependence with κ is found in the difference

between the forbidden line temperatures, TFL, and the hydrogen recombination temperature

Trec. The helium recombination temperature could equally well be used in the place of the

hydrogen recombination temperature, since the difference between the two is small for all

models; see Table 6.

The high-quality echelle spectroscopy of galactic and extragalactic H ii regions shows

that there is indeed a systematic a difference between TFL and Trec. Here, we have collected

the data the galactic H ii regions from M 42 (Esteban et al. 2004), NGC 3576 (Garcıa-Rojas

et al. 2004), S311 (Garcıa-Rojas et al. 2005), M20 & NGC 3602 (Garcıa-Rojas & Esteban

2006), M 8 & M 17 (Garcıa-Rojas & Esteban 2007). For the extragalactic H II regions we

have data for 30 Dor (Peimbert 2003), NGC595 (Lopez-Sanchez et al. 2012), NGC 595, NGC

604, VS 24, VS 44, NGC 2365 and K 932 (Esteban et al. 2009). However, instead of using

the forbidden line temperatures given by these authors, we have used the measured fluxes,

and made an independent estimate of the temperatures implied by these using the Nicholls

et al. (2013) analytic equations. This ensures that the derived temperatures are consistent

with the new atomic data used here. Noting that the helium recombination temperatures

and the hydrogen recombination line temperatures are very similar, we have used the average

of these (when available) to estimate Trec. In the absence of either we have used the other

to give our estimate of Trec. The error bars on the temperatures are assumed to be the same

as given by the authors cited above.

It should be noted that, in all cases, the temperatures are derived for only a small

patch of the total H ii region. These ‘pencil-beam’ observations do not therefore provide a

temperature which is representative of the nebula as a whole. This may be a problem when

comparing the data with the models.

With this data we have constructed Figure 5, which shows forbidden line temperatures

plotted for two ions arising in the high-ionization zones of H ii regions, O III and Ar III,

and for two ions arising in the low-ionization zones, O II and N II, compared with the

recombination temperatures as derived above. In general the κ- distribution models provide

a better fit than the Maxwell-Boltzmann case. There may well be an intrinsic scatter in the

κ appropriate to individual H ii regions. However, the data is mostly consistent with a fairly

moderate κ ∼ 20, or somewhat higher. This represents only a very mild deviation from the

Maxwell-Boltzmann case, but is sufficient to significantly affect our estimates of forbidden

line and recombination temperatures. In the analysis which follows we will adopt κ ∼ 20.

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4000 6000 8000 10000 12000 14000 16000

4000

6000

8000

10000

12000

14000

16000

T [O III]

T re

c

9.17

8.99

8.69

8.39

8.177.99

7.697.39

κ = 10

κ = 20κ = 50κ = inf.

12+lo

g(O/H)

4000 6000 8000 10000 12000 14000 16000

4000

6000

8000

10000

12000

14000

16000

T [O II]

T re

c

9.17

8.99

8.69

8.398.17

7.997.69

7.39

12+log(O/H)

κ = in

f.

κ = 50

κ = 20

κ = 10

4000 6000 8000 10000 12000 14000 16000

4000

6000

8000

10000

12000

14000

16000

T [N II]

T re

c

9.17

8.99

8.69

8.398.17

7.997.69

7.39

κ = in

f.

κ = 50

κ = 20

κ = 10

4000 6000 8000 10000 12000 14000 16000

4000

6000

8000

10000

12000

14000

16000

T [Ar III]T

rec

9.17

8.99

8.69

8.39

8.17

7.99

7.69 7.39

κ = in

f.

κ = 50

κ = 20

κ = 10

12+log(O/H)

(a) (b)

(c) (d)

Fig. 5.— The relationship between the forbidden line and recombination line temperatures.

The observations for the galactic and extragalactic H ii regions derived from the high-quality

echelle data cited in the text are shown with error bars. The models at each abundance,

and for each set of log q are shown as ‘worms’ in which the head represents log q = 8.5 and

the tail log q = 6.5. Each value of κ is coded by color, as indicated. Note the difference in

behavior between the ions arising in the high-ionisation zones of the H ii region; O III and

Ar III (panels (a) and (b)), and those arising from the low-ionisation regions ; O II and N II

(panels (c) and (d)). From this figure, we conclude that the best-fit value of κ ∼ 20, or

possibly somewhat higher.

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6. Effect of κ on UV and IR Lines

6.1. The UV lines of carbon

The UV spectrum of H ii regions is rather sparse (Garnett et al. 1995a), and as a

consequence only a few observations have been obtained in this wavelength region, mostly

by Garnett and his collaborators (Garnett et al. 1995b, 1999). The strongest lines are

generally the C III] λλ1906, 9 doublet and the C II] λ2326 multiplet. Si III] λλ1883, 92 are

sometimes seen, as well as the [O II] λλ2470 line.

Here we will consider only the effect of the κ−distribution on the important carbon

lines. The effect on the Si III] λλ1883, 92 lines is essentially the same as for the C III]

λλ1906, 9 doublet, and the effect on the [O II] λλ2470 line is similar to that of the C II]

λ2326 multiplet. In Figure 6 we plot the enhancement in the line intensity for κ = 20

compared with κ = ∞, against the predicted line flux relative to Hβ computed for models

with κ = ∞. The enhancement of line intensity is very significant for metallicities greater

than two times solar. The reason for these large correction factor is that the temperature

of the H ii region is low, and the hot tail in the κ electron energy distribution becomes very

important. However, there are no UV measurements for H ii regions in this metallicity range,

so the computations cannot be checked. For lower metallicities, the corrections are much

smaller, and the carbon lines are generally affected by less than a factor of two. Nonetheless,

these corrections may well be important where UV lines are being used to estimate the C/O

ratio.

6.2. The IR lines

By contrast with the UV, the effect of of κ on the IR lines is very weak indeed. At the

high abundance end, the intensities of the strong lines are weakened by only 2 − 4%, even

at κ = 10. The effect becomes more noticeable for low abundance H ii regions, with line

intensities being weakened by as much as 25%. This is easily understood by reference to

the “banana curves” of Nicholls et al. (2012, 2013), which show that only weak κ−related

changes are expected in the excitation rates of the IR lines for typical nebular temperatures.

More problematic is the fact that the models do no give a very good description of the

observed spectrum of H ii regions. Snijders, Kewley & van der Werf (2007) compared the

Mappings models with the observations of Giveon et al. (2002), and devised two new mid-

IR diagnostics based upon the excitation-dependent ratios [Ne III] 15.56 µm/[Ne II] 12.81

µm, [S IV] 10.51 µm/[S III] 18.71 µm, [S III] 18.71 µm/[Ne II] 12.81 µm and [S IV] 10.51

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-0.5 0.0 0.5 1.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

log (f)

log C

III]/

H-Be

ta

-0.2 0.0 0.2 0.5 0.8 1.0

-2.0

-1.5

-1.0

-0.5

log (f)

log C

II]/H

-Bet

a9.17

8.99 8.99

9.17

8.69 8.69

8.39

8.39

8.17

8.17

7.99

7.99

7.69

7.69

7.39

7.39

12+log(O/H)

12+log(O/H)

log q

log q

6.5

8.5

6.5

8.5

Fig. 6.— The effect of κ = 20 on the C III] λλ1906, 9 doublet (left) and the C II] λ2326

multiplet (right). The vertical axis is the predicted line flux relative to Hβ for κ = ∞, and

the horizontal axis is the factor, f , by which the line intensity has to be multiplied to give

the predicted intensity for κ = 20. The effect of κ is most evident at high abundance, where

line intensities may be enhanced by as much as a factor of ten.

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µm/[Ar III] 8.99 µm. In Figure 7 we plot one of these; the [Ne III] 15.56 µm/[Ne II] 12.81

µm vs. [S IV] 10.51 µm/[S III] 18.71 µm and a new one, [Ne III] 15.56 µm/[Ne II] 12.81 µm

vs. /[Ar III] 8.99 µm / [Ne II] 12.81 µm, along with the Giveon et al. (2002) data. Here the

grids are shown only for κ =∞ - the grids for κ = 20 fully overlay these.

The offsets between the theory and the observation require explanation. First, let us

consider the possibility that the intensity of the [Ne II] 12.81 µm line is in error. If this were

the case, the grid on the LHS of Figure 7 would move closer to the observations. However,

the effect on the RHS diagram would simply be to translate the curve along the 45 degree

line, leading to no improvement here. Likewise, the [Ne III] 15.56 µm line intensity cannot

be the source of the problems, since changing this lines translates both grids sideways in the

same direction, so the fit of one is improved only at the expense of the other.

A more likely explanation is that the [S IV] 10.51 µm/[S III] 18.71 µm ratio is in error,

particularly at the high abundance end. Snijders, Kewley & van der Werf (2007) showed that

a much better fit between observations and theory can be obtained if the mean effective age

of the exciting clusters is somewhat older than we have used here. This allows an appreciable

population of Wolf-Rayet stars to develop. These stars have higher effective temperatures,

can excite the species with higher ionisation potentials and so produce more S IV ions in

the nebula, resulting in a stronger [S IV] 10.51 µm line. To explain the offset in the [Ar III]

8.99 µm / [Ne II] 12.81µm ratio, we would have to appeal to errors in either the atomic

data for the [Ar III] line or else errors in the charge-exchange rates which strongly affect the

ionisation balance of Ar. All of these issues point to the need for more work in refining the

predictions of the models in the IR.

In the far-IR, we have identified a very promising abundance - ionisation parameter

diagnostic. This is shown in Figure 8 where we plot [N III] 57.34 µm/[O III] 51.81 µm vs.

[O IV] 25.89 µm/[O III] 51.81 µm as delivered by the models. This grid is little affected by κ,

and provides a very clean separation between the abundance and the ionisation parameter.

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-1.5 -1.0 -0.5 0.0 0.5 1.0

-3.0

-2.0

-1.0

0.0

log [Ne III]/[Ne II]

log [S

IV]/[S

III]

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

log [Ne III]/[Ne II]

log [A

r III]/

[Ne

II]

9.39

9.17

8.99

8.69

7.398.39

12+log(O/H)

8.58.0

7.5

7.0

6.5

log q

Fig. 7.— The mid-IR diagnostics, [Ne III] 15.56 µm/[Ne II] 12.81 µm vs. [S IV] 10.51

µm/[S III] 18.71 µm (left), and [Ne III] 15.56 µm/[Ne II] 12.81 µm vs. /[Ar III] 8.99 µm /

[Ne II] 12.81µm (right) plotted for κ =∞. The points represent the Giveon et al. (2002) data

for Galactic and Magellanic Cloud H ii regions. The probable cause of the offset between

theory and observation is discussed in the text.

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-1.5 -1.0 -0.5 0.0-4.0

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

log [N III]/[O III]

log [O

IV]/[O

III]

9.39

9.17

8.99

8.69

8.39

12+log(O/H)

8.5

8.0

7.5

7.0

6.5

log q

8.177.99

7.697.39

Fig. 8.— A far-IR diagnostic for abundance and ionisation parameter, [N III] 57.34

µm/[O III] 51.81 µm vs. [O IV] 25.89 µm/[O III] 51.81 µm . The grid is shown for κ = ∞,

and gray circles represent the κ = 20 case. The effect of κ on this diagnostic is very small.

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7. Strong Line Ratio Diagnostics

7.1. Veilleux & Osterbrock Diagnostics

Following the pioneering work of Baldwin, Phillips & Terlevich (1981), Veilleux & Oster-

brock (1987) (VO87) exploited the utility of diagnostics based upon the ratio of the strong

red lines; [N II]/Hα, [S II]/Hα and [O I]/Hα plotted against the ratio [O III] λ5007/Hβ.

These ratios have the great advantage of using lines close together in wavelength, so that the

reddening correction for dust is negligible. They noted that the H ii regions are confined to

a rather narrow strip on these diagrams, while Seyferts and LINERS lay systematically re-

spectively above and to the right of the H ii region sequence. These diagrams are therefore of

great utility in determining the mode of excitation for photoionised objects. The permitted

H ii region and starburst region was established in Kauffmann et al. (2006) and the formal

division between the starburst, Seyfert and LINER zones on these diagrams was established

empirically by Kewley et al. (2006) using the very extensive SDSS spectrophotometry.

A number of theoretical attempts to reproduce the narrow H ii region and starburst

sequence have been made. Dopita et al. (2000) demonstrated that the narrowness of the

the sequence could be understood (in part) as a result of the folding of the log(Z) : log(q)

surface which ensures that H ii regions having a wide range in these parameters occupy

the same region of the diagnostic diagram. Dopita et al. (2006b) demonstrated that the

ionisation parameter, the hardness of the ionising spectrum and the metallicity are tightly

correlated, and provided a theoretical explanation of why this should be the case. Both of

these effects clearly play a role in making for a tight H ii region and starburst sequence.

The fundamental difficulty with the theoretical models is that the ‘fold’ in the surface was

not the correct shape, presumably due to a combination of errors or incompatibilities in

the stellar atmospheres used, issues with the atomic data used, or errors in the modelling

procedure, especially in the treatment of the geometry of the H ii region and in the treatment

of dust absorption in the H ii region. Dopita et al. (2006b) made an attempt to take into

account the time evolution of the spectrum of the H ii regions as the stellar cluster ages and

as the nebular shell expands. This analysis showed that the more recent STARBURST 99

atmospheres were definitely too soft in their EUV spectra, as a consequence of the use of

non-clumpy stellar winds. This analysis also showed that most extragalactic H ii regions are

observed when they are very young (. 2 Myr); shortly after the absorbing placental dust

cloud is dispersed, when the pressure – and hence the emissivity – in the H ii region is high,

and before the central stars fade in their EUV photon production rate. All of these factors

militate to making them easily observable while very young.

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-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log [N II]/H-Alpha

log

[O II

I]/H-

Beta

12+log(O/H)

7.39

7.69

7.998.17

8.398.69

8.99

9.17

log q

6.5

7.0

7.58.08.5

Fig. 9.— The VO87 plot of [N II]λ6584/Hα vs. [O III] λ5007/Hβ. The grey dots represent

the SDSS dataset as used by Kewley et al. (2006), while the points with error bars are from

the van Zee et al. (1998) dataset. The delineation of the two AGN sequences in the upper

right-hand side of the diagram, the Seyferts (upper) and LINERS (lower) is very clear on

this plot. The models grids on this and all subsequent diagnostic diagrams are shown for

two values of kappa; κ =∞ (black lines) and κ = 20 (green lines). Note that the effect of κ

is relatively small in this diagnostic.

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– 30 –

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log [S II]/H-Alpha

log

[O II

I]/H-

Beta

12+log(O/H)

9.17

8.99

8.69

7.39

7.69

7.99

log q

6.5

7.0

7.58.0

8.5

Fig. 10.— As figure 9 but for the VO87 plot of [S II]λλ6717, 31/Hα vs. [O III] λ5007/Hβ.

The models seem to predict slightly too weak [S II] line intensities.

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– 31 –

The models presented here represent a great improvement upon the earlier work of

our group, although we should note in passing that the models of Stasinska (2006) provide a

rather good description to the upper envelope of the H ii region-like points on these diagrams.

In Figure 9, we present the VO87 plot of [N II]λ6584/Hα vs. [O III] λ5007/Hβ. This figure

should be compared to Figure 2 of Dopita et al. (2000), showing the improvement in the fit

of the theory compared with the observations. Important contributors to this improvement

are the proper treatment of the EUV absorption dust, improved atomic data, the use of

spherical models, and the fact that the nebular abundance set is now fully compatible with

the stellar model atmospheres.

In Figure 10, we present the VO87 plot for [S II]λλ6717, 31/Hα vs. [O III] λ5007/Hβ.

Once again there is a great improvement in the fit between theory and observation c.f. Figure

3 of Dopita et al. (2000). However, the [S II] lines are perhaps about 0.1 dex too weak. At

the high abundance end, the observed sequence is best explained by the H ii regions having a

roughly constant log(q), roughly between 7.0–7.5. This is confirmed in the many diagnostics

presented below.

We have not attempted to provide the third diagnostic, [O I]λ6300/Hα vs. [O III] λ5007/Hβ.

This is because the [O I] line arises in a very narrow zone close to the ionisation front, where

shocks and non-equilibrium heating may well be important. Dopita et al. (1997) noted that

shocks have a significant effect on this line ratio even when the ratio of mechanical energy

to photon energy flux is as small as 10−3. We therefore regard our computations of this line

as much more unreliable than the other two. However, the intensity of the line is given in

Table 5, if the theoretical values are required by the reader for any reason.

Closely related to the above diagnostics is that of [O II]λλ3727, 9/Hβ vs. [O III] λ5007/Hβ.

or completeness, this ratio is shown in Figure 11. The observational errors on the x− axis

are somewhat greater because of uncertain reddening corrections.

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– 32 –

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log [OII]/H-Beta

log [O

III]/

H-Be

ta

log q

8.58.0

7.5

7.0

6.57.39

7.69

7.998.178.39 8.69

8.99

9.17

12+log(O/H)

Fig. 11.— As figure 9 but for [O II]λλ3727, 9/Hβ vs. [O III] λ5007/Hβ.

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– 33 –

7.2. Excitation-Dependent Diagnostics

Baldwin, Phillips & Terlevich (1981) were the first to emphasise the importance of

nebular excitation, measured by ratios such as [O III]λ5007/[O II]λ3727, 9 in distinguishing

and separating the various modes of ionisation commonly observed in nature (H ii regions,

planetary nebulae (PNe), power-law ionised or shock excited). Within a given class of

object, such ratios are also sensitive to the ionisation parameter. For H ii regions, Bald-

win, Phillips & Terlevich (1981) showed that [O III] λ5007/Hβ is also correlated with

[O III]λ5007/[O II]λλ3727, 9, as it is separately in the case of PNe. In Figure 12, we show

how well these two line ratios track each other. As it stands, this plot is not very useful.

It neither effectively separates 12+log(O/H) from log q, nor does it reveal the AGN as a

separate branch.

A better excitation-dependent diagnostic is obtained if we substitute the excitation-

dependent ratio [O III]λ5007/[S II]λλ6717, 31 for [O III] λ5007/Hβ, as shown in Figure 13.

Both ratios provide a similar sensitivity to ionisation parameter at abundances less than

solar, and in this abundance range the abundance sensitivity is also weak. Clearly we can

substitute [S II]λλ6717, 31 in place of [O II]λλ3727, 9, if necessary. This is useful if reddening

corrections are uncertain, or if the nebular spectra obtained do not extend much below Hβ.

Given the similar sensitivity of both [O III] λ5007/Hβ and [O III]λ5007/[O II]λλ3727, 9

ratios to both excitation and chemical abundance, we examine the substitution of the second

for the first in the Baldwin, Phillips & Terlevich (1981) and Veilleux & Osterbrock (1987)

diagnostic diagram in Figure 14. This diagram is, in fact, another Baldwin, Phillips &

Terlevich (1981) diagram (with transposition of the axes). Again, as in Figure 9 , there is a

clean separation of the AGN excited objects from the narrow H ii region sequence.

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– 34 –

12+log(O/H)

-2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log [O III]/H-Beta

log

[O II

I]/[O

II]

12+log(O/H)

9.17

8.99

8.69

8.39

7.39 7.69 7.998.17

log q

8.58.0

7.0

7.5

6.5

12+log(O/H)

Fig. 12.— The excitation-sensitive ratios [O III]λ5007/[O II]λλ3727, 9 and [O III] λ5007/Hβ

plotted against each other. This is a transposed version of one of the BPT diagnostics.

Clearly, [O III] λ5007/Hβ shows a rather greater sensitivity to the chemical abundance, but

both depend upon a mixture of both 12+log(O/H) and log q. Neither can be used alone to

estimate the excitation.

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– 35 –

-2.0 -1.0 0.0 1.0 2.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

log [O III]/[S II]

log

[O II

I]/[O

II]

Fig. 13.— The excitation-sensitive ratio [O III]λ5007/[S II]λ6717, 31 plotted against a second

excitation-sensitive ratio [O III]λ5007/[O II]λλ3727, 9. The two ratios show good sensitivity

to ionisation parameter at abundances less than solar, and the two AGN sequences are now

clearly distinguished. Due to the great degeneracy of the theoretical curves on this plot, we

have not attempted to label the individual curves. Suffice it to note that the high abundance

objects are located in the lower left-hand corner of the plot.

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– 36 –

-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log [N II]/H-Alpha

log

[O II

I]/[O

II]

12+log(O/H)9.39

9.17

8.99

8.69

8.398.177.99

7.697.39

log q

6.5

7.0

7.58.08.5

Fig. 14.— [N II]λ6584/Hα vs.[O III]λ5007/[O II]λλ3727, 9. This is one of the BPT diagnos-

tics, with axes transposed. Both this diagram and Figure 9 provide a clean separation of

the H ii region sequence from the Seyfert and LINER branches. However, this figure might

prove more useful in separating the Seyfert and LINER branches than Figure 9.

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7.3. Abundance-Sensitive Diagnostics

7.3.1. The R23 Diagnostic

It has been traditional to use the ratio of a forbidden line to a hydrogen recombination

line in the quest to determine chemical abundance. However, all such ratios are two-valued

in terms of abundance. As a consequence, a great deal of effort has been expended in

identifying the appropriate ‘branch’ a particular H ii region lies upon in diagnostics such as

the R23 ratio, ([O II] λλ3727,9 + [O III] λλ4959,5007)/Hβ (Pagel et al. 1979), or in similar

ratios such as S23 = ([S II] λλ6717,31 + [S III] λλ9069,9532)/Hβ (Diaz, & Perez-Montero

2000; Oey et al. 2002).

For the R23 ratio, in particular, the use of both the visible forbidden line of [O III] and

the UV [O II] together mixes two regions of different H ii region temperatures, and makes

the maximum of this line ratio very broad in terms of abundance. This makes the actual

abundance very difficult to estimate in the region of the maximum, and it becomes critical

to have a good estimate of the ionisation parameter to remove the residual sensitivity of the

R23 ratio to this parameter. This point was emphasized by McGaugh (1991)

These problems become very evident in Figure 15, in which we plot the R23 ratio,

([O II] λλ3727,9 + [O III] λλ4959,5007)/Hβ (Pagel et al. 1979), against the excitation-

sensitive [O III]λ5007/[O II]λl3727, 9 ratio, as was done by McGaugh (1991). First, the

ratio is only weakly dependent on abundance for a broad range of abundance; 8.3 > 12 +

log(O/H) > 9.0, approximately. Second, in this range the sensitivity to the ionisation

parameter is as great as to the abundance. Elsewhere, the ratio is two-valued leading to

the associated problems of determining whether the abundance solution lies on the low-

or high- abundance branches. All these issues apply whether or not the electrons have a

κ−distribution. In conclusion therefore, we strongly recommend against use of the R23 ratio,

([O II] λλ3727,9 + [O III] λλ4959,5007)/Hβ in attempts to determine chemical abundances,

and advise observers to treat any such attempts with a great deal of caution.

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-1.0 -0.5 0.0 0.5 1.0 1.5-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

log R23

log [O

III]/[O

II]

12+log(O/H) 9.17

8.99

8.698.39

8.177.99

7.697.39

log q

8.58.0

7.5

7.0

6.5

Fig. 15.— The R23 ratio, ([O II] λλ3727,9 + [O III] λλ4959,5007)/Hβ (Pagel et al. 1979)

plotted against the excitation-sensitive [O III]λ5007/[O II]λλ3727, 9 ratio. This diagram

graphically illustrates the serious problems associated with any attempt to derive the chem-

ical abundance from the R23 ratio alone. We strongly recommend against the use of this

ratio as an abundance diagnostic.

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– 39 –

7.3.2. Ratios of Strong Forbidden Lines

Unlike the R23 diagostic, and others which use the ratio of a forbidden line to a hydrogen

recombination line, a number of purely forbidden line ratios are known to vary monotonically

with abundance, such as the [N II] λ6584/[O II] λλ3727,29 ratio (Dopita et al. 2000), or

the [Ar III]λ7135/[O III]λ5007 and the [S III]λ9069/[O III]λ5007 ratios (Stasinska 2006).

Th use of such pairs of forbidden line ratios to unambiguously separate the abundance

and the ionisation parameter was pioneered by Evans & Dopita (1985, 1986). It seems it

seems somewhat surprising that ratios such as these have since not been much more widely

employed for strong line abundance diagnostics. Perhaps this is the result of a natural

psychological pressure to include hydrogen if an attempt is being made to determine the

abundance of a heavy element with respect to hydrogen.

In Figure 16 we show the two ratios used by (Stasinska 2006). Here we have used

the excitation-sensitive [S III]λ9069/[S II]λ6717, 31 ratio as the prime ionisation parameter

diagnostic. Both abundance indicators are similar, being relatively insensitive to abundance

below 12 + log(O/H) < 8.0, and showing considerable sensitivity to ionisation parameter.

The data sets we are using do not have the [S III]λ9069 line fluxes, and so cannot be plotted

on these diagrams. In addition, the excitation-sensitive [O III]λ5007/[S II]λ6717, 31 ratio

cannot be substituted on the y−axis, as the ratios then become degenerate.

As pointed out by (Stasinska 2006), these ratios work because they (indirectly) measure

the electron temperature in the high-ionisation zone of the H ii region. At high abundances

the temperature of this zone changes rapidly with abundance, giving the observed sensitivity

at the high abundance end, but at the low-abundance end of the scale, the temperature

sensitivity to abundance is much weaker.

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-1.0 0.0 1.0 2.0 3.0

-0.5

0.0

0.5

log [S III]/[O III]

log [S

III]/[S

II]

12+log(O/H) 9.178.99

8.698.39

8.5

8.0

7.5

7.0

6.5

log q 7.39

9.39

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-0.5

0.0

0.5

log [Ar III]/[O III]

log [S

III]/[S

II]8.5

8.0

7.5

7.0

6.5

log q

9.3912+log(O/H)9.17

8.998.69

8.397.39

Fig. 16.— The Stasinska (2006) abundance-sensitive ratios plotted against the excitation-

sensitive [S III]λ9069/[S II]λ6717, 31 ratio. As before, the black grids correspond to κ = ∞and the green labelled grids are for κ = 20. The data sets we are using do not give the

[S III]λ9069 line fluxes, and so cannot be plotted on these diagrams. Note that the behaviour

of both abundance indicators is similar, being relatively insensitive to abundance below

12 + log(O/H) < 8.0, and showing considerable sensitivity to ionisation parameter.

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7.3.3. [N II]/[O II] as an abundance diagnostic

Dopita et al. (2000) separated the effects of abundance and ionisation parameter by using

[N II] λ6584/[O II] λλ3727,29 as the prime abundance diagnostic, and using the excitation-

sensitive [O III]λ5007/[O II]λλ3727, 9 ratio as the prime ionisation parameter diagnostic. Our

re-computation of this diagnostic is shown in Figure 17. The [N II] λ6584/[O II] λλ3727,29

ratio is particularly sensitive to abundance for two reasons. First, nitrogen has a large

secondary component of nucleosynthesis at high abundance, see Figure 3, which ensures an

increase of [N II]/[O II], and second, the nebular electron temperature falls systematically

as the abundance increases. This ensures that collisional excitations of the [O II]λλ3727, 9

lines are quenched at the high abundance end of the scale.

Several points are to be noted. First, the effect of the κ-distribution on the implied

chemical composition is small, but nonetheless significant. In general, the κ-distribution leads

to systematically higher derived chemical abundances. Likewise, the κ-distribution tends to

systematically decrease the derived ionisation parameters. The most significant difference

occurs in the high-q low-Z regime. Second, the vertical scatter of the observational points

on this figure can be ascribed to intrinsic variability in log q between different H ii regions.

Most of the van Zee et al. (1998) H ii regions have log q in the range 7.0–7.5, with the high-q

outliers tending to be associated with low-abundance H ii regions. Third, the SDSS galaxies

display a systematically smaller abundance spread than the van Zee et al. (1998) sample,

consistent with the fact that the SDSS spectra are heavily weighted towards the central

regions of galaxies, while most of the van Zee et al. (1998) H ii regions are located in the

spiral arms, which have lower oxygen abundance due to the presence of galactic abundance

gradients. A few of the van Zee et al. (1998) H ii regions have extremely high abundances.

These H ii regions are located in very luminous disk galaxies such as NGC 1068, NGC 1637

and NGC 3184. Lastly, the SDSS galaxies clearly show the AGN branches emerging in the

vertical direction from the main cloud of galaxies. This implies that most of the AGN in the

Local Universe are associated with super-solar chemical abundances; 12+log(O/H)& 9.0.

We had already demonstrated in Figure 13, above, that either [O III]λ5007/[O II]λλ3727, 9

or [O III]λ5007/[S II]λ6717, 31 can provide good excitation diagnostics. Figure 18 shows the

effect of making this substitution in the Dopita et al. (2000) diagnostic which we have just

discussed. The abundances implied by both diagnostics agree closely, as they should, since

only the [N II] λ6584/[O II] λλ3727,29 is sensitive to abundance. However, the scatter in

the inferred log(q) is reduced in Figure 18. This is almost certainly because the reddening

corrections and their associated errors are much smaller for the [O III]/[S II] ratio than for

the [O III]/[O II] ratio. It is now evident that the observed range of ionisation parameter

for either the spiral arm H ii regions or the SDSS nuclear spectra is rather restricted; most

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– 42 –

objects are located in the narrow band 6.9 . log(q) . 7.6.

If we try to use the excitation-sensitive [O III]λ5007/Hβ on the y-axis, we obtain the

diagnostic diagram in Figure 19. This is degenerate in terms of the ionisation parameter

over a wide range for higher values of log(q). This diagram is probably better suited to

separate the AGN galaxies from the normal star-forming galaxies, despite the fact that it

distinguishes between the LINER and Seyfert sequences rather poorly.

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-2.0 -1.0 0.0 1.0 2.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

log [N II]/[O II]

log

[O II

I]/[O

II]

12+log(O/H)9.39

9.178.99

8.69

8.398.17

7.997.69

7.39

log q

8.58.0

7.5

7.0

6.5

Fig. 17.— The Dopita et al. (2000) diagnostic diagram. This clearly separates the abundance

from the ionisation parameter. Note that the SDSS galaxies and the van Zee et al. (1998)

sample of H ii regions have a relatively restricted range of abundance parameters. Also, the

AGN sequence is quite distinct in this diagnostic.

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-2.0 -1.0 0.0 1.0 2.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

log [N II]/[O II]

log

[O II

I]/[S

II]

12+log(O/H)

9.17

8.99

8.69

8.398.17

7.997.69

7.39

log q

6.5

7.0

7.58.08.5

Fig. 18.— As Figure 17, above, but substituting [O III]λ5007/[S II]λ6717, 31 in the place

of [O III]λ5007/[O II]λλ3727, 9. The [O III]/[S II] ratio is more sensitive to abundance,

but some of the scatter is reduced because the [O III]/[S II] ratio is much less sensitive to

reddening corrections than the [O III]/[O II] ratio. The ionisation parameter is more closely

confined to 7.6 & log(q) & 6.9. The two grids agree closely as to the abundance of the

H ii regions.

.

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-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log[N II]/[O II]

log

[O II

I]/H-

Beta

7.39

7.697.99

8.17

12+log(O/H)

8.39 8.69

8.99

9.17

8.58.07.5

7.0

6.5

log q

Fig. 19.— As Figure 17, above, but substituting [O III]λ5007/Hβ in the place of

[O III]λ5007/[O II]λλ3727, 9. This is not so useful to determine log(q), but the sharp upper

boundary of the theoretical models suggests that this diagram is very useful for distinguishing

AGN and transitional types from the normal star-forming galaxies.

.

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7.3.4. [N II]/[S II] as an abundance diagnostic

Given that [N II] λ6584/[O II] λλ3727,29 is the ratio of an element formed in inter-

mediate mass stars to a standard α-process element, it is reasonable to ask whether an-

other α-process element could be substituted for oxygen. An obvious candidate to use is

[S II]λ6717, 31. In Figure 20 we compare [N II]λ6584/[S II]λ6717, 31 to the [N II] λ6584/[O II] λλ3727,29

ratio. Both ratios are sensitive to abundance, except that for [N II]λ6584/[S II]λ6717, 31

there is a greater sensitivity to the ionisation parameter, which is a consequence of the mis-

match of the ionisation potential of S II as compared to either N II or O II. In addition, the

sensitivity of the ratio to abundance is less, because the ratio of collisional excitation rates

of [N II] and [S II] is a very weak function of nebular temperature.

The great advantage in the use of [N II]/[S II] as an abundance diagnostic is that

reddening corrections are negligible, facilitating an accurate determination of the line ratio.

To minimise the reddening corrections in the determination of the excitation, an obvious

choice is to use the [O III]/[S II] ratio, since the S II line is close to Hα, the O III line is

close to Hβ, and the intrinsic Balmer Decrement is well defined. In this context, we should

note that our models provide a systematically higher Hα/Hβ ratio than the standard Case B

recombination value, as can be seen in Table 5. This is a result of an important contribution

of collisional excitation from the metastable 21S1/2 level to the Hα line flux, since there is a

large resonance just above threshold in the collisional cross section of this line.

Figure 21 shows [N II]/[S II] vs. [O III]/[S II]. This new diagnostic is very useful, since it

provides an excellent discrimination between 12+log(O/H) and log(q) over the full range of

both these parameters. Comparing with Figure 18, it is clear that observational data provide

very similar solutions for both of these parameters. In addition, spectra of limited wavelength

coverage and poor spectrophotometric calibration can be used to provide robust solutions

for both 12+log(O.H) and log(q). Finally, for this diagnostic it hardly matters whether the

κ-distribution applies or not, since both theoretical grids overlap almost perfectly.

A useful diagnostic is also obtained if we substitute [O III]/Hβ for [O III]/[S II] as our

excitation-dependent diagnostic ratio. This is shown in Figure 22. This suffers a little from

the issues of Figure 19 in that it is not very capable of distinguishing q at the high ionisation

parameter limit. This tendency is more marked at the low-abundance end. However, the

AGN sequence is well distinguished, and like Figure 21, it has the advantage that spectra of

limited wavelength coverage and poor spectrophotometric calibration can be used to provide

a good solution.

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– 47 –

-1.0 -0.5 0.0 0.5-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

log [N II]/[S II]

log

[N II

]/[O

II]

12+log(O/H)

9.39

9.17

8.99

8.69

8.39

8.177.99

7.697.39

log q

8.58.0

7.57.0

6.5

Fig. 20.— [N II]/[S II] and [N II]/[O II] compared as abundance diagnostics. Clearly both

are sensitive to abundance, but for [N II]/[S II] the sensitivity is weaker, and there is a greater

sensitivity to log(q). The AGN sequence is not distinguished in this diagnostic diagram.

.

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– 48 –

-1.5 -1.0 -0.5 0.0 0.5 1.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

log [N II]/[S II]

log

[O II

I]/[S

II]

12+log(O/H)

9.39

9.17

8.99

8.698.398.177.997.697.39

log q

8.58.0

7.0

7.5

6.5

Fig. 21.— [N II]/[S II] vs. [O III]/[S II]. This new diagnostic diagram is valuable for several

reasons. First, it provides an excellent separation of log(q) and 12+log(O/H). Second, the

reddening corrections are simple to make. Third, only a limited spectral coverage is required.

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– 49 –

-1.0 -0.5 0.0 0.5-3.0

-2.0

-1.0

0.0

1.0

log [N II]/[S II]

log

[O II

I]/H-

Beta

7.39

7.697.99

8.17 8.39 8.69

8.99

9.17

9.3912+log(O/H)

log q

7.0

8.58.0

7.5

Fig. 22.— [N II]/[S II] vs. [O III]/Hβ. This new diagnostic diagram is useful for the same

reasons as Figure 21, except perhaps at the high ionisation parameter, low abundance limit.

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7.3.5. The Alloin et al. (1979) abundance diagnostic

Alloin et al. (1979) suggested that the ratio [O III]/[N II] could provide a good abun-

dance diagnostic since they demonstrated a good correlation between this ratio and the

measured electron temperature, and in turn the electron temperature is inversely correlated

with chemical composition (c.f. Figure 4, above). However, as we have amply demonstrated

above, no one ratio provides either a clean abundance diagnostic or a clean ionisation pa-

rameter diagnostic. All are sensitive to both parameters. Figure 23 brings out this point.

Here, we have plotted [O III]/[N II] against the the excitation-dependent [O III]/[O II] ratio.

This figure also provides a clean separation of the abundance from the ionisation parameter

over the full range of these parameters, and shows very little sensitivity to the value of κ.

-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

log [O III]/[N II]

log

[O II

I]/[O

II]

12+log(O/H)

9.399.17

8.99

8.69

8.398.17

7.997.69

7.39

log q

8.58.0

7.5

7.0

6.5

Fig. 23.— The Alloin et al. (1979) abundance-sensitive diagnostic [O III]/[N II] plotted

against the excitation-dependent [O III]/[O II] ratio. Both ratios are also sensitive to log q,

but provide sufficient sensitivity to both abundance and ionisation parameter to make this

a useful diagnostic diagram. In addition, the AGN branch is quite distinct.

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8. Applying the Abundance Diagnostics

8.1. Self-Consistency

Before applying the new diagnostics, it is mandatory to check them for self-consistency.

For this purpose, we have selected the four best diagnostics on the grounds that they should

adequately separate the two parameters, log(q) and 12+log(O/H), and be sensitive to these

over the full range of both parameters. Bearing in mind that many of the diagnostics are

not truly independent, since they employ the same line ratios in at least one axis, we have

selected a subset of four, two based upon [N II]/[O II], and two based upon [N II]/[S II]:

1. [N II]/[O II] vs. [O III]/[O II]

2. [N II]/[O II] vs. [O III]/[S II]

3. [N II]/[S II] vs. [O III]/Hβ, and

4. [N II]/[S II] vs. [O III]/[S II].

For the observational test set we have used the homogeneous van Zee et al. (1998)

observations, which cover a wide abundance range of H ii regions in several galaxies. For

each of these, we have graphically solved for the implied oxygen abundance (to the nearest

0.01dex) and for the ionisation parameter (to the nearest 0.1dex) using our four diagnostics.

A value of κ = 20 was assumed, on the basis of the discussion in Section 5. We then formed

a global average for each of the parameters using all for diagnostics. The result is shown in

Figure 24 for the chemical abundances, and in Figure 25 for the ionisation parameter.

It is clear that all four methods are in remarkably close agreement with each other.

For those abundance diagnostics involving [O II], the scatter is somewhat larger, presum-

ably reflecting increased photometric and reddening correction errors. As expected, the

[N II]/[S II] vs. [O III]/[S II] diagnostic gives the smallest scatter. There appears to be little

or no systematic difference in derived abundance as a function of abundance for any of the

diagnostics.

For the ionisation parameter, [N II]/[O II] vs. [O III]/[S II] gives the smallest scatter.

For [N II]/[O II] vs. [O III]/[O II] a small systematic trend towards higher derived log(q) at

higher q is apparent. [N II]/[S II] vs. [O III]/[S II] gives the greatest scatter in derived log(q).

However these effects are small, and the global solution using all four diagnostics appears to

be robust.

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7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

12+l

og(O

/H)

log[N II]/[O II] vs. log[O III]/[O II]

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

12+l

og(O

/H)

log[N II]/[O II] vs. log[O III]/[S II]

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

12+l

og(O

/H)

log[N II]/[S II] vs. log[O III]/H-Beta

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

12+l

og(O

/H)

log[N II]/[S II] vs. log[O III]/[S II]

(a) (b)

(c) (d)

Fig. 24.— Chemical abundances derived for the van Zee et al. (1998) H ii regions using each

of the four diagnostics given on the label, plotted against the average of all four.

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– 53 –

6.8 7.0 7.2 7.5 7.8 8.0 8.2

6.8

7.0

7.2

7.5

7.8

8.0

8.2

log

q

6.8 7.0 7.2 7.5 7.8 8.0 8.2

6.8

7.0

7.2

7.5

7.8

8.0

8.2

log

q

6.8 7.0 7.2 7.5 7.8 8.0 8.2

6.8

7.0

7.2

7.5

7.8

8.0

8.2

log

q

6.8 7.0 7.2 7.5 7.8 8.0 8.2

6.8

7.0

7.2

7.5

7.8

8.0

8.2

log

q

log[N II]/[O II] vs. log[O III]/[S II]log[N II]/[O II] vs. log[O III]/[O II]

log[N II]/[S II] vs. log[O III]/[S II]log[N II]/[S II] vs. log[O III]/H-Beta

<log q> <log q>

<log q><log q>

(d)

(b)(a)

(c)

Fig. 25.— As figure 24, but for the derived ionisation parameter.

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8.2. Comparison with Kewley & Dopita (2002)

Given that the Kewley & Dopita (2002) work was based upon an earlier version of the

MAPPINGS code, it is interesting to see how our new abundance diagnostics compare with

that earlier work. The main changes in the code that have occurred in the eleven years since

are:

• A proper match of the stellar and nebular abundances.

• Use of Grevesse et al. (2010) revised abundance set and new CN abundance variations.

• Inclusion of the effect of radiation pressure.

• Use of spherical geometry rather than plane parallel geometry.

• Improved atomic data (as described above)

• Inclusion of the possibility of κ-distributed electrons.

Again, we have used the homogeneous van Zee et al. (1998) observations to facilitate

this comparison, reducing the data with the procedure described in Kewley & Dopita (2002).

This provides four abundance diagnostics, based on, respectively, the R23 calibration, the

[N II]/[O II] vs. [O III]/[O II] diagnostic, the [N II]/[S II] vs. [O III]/[O II] and the [N II]/Hα

ratio. The results are shown in Figure 26.

The correlation between our abundances and the Kewley & Dopita (2002) R23 abun-

dances is good at the high abundance end. However, the scatter is large in the region

8.2 . 12 + log(O/H) . 8.7, where the R23 indicator is almost insensitive to O/H. The

[N II]/Hα method produces large scatter, with a systematic offset at the high abundance

limit. As expected, the [N II]/[O II] vs. [O III]/[O II] diagnostics agree very well with

one another. The systematic offset can be largely ascribed to the re-calibration of the N/O

abundance with respect to O/H (which provides both an offset and the curvature seen at

low abundance) and the change in the stellar EUV spectra. However, the [N II]/[S II] vs.

[O III]/[O II] diagnostic shows both a large (∼ 0.3dex) offset and marked curvature.

The average of all four Kewley & Dopita (2002) diagnostics is given in Figure 27. The

overall correlation is good, and this implies that previous results on the chemical composition

of galaxies based on the Kewley & Dopita (2002) diagnostics do not need revision except

perhaps at the low- and high-abundance extremes.

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7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

<12+

log(

O/H

)> K

D02

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

<12+

log(

O/H

)> K

D02

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

12+log(O/H)

12+l

og(O

/H)

KD02

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

12+log(O/H)

12+l

og(O

/H)

KD02

(a) R23 (b) [N II]/H-alpha

(c) [N II]/[O II] (d) [N II]/[S II]

Fig. 26.— The abundances derived from the van Zee et al. (1998) H ii regions using the

Kewley & Dopita (2002) abundance diagnostics, compared with those of this paper. In

panels (a) and (b) we compare the R23 method and the [N II]/Hα method with the mean

of our abundance diagnostics. The error bars show the internal RMS dispersion for our

abundance estimates. In panels (c) and (d) we use the [N II]/[O II] vs. [O III]/[O II] and the

[N II]/[S II] vs. [O III]/[O II] diagnostics from the Kewley & Dopita (2002) paper, compared

with these same diagnostics from this paper.

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7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

<12+

log(

O/H

)> K

D02

Fig. 27.— The mean of the Kewley & Dopita (2002) diagnostics plotted against the mean of

the diagnostics used in this paper. The error bars are the RMS scatter of the four diagnostics

used to create the mean in each case. The systematic offset can be largely ascribed to the

offset of the [N II]/[O II] and [N II]/[S II] diagnostics.

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8.3. Comparison with van Zee et al. (1998)

In their paper, van Zee et al. (1998) used a hybrid technique to determine abundances,

based upon both strong lines and on a calibration of the excitation with the Te measured for

a small subset of her sample. In essence, therefore, this is essentially a Te-based calibration,

similar to those used by Pilyugin and his collaborators (Pilyugin 2001a,b; Pilyugin & Thuan

2005; Pilyugin & Mattsson 2011a; Pilyugin et al. 2012). In Figure 28 we show the correlation

between the van Zee et al. (1998) abundances and those derived in this paper. Note that,

although the correlation is very good, there is a small systematic offset between the two in

the same sense as as is usually found for strong line methods calibrated using photoionisation

models compared with methods based on Te (see the discussion of this in the Introduction).

van Zee et al. (1998) also compared their data with abundances determined by two strong

line methods based upon the R23 ratio; that of Zaritsky, Kennicutt & Huchra (1994) and

of Edmunds & Pagel (1984). The comparison of these two methods with our abundances is

shown in Figure 29. Note that the Zaritsky, Kennicutt & Huchra (1994) method is applicable

only to the high abundance branch, which is why the scatter increases below 12+log(O/H)∼8.7. Otherwise this method agrees rather closely with our results. As previously found in

Kewley & Dopita (2002), the Edmunds & Pagel (1984) method is subject to large systematic

errors.

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7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

12+l

og(O

/H) (

vZ)

Fig. 28.— The abundances derived by van Zee et al. (1998) for their H ii regions compared

with the abundances derived here. Note the close similarity with Figure 27. Here the

systematic offset of ∼ 0.2 dex. can be understood as another manifestation of the systematic

offset always found between strong-line and Te-based abundance determinations (Lopez-

Sanchez et al. 2012).

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7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>

12+l

og(O

/H) (

ZKH

)

7.6 7.8 8.0 8.2 8.4 8.6 8.8 9.0 9.2 9.4

7.6

7.8

8.0

8.2

8.4

8.6

8.8

9.0

9.2

9.4

<12+log(O/H)>12

+log

(O/H

) (EP

84)

(a) (b)

Fig. 29.— The abundances derived here for the van Zee et al. (1998) H ii regions compared

with those derived from the methods of Zaritsky, Kennicutt & Huchra (1994) and of Edmunds

& Pagel (1984). Both of these are R23 techniques, but the Zaritsky, Kennicutt & Huchra

(1994) method is applicable only to the high abundance branch, which is why the scatter

increases below 12+log(O/H)∼ 8.7. The Edmunds & Pagel (1984) method is clearly subject

to large systematic errors.

8.4. An automated technique to derive abundances

In this paper we have presented a grid of models covering a wide range of abundance

and ionisation parameters typical of H ii regions in galaxies. However, given an observed

set of ratios, we need to implement a two dimensional interpolation routine to read the

diagnostic line ratio grid between the nodes actually computed. For this purpose, we have

implemented a dedicated Python module to perform this task automatically - the pyqz mod-

ule. This module relies on the griddata function in the scipy.interpolate module to perform a

two dimensional fit to a given diagnostic grid. The griddata routine allows either a linear or

piecewise cubic spline fit to a N-dimensional unstructured dataset. We refer the reader to

the Scipy Reference Guide for more information on the griddata function 2.

As discussed in Section 7, several diagnostic grids allow a clear separation of both log q

and 12+log(O/H). In Figure 30 and 31, we use our pyqz module to test how well these

different grids can be interpolated to recover the value of log q or 12+log(O/H), respectively.

2The information page for the griddata function is located at:

http://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.griddata.html .

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Each row corresponds to a different diagnostic grid labelled accordingly. In the left and

middle column, we show the result of the interpolation performed using the linear or piecewise

cubic approach. In the right column, we show the difference, in %, between the two different

interpolation results. The grids in this case are computed for κ = 20. The error maps in

Figure 30 and 31 do not represent absolute error on the interpolation results. Nevertheless,

they indicate how well a given grid can be read. In most cases, the difference between the

two interpolation methods is lower than 5%. These grids provide consistent results between

the two different interpolation methods, with errors below 1% for most of the interpolation

region.

For both the log q and 12+log(O/H) grids, we mark with a black star which interpo-

lation method (linear or piecewise cubic) provides the smoothest result, based on a visual

comparison of the two different interpolated grid. The absolute grid error associated with

the best interpolation method can be expected to be smaller than the error map provided

in the right column, which can be used as an upper estimate of the uncertainty associated

with reading a given diagnostic grid. We note that the error associated with reading of

the grid is much smaller than errors associated with the computation of the grid itself, and

observational errors affecting line ratios.

Our pyqz Python module (v0.4) is made freely available for the community to use

under the GNU General Public License, and can be downloaded from the Australian Na-

tional University Data Commons online repository (doi:10.4225/13/516366F6F24ED). This

module allows observers to interpolate within any of the line ratio grids listed in Table 7

for κ ∈ [10, 20, 50,∞]. With any given set of observed line ratios the module returns the

corresponding log q and 12+log(O/H) values for the chosen value of κ if the observed ratios

lie within a readable region of the grid (with no wrapping present). The specific readable

regions, for all diagnostic grids and κ, are listed in Table 7

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-2-101

[OIII

]/[S

II]

7.69 8.17 8.69 9.1712+log(O/H)

1 2 3 4 5%

-2-101

[OIII

]/Hβ

-1.5 -0.5 0.5

-2-101

[OIII

]/[O

II]

-1.5 -0.5 0.5[NII]/[SII]

-1.5 -0.5 0.5

-2-101

[OIII

]/[O

II]

-1.5 -0.5 0.5

-2-101

[OIII

]/[S

II]

-1.5 -0.5 0.5[NII]/[OII]

-1.5 -0.5 0.5

Fig. 30.— Side-by-side comparison between a linear and piecewise cubic interpolation of

different diagnostic grids that allow for unambiguous reading of the logO/H value. The

third column shows the difference in % between the two different interpolation methods,

and is indicative of how accurately a given diagnostic grid can be read. These grids are for

κ = 20.

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-2-101

[OIII

]/[S

II]

7.0 7.5 8.0log q

1 2 3 4 5%

-2-101

[OIII

]/Hβ

-1.5 -0.5 0.5

-2-101

[OIII

]/[O

II]

-1.5 -0.5 0.5[NII]/[SII]

-1.5 -0.5 0.5

-2-101

[OIII

]/[O

II]

-1.5 -0.5 0.5

-2-101

[OIII

]/[S

II]

-1.5 -0.5 0.5[NII]/[OII]

-1.5 -0.5 0.5

Fig. 31.— As figure 30, but for the ionisation parameter log(q).

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8.5. Implications of κ for Te - based abundance diagnostics

In a future paper we propose to examine in more detail what are the implications of

κ-distributed electrons on abundances derived by Te methods. However, here we will give an

outline explanation of how κ could help to address the long-standing discrepancy between

the abundance scales defined by strong line techniques and that defined by the Te method.

The κ-distributed electrons affect the Te method in three separate ways. First, as pointed

out by Nicholls et al. (2012, 2013), the κ-distribution directly affects the electron temperature

measured by the usual temperature-sensitive line ratios such as [O III] λ4363 / [O III] λ5007.

This effect is most marked at the high abundance end of the scale (low electron temperature

end), as can be seen in Table 6. This effect dies away for abundances below about 0.3

solar (although errors caused by use of the older temperature-averaged collisional strengths

persist down to much lower abundances; Nicholls et al. (2013)). Since the inferred electron

temperature is higher than the electron temperature for Maxwell-Boltzmann distributed

electrons, the effect of this is to systematically underestimate the true abundance through

the Te method.

The second factor is that, at the temperatures typical of H ii regions, collisional ex-

citation rates for strong lines such as [O III] λ5007 and [O II]λλ3727, 9 are reduced in a κ

distribution, while the strengths of the recombination lines are increased. This weakens these

lines relative to the Balmer lines, leading to a further underestimate of the ionic abundances

and adding to the systematic offset between strong-line techniques and the Te method. The

weakening of these forbidden lines with respect to the hydrogen recombination lines is more

significant at the low end of the abundance scale, as can be clearly seen in Figures 9 or 19.

We have estimated the size of these three effects for κ = 20 using the ratio of the

collisional excitation rates implied by the inferred electron temperatures given in Table 6

for κ = 20 and κ = ∞; the Maxwell-Boltzmann case. This correction factor has to be

further corrected by multiplying it with the ratio of the forbidden line considered - in this

case, [O III] λ5007 and [O II] λλ3727, 9 evaluated at κ = ∞ and κ = 20. In effect, we are

assuming that the derived abundance scales as the chosen line ratio with respect to Hβ. The

line strengths are drawn from Table 4.

The result of these computations is shown in Figure 32, which gives the estimated

offset between the model-based strong-line method and the Te method for the ionic ratios

O++/H+ and O+/H+, which are fundamental for deriving O/H in the Te method. Typical

offsets lie between 0.2 and 0.4 dex, which are very similar to the observed offset - see (for

example) Lopez-Sanchez et al. (2012), fig 12. We conclude that κ-distributed electrons

may well provide the key to resolving the long-standing abundance discrepancy problem in

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H ii regions.

7.50 8.00 8.50 9.00

0.10

0.20

0.30

0.40

0.50

0.60

12 + log(O/H)

6.5

7.0

7.5

8.08.5

log q

++

7.50 8.00 8.50 9.00

0.10

0.20

0.30

0.40

0.50

0.60

12 + log(O/H)

Δ lo

g(O

/ H

)++

+

log q

Δ lo

g(O

/ H

)7.06.5

7.5

8.08.5

Fig. 32.— The offset in abundance implied between the strong line techniques and the Temethod for O++/H+ (left) and O+/H+ (right), for an assumed value of κ = 20. The x-axis is

the true nebular abundance. The theoretical offset is close to the actual difference observed

for H ii regions (Lopez-Sanchez et al. 2012), suggesting that κ-distributed electrons might

be capable of resolving this long-standing abundance discrepancy problem.

9. Conclusions

In this paper we have investigated the consequences of the assumption of κ-distributed

electrons rather than Maxwell-Boltzmann distributed electrons on strong line abundance

diagnostics. These models also account for the impact of new atomic data on collisional

excitation rates and transition probabilities, and the effect of the revised solar abundance

scale (Grevesse et al. 2010).

We have treated κ as a free variable in the grid of models presented here, so that

observers can elect either to use or not to use κ. However, with a κ ∼ 20, or somewhat

larger, the observed offset between the recombination temperature of bright H ii regions

and the electron temperatures inferred for both the high- and low-excitation zones can be

explained.

With κ ∼ 20, the UV lines of high-abundance, low-electron temperature H ii regions are

predicted to be very strongly enhanced, whereas the effect of κ on the mid- and far-IR lines

Page 65: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 65 –

is weak, ranging from 2− 25%. Our models clearly have some issues in their predictions of

the intensities of some of the mid-IR lines, which is likely to be due to our choice of low

density, and zero age (Snijders, Kewley & van der Werf 2007).

For the strong lines at optical wavelengths, we have developed a new set of diagnostic

diagrams which rely on the ratios of two forbidden lines rather than the ratio of a forbidden

line to a recombination line of hydrogen, as has mostly been used hitherto. These new

diagnostics cleanly separate the two parameters which principally determine the strong line

emission spectrum: the chemical abundance set and the ionisation parameter.

However, the derived abundance scale derived in this paper suffers from the weakness

of relying on the ratio of [N II] to either of the α-process ions, [O II] or [S II] . Thus, it is

highly sensitive to how well the N/O vs. O/H calibration shown in Figure 3 can be made.

This relationship clearly has scatter, especially at the low abundance end, and the reasons

for this have been discussed by many authors (Matteucci & Tosi 1985; Henry, Edmunds &

Koppen 2000; Contini et al 2002; Lopez-Sanchez & Esteban 2010) - see the recent summary

by Pilyugin & Thuan (2011b). For a given change in the N/O ratio at fixed O/H, the

calibrations involving the [N II]/[S II] ratio will be more affected than those which depend

upon the [N II]/I [O II] ratio, since the total range in the [N II]/[S II] ratio is more restricted

than that of the [N II]/[O II] ratio. In addition, the ratio of the secondary nucleosynthetic

production of nitrogen to the primary component is sensitive to the IMF, which may change

between galaxies. Nonetheless, the fact that the derived abundance is monotonic with the

abundance sensitive ratio used is a notable advantage compared to the use of the ratio of

a forbidden line to a recombination line of hydrogen, which must always be a two-valued

function of abundance. The latter ratios then have to be calibrated with an assumption

of which solution branch applies, and furthermore there is a wide range of abundance over

which the ratio of a forbidden line to a recombination line of hydrogen is insensitive to

changes in the abundance.

The prime effect of the new atomic data and the self-consistency between the abundance

set used in the stellar atmospheres and the abundance set used in the H ii region models is

to produce, for the first time, a fully consistent solution for the nebular abundances and the

nebular ionisation parameter between some half dozen strong-line diagnostics. This greatly

increases confidence in their use, as well as in the N/O vs. O/H calibration used here.

κ ∼ 20 assists in resolving the long-standing abundance discrepancy between the strong-

line and Te based techniques of deriving the nebular abundance. At the high abundance end,

κ increases the electron temperature measured from the ratio of two forbidden lines, which

leads to the Te method delivering too low abundances. At the low abundance end, the

effect of κ is to decrease the forbidden lines relative to the recombination lines of hydrogen.

Page 66: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 66 –

This also will lead to the Te method delivering too low abundances. These effects seem, in

principal, to account for all of the abundance discrepancy between the strong-line and Te+

ICF based techniques. This important point will be examined in greater detail in a future

paper.

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Table 2. Solar abundance set (Z) and the logarithmic

depletion factors (D) adopted for each element.

Element log(Z) log(D)

H 0.00 0.00

He -1.01 0.00

C -3.57 -0.30

N -4.60 -0.05

O -3.31 -0.07

Ne -4.07 0.00

Na -5.75 -1.00

Mg -4.40 -1.08

Al -5.55 -1.39

Si -4.49 -0.81

S -4.86 0.00

Cl -6.63 -1.00

Ar -5.60 0.00

Ca -5.66 -2.52

Fe -4.50 -1.31

Ni -5.78 -2.00

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– 74 –

Table 3. The C and N abundances as a function of O/H.

(Solar: 12 + log(O/H) = 8.69)

12 + log(O/H) log(N/H) log(C/H)

7.39 -6.61 -5.58

7.50 -6.47 -5.44

7.69 -6.23 -5.20

7.99 -5.79 -4.76

8.17 -5.51 -4.48

8.39 -5.14 -4.11

8.69 -4.60 -3.57

8.80 -4.40 -3.37

8.99 -4.04 -3.01

9.17 -3.67 -2.64

9.39 -3.17 -2.14

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– 75 –

Tab

le4.

The

‘blu

e’line

fluxes

give

nby

the

MA

PP

ING

S4

model

sre

lati

vetoFHβ

=1.

0.

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

5.0Z

;κ=∞

8.50

0.0105

0.0148

0.0002

0.0003

0.4447

0.0000

0.0941

1.0000

0.0021

0.0061

0.0529

0.0000

0.0000

0.0001

8.25

0.0067

0.0095

0.0001

0.0002

0.4458

0.0000

0.0923

1.0000

0.0014

0.0039

0.0498

0.0000

0.0000

0.0000

8.00

0.0048

0.0068

0.0001

0.0002

0.4470

0.0000

0.0907

1.0000

0.0010

0.0029

0.0472

0.0000

0.0000

0.0000

7.75

0.0039

0.0055

0.0001

0.0002

0.4481

0.0000

0.0889

1.0000

0.0008

0.0023

0.0452

0.0000

0.0000

0.0000

7.50

0.0030

0.0043

0.0001

0.0002

0.4488

0.0000

0.0873

1.0000

0.0006

0.0017

0.0438

0.0000

0.0000

0.0000

7.25

0.0019

0.0027

0.0000

0.0001

0.4486

0.0000

0.0841

1.0000

0.0003

0.0010

0.0423

0.0000

0.0000

0.0000

7.00

0.0008

0.0012

0.0000

0.0001

0.4472

0.0000

0.0793

1.0000

0.0001

0.0004

0.0407

0.0000

0.0000

0.0000

6.75

0.0003

0.0004

0.0000

0.0000

0.4442

0.0000

0.0728

1.0000

0.0000

0.0001

0.0396

0.0000

0.0000

0.0000

6.50

0.0000

0.0001

0.0000

0.0000

0.4394

0.0000

0.0635

1.0000

0.0000

0.0000

0.0392

0.0000

0.0000

0.0000

5.0Z

;κ=

50

8.50

0.0204

0.0285

0.0004

0.0004

0.4446

0.0000

0.0920

1.0000

0.0036

0.0104

0.0512

0.0000

0.0000

0.0001

8.25

0.0143

0.0200

0.0003

0.0004

0.4456

0.0000

0.0902

1.0000

0.0025

0.0073

0.0483

0.0000

0.0000

0.0001

8.00

0.0113

0.0159

0.0002

0.0004

0.4468

0.0000

0.0884

1.0000

0.0020

0.0058

0.0458

0.0000

0.0000

0.0001

7.75

0.0098

0.0138

0.0002

0.0004

0.4478

0.0000

0.0867

1.0000

0.0017

0.0048

0.0439

0.0000

0.0000

0.0001

7.50

0.0085

0.0120

0.0002

0.0004

0.4486

0.0000

0.0851

1.0000

0.0013

0.0037

0.0426

0.0000

0.0000

0.0000

7.25

0.0062

0.0086

0.0001

0.0003

0.4483

0.0000

0.0820

1.0000

0.0007

0.0021

0.0411

0.0000

0.0000

0.0000

7.00

0.0034

0.0047

0.0001

0.0002

0.4469

0.0000

0.0774

1.0000

0.0003

0.0008

0.0396

0.0000

0.0000

0.0000

6.75

0.0015

0.0021

0.0000

0.0001

0.4440

0.0000

0.0712

1.0000

0.0001

0.0002

0.0385

0.0000

0.0000

0.0000

6.50

0.0003

0.0004

0.0000

0.0000

0.4394

0.0000

0.0626

1.0000

0.0000

0.0000

0.0383

0.0000

0.0000

0.0000

5.0Z

;κ=

20

8.50

0.0437

0.0602

0.0011

0.0008

0.4444

0.0000

0.0890

1.0000

0.0075

0.0216

0.0487

0.0000

0.0000

0.0004

8.25

0.0338

0.0467

0.0008

0.0008

0.4453

0.0000

0.0870

1.0000

0.0056

0.0161

0.0461

0.0000

0.0000

0.0003

8.00

0.0296

0.0408

0.0007

0.0008

0.4465

0.0000

0.0851

1.0000

0.0047

0.0137

0.0438

0.0000

0.0000

0.0003

7.75

0.0281

0.0386

0.0007

0.0009

0.4475

0.0000

0.0833

1.0000

0.0041

0.0117

0.0420

0.0000

0.0000

0.0003

7.50

0.0268

0.0366

0.0006

0.0010

0.4481

0.0000

0.0817

1.0000

0.0031

0.0090

0.0408

0.0000

0.0000

0.0002

7.25

0.0235

0.0319

0.0005

0.0011

0.4480

0.0000

0.0792

1.0000

0.0019

0.0056

0.0396

0.0000

0.0000

0.0002

7.00

0.0153

0.0205

0.0002

0.0008

0.4465

0.0000

0.0748

1.0000

0.0008

0.0022

0.0381

0.0000

0.0000

0.0001

6.75

0.0074

0.0096

0.0001

0.0005

0.4436

0.0000

0.0687

1.0000

0.0002

0.0006

0.0369

0.0000

0.0000

0.0001

6.50

0.0021

0.0026

0.0000

0.0002

0.4391

0.0000

0.0607

1.0000

0.0000

0.0001

0.0367

0.0000

0.0000

0.0000

5.0Z

;κ=

10

8.50

0.1030

0.1361

0.0033

0.0018

0.4438

0.0001

0.0835

1.0000

0.0193

0.0558

0.0447

0.0000

0.0000

0.0015

8.25

0.0900

0.1183

0.0027

0.0018

0.4446

0.0001

0.0815

1.0000

0.0159

0.0460

0.0425

0.0000

0.0000

0.0013

8.00

0.0876

0.1137

0.0026

0.0020

0.4457

0.0000

0.0795

1.0000

0.0142

0.0410

0.0404

0.0000

0.0000

0.0012

Page 76: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 76 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

7.75

0.0906

0.1158

0.0026

0.0025

0.4466

0.0000

0.0776

1.0000

0.0122

0.0353

0.0389

0.0000

0.0000

0.0012

7.50

0.0934

0.1181

0.0024

0.0030

0.4472

0.0000

0.0760

1.0000

0.0091

0.0262

0.0378

0.0000

0.0000

0.0013

7.25

0.0887

0.1110

0.0018

0.0034

0.4469

0.0000

0.0737

1.0000

0.0053

0.0153

0.0368

0.0000

0.0000

0.0012

7.00

0.0660

0.0796

0.0010

0.0032

0.4455

0.0000

0.0698

1.0000

0.0021

0.0061

0.0354

0.0000

0.0000

0.0009

6.75

0.0368

0.0407

0.0004

0.0023

0.4427

0.0000

0.0644

1.0000

0.0006

0.0017

0.0343

0.0000

0.0000

0.0005

6.50

0.0126

0.0116

0.0001

0.0012

0.4385

0.0000

0.0574

1.0000

0.0001

0.0003

0.0341

0.0000

0.0000

0.0002

3.0Z

;κ=∞

8.50

0.2716

0.3893

0.0226

0.0037

0.4542

0.0003

0.0768

1.0000

0.1242

0.3591

0.0388

0.0001

0.0001

0.0016

8.25

0.2880

0.4139

0.0214

0.0042

0.4550

0.0002

0.0761

1.0000

0.1162

0.3358

0.0384

0.0001

0.0001

0.0016

8.00

0.3166

0.4555

0.0207

0.0051

0.4560

0.0002

0.0753

1.0000

0.1095

0.3164

0.0381

0.0001

0.0001

0.0018

7.75

0.3512

0.5055

0.0199

0.0066

0.4568

0.0001

0.0742

1.0000

0.0994

0.2875

0.0377

0.0001

0.0002

0.0019

7.50

0.3806

0.5478

0.0182

0.0085

0.4575

0.0001

0.0728

1.0000

0.0811

0.2345

0.0372

0.0001

0.0002

0.0020

7.25

0.3884

0.5589

0.0149

0.0107

0.4578

0.0001

0.0709

1.0000

0.0547

0.1581

0.0363

0.0001

0.0002

0.0019

7.00

0.3620

0.5208

0.0104

0.0125

0.4578

0.0000

0.0684

1.0000

0.0286

0.0827

0.0350

0.0000

0.0002

0.0017

6.75

0.3058

0.4398

0.0062

0.0134

0.4575

0.0000

0.0652

1.0000

0.0118

0.0340

0.0333

0.0000

0.0003

0.0014

6.50

0.2356

0.3388

0.0032

0.0130

0.4569

0.0000

0.0614

1.0000

0.0041

0.0117

0.0312

0.0000

0.0003

0.0011

3.0Z

;κ=

50

8.50

0.3144

0.4499

0.0272

0.0041

0.4539

0.0005

0.0749

1.0000

0.1458

0.4213

0.0378

0.0001

0.0001

0.0020

8.25

0.3371

0.4836

0.0260

0.0047

0.4547

0.0004

0.0743

1.0000

0.1374

0.3972

0.0375

0.0001

0.0001

0.0021

8.00

0.3759

0.5400

0.0255

0.0055

0.4556

0.0004

0.0732

1.0000

0.1301

0.3760

0.0372

0.0001

0.0003

0.0023

7.75

0.4245

0.6100

0.0248

0.0076

0.4564

0.0003

0.0724

1.0000

0.1176

0.3400

0.0368

0.0001

0.0002

0.0026

7.50

0.4692

0.6743

0.0227

0.0100

0.4571

0.0002

0.0709

1.0000

0.0945

0.2730

0.0362

0.0001

0.0002

0.0028

7.25

0.4880

0.7012

0.0185

0.0128

0.4574

0.0002

0.0691

1.0000

0.0622

0.1797

0.0354

0.0001

0.0002

0.0028

7.00

0.4643

0.6670

0.0130

0.0153

0.4573

0.0001

0.0666

1.0000

0.0320

0.0924

0.0341

0.0001

0.0003

0.0027

6.75

0.4009

0.5757

0.0078

0.0167

0.4570

0.0000

0.0635

1.0000

0.0131

0.0377

0.0324

0.0000

0.0003

0.0022

6.50

0.3163

0.4540

0.0041

0.0167

0.4565

0.0000

0.0598

1.0000

0.0045

0.0130

0.0304

0.0000

0.0003

0.0017

3.0Z

;κ=

20

8.50

0.3713

0.5295

0.0346

0.0045

0.4535

0.0012

0.0721

1.0000

0.1810

0.5232

0.0364

0.0001

0.0001

0.0026

8.25

0.4043

0.5783

0.0335

0.0053

0.4542

0.0010

0.0715

1.0000

0.1718

0.4965

0.0361

0.0001

0.0001

0.0028

8.00

0.4588

0.6570

0.0331

0.0066

0.4550

0.0009

0.0706

1.0000

0.1624

0.4694

0.0357

0.0001

0.0001

0.0032

7.75

0.5298

0.7591

0.0322

0.0088

0.4558

0.0008

0.0696

1.0000

0.1447

0.4183

0.0354

0.0001

0.0002

0.0036

7.50

0.5966

0.8549

0.0293

0.0119

0.4563

0.0006

0.0682

1.0000

0.1128

0.3260

0.0348

0.0001

0.0002

0.0041

7.25

0.6321

0.9056

0.0236

0.0156

0.4566

0.0004

0.0663

1.0000

0.0716

0.2071

0.0339

0.0001

0.0002

0.0043

7.00

0.6132

0.8784

0.0164

0.0191

0.4565

0.0002

0.0640

1.0000

0.0358

0.1034

0.0327

0.0001

0.0003

0.0042

Page 77: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 77 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

6.75

0.5423

0.7765

0.0099

0.0216

0.4562

0.0001

0.0610

1.0000

0.0144

0.0415

0.0311

0.0001

0.0003

0.0037

6.50

0.4428

0.6336

0.0053

0.0223

0.4557

0.0000

0.0575

1.0000

0.0049

0.0143

0.0292

0.0001

0.0004

0.0030

3.0Z

;κ=

10

8.50

0.4468

0.6319

0.0478

0.0052

0.4525

0.0034

0.0674

1.0000

0.2441

0.7056

0.0340

0.0002

0.0001

0.0035

8.25

0.5009

0.7108

0.0467

0.0062

0.4532

0.0032

0.0668

1.0000

0.2317

0.6698

0.0337

0.0002

0.0001

0.0039

8.00

0.5854

0.8324

0.0461

0.0079

0.4539

0.0029

0.0660

1.0000

0.2154

0.6227

0.0333

0.0002

0.0001

0.0046

7.75

0.6944

0.9885

0.0443

0.0108

0.4545

0.0025

0.0649

1.0000

0.1850

0.5346

0.0329

0.0003

0.0002

0.0056

7.50

0.8030

1.1440

0.0395

0.0150

0.4550

0.0019

0.0636

1.0000

0.1372

0.3965

0.0324

0.0003

0.0002

0.0066

7.25

0.8721

1.2430

0.0313

0.0203

0.4552

0.0012

0.0619

1.0000

0.0828

0.2394

0.0316

0.0002

0.0003

0.0074

7.00

0.8662

1.2340

0.0216

0.0258

0.4552

0.0006

0.0596

1.0000

0.0397

0.1149

0.0304

0.0002

0.0003

0.0075

6.75

0.7891

1.1230

0.0131

0.0302

0.4549

0.0002

0.0569

1.0000

0.0157

0.0454

0.0289

0.0002

0.0004

0.0069

6.50

0.6641

0.9438

0.0072

0.0322

0.0001

0.0535

0.0000

1.0000

0.0054

0.0156

0.0271

0.0001

0.0004

0.0058

2.0Z

;κ=∞

8.50

0.5862

0.8442

0.0991

0.0077

0.4593

0.0023

0.0630

1.0000

0.5160

1.4920

0.0329

0.0003

0.0005

0.0026

8.25

0.6283

0.9058

0.0960

0.0083

0.4595

0.0021

0.0628

1.0000

0.4930

1.4250

0.0329

0.0003

0.0006

0.0028

8.00

0.7061

1.0190

0.0938

0.0097

0.4598

0.0019

0.0626

1.0000

0.4666

1.3490

0.0329

0.0003

0.0006

0.0031

7.75

0.8266

1.1930

0.0911

0.0123

0.4603

0.0016

0.0622

1.0000

0.4233

1.2240

0.0329

0.0003

0.0007

0.0035

7.50

0.9796

1.4140

0.0855

0.0164

0.4609

0.0014

0.0616

1.0000

0.3498

1.0110

0.0328

0.0003

0.0008

0.0041

7.25

1.1300

1.6310

0.0747

0.0225

0.4612

0.0010

0.0607

1.0000

0.2467

0.7131

0.0325

0.0003

0.0011

0.0047

7.00

1.2210

1.7630

0.0587

0.0301

0.4614

0.0006

0.0595

1.0000

0.1399

0.4044

0.0319

0.0003

0.0014

0.0051

6.75

1.2090

1.7440

0.0405

0.0383

0.4613

0.0003

0.0578

1.0000

0.0628

0.1816

0.0310

0.0002

0.0017

0.0051

6.50

1.0970

1.5840

0.0248

0.0452

0.4610

0.0001

0.0556

1.0000

0.0235

0.0679

0.0296

0.0002

0.0021

0.0046

2.0Z

;κ=

50

8.50

0.6060

0.8718

0.1082

0.0075

0.4588

0.0036

0.0615

1.0000

0.5587

1.6150

0.0321

0.0003

0.0005

0.0028

8.25

0.6559

0.9447

0.1051

0.0083

0.4590

0.0033

0.0613

1.0000

0.5329

1.5400

0.0321

0.0003

0.0005

0.0030

8.00

0.7441

1.0720

0.1026

0.0098

0.4594

0.0030

0.0611

1.0000

0.5010

1.4480

0.0321

0.0003

0.0005

0.0034

7.75

0.8807

1.2700

0.0993

0.0125

0.4599

0.0027

0.0607

1.0000

0.4494

1.2990

0.0321

0.0004

0.0006

0.0040

7.50

1.0550

1.5210

0.0926

0.0170

0.4603

0.0023

0.0601

1.0000

0.3653

1.0560

0.0320

0.0004

0.0008

0.0047

7.25

1.2240

1.7640

0.0802

0.0236

0.4607

0.0017

0.0593

1.0000

0.2526

0.7300

0.0317

0.0004

0.0010

0.0055

7.00

1.3230

1.9080

0.0623

0.0319

0.4608

0.0010

0.0581

1.0000

0.1403

0.4056

0.0311

0.0003

0.0013

0.0061

6.75

1.3120

1.8920

0.0427

0.0409

0.4607

0.0004

0.0564

1.0000

0.0621

0.1794

0.0302

0.0003

0.0017

0.0061

6.50

1.1990

1.7280

0.0261

0.0487

0.4604

0.0002

0.0542

1.0000

0.0230

0.0665

0.0289

0.0002

0.0022

0.0056

2.0Z

;κ=

20

8.50

0.6082

0.8733

0.1190

0.0070

0.4581

0.0063

0.0593

1.0000

0.6125

1.7700

0.0309

0.0004

0.0003

0.0029

Page 78: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 78 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

8.25

0.6645

0.9553

0.1153

0.0078

0.4582

0.0059

0.0591

1.0000

0.5817

1.6810

0.0309

0.0004

0.0003

0.0032

8.00

0.7658

1.1020

0.1122

0.0094

0.4586

0.0055

0.0589

1.0000

0.5414

1.5650

0.0309

0.0004

0.0004

0.0036

7.75

0.9173

1.3200

0.1074

0.0122

0.4590

0.0049

0.0585

1.0000

0.4765

1.3770

0.0308

0.0004

0.0005

0.0044

7.50

1.1070

1.5940

0.0985

0.0168

0.4594

0.0040

0.0579

1.0000

0.3769

1.0900

0.0307

0.0005

0.0006

0.0053

7.25

1.2820

1.8460

0.0833

0.0235

0.4597

0.0028

0.0571

1.0000

0.2515

0.7270

0.0304

0.0005

0.0008

0.0063

7.00

1.3760

1.9800

0.0631

0.0320

0.4597

0.0016

0.0559

1.0000

0.1344

0.3885

0.0298

0.0004

0.0011

0.0070

6.75

1.3460

1.9370

0.0421

0.0411

0.4595

0.0007

0.0543

1.0000

0.0572

0.1653

0.0289

0.0003

0.0014

0.0070

6.50

1.2170

1.7520

0.0251

0.0490

0.4592

0.0002

0.0522

1.0000

0.0205

0.0592

0.0276

0.0002

0.0019

0.0064

2.0Z

;κ=

10

8.50

0.5729

0.8190

0.1302

0.0062

0.4567

0.0129

0.0556

1.0000

0.6676

1.9300

0.0289

0.0005

0.0001

0.0029

8.25

0.6371

0.9121

0.1254

0.0071

0.4568

0.0121

0.0555

1.0000

0.6285

1.8170

0.0289

0.0005

0.0001

0.0032

8.00

0.7463

1.0690

0.1199

0.0087

0.4571

0.0111

0.0552

1.0000

0.5731

1.6560

0.0288

0.0005

0.0001

0.0037

7.75

0.9042

1.2960

0.1114

0.0116

0.4574

0.0096

0.0548

1.0000

0.4862

1.4050

0.0287

0.0005

0.0002

0.0046

7.50

1.0870

1.5580

0.0976

0.0161

0.4576

0.0074

0.0543

1.0000

0.3633

1.0500

0.0285

0.0005

0.0002

0.0058

7.25

1.2430

1.7830

0.0782

0.0227

0.4577

0.0047

0.0535

1.0000

0.2248

0.6499

0.0282

0.0005

0.0003

0.0069

7.00

1.3170

1.8880

0.0563

0.0311

0.4576

0.0023

0.0524

1.0000

0.1104

0.3190

0.0276

0.0005

0.0004

0.0077

6.75

1.2780

1.8330

0.0362

0.0405

0.4574

0.0009

0.0508

1.0000

0.0436

0.1260

0.0267

0.0004

0.0006

0.0077

6.50

1.1670

1.6740

0.0214

0.0492

0.4571

0.0003

0.0488

1.0000

0.0149

0.0431

0.0255

0.0003

0.0009

0.0071

1.0Z

;κ=∞

8.50

0.8748

1.2640

0.2697

0.0113

0.4641

0.0150

0.0480

1.0000

1.3340

3.8560

0.0268

0.0007

0.0006

0.0025

8.25

0.9168

1.3250

0.2628

0.0119

0.4641

0.0143

0.0479

1.0000

1.2870

3.7200

0.0269

0.0007

0.0006

0.0026

8.00

1.0070

1.4550

0.2551

0.0131

0.4641

0.0135

0.0479

1.0000

1.2160

3.5160

0.0269

0.0007

0.0007

0.0028

7.75

1.1790

1.7040

0.2458

0.0155

0.4643

0.0125

0.0479

1.0000

1.1050

3.1940

0.0269

0.0008

0.0008

0.0032

7.50

1.4610

2.1120

0.2327

0.0202

0.4645

0.0110

0.0478

1.0000

0.9331

2.6970

0.0270

0.0008

0.0010

0.0040

7.25

1.8350

2.6530

0.2117

0.0279

0.4647

0.0087

0.0476

1.0000

0.6946

2.0080

0.0270

0.0009

0.0013

0.0051

7.00

2.1960

3.1750

0.1788

0.0395

0.4649

0.0057

0.0474

1.0000

0.4274

1.2360

0.0269

0.0009

0.0018

0.0063

6.75

2.3950

3.4640

0.1358

0.0549

0.4649

0.0029

0.0471

1.0000

0.2082

0.6018

0.0268

0.0008

0.0026

0.0072

6.50

2.3760

3.4360

0.0920

0.0726

0.4647

0.0011

0.0465

1.0000

0.0818

0.2365

0.0263

0.0007

0.0036

0.0073

1.0Z

;κ=

50

8.50

0.8257

1.1920

0.2704

0.0101

0.4635

0.0196

0.0468

1.0000

1.3390

3.8690

0.0262

0.0007

0.0004

0.0023

8.25

0.8691

1.2550

0.2633

0.0106

0.4635

0.0187

0.0468

1.0000

1.2900

3.7290

0.0262

0.0007

0.0004

0.0024

8.00

0.9604

1.3870

0.2547

0.0118

0.4636

0.0176

0.0468

1.0000

1.2160

3.5140

0.0262

0.0008

0.0005

0.0027

7.75

1.1320

1.6360

0.2438

0.0141

0.4637

0.0161

0.0468

1.0000

1.0980

3.1730

0.0262

0.0008

0.0006

0.0031

7.50

1.4090

2.0350

0.2280

0.0185

0.4638

0.0139

0.0467

1.0000

0.9158

2.6470

0.0263

0.0009

0.0007

0.0039

Page 79: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 79 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

7.25

1.7610

2.5440

0.2035

0.0258

0.4640

0.0107

0.0466

1.0000

0.6680

1.9310

0.0263

0.0009

0.0009

0.0050

7.00

2.0750

2.9990

0.1672

0.0363

0.4641

0.0067

0.0464

1.0000

0.3987

1.1520

0.0262

0.0009

0.0014

0.0062

6.75

2.2090

3.1930

0.1226

0.0499

0.4640

0.0032

0.0461

1.0000

0.1864

0.5388

0.0260

0.0008

0.0020

0.0069

6.50

2.1260

3.0730

0.0797

0.0651

0.4637

0.0012

0.0456

1.0000

0.0699

0.2020

0.0256

0.0006

0.0028

0.0067

1.0Z

;κ=

20

8.50

0.7338

1.0580

0.2640

0.0083

0.4625

0.0266

0.0452

1.0000

1.3120

3.7920

0.0251

0.0008

0.0002

0.0021

8.25

0.7772

1.1210

0.2563

0.0088

0.4625

0.0254

0.0452

1.0000

1.2610

3.6460

0.0251

0.0008

0.0002

0.0022

8.00

0.8660

1.2500

0.2462

0.0098

0.4625

0.0237

0.0452

1.0000

1.1810

3.4130

0.0251

0.0008

0.0003

0.0024

7.75

1.0280

1.4840

0.2319

0.0120

0.4625

0.0213

0.0451

1.0000

1.0510

3.0380

0.0252

0.0008

0.0003

0.0029

7.50

1.2770

1.8440

0.2110

0.0158

0.4626

0.0177

0.0451

1.0000

0.8534

2.4670

0.0252

0.0008

0.0004

0.0036

7.25

1.5680

2.2630

0.1803

0.0219

0.4626

0.0127

0.0450

1.0000

0.5943

1.7180

0.0252

0.0009

0.0006

0.0046

7.00

1.7770

2.5660

0.1393

0.0304

0.4625

0.0072

0.0450

1.0000

0.3306

0.9555

0.0251

0.0008

0.0008

0.0055

6.75

1.7880

2.5800

0.0944

0.0407

0.4621

0.0030

0.0448

1.0000

0.1409

0.4073

0.0248

0.0007

0.0012

0.0058

6.50

1.6090

2.3230

0.0561

0.0510

0.4615

0.0010

0.0443

1.0000

0.0477

0.1378

0.0244

0.0005

0.0016

0.0053

1.0Z

;κ=

10

8.50

0.5761

0.8286

0.2395

0.0063

0.4604

0.0366

0.0425

1.0000

1.1910

3.4440

0.0234

0.0007

0.0001

0.0016

8.25

0.6160

0.8864

0.2303

0.0067

0.4604

0.0347

0.0425

1.0000

1.1360

3.2830

0.0234

0.0008

0.0001

0.0017

8.00

0.6941

0.9991

0.2167

0.0076

0.4603

0.0317

0.0426

1.0000

1.0430

3.0150

0.0234

0.0008

0.0001

0.0020

7.75

0.8281

1.1920

0.1960

0.0094

0.4603

0.0271

0.0426

1.0000

0.8923

2.5790

0.0234

0.0008

0.0002

0.0024

7.50

1.0110

1.4560

0.1665

0.0125

0.4601

0.0204

0.0427

1.0000

0.6734

1.9460

0.0234

0.0008

0.0002

0.0030

7.25

1.1780

1.6960

0.1284

0.0171

0.4599

0.0125

0.0428

1.0000

0.4161

1.2030

0.0234

0.0007

0.0003

0.0037

7.00

1.2220

1.7590

0.0868

0.0230

0.4595

0.0057

0.0428

1.0000

0.1952

0.5641

0.0232

0.0006

0.0004

0.0041

6.75

1.1060

1.5900

0.0507

0.0294

0.4589

0.0019

0.0427

1.0000

0.0682

0.1971

0.0230

0.0004

0.0006

0.0038

6.50

0.9097

1.3080

0.0265

0.0354

0.4583

0.0005

0.0423

1.0000

0.0190

0.0550

0.0225

0.0003

0.0009

0.0032

0.5Z

;κ=∞

8.50

0.9135

1.3210

0.3909

0.0112

0.4674

0.0446

0.0420

1.0000

1.7650

5.1020

0.0249

0.0011

0.0002

0.0016

8.25

0.9385

1.3570

0.3863

0.0115

0.4674

0.0436

0.0420

1.0000

1.7370

5.0210

0.0249

0.0011

0.0002

0.0017

8.00

0.9963

1.4410

0.3778

0.0122

0.4674

0.0417

0.0420

1.0000

1.6780

4.8510

0.0249

0.0011

0.0002

0.0018

7.75

1.1190

1.6190

0.3638

0.0136

0.4674

0.0388

0.0420

1.0000

1.5660

4.5260

0.0249

0.0012

0.0002

0.0020

7.50

1.3490

1.9510

0.3415

0.0166

0.4674

0.0341

0.0421

1.0000

1.3670

3.9530

0.0250

0.0012

0.0003

0.0024

7.25

1.6970

2.4560

0.3066

0.0219

0.4674

0.0268

0.0422

1.0000

1.0590

3.0620

0.0250

0.0012

0.0004

0.0030

7.00

2.0820

3.0130

0.2565

0.0304

0.4673

0.0174

0.0423

1.0000

0.6784

1.9610

0.0251

0.0012

0.0005

0.0038

6.75

2.3170

3.3520

0.1939

0.0422

0.4670

0.0085

0.0425

1.0000

0.3361

0.9715

0.0251

0.0011

0.0008

0.0044

6.50

2.2860

3.3080

0.1305

0.0566

0.4665

0.0031

0.0426

1.0000

0.1285

0.3714

0.0250

0.0009

0.0012

0.0045

Page 80: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 80 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

1.0Z

;κ=

50

8.50

0.8099

1.1710

0.3698

0.0096

0.4665

0.0492

0.0411

1.0000

1.6870

4.8760

0.0243

0.0010

0.0001

0.0014

8.25

0.8335

1.2050

0.3649

0.0098

0.4664

0.0480

0.0411

1.0000

1.6580

4.7920

0.0243

0.0010

0.0001

0.0015

8.00

0.8872

1.2830

0.3553

0.0104

0.4664

0.0458

0.0411

1.0000

1.5960

4.6120

0.0242

0.0011

0.0001

0.0016

7.75

0.9998

1.4460

0.3389

0.0117

0.4663

0.0421

0.0411

1.0000

1.4760

4.2670

0.0242

0.0011

0.0002

0.0017

7.50

1.2050

1.7430

0.3123

0.0144

0.4662

0.0360

0.0412

1.0000

1.2670

3.6610

0.0243

0.0011

0.0002

0.0021

7.25

1.5040

2.1760

0.2720

0.0190

0.4661

0.0270

0.0413

1.0000

0.9509

2.7490

0.0243

0.0011

0.0003

0.0027

7.00

1.8020

2.6060

0.2179

0.0261

0.4658

0.0162

0.0415

1.0000

0.5784

1.6720

0.0243

0.0010

0.0004

0.0033

6.75

1.9270

2.7880

0.1558

0.0357

0.4654

0.0072

0.0418

1.0000

0.2673

0.7726

0.0243

0.0009

0.0005

0.0037

6.50

1.8160

2.6260

0.0986

0.0468

0.4649

0.0024

0.0420

1.0000

0.0948

0.2739

0.0243

0.0007

0.0008

0.0036

1.0Z

;κ=

20

8.50

0.6589

0.9519

0.3312

0.0074

0.4650

0.0536

0.0397

1.0000

1.5320

4.4280

0.0232

0.0009

0.0001

0.0012

8.25

0.6797

0.9820

0.3254

0.0076

0.4649

0.0520

0.0397

1.0000

1.5000

4.3350

0.0232

0.0010

0.0001

0.0012

8.00

0.7263

1.0490

0.3140

0.0081

0.4648

0.0491

0.0397

1.0000

1.4320

4.1380

0.0232

0.0010

0.0001

0.0013

7.75

0.8219

1.1880

0.2938

0.0092

0.4647

0.0440

0.0398

1.0000

1.3010

3.7600

0.0232

0.0010

0.0001

0.0014

7.50

0.9890

1.4290

0.2613

0.0113

0.4644

0.0358

0.0399

1.0000

1.0780

3.1150

0.0232

0.0010

0.0001

0.0017

7.25

1.2100

1.7490

0.2152

0.0150

0.4641

0.0246

0.0401

1.0000

0.7603

2.1970

0.0232

0.0009

0.0001

0.0022

7.00

1.3840

1.9990

0.1594

0.0203

0.4635

0.0131

0.0405

1.0000

0.4205

1.2150

0.0232

0.0008

0.0002

0.0026

6.75

1.3800

1.9940

0.1038

0.0268

0.4628

0.0050

0.0409

1.0000

0.1721

0.4974

0.0232

0.0006

0.0003

0.0027

6.50

1.2020

1.7370

0.0593

0.0335

0.4621

0.0014

0.0412

1.0000

0.0539

0.1558

0.0231

0.0004

0.0004

0.0024

1.0Z

;κ=

10

8.50

0.4504

0.6494

0.2612

0.0050

0.4622

0.0546

0.0374

1.0000

1.2270

3.5470

0.0215

0.0008

0.0000

0.0008

8.25

0.4666

0.6728

0.2541

0.0051

0.4621

0.0524

0.0374

1.0000

1.1900

3.4400

0.0215

0.0008

0.0000

0.0008

8.00

0.5018

0.7236

0.2396

0.0055

0.4620

0.0481

0.0375

1.0000

1.1120

3.2130

0.0214

0.0008

0.0000

0.0009

7.75

0.5708

0.8233

0.2143

0.0064

0.4617

0.0407

0.0376

1.0000

0.9658

2.7920

0.0214

0.0008

0.0000

0.0010

7.50

0.6797

0.9803

0.1762

0.0080

0.4612

0.0297

0.0379

1.0000

0.7353

2.1250

0.0214

0.0007

0.0000

0.0012

7.25

0.7925

1.1430

0.1293

0.0106

0.4605

0.0173

0.0383

1.0000

0.4518

1.3060

0.0214

0.0006

0.0001

0.0015

7.00

0.8220

1.1850

0.0828

0.0139

0.4597

0.0073

0.0388

1.0000

0.2051

0.5929

0.0214

0.0005

0.0001

0.0016

6.75

0.7256

1.0450

0.0461

0.0176

0.4590

0.0021

0.0395

1.0000

0.0669

0.1934

0.0215

0.0003

0.0001

0.0015

6.50

0.5705

0.8210

0.0231

0.0210

0.4586

0.0005

0.0399

1.0000

0.0172

0.0496

0.0214

0.0002

0.0002

0.0012

0.3Z

;κ=∞

8.50

0.7972

1.1530

0.3938

0.0095

0.4696

0.0651

0.0392

1.0000

1.6890

4.8810

0.0240

0.0011

0.0001

0.0011

8.25

0.8101

1.1720

0.3911

0.0097

0.4696

0.0642

0.0392

1.0000

1.6730

4.8350

0.0240

0.0011

0.0001

0.0011

8.00

0.8419

1.2180

0.3839

0.0100

0.4696

0.0619

0.0392

1.0000

1.6310

4.7130

0.0240

0.0012

0.0001

0.0011

Page 81: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 81 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

7.75

0.9134

1.3220

0.3687

0.0108

0.4695

0.0574

0.0392

1.0000

1.5370

4.4410

0.0240

0.0012

0.0001

0.0012

7.50

1.0570

1.5300

0.3415

0.0126

0.4693

0.0495

0.0393

1.0000

1.3550

3.9180

0.0240

0.0012

0.0002

0.0014

7.25

1.2960

1.8760

0.2989

0.0159

0.4690

0.0376

0.0395

1.0000

1.0590

3.0600

0.0240

0.0012

0.0002

0.0017

7.00

1.5780

2.2830

0.2415

0.0214

0.4685

0.0231

0.0398

1.0000

0.6769

1.9560

0.0240

0.0011

0.0003

0.0022

6.75

1.7470

2.5290

0.1765

0.0292

0.4679

0.0106

0.0402

1.0000

0.3290

0.9510

0.0241

0.0009

0.0004

0.0025

6.50

1.7000

2.4600

0.1158

0.0390

0.4672

0.0036

0.0406

1.0000

0.1210

0.3497

0.0241

0.0007

0.0006

0.0025

0.3Z

;κ=

50

8.50

0.6762

0.9782

0.3562

0.0079

0.4682

0.0646

0.0383

1.0000

1.5500

4.4790

0.0233

0.0010

0.0001

0.0002

8.25

0.6878

0.9950

0.3530

0.0080

0.4682

0.0635

0.0383

1.0000

1.5320

4.4290

0.0233

0.0010

0.0001

0.0009

8.00

0.7158

1.0360

0.3447

0.0083

0.4681

0.0608

0.0384

1.0000

1.4870

4.2970

0.0233

0.0011

0.0001

0.0009

7.75

0.7788

1.1270

0.3276

0.0090

0.4680

0.0556

0.0384

1.0000

1.3870

4.0090

0.0233

0.0011

0.0001

0.0010

7.50

0.9036

1.3070

0.2975

0.0105

0.4677

0.0466

0.0385

1.0000

1.1990

3.4650

0.0233

0.0011

0.0001

0.0012

7.25

1.1020

1.5940

0.2521

0.0134

0.4672

0.0337

0.0387

1.0000

0.9032

2.6110

0.0233

0.0010

0.0001

0.0015

7.00

1.3120

1.8990

0.1948

0.0179

0.4666

0.0192

0.0391

1.0000

0.5456

1.5770

0.0233

0.0009

0.0002

0.0018

6.75

1.3970

2.0210

0.1349

0.0241

0.4658

0.0080

0.0396

1.0000

0.2464

0.7121

0.0234

0.0007

0.0003

0.0020

6.50

1.2970

1.8770

0.0835

0.0315

0.4651

0.0024

0.0401

1.0000

0.0839

0.2426

0.0234

0.0005

0.0004

0.0019

0.3Z

;κ=

20

8.50

0.5186

0.7497

0.3000

0.0058

0.4660

0.0615

0.0371

1.0000

1.3320

3.8490

0.0222

0.0009

0.0000

0.0007

8.25

0.5282

0.7636

0.2962

0.0059

0.4659

0.0602

0.0371

1.0000

1.3120

3.7930

0.0222

0.0009

0.0000

0.0007

8.00

0.5513

0.7969

0.2865

0.0061

0.4658

0.0569

0.0371

1.0000

1.2620

3.6470

0.0222

0.0009

0.0000

0.0007

7.75

0.6024

0.8710

0.2670

0.0067

0.4655

0.0506

0.0372

1.0000

1.1550

3.3370

0.0222

0.0009

0.0000

0.0008

7.50

0.7008

1.0130

0.2338

0.0080

0.4651

0.0403

0.0373

1.0000

0.9612

2.7780

0.0222

0.0009

0.0001

0.0009

7.25

0.8442

1.2210

0.1872

0.0102

0.4644

0.0268

0.0377

1.0000

0.6783

1.9610

0.0222

0.0008

0.0001

0.0011

7.00

0.9643

1.3940

0.1342

0.0135

0.4637

0.0135

0.0382

1.0000

0.3713

1.0730

0.0222

0.0006

0.0001

0.0013

6.75

0.9584

1.3850

0.0850

0.0177

0.4629

0.0049

0.0388

1.0000

0.1482

0.4284

0.0223

0.0005

0.0001

0.0014

6.50

0.8237

1.1900

0.0478

0.0220

0.4621

0.0013

0.0395

1.0000

0.0447

0.1292

0.0223

0.0003

0.0002

0.0012

0.3Z

;κ=

10

8.50

0.3287

0.4744

0.2192

0.0037

0.4626

0.0535

0.0351

1.0000

0.9962

2.8800

0.0205

0.0006

0.0000

0.0004

8.25

0.3357

0.4844

0.2144

0.0038

0.4625

0.0517

0.0351

1.0000

0.9732

2.8130

0.0205

0.0006

0.0000

0.0004

8.00

0.3523

0.5085

0.2030

0.0040

0.4623

0.0475

0.0351

1.0000

0.9169

2.6500

0.0204

0.0006

0.0000

0.0005

7.75

0.3883

0.5604

0.1809

0.0044

0.4619

0.0399

0.0352

1.0000

0.8026

2.3200

0.0204

0.0006

0.0000

0.0005

7.50

0.4517

0.6518

0.1465

0.0053

0.4613

0.0286

0.0355

1.0000

0.6137

1.7740

0.0204

0.0006

0.0000

0.0006

7.25

0.5242

0.7563

0.1045

0.0069

0.4605

0.0161

0.0361

1.0000

0.3757

1.0860

0.0204

0.0005

0.0000

0.0007

7.00

0.5449

0.7857

0.0649

0.0089

0.4597

0.0065

0.0368

1.0000

0.1679

0.4852

0.0205

0.0003

0.0000

0.0008

Page 82: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 82 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

6.75

0.4773

0.6877

0.0353

0.0112

0.4589

0.0018

0.0378

1.0000

0.0530

0.1533

0.0207

0.0002

0.0001

0.0007

6.50

0.3690

0.5312

0.0175

0.0135

0.4586

0.0004

0.0386

1.0000

0.0131

0.0378

0.0208

0.0001

0.0001

0.0006

0.2Z

;κ=∞

8.50

0.6113

0.8847

0.3519

0.0077

0.4703

0.0708

0.0380

1.0000

1.4680

4.2430

0.0237

0.0010

0.0001

0.0007

8.25

0.6182

0.8946

0.3496

0.0078

0.4703

0.0698

0.0380

1.0000

1.4560

4.2080

0.0237

0.0010

0.0001

0.0007

8.00

0.6353

0.9195

0.3432

0.0080

0.4702

0.0673

0.0380

1.0000

1.4220

4.1110

0.0237

0.0010

0.0001

0.0007

7.75

0.6760

0.9784

0.3293

0.0084

0.4701

0.0622

0.0380

1.0000

1.3460

3.8900

0.0236

0.0010

0.0001

0.0007

7.50

0.7636

1.1050

0.3035

0.0095

0.4699

0.0532

0.0381

1.0000

1.1950

3.4550

0.0236

0.0010

0.0001

0.0008

7.25

0.9221

1.3350

0.2629

0.0117

0.4695

0.0398

0.0383

1.0000

0.9432

2.7260

0.0236

0.0010

0.0001

0.0010

7.00

1.1270

1.6320

0.2096

0.0154

0.4690

0.0240

0.0387

1.0000

0.6099

1.7630

0.0237

0.0009

0.0002

0.0013

6.75

1.2650

1.8310

0.1516

0.0209

0.4682

0.0107

0.0393

1.0000

0.2981

0.8617

0.0238

0.0007

0.0002

0.0014

6.50

1.2380

1.7910

0.0989

0.0278

0.4674

0.0035

0.0400

1.0000

0.1088

0.3144

0.0239

0.0006

0.0004

0.0015

0.2Z

;κ=

50

8.50

0.5035

0.7285

0.3093

0.0062

0.4690

0.0660

0.0372

1.0000

1.3100

3.7900

0.0229

0.0009

0.0001

0.0006

8.25

0.5095

0.7371

0.3066

0.0063

0.4690

0.0649

0.0372

1.0000

1.3000

3.7600

0.0229

0.0009

0.0001

0.0006

8.00

0.5244

0.7587

0.2996

0.0064

0.4690

0.0622

0.0372

1.0000

1.2600

3.6500

0.0229

0.0009

0.0001

0.0006

7.75

0.5598

0.8100

0.2845

0.0069

0.4690

0.0566

0.0372

1.0000

1.1800

3.4200

0.0229

0.0009

0.0001

0.0006

7.50

0.6356

0.9197

0.2572

0.0078

0.4680

0.0470

0.0374

1.0000

1.0300

2.9800

0.0229

0.0009

0.0001

0.0007

7.25

0.7677

1.1110

0.2160

0.0097

0.4676

0.0335

0.0377

1.0000

0.7846

2.2680

0.0229

0.0008

0.0001

0.0008

7.00

0.9228

1.3350

0.1651

0.0128

0.4668

0.0188

0.0381

1.0000

0.4796

1.3860

0.0229

0.0007

0.0001

0.0010

6.75

0.9974

1.4430

0.1135

0.0171

0.4660

0.0077

0.0388

1.0000

0.2178

0.6294

0.0231

0.0006

0.0002

0.0011

6.50

0.9311

1.3470

0.0700

0.0222

0.4651

0.0023

0.0396

1.0000

0.0736

0.2128

0.0232

0.0004

0.0002

0.0011

0.2Z

;κ=

20

8.50

0.3725

0.5386

0.2518

0.0045

0.4660

0.0585

0.0360

1.0000

1.0900

3.1600

0.0218

0.0007

0.0000

0.0004

8.25

0.3773

0.5455

0.2488

0.0045

0.4660

0.0572

0.0360

1.0000

1.0800

3.1200

0.0218

0.0007

0.0000

0.0004

8.00

0.3894

0.5630

0.2409

0.0046

0.4660

0.0541

0.0360

1.0000

1.0400

3.0100

0.0218

0.0007

0.0000

0.0004

7.75

0.4181

0.6046

0.2244

0.0050

0.4660

0.0480

0.0361

1.0000

0.9580

2.7700

0.0218

0.0007

0.0000

0.0005

7.50

0.4782

0.6914

0.1959

0.0058

0.4650

0.0379

0.0363

1.0000

0.8040

2.3200

0.0218

0.0007

0.0001

0.0005

7.25

0.5749

0.8313

0.1558

0.0072

0.4650

0.0250

0.0367

1.0000

0.5730

1.6600

0.0218

0.0006

0.0001

0.0006

7.00

0.6666

0.9638

0.1107

0.0095

0.4640

0.0125

0.0373

1.0000

0.3180

0.9180

0.0218

0.0005

0.0001

0.0007

6.75

0.6733

0.9732

0.0698

0.0123

0.4630

0.0044

0.0382

1.0000

0.1270

0.3680

0.0220

0.0004

0.0001

0.0008

6.50

0.5814

0.8402

0.0393

0.0154

0.4620

0.0011

0.0391

1.0000

0.0381

0.1100

0.0222

0.0002

0.0002

0.0007

0.2Z

;κ=

10

8.50

0.2257

0.3258

0.1768

0.0027

0.4630

0.0469

0.0341

1.0000

0.7910

2.2900

0.0201

0.0005

0.0000

0.0002

Page 83: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 83 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

8.25

0.2291

0.3307

0.1732

0.0028

0.4620

0.0453

0.0341

1.0000

0.7740

2.2400

0.0201

0.0005

0.0000

0.0002

8.00

0.2378

0.3432

0.1644

0.0029

0.4620

0.0417

0.0341

1.0000

0.7320

2.1200

0.0200

0.0005

0.0000

0.0003

7.75

0.2581

0.3726

0.1466

0.0031

0.4618

0.0350

0.0343

1.0000

0.6450

1.8640

0.0200

0.0005

0.0000

0.0003

7.50

0.2977

0.4298

0.1185

0.0038

0.4610

0.0250

0.0346

1.0000

0.4980

1.4400

0.0200

0.0004

0.0000

0.0003

7.25

0.3490

0.5037

0.0841

0.0048

0.4600

0.0140

0.0352

1.0000

0.3080

0.8910

0.0201

0.0003

0.0000

0.0004

7.00

0.3704

0.5343

0.0519

0.0062

0.4600

0.0056

0.0362

1.0000

0.1390

0.4030

0.0202

0.0002

0.0000

0.0004

6.75

0.3289

0.4740

0.0282

0.0078

0.4590

0.0015

0.0373

1.0000

0.0440

0.1270

0.0205

0.0002

0.0001

0.0004

6.50

0.2544

0.3663

0.0141

0.0093

0.4580

0.0003

0.0385

1.0000

0.0107

0.0311

0.0207

0.0001

0.0001

0.0003

0.1Z

;κ=∞

8.50

0.3394

0.4913

0.2298

0.0046

0.4700

0.0557

0.0366

1.0000

0.9360

2.7100

0.0232

0.0006

0.0001

0.0003

8.25

0.3417

0.4945

0.2283

0.0047

0.4700

0.0549

0.0366

1.0000

0.9290

2.6900

0.0232

0.0006

0.0001

0.0003

8.00

0.3476

0.5031

0.2240

0.0047

0.4700

0.0528

0.0367

1.0000

0.9090

2.6300

0.0232

0.0006

0.0001

0.0003

7.75

0.3631

0.5256

0.2146

0.0049

0.4700

0.0485

0.0367

1.0000

0.8630

2.4900

0.0232

0.0007

0.0001

0.0003

7.50

0.4002

0.5793

0.1971

0.0054

0.4700

0.0412

0.0368

1.0000

0.7720

2.2300

0.0232

0.0007

0.0001

0.0003

7.25

0.4755

0.6883

0.1696

0.0065

0.4690

0.0304

0.0371

1.0000

0.6170

1.7800

0.0232

0.0006

0.0001

0.0004

7.00

0.5855

0.8474

0.1343

0.0084

0.4690

0.0182

0.0377

1.0000

0.4060

1.1700

0.0233

0.0005

0.0001

0.0005

6.75

0.6715

0.9719

0.0969

0.0112

0.4680

0.0081

0.0384

1.0000

0.2020

0.5840

0.0234

0.0004

0.0002

0.0006

6.50

0.6666

0.9648

0.0636

0.0148

0.4680

0.0026

0.0394

1.0000

0.0739

0.2140

0.0237

0.0003

0.0003

0.0006

0.1Z

;κ=

50

8.50

0.2725

0.3944

0.1975

0.0037

0.4690

0.0494

0.0359

1.0000

0.8210

2.3700

0.0225

0.0005

0.0000

0.0002

8.25

0.2744

0.3971

0.1958

0.0037

0.4690

0.0485

0.0359

1.0000

0.8130

2.3500

0.0225

0.0005

0.0000

0.0002

8.00

0.2796

0.4047

0.1913

0.0037

0.4690

0.0464

0.0359

1.0000

0.7920

2.2900

0.0225

0.0005

0.0000

0.0002

7.75

0.2932

0.4244

0.1815

0.0039

0.4680

0.0420

0.0360

1.0000

0.7450

2.1500

0.0224

0.0006

0.0000

0.0002

7.50

0.3257

0.4714

0.1637

0.0043

0.4680

0.0347

0.0362

1.0000

0.6540

1.8900

0.0224

0.0005

0.0000

0.0003

7.25

0.3893

0.5633

0.1368

0.0053

0.4680

0.0245

0.0365

1.0000

0.5040

1.4600

0.0224

0.0005

0.0001

0.0003

7.00

0.4740

0.6859

0.1040

0.0068

0.4670

0.0137

0.0371

1.0000

0.3140

0.9080

0.0225

0.0004

0.0001

0.0004

6.75

0.5247

0.7591

0.0715

0.0091

0.4660

0.0056

0.0380

1.0000

0.1450

0.4190

0.0227

0.0003

0.0001

0.0004

6.50

0.4966

0.7184

0.0445

0.0118

0.4650

0.0016

0.0391

1.0000

0.0491

0.1420

0.0230

0.0002

0.0002

0.0004

0.1Z

;κ=

20

8.50

0.1953

0.2824

0.1566

0.0026

0.4660

0.0413

0.0348

1.0000

0.6680

1.9300

0.0214

0.0004

0.0000

0.0002

8.25

0.1968

0.2846

0.1548

0.0026

0.4660

0.0403

0.0348

1.0000

0.6600

1.9100

0.0214

0.0004

0.0000

0.0002

8.00

0.2010

0.2907

0.1500

0.0026

0.4660

0.0381

0.0348

1.0000

0.6380

1.8500

0.0213

0.0004

0.0000

0.0002

7.75

0.2122

0.3069

0.1398

0.0028

0.4660

0.0336

0.0349

1.0000

0.5900

1.7100

0.0213

0.0004

0.0000

0.0002

7.50

0.2385

0.3449

0.1218

0.0031

0.4650

0.0265

0.0352

1.0000

0.4990

1.4400

0.0213

0.0004

0.0000

0.0002

Page 84: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 84 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

7.25

0.2861

0.4138

0.0965

0.0039

0.4640

0.0173

0.0356

1.0000

0.3610

1.0400

0.0213

0.0004

0.0000

0.0002

7.00

0.3385

0.4895

0.0684

0.0050

0.4630

0.0086

0.0364

1.0000

0.2040

0.5890

0.0215

0.0003

0.0000

0.0003

6.75

0.3505

0.5067

0.0433

0.0065

0.4630

0.0031

0.0375

1.0000

0.0830

0.2400

0.0217

0.0002

0.0001

0.0003

6.50

0.3064

0.4428

0.0246

0.0081

0.4620

0.0008

0.0388

1.0000

0.0248

0.0718

0.0220

0.0001

0.0001

0.0003

0.1Z

;κ=

10

8.50

0.1136

0.1640

0.1066

0.0015

0.4620

0.0309

0.0330

1.0000

0.4700

1.3600

0.0196

0.0003

0.0000

0.0001

8.25

0.1147

0.1656

0.1046

0.0015

0.4620

0.0299

0.0331

1.0000

0.4610

1.3300

0.0196

0.0003

0.0000

0.0001

8.00

0.1178

0.1700

0.0994

0.0016

0.4620

0.0275

0.0331

1.0000

0.4380

1.2700

0.0196

0.0003

0.0000

0.0001

7.75

0.1259

0.1818

0.0888

0.0017

0.4615

0.0229

0.0332

1.0000

0.3878

1.1210

0.0196

0.0003

0.0000

0.0001

7.50

0.1438

0.2077

0.0716

0.0020

0.4610

0.0163

0.0336

1.0000

0.3020

0.8730

0.0196

0.0002

0.0000

0.0001

7.25

0.1705

0.2461

0.0507

0.0025

0.4600

0.0091

0.0344

1.0000

0.1900

0.5490

0.0197

0.0002

0.0000

0.0001

7.00

0.1861

0.2686

0.0313

0.0032

0.4590

0.0037

0.0355

1.0000

0.0875

0.2530

0.0199

0.0001

0.0000

0.0002

6.75

0.1690

0.2436

0.0172

0.0040

0.4590

0.0010

0.0369

1.0000

0.0280

0.0808

0.0203

0.0001

0.0000

0.0001

6.50

0.1316

0.1895

0.0087

0.0048

0.4580

0.0002

0.0385

1.0000

0.0068

0.0196

0.0207

0.0001

0.0000

0.0001

0.05Z

;κ=∞

8.50

0.1801

0.2606

0.1275

0.0025

0.4698

0.0335

0.0361

1.0000

0.5135

1.4840

0.0230

0.0004

0.0000

0.0001

8.25

0.1809

0.2618

0.1266

0.0025

0.4698

0.0330

0.0361

1.0000

0.5098

1.4740

0.0230

0.0004

0.0000

0.0001

8.00

0.1832

0.2652

0.1243

0.0025

0.4700

0.0317

0.0361

1.0000

0.4990

1.4400

0.0230

0.0004

0.0000

0.0001

7.75

0.1898

0.2748

0.1191

0.0026

0.4700

0.0291

0.0361

1.0000

0.4750

1.3700

0.0230

0.0004

0.0000

0.0001

7.50

0.2068

0.2993

0.1093

0.0028

0.4700

0.0246

0.0363

1.0000

0.4260

1.2300

0.0230

0.0004

0.0000

0.0001

7.25

0.2433

0.3522

0.0938

0.0034

0.4690

0.0181

0.0366

1.0000

0.3420

0.9890

0.0230

0.0003

0.0000

0.0002

7.00

0.2995

0.4336

0.0739

0.0043

0.4690

0.0107

0.0372

1.0000

0.2270

0.6550

0.0231

0.0003

0.0001

0.0002

6.75

0.3459

0.5007

0.0531

0.0058

0.4680

0.0047

0.0380

1.0000

0.1130

0.3280

0.0232

0.0002

0.0001

0.0002

6.50

0.3450

0.4993

0.0348

0.0077

0.4680

0.0015

0.0390

1.0000

0.0414

0.1200

0.0235

0.0002

0.0001

0.0003

0.05Z

;κ=

50

8.50

0.1434

0.2074

0.1088

0.0020

0.4682

0.0292

0.0354

1.0000

0.4476

1.2940

0.0223

0.0003

0.0000

0.0001

8.25

0.1440

0.2085

0.1079

0.0020

0.4682

0.0287

0.0354

1.0000

0.4438

1.2830

0.0223

0.0003

0.0000

0.0001

8.00

0.1461

0.2114

0.1055

0.0020

0.4681

0.0274

0.0354

1.0000

0.4330

1.2520

0.0222

0.0003

0.0000

0.0001

7.75

0.1520

0.2199

0.1001

0.0021

0.4680

0.0248

0.0354

1.0000

0.4081

1.1800

0.0222

0.0003

0.0000

0.0001

7.50

0.1670

0.2416

0.0902

0.0023

0.4678

0.0204

0.0356

1.0000

0.3590

1.0380

0.0222

0.0003

0.0000

0.0001

7.25

0.1980

0.2865

0.0751

0.0027

0.4674

0.0144

0.0360

1.0000

0.2781

0.8040

0.0222

0.0003

0.0000

0.0001

7.00

0.2416

0.3496

0.0569

0.0035

0.4667

0.0080

0.0367

1.0000

0.1743

0.5038

0.0223

0.0002

0.0000

0.0002

6.75

0.2694

0.3898

0.0390

0.0047

0.4658

0.0032

0.0376

1.0000

0.0808

0.2336

0.0225

0.0002

0.0000

0.0002

6.50

0.2560

0.3704

0.0242

0.0060

0.4650

0.0009

0.0388

1.0000

0.0273

0.0789

0.0229

0.0001

0.0001

0.0002

Page 85: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 85 –

Tab

le4—

Con

tinued

[OII]

[NII]

[NeIII]

[SII]

[OIII]

HeI

[OIII]

[OIII]

HeI

[ArIII]

[NI]

[NII]

log(q)

3727

3729

3869

4068,78

4340

4363

4471

4861

4959

5007

5016

5192

5198,00

5755

0.05Z

;κ=

20

8.50

0.1016

0.1469

0.0856

0.0014

0.4656

0.0239

0.0343

1.0000

0.3620

1.0460

0.0211

0.0002

0.0000

0.0001

8.25

0.1022

0.1477

0.0847

0.0014

0.4656

0.0234

0.0343

1.0000

0.3579

1.0340

0.0211

0.0002

0.0000

0.0001

8.00

0.1039

0.1502

0.0821

0.0014

0.4655

0.0221

0.0343

1.0000

0.3466

1.0020

0.0211

0.0002

0.0000

0.0001

7.75

0.1087

0.1573

0.0765

0.0014

0.4653

0.0195

0.0344

1.0000

0.3210

0.9279

0.0211

0.0002

0.0000

0.0001

7.50

0.1210

0.1750

0.0666

0.0016

0.4649

0.0153

0.0347

1.0000

0.2724

0.7874

0.0211

0.0002

0.0000

0.0001

7.25

0.1445

0.2090

0.0526

0.0020

0.4642

0.0099

0.0352

1.0000

0.1979

0.5721

0.0211

0.0002

0.0000

0.0001

7.00

0.1718

0.2485

0.0371

0.0026

0.4633

0.0049

0.0360

1.0000

0.1123

0.3247

0.0213

0.0001

0.0000

0.0001

6.75

0.1792

0.2591

0.0234

0.0033

0.4624

0.0017

0.0372

1.0000

0.0459

0.1325

0.0215

0.0001

0.0000

0.0001

6.50

0.1571

0.2271

0.0133

0.0041

0.4616

0.0004

0.0385

1.0000

0.0137

0.0395

0.0219

0.0001

0.0000

0.0001

0.05Z

;κ=

10

8.50

0.0582

0.0841

0.0576

0.0008

0.4617

0.0175

0.0326

1.0000

0.2523

0.7292

0.0194

0.0001

0.0000

0.0000

8.25

0.0586

0.0847

0.0566

0.0008

0.4617

0.0169

0.0326

1.0000

0.2478

0.7163

0.0194

0.0001

0.0000

0.0000

8.00

0.0599

0.0865

0.0539

0.0008

0.4616

0.0155

0.0326

1.0000

0.2358

0.6817

0.0194

0.0001

0.0000

0.0000

7.75

0.0635

0.0917

0.0481

0.0009

0.4612

0.0129

0.0328

1.0000

0.2095

0.6057

0.0194

0.0001

0.0000

0.0000

7.50

0.0720

0.1040

0.0388

0.0010

0.4606

0.0092

0.0332

1.0000

0.1636

0.4730

0.0194

0.0001

0.0000

0.0000

7.25

0.0854

0.1233

0.0273

0.0013

0.4599

0.0051

0.0340

1.0000

0.1032

0.2984

0.0195

0.0001

0.0000

0.0001

7.00

0.0940

0.1357

0.0168

0.0016

0.4592

0.0020

0.0352

1.0000

0.0477

0.1379

0.0197

0.0001

0.0000

0.0001

6.75

0.0859

0.1238

0.0092

0.0021

0.4586

0.0006

0.0367

1.0000

0.0153

0.0441

0.0202

0.0000

0.0000

0.0001

6.50

0.0669

0.0964

0.0047

0.0025

0.4582

0.0001

0.0383

1.0000

0.0037

0.0107

0.0207

0.0000

0.0000

0.0000

Page 86: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 86 –

Tab

le5.

The

‘red

’line

fluxes

give

nby

the

MA

PP

ING

S4

model

sre

lati

vetoFHβ

=1.

0.

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

5.0Z

;κ=∞

8.50

0.3218

0.0012

0.0001

0.0565

3.3420

0.1661

0.0880

0.0267

0.0188

0.0052

0.0000

0.0013

0.0559

0.1403

8.25

0.3130

0.0010

0.0001

0.0472

3.3210

0.1387

0.0863

0.0259

0.0182

0.0044

0.0000

0.0011

0.0488

0.1227

8.00

0.3037

0.0010

0.0000

0.0429

3.2950

0.1263

0.0844

0.0277

0.0194

0.0042

0.0000

0.0010

0.0457

0.1147

7.75

0.2942

0.0011

0.0000

0.0422

3.2730

0.1243

0.0823

0.0322

0.0226

0.0045

0.0000

0.0011

0.0447

0.1122

7.50

0.2865

0.0012

0.0000

0.0416

3.2580

0.1223

0.0804

0.0375

0.0263

0.0047

0.0000

0.0011

0.0422

0.1059

7.25

0.2758

0.0011

0.0000

0.0355

3.2660

0.1044

0.0775

0.0378

0.0266

0.0040

0.0000

0.0010

0.0339

0.0851

7.00

0.2620

0.0008

0.0000

0.0235

3.3000

0.0692

0.0733

0.0298

0.0210

0.0026

0.0000

0.0006

0.0209

0.0525

6.75

0.2449

0.0005

0.0000

0.0124

3.3670

0.0365

0.0678

0.0187

0.0132

0.0012

0.0000

0.0003

0.0099

0.0248

6.50

0.2206

0.0002

0.0000

0.0035

3.4790

0.0103

0.0597

0.0065

0.0046

0.0002

0.0000

0.0001

0.0025

0.0063

5.0Z

;κ=

50

8.50

0.3138

0.0015

0.0002

0.0683

3.3460

0.2009

0.0860

0.0318

0.0224

0.0066

0.0001

0.0016

0.0620

0.1558

8.25

0.3048

0.0013

0.0001

0.0592

3.3250

0.1741

0.0842

0.0318

0.0223

0.0057

0.0001

0.0014

0.0555

0.1394

8.00

0.2954

0.0013

0.0001

0.0560

3.3010

0.1647

0.0822

0.0351

0.0246

0.0057

0.0000

0.0014

0.0530

0.1332

7.75

0.2861

0.0015

0.0001

0.0570

3.2790

0.1677

0.0801

0.0420

0.0295

0.0062

0.0000

0.0015

0.0526

0.1322

7.50

0.2786

0.0017

0.0001

0.0579

3.2640

0.1704

0.0783

0.0502

0.0353

0.0065

0.0000

0.0016

0.0501

0.1259

7.25

0.2681

0.0017

0.0000

0.0516

3.2730

0.1518

0.0753

0.0529

0.0372

0.0056

0.0000

0.0014

0.0407

0.1023

7.00

0.2552

0.0014

0.0000

0.0368

3.3060

0.1083

0.0715

0.0449

0.0317

0.0037

0.0000

0.0009

0.0260

0.0654

6.75

0.2388

0.0009

0.0000

0.0208

3.3730

0.0613

0.0662

0.0303

0.0215

0.0017

0.0000

0.0004

0.0128

0.0321

6.50

0.2167

0.0004

0.0000

0.0070

3.4820

0.0207

0.0588

0.0125

0.0089

0.0004

0.0000

0.0001

0.0037

0.0092

5.0Z

;κ=

20

8.50

0.3019

0.0019

0.0004

0.0862

3.3520

0.2536

0.0830

0.0394

0.0278

0.0091

0.0005

0.0022

0.0716

0.1798

8.25

0.2927

0.0018

0.0003

0.0782

3.3330

0.2299

0.0811

0.0408

0.0288

0.0081

0.0004

0.0020

0.0654

0.1643

8.00

0.2832

0.0018

0.0003

0.0777

3.3090

0.2287

0.0790

0.0471

0.0331

0.0084

0.0003

0.0020

0.0643

0.1615

7.75

0.2739

0.0021

0.0002

0.0821

3.2890

0.2415

0.0768

0.0581

0.0408

0.0091

0.0003

0.0022

0.0645

0.1621

7.50

0.2665

0.0025

0.0002

0.0864

3.2750

0.2542

0.0750

0.0717

0.0504

0.0096

0.0002

0.0023

0.0619

0.1554

7.25

0.2577

0.0028

0.0001

0.0841

3.2800

0.2474

0.0725

0.0819

0.0577

0.0089

0.0002

0.0021

0.0531

0.1333

7.00

0.2454

0.0025

0.0001

0.0643

3.3150

0.1891

0.0688

0.0749

0.0530

0.0060

0.0001

0.0014

0.0349

0.0878

6.75

0.2296

0.0018

0.0000

0.0381

3.3820

0.1121

0.0637

0.0533

0.0379

0.0028

0.0000

0.0028

0.0173

0.0435

6.50

0.2094

0.0010

0.0000

0.0151

3.4900

0.0445

0.0569

0.0255

0.0183

0.0008

0.0000

0.0002

0.0056

0.0140

5.0Z

;κ=

10

8.50

0.2812

0.0026

0.0011

0.1130

3.3670

0.3324

0.0777

0.0511

0.0364

0.0136

0.0028

0.0033

0.0850

0.2136

8.25

0.2722

0.0025

0.0009

0.1096

3.3500

0.3225

0.0757

0.0558

0.0396

0.0128

0.0023

0.0031

0.0808

0.2030

8.00

0.2626

0.0027

0.0009

0.1158

3.3270

0.3406

0.0735

0.0677

0.0479

0.0136

0.0021

0.0033

0.0816

0.2051

Page 87: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 87 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

7.75

0.2536

0.0032

0.0008

0.1274

3.3090

0.3749

0.0713

0.0862

0.0610

0.0148

0.0020

0.0036

0.0825

0.2073

7.50

0.2466

0.0040

0.0008

0.1387

3.2980

0.4079

0.0695

0.1097

0.0776

0.0152

0.0020

0.0037

0.0790

0.1984

7.25

0.2388

0.0049

0.0006

0.1396

3.3060

0.4107

0.0673

0.1303

0.0922

0.0139

0.0018

0.0033

0.0677

0.1702

7.00

0.2279

0.0050

0.0004

0.1155

3.3390

0.3399

0.0640

0.1296

0.0921

0.0096

0.0011

0.0023

0.0464

0.1165

6.75

0.2139

0.0042

0.0002

0.0767

3.4030

0.2257

0.0595

0.1031

0.0739

0.0049

0.0003

0.0012

0.0247

0.0620

6.50

0.1967

0.0027

0.0001

0.0368

3.5050

0.1084

0.0537

0.0586

0.0427

0.0016

0.0000

0.0004

0.0091

0.0228

3.0Z

;κ=∞

8.50

0.2399

0.0113

0.0033

0.1468

3.1290

0.4318

0.0680

0.0999

0.0694

0.0682

0.0040

0.0164

0.2564

0.6441

8.25

0.2358

0.0124

0.0034

0.1674

3.1080

0.4925

0.0670

0.1198

0.0829

0.0725

0.0040

0.0175

0.2794

0.7017

8.00

0.2308

0.0147

0.0035

0.2002

3.0850

0.5891

0.0657

0.1553

0.1073

0.0799

0.0041

0.0193

0.3131

0.7865

7.75

0.2252

0.0183

0.0036

0.2449

3.0620

0.7206

0.0642

0.2128

0.1470

0.0883

0.0041

0.0213

0.3480

0.8742

7.50

0.2192

0.0232

0.0036

0.2950

3.0450

0.8679

0.0626

0.2975

0.2054

0.0935

0.0040

0.0226

0.3680

0.9244

7.25

0.2126

0.0289

0.0033

0.3347

3.0350

0.9847

0.0607

0.4052

0.2797

0.0910

0.0035

0.0220

0.3572

0.8974

7.00

0.2050

0.0348

0.0026

0.3458

3.0350

1.0180

0.0586

0.5182

0.3577

0.0788

0.0029

0.0190

0.3115

0.7824

6.75

0.1961

0.0402

0.0019

0.3246

3.0410

0.9551

0.0560

0.6114

0.4222

0.0601

0.0022

0.0145

0.2439

0.6127

6.50

0.1856

0.0447

0.0012

0.2809

3.0530

0.8264

0.0530

0.6606

0.4563

0.0398

0.0015

0.0096

0.1731

0.4349

3.0Z

;κ=

50

8.50

0.2336

0.0113

0.0040

0.1469

3.1340

0.4321

0.0663

0.1009

0.0701

0.0699

0.0061

0.0169

0.2572

0.6461

8.25

0.2297

0.0124

0.0041

0.1680

3.1150

0.4944

0.0653

0.1212

0.0840

0.0743

0.0063

0.0179

0.2796

0.7023

8.00

0.2249

0.0147

0.0043

0.2018

3.0920

0.5938

0.0641

0.1575

0.1091

0.0817

0.0066

0.0197

0.3118

0.7832

7.75

0.2194

0.0184

0.0045

0.2478

3.0700

0.7291

0.0626

0.2163

0.1496

0.0898

0.0069

0.0217

0.3442

0.8645

7.50

0.2136

0.0235

0.0046

0.2994

3.0540

0.8809

0.0610

0.3028

0.2093

0.0945

0.0070

0.0228

0.3612

0.9072

7.25

0.2072

0.0298

0.0042

0.3404

3.0450

1.0010

0.0592

0.4136

0.2859

0.0912

0.0067

0.0220

0.3481

0.8744

7.00

0.1997

0.0363

0.0035

0.3531

3.0440

1.0390

0.0571

0.5313

0.3672

0.0789

0.0059

0.0190

0.3025

0.7599

6.75

0.1910

0.0428

0.0025

0.3334

3.0500

0.9809

0.0546

0.6311

0.4363

0.0601

0.0047

0.0145

0.2366

0.5944

6.50

0.1808

0.0483

0.0016

0.2906

3.0630

0.8550

0.0516

0.6873

0.4753

0.0397

0.0034

0.0096

0.1678

0.4216

3.0Z

;κ=

20

8.50

0.3713

0.5295

0.0346

0.0045

0.4535

0.0012

0.0721

1.0000

0.1810

0.5232

0.0364

0.0001

0.0001

0.0026

8.25

0.4043

0.5783

0.0335

0.0053

0.4542

0.0010

0.0715

1.0000

0.1718

0.4965

0.0361

0.0001

0.0001

0.0028

8.00

0.4588

0.6570

0.0331

0.0066

0.4550

0.0009

0.0706

1.0000

0.1624

0.4694

0.0357

0.0001

0.0001

0.0032

7.75

0.5298

0.7591

0.0322

0.0088

0.4558

0.0008

0.0696

1.0000

0.1447

0.4183

0.0354

0.0001

0.0002

0.0036

7.50

0.5966

0.8549

0.0293

0.0119

0.4563

0.0006

0.0682

1.0000

0.1128

0.3260

0.0348

0.0001

0.0002

0.0041

7.25

0.6321

0.9056

0.0236

0.0156

0.4566

0.0004

0.0663

1.0000

0.0716

0.2071

0.0339

0.0001

0.0002

0.0043

7.00

0.6132

0.8784

0.0164

0.0191

0.4565

0.0002

0.0640

1.0000

0.0358

0.1034

0.0327

0.0001

0.0003

0.0042

Page 88: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 88 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

6.75

0.5423

0.7765

0.0099

0.0216

0.4562

0.0001

0.0610

1.0000

0.0144

0.0415

0.0311

0.0001

0.0003

0.0037

6.50

0.4428

0.6336

0.0053

0.0223

0.4557

0.0000

0.0575

1.0000

0.0049

0.0143

0.0292

0.0001

0.0004

0.0030

3.0Z

;κ=

10

8.50

0.2090

0.0096

0.0068

0.1322

3.1670

0.3890

0.0594

0.0959

0.0670

0.0715

0.0177

0.0172

0.2423

0.6087

8.25

0.2057

0.0108

0.0072

0.1542

3.1510

0.4538

0.0585

0.1169

0.0815

0.0756

0.0195

0.0182

0.2608

0.6551

8.00

0.2016

0.0130

0.0078

0.1887

3.1330

0.5552

0.0574

0.1537

0.1070

0.0818

0.0224

0.0197

0.2849

0.7157

7.75

0.1969

0.0169

0.0084

0.2359

3.1160

0.6942

0.0562

0.2134

0.1484

0.0877

0.0260

0.0212

0.3059

0.7685

7.50

0.1918

0.0226

0.0087

0.2890

3.1030

0.8504

0.0548

0.3017

0.2097

0.0897

0.0296

0.0216

0.3121

0.7839

7.25

0.1861

0.0303

0.0081

0.3326

3.0970

0.9787

0.0531

0.4176

0.2902

0.0847

0.0317

0.0204

0.2943

0.7393

7.00

0.1795

0.0395

0.0068

0.3494

3.0980

1.0280

0.0513

0.5459

0.3794

0.0721

0.0309

0.0174

0.2521

0.6332

6.75

0.1715

0.0495

0.0051

0.3366

3.1060

0.9904

0.0490

0.6627

0.4606

0.0546

0.0275

0.0132

0.1961

0.4925

6.50

0.1622

0.0590

0.0034

0.3016

3.1200

0.8873

0.0463

0.7395

0.5142

0.0359

0.0224

0.0087

0.1391

0.3493

2.0Z

;κ=∞

8.50

0.1865

0.0283

0.0094

0.1255

3.0100

0.3694

0.0533

0.1419

0.0983

0.1329

0.0145

0.0321

0.3991

1.0030

8.25

0.1856

0.0292

0.0096

0.1400

3.0050

0.4118

0.0531

0.1593

0.1102

0.1385

0.0149

0.0334

0.4228

1.0620

8.00

0.1842

0.0317

0.0102

0.1656

2.9970

0.4874

0.0527

0.1929

0.1334

0.1479

0.0159

0.0357

0.4571

1.1480

7.75

0.1821

0.0366

0.0110

0.2067

2.9870

0.6083

0.0521

0.2538

0.1754

0.1594

0.0174

0.0385

0.4954

1.2440

7.50

0.1794

0.0446

0.0117

0.2629

2.9780

0.7735

0.0513

0.3544

0.2447

0.1689

0.0191

0.0408

0.5244

1.3170

7.25

0.1762

0.0569

0.0119

0.3248

2.9710

0.9555

0.0504

0.5043

0.3481

0.1706

0.0207

0.0412

0.5274

1.3250

7.00

0.1724

0.0745

0.0111

0.3736

2.9680

1.0990

0.0494

0.7042

0.4859

0.1600

0.0214

0.0386

0.4933

1.2390

6.75

0.1677

0.0975

0.0094

0.3927

2.9700

1.1550

0.0480

0.9368

0.6462

0.1366

0.0203

0.0330

0.4241

1.0650

6.50

0.1616

0.1249

0.0070

0.3807

2.9750

1.1200

0.0463

1.1680

0.8055

0.1043

0.0175

0.0252

0.3351

0.8417

2.0Z

;κ=

50

8.50

0.1820

0.0255

0.0103

0.1194

3.0190

0.3513

0.0520

0.1352

0.0938

0.1301

0.0175

0.0314

0.3865

0.9708

8.25

0.1812

0.0266

0.0106

0.1337

3.0140

0.3934

0.0518

0.1526

0.1057

0.1356

0.0184

0.0327

0.4092

1.0280

8.00

0.1797

0.0292

0.0113

0.1589

3.0060

0.4674

0.0514

0.1859

0.1286

0.1443

0.0200

0.0348

0.4411

1.1080

7.75

0.1777

0.0340

0.0122

0.1991

2.9970

0.5857

0.0508

0.2457

0.1699

0.1548

0.0225

0.0373

0.4760

1.1960

7.50

0.1752

0.0423

0.0130

0.2541

2.9880

0.7476

0.0501

0.3448

0.2383

0.1632

0.0256

0.0394

0.5014

1.2600

7.25

0.1721

0.0548

0.0132

0.3141

2.9810

0.9241

0.0493

0.4919

0.3399

0.1639

0.0285

0.0396

0.5015

1.2600

7.00

0.1684

0.0727

0.0123

0.3607

2.9790

1.0610

0.0482

0.6873

0.4748

0.1529

0.0299

0.0369

0.4662

1.1710

6.75

0.1639

0.0963

0.0103

0.3786

2.9810

1.1140

0.0469

0.9156

0.6323

0.1299

0.0288

0.0313

0.3989

1.0020

6.50

0.1579

0.1247

0.0077

0.3674

2.9860

1.0810

0.0452

1.1440

0.7897

0.0988

0.0252

0.0238

0.3141

0.7890

2.0Z

;κ=

20

8.50

0.1754

0.0202

0.0113

0.1073

3.0370

0.3158

0.0501

0.1215

0.0843

0.1238

0.0213

0.0299

0.3623

0.9101

Page 89: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 89 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

8.25

0.1747

0.0212

0.0117

0.1208

3.0320

0.3553

0.0499

0.1380

0.0957

0.1286

0.0228

0.0310

0.3829

0.9618

8.00

0.1733

0.0236

0.0125

0.1446

3.0250

0.4256

0.0496

0.1698

0.1177

0.1362

0.0255

0.0329

0.4110

1.0330

7.75

0.1714

0.0281

0.0134

0.1823

3.0160

0.5363

0.0490

0.2264

0.1568

0.1449

0.0296

0.0350

0.4399

1.1050

7.50

0.1690

0.0357

0.0142

0.2332

3.0080

0.6862

0.0484

0.3189

0.2207

0.1511

0.0347

0.0365

0.4583

1.1510

7.25

0.1662

0.0473

0.0142

0.2875

3.0030

0.8457

0.0476

0.4549

0.3148

0.1498

0.0393

0.0362

0.4521

1.1360

7.00

0.1627

0.0640

0.0130

0.3275

3.0030

0.9636

0.0466

0.6340

0.4386

0.1378

0.0415

0.0333

0.4139

1.0400

6.75

0.1584

0.0861

0.0106

0.3396

3.0070

0.9992

0.0453

0.8403

0.5812

0.1151

0.0397

0.0278

0.3477

0.8735

6.50

0.1527

0.1132

0.0078

0.3259

3.0140

0.9590

0.0437

1.0440

0.7222

0.0857

0.0347

0.0207

0.2687

0.6750

2.0Z

;κ=

10

8.50

0.1648

0.0144

0.0123

0.0854

3.0680

0.2514

0.0471

0.1016

0.0707

0.1093

0.0261

0.0264

0.3133

0.7871

8.25

0.1642

0.0154

0.0128

0.0972

3.0640

0.2860

0.0469

0.1168

0.0812

0.1130

0.0287

0.0273

0.3302

0.8294

8.00

0.1630

0.0175

0.0136

0.1176

3.0570

0.3461

0.0466

0.1454

0.1010

0.1183

0.0331

0.0286

0.3509

0.8814

7.75

0.1613

0.0214

0.0144

0.1493

3.0480

0.4394

0.0461

0.1953

0.1356

0.1234

0.0395

0.0298

0.3685

0.9257

7.50

0.1592

0.0280

0.0147

0.1907

3.0410

0.5610

0.0456

0.2752

0.1910

0.1250

0.0470

0.0302

0.3731

0.9372

7.25

0.1568

0.0384

0.0142

0.2331

3.0380

0.6860

0.0449

0.3915

0.2717

0.1201

0.0534

0.0290

0.3563

0.8951

7.00

0.1536

0.0539

0.0125

0.2631

3.0400

0.7740

0.0439

0.5445

0.3778

0.1074

0.0561

0.0259

0.3166

0.7954

6.75

0.1495

0.0753

0.0100

0.2703

3.0440

0.7952

0.0428

0.7220

0.5009

0.0874

0.0537

0.0211

0.2592

0.6510

6.50

0.1439

0.1021

0.0073

0.2600

3.0510

0.7650

0.0412

0.9012

0.6250

0.0636

0.0480

0.0153

0.1972

0.4953

1.0Z

;κ=∞

8.50

0.1356

0.0386

0.0194

0.0704

2.9180

0.2072

0.0388

0.1596

0.1106

0.1642

0.0315

0.0396

0.4139

1.0400

8.25

0.1355

0.0395

0.0199

0.0745

2.9180

0.2193

0.0388

0.1684

0.1167

0.1685

0.0325

0.0406

0.4293

1.0780

8.00

0.1354

0.0418

0.0209

0.0830

2.9170

0.2443

0.0387

0.1875

0.1298

0.1750

0.0350

0.0422

0.4544

1.1410

7.75

0.1351

0.0469

0.0223

0.0994

2.9140

0.2924

0.0387

0.2264

0.1567

0.1831

0.0400

0.0442

0.4852

1.2190

7.50

0.1346

0.0570

0.0241

0.1271

2.9090

0.3738

0.0385

0.2979

0.2062

0.1915

0.0485

0.0462

0.5125

1.2870

7.25

0.1339

0.0744

0.0254

0.1660

2.9040

0.4883

0.0383

0.4171

0.2886

0.1973

0.0601

0.0476

0.5258

1.3210

7.00

0.1331

0.1020

0.0255

0.2081

2.9010

0.6124

0.0381

0.5972

0.4131

0.1957

0.0715

0.0472

0.5136

1.2900

6.75

0.1322

0.1425

0.0233

0.2392

2.9010

0.7037

0.0378

0.8431

0.5831

0.1821

0.0773

0.0439

0.4693

1.1790

6.50

0.1307

0.1979

0.0193

0.2502

2.9040

0.7362

0.0374

1.1450

0.7917

0.1559

0.0749

0.0376

0.3979

0.9996

1.0Z

;κ=

50

8.50

0.1325

0.0316

0.0195

0.0640

2.9320

0.1883

0.0379

0.1443

0.1000

0.1554

0.0325

0.0375

0.3912

0.9826

8.25

0.1325

0.0324

0.0200

0.0679

2.9320

0.1997

0.0379

0.1527

0.1058

0.1595

0.0338

0.0385

0.4060

1.0200

8.00

0.1323

0.0345

0.0210

0.0759

2.9310

0.2234

0.0379

0.1708

0.1183

0.1655

0.0368

0.0399

0.4297

1.0790

7.75

0.1321

0.0390

0.0225

0.0913

2.9290

0.2687

0.0378

0.2073

0.1436

0.1727

0.0426

0.0417

0.4578

1.1500

7.50

0.1317

0.0477

0.0240

0.1171

2.9250

0.3446

0.0377

0.2741

0.1898

0.1795

0.0522

0.0433

0.4810

1.2080

Page 90: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 90 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

7.25

0.1311

0.0629

0.0250

0.1528

2.9220

0.4495

0.0375

0.3843

0.2660

0.1832

0.0647

0.0442

0.4887

1.2280

7.00

0.1306

0.0869

0.0244

0.1900

2.9220

0.5590

0.0374

0.5484

0.3795

0.1791

0.0759

0.0432

0.4706

1.1820

6.75

0.1299

0.1219

0.0216

0.2150

2.9250

0.6324

0.0372

0.7689

0.5320

0.1635

0.0797

0.0395

0.4218

1.0600

6.50

0.1287

0.1696

0.0172

0.2203

2.9320

0.6481

0.0368

1.0330

0.7146

0.1366

0.0744

0.0330

0.3492

0.8771

1.0Z

;κ=

20

8.50

0.1281

0.0222

0.0190

0.0539

2.9590

0.1585

0.0367

0.1205

0.0836

0.1404

0.0326

0.0339

0.3528

0.8861

8.25

0.1281

0.0229

0.0196

0.0574

2.9590

0.1689

0.0366

0.1282

0.0889

0.1440

0.0343

0.0347

0.3664

0.9205

8.00

0.1280

0.0245

0.0206

0.0646

2.9600

0.1901

0.0366

0.1445

0.1001

0.1491

0.0378

0.0360

0.3874

0.9731

7.75

0.1278

0.0279

0.0218

0.0782

2.9590

0.2300

0.0366

0.1769

0.1226

0.1543

0.0443

0.0372

0.4103

1.0310

7.50

0.1276

0.0346

0.0228

0.1004

2.9600

0.2954

0.0365

0.2351

0.1629

0.1581

0.0545

0.0381

0.4251

1.0680

7.25

0.1274

0.0462

0.0228

0.1298

2.9630

0.3820

0.0365

0.3289

0.2278

0.1574

0.0665

0.0380

0.4218

1.0600

7.00

0.1273

0.0641

0.0211

0.1578

2.9690

0.4642

0.0364

0.4643

0.3216

0.1487

0.0745

0.0359

0.3925

0.9859

6.75

0.1271

0.0897

0.0174

0.1718

2.9810

0.5056

0.0364

0.6382

0.4419

0.1299

0.0731

0.0314

0.3363

0.8448

6.50

0.1264

0.1233

0.0128

0.1679

2.9950

0.4941

0.0362

0.8336

0.5769

0.1027

0.0631

0.0248

0.2637

0.6625

1.0Z

;κ=

10

8.50

0.1212

0.0139

0.0172

0.0385

3.0110

0.1134

0.0347

0.0904

0.0628

0.1132

0.0307

0.0273

0.2837

0.7125

8.25

0.1213

0.0144

0.0177

0.0414

3.0120

0.1217

0.0347

0.0969

0.0673

0.1160

0.0327

0.0280

0.2948

0.7406

8.00

0.1214

0.0156

0.0185

0.0470

3.0150

0.1384

0.0348

0.1107

0.0768

0.1190

0.0367

0.0287

0.3101

0.7790

7.75

0.1216

0.0182

0.0191

0.0574

3.0190

0.1690

0.0348

0.1373

0.0953

0.1206

0.0434

0.0291

0.3226

0.8103

7.50

0.1220

0.0232

0.0188

0.0736

3.0260

0.2165

0.0349

0.1837

0.1275

0.1187

0.0525

0.0286

0.3220

0.8089

7.25

0.1226

0.0317

0.0172

0.0928

3.0340

0.2729

0.0351

0.2551

0.1770

0.1115

0.0604

0.0000

0.3013

0.7568

7.00

0.1233

0.0448

0.0141

0.1066

3.0400

0.3137

0.0353

0.3525

0.2445

0.0974

0.0611

0.0235

0.2589

0.6504

6.75

0.1237

0.0630

0.0102

0.1075

3.0410

0.3163

0.0354

0.4688

0.3251

0.0775

0.0531

0.0187

0.2021

0.5077

6.50

0.1231

0.0869

0.0066

0.0980

3.0430

0.2884

0.0352

0.5915

0.4099

0.0552

0.0415

0.0133

0.1445

0.3631

0.5Z

;κ=∞

8.50

0.1156

0.0338

0.0253

0.0333

2.8630

0.0980

0.0330

0.1363

0.0946

0.1407

0.0430

0.0339

0.3269

0.8212

8.25

0.1156

0.0343

0.0258

0.0342

2.8640

0.1008

0.0330

0.1398

0.0969

0.1431

0.0441

0.0345

0.3338

0.8384

8.00

0.1156

0.0355

0.0268

0.0364

2.8640

0.1071

0.0330

0.1479

0.1026

0.1475

0.0466

0.0356

0.3476

0.8731

7.75

0.1156

0.0384

0.0284

0.0410

2.8640

0.1206

0.0330

0.1661

0.1152

0.1533

0.0521

0.0370

0.3690

0.9269

7.50

0.1157

0.0447

0.0301

0.0498

2.8650

0.1466

0.0331

0.2029

0.1407

0.1583

0.0623

0.0382

0.3911

0.9824

7.25

0.1159

0.0568

0.0310

0.0642

2.8670

0.1889

0.0331

0.2694

0.1868

0.1602

0.0779

0.0386

0.4012

1.0080

7.00

0.1163

0.0777

0.0301

0.0825

2.8710

0.2428

0.0332

0.3765

0.2611

0.1569

0.0947

0.0379

0.3908

0.9818

6.75

0.1170

0.1107

0.0268

0.0984

2.8770

0.2895

0.0335

0.5325

0.3691

0.1462

0.1034

0.0353

0.3566

0.8957

6.50

0.1178

0.1582

0.0216

0.1051

2.8840

0.3093

0.0337

0.7372

0.5107

0.1272

0.0982

0.0307

0.3021

0.7590

Page 91: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 91 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

1.0Z

;κ=

50

8.50

0.1131

0.0267

0.0237

0.0293

2.8820

0.0863

0.0323

0.1198

0.0831

0.1298

0.0402

0.0313

0.3020

0.7585

8.25

0.1131

0.0271

0.0242

0.0302

2.8830

0.0889

0.0323

0.1230

0.0853

0.1321

0.0413

0.0319

0.3084

0.7748

8.00

0.1132

0.0282

0.0252

0.0322

2.8840

0.0946

0.0323

0.1305

0.0905

0.1361

0.0438

0.0328

0.3213

0.8070

7.75

0.1133

0.0306

0.0266

0.0363

2.8850

0.1069

0.0324

0.1471

0.1020

0.1409

0.0491

0.0340

0.3404

0.8552

7.50

0.1135

0.0358

0.0278

0.0443

2.8880

0.1303

0.0324

0.1806

0.1252

0.1442

0.0588

0.0348

0.3582

0.8999

7.25

0.1140

0.0457

0.0279

0.0570

2.8930

0.1676

0.0326

0.2404

0.1667

0.1437

0.0727

0.0347

0.3621

0.9096

7.00

0.1147

0.0629

0.0260

0.0724

2.9030

0.2130

0.0328

0.3352

0.2324

0.1375

0.0858

0.0332

0.3447

0.8658

6.75

0.1159

0.0894

0.0220

0.0843

2.9150

0.2479

0.0331

0.4700

0.3256

0.1244

0.0891

0.0300

0.3051

0.7664

6.50

0.1170

0.1268

0.0168

0.0872

2.9300

0.2566

0.0335

0.6408

0.4437

0.1045

0.0798

0.0252

0.2497

0.6273

1.0Z

;κ=

20

8.50

0.1098

0.0179

0.0209

0.0236

2.9250

0.0694

0.0314

0.0958

0.0665

0.1125

0.0352

0.0271

0.2622

0.6586

8.25

0.1098

0.0182

0.0214

0.0243

2.9260

0.0716

0.0314

0.0986

0.0684

0.1144

0.0363

0.0276

0.2680

0.6731

8.00

0.1099

0.0190

0.0222

0.0260

2.9280

0.0765

0.0314

0.1050

0.0729

0.1177

0.0387

0.0284

0.2791

0.7010

7.75

0.1102

0.0207

0.0233

0.0295

2.9330

0.0868

0.0315

0.1194

0.0828

0.1210

0.0436

0.0292

0.2944

0.7396

7.50

0.1107

0.0245

0.0237

0.0361

2.9410

0.1063

0.0317

0.1479

0.1026

0.1216

0.0520

0.0294

0.3053

0.7668

7.25

0.1116

0.0317

0.0226

0.0462

2.9550

0.1360

0.0319

0.1976

0.1370

0.1175

0.0627

0.0284

0.2996

0.7527

7.00

0.1129

0.0438

0.0197

0.0573

2.9730

0.1686

0.0323

0.2737

0.1897

0.1078

0.0698

0.0260

0.2730

0.6858

6.75

0.1146

0.0618

0.0153

0.0637

2.9950

0.1874

0.0328

0.3762

0.2607

0.0925

0.0666

0.0223

0.2289

0.5750

6.50

0.1163

0.0859

0.0106

0.0622

3.0160

0.1830

0.0333

0.4969

0.3440

0.0731

0.0544

0.0176

0.1761

0.4424

1.0Z

;κ=

10

8.50

0.1046

0.0104

0.0161

0.0156

3.0010

0.0458

0.0299

0.0666

0.0462

0.0843

0.0272

0.0203

0.1972

0.4954

8.25

0.1047

0.0106

0.0164

0.0161

3.0040

0.0475

0.0299

0.0688

0.0478

0.0857

0.0282

0.0207

0.2017

0.5067

8.00

0.1049

0.0111

0.0170

0.0174

3.0090

0.0511

0.0300

0.0740

0.0514

0.0877

0.0302

0.0212

0.2097

0.5268

7.75

0.1054

0.0124

0.0174

0.0199

3.0190

0.0587

0.0302

0.0855

0.0593

0.0883

0.0342

0.0213

0.2184

0.5486

7.50

0.1065

0.0151

0.0167

0.0246

3.0340

0.0723

0.0305

0.1078

0.0748

0.0851

0.0401

0.0205

0.2180

0.5476

7.25

0.1083

0.0201

0.0144

0.0310

3.0550

0.0911

0.0310

0.1450

0.1006

0.0769

0.0456

0.0186

0.2001

0.5027

7.00

0.1107

0.0285

0.0109

0.0363

3.0740

0.1067

0.0317

0.1985

0.1377

0.0648

0.0453

0.0156

0.1668

0.4191

6.75

0.1135

0.0405

0.0074

0.0368

3.0830

0.1084

0.0325

0.2650

0.1838

0.0505

0.0377

0.0122

0.1264

0.3176

6.50

0.1157

0.0562

0.0045

0.0331

3.0730

0.0973

0.0331

0.3373

0.2337

0.0359

0.0276

0.0087

0.0882

0.2215

0.3Z

;κ=∞

8.50

0.1063

0.0274

0.0246

0.0185

2.8550

0.0543

0.0303

0.1082

0.0751

0.1097

0.0435

0.0265

0.2466

0.6195

8.25

0.1063

0.0277

0.0249

0.0187

2.8550

0.0552

0.0303

0.1097

0.0762

0.1108

0.0442

0.0267

0.2496

0.6270

8.00

0.1063

0.0283

0.0255

0.0195

2.8560

0.0573

0.0303

0.1135

0.0788

0.1133

0.0459

0.0273

0.2564

0.6440

Page 92: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 92 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

7.75

0.1064

0.0299

0.0267

0.0211

2.8580

0.0621

0.0304

0.1225

0.0851

0.1169

0.0498

0.0282

0.2687

0.6750

7.50

0.1067

0.0335

0.0279

0.0245

2.8610

0.0721

0.0305

0.1423

0.0988

0.1197

0.0573

0.0289

0.2835

0.7122

7.25

0.1073

0.0410

0.0280

0.0306

2.8670

0.0900

0.0307

0.1808

0.1255

0.1193

0.0695

0.0288

0.2901

0.7287

7.00

0.1084

0.0551

0.0260

0.0391

2.8750

0.1151

0.0310

0.2464

0.1710

0.1142

0.0828

0.0275

0.2792

0.7012

6.75

0.1099

0.0783

0.0221

0.0471

2.8850

0.1386

0.0314

0.3455

0.2397

0.1043

0.0883

0.0252

0.2504

0.6290

6.50

0.1116

0.1126

0.0171

0.0506

2.8950

0.1489

0.0319

0.4794

0.3324

0.0899

0.0813

0.0217

0.2092

0.5254

hline0.3Z

;κ=

50

8.50

0.1043

0.0212

0.0219

0.0159

2.8820

0.0467

0.0298

0.0929

0.0645

0.0988

0.0380

0.0238

0.2226

0.5591

8.25

0.1043

0.0214

0.0221

0.0161

2.8820

0.0474

0.0298

0.0943

0.0654

0.0998

0.0386

0.0241

0.2253

0.5660

8.00

0.1044

0.0219

0.0227

0.0168

2.8830

0.0493

0.0298

0.0978

0.0679

0.1020

0.0402

0.0246

0.2315

0.5814

7.75

0.1046

0.0232

0.0237

0.0182

2.8860

0.0536

0.0299

0.1059

0.0735

0.1049

0.0436

0.0253

0.2424

0.6090

7.50

0.1050

0.0262

0.0245

0.0213

2.8920

0.0625

0.0300

0.1239

0.0860

0.1066

0.0503

0.0257

0.2543

0.6389

7.25

0.1059

0.0324

0.0239

0.0266

2.9020

0.0783

0.0302

0.1586

0.1100

0.1045

0.0604

0.0252

0.2563

0.6439

7.00

0.1072

0.0438

0.0213

0.0338

2.9140

0.0993

0.0306

0.2166

0.1502

0.0977

0.0699

0.0236

0.2407

0.6047

6.75

0.1091

0.0622

0.0173

0.0397

2.9290

0.1167

0.0312

0.3017

0.2092

0.0867

0.0710

0.0209

0.2095

0.5261

6.50

0.1113

0.0887

0.0127

0.0412

2.9430

0.1213

0.0318

0.4127

0.2859

0.0723

0.0618

0.0174

0.1691

0.4248

0.3Z

;κ=

20

8.50

0.1016

0.0138

0.0180

0.0123

2.9310

0.0362

0.0290

0.0719

0.0499

0.0827

0.0305

0.0200

0.1872

0.4701

8.25

0.1016

0.0139

0.0182

0.0125

2.9320

0.0369

0.0290

0.0731

0.0507

0.0836

0.0311

0.0202

0.1895

0.4761

8.00

0.1017

0.0143

0.0187

0.0131

2.9350

0.0384

0.0291

0.0760

0.0527

0.0854

0.0324

0.0206

0.1948

0.4894

7.75

0.1020

0.0152

0.0194

0.0143

2.9400

0.0420

0.0291

0.0830

0.0576

0.0873

0.0353

0.0211

0.2036

0.5115

7.50

0.1027

0.0173

0.0196

0.0168

2.9510

0.0495

0.0293

0.0984

0.0683

0.0873

0.0406

0.0211

0.2111

0.5303

7.25

0.1040

0.0218

0.0182

0.0211

2.9670

0.0621

0.0297

0.1274

0.0884

0.0830

0.0479

0.0200

0.2067

0.5192

7.00

0.1059

0.0299

0.0152

0.0263

2.9890

0.0773

0.0303

0.1741

0.1207

0.0745

0.0526

0.0180

0.1858

0.4668

6.75

0.1085

0.0422

0.0113

0.0295

3.0130

0.0867

0.0310

0.2388

0.1655

0.0629

0.0493

0.0152

0.1534

0.3852

6.50

0.1113

0.0589

0.0076

0.0289

3.0350

0.0849

0.0318

0.3168

0.2194

0.0495

0.0393

0.0119

0.1166

0.2930

0.3Z

;κ=

10

8.50

0.0972

0.0077

0.0127

0.0078

3.0160

0.0229

0.0278

0.0479

0.0333

0.0594

0.0211

0.0143

0.1353

0.3399

8.25

0.0973

0.0078

0.0128

0.0079

3.0180

0.0233

0.0278

0.0488

0.0339

0.0601

0.0216

0.0145

0.1372

0.3445

8.00

0.0975

0.0080

0.0131

0.0083

3.0230

0.0245

0.0279

0.0512

0.0355

0.0612

0.0226

0.0148

0.1411

0.3543

7.75

0.0981

0.0087

0.0134

0.0092

3.0340

0.0271

0.0281

0.0569

0.0395

0.0616

0.0247

0.0149

0.1464

0.3678

7.50

0.0994

0.0102

0.0128

0.0110

3.0510

0.0325

0.0284

0.0693

0.0481

0.0591

0.0283

0.0143

0.1469

0.3691

7.25

0.1015

0.0135

0.0107

0.0138

3.0740

0.0406

0.0290

0.0915

0.0635

0.0526

0.0317

0.0127

0.1344

0.3376

7.00

0.1046

0.0190

0.0078

0.0163

3.0940

0.0480

0.0299

0.1246

0.0865

0.0434

0.0313

0.0105

0.1103

0.2770

Page 93: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 93 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

6.75

0.1083

0.0272

0.0051

0.0167

3.1030

0.0490

0.0310

0.1667

0.1156

0.0333

0.0255

0.0080

0.0822

0.2065

6.50

0.1118

0.0379

0.0030

0.0149

3.0930

0.0439

0.0320

0.2133

0.1478

0.0237

0.0183

0.0057

0.0567

0.1425

0.2Z

;κ=∞

8.50

0.1022

0.0225

0.0205

0.0108

2.8650

0.0317

0.0292

0.0847

0.0588

0.0823

0.0361

0.0199

0.1806

0.4537

8.25

0.1022

0.0227

0.0207

0.0109

2.8660

0.0320

0.0292

0.0854

0.0593

0.0829

0.0365

0.0200

0.1822

0.4576

8.00

0.1023

0.0231

0.0211

0.0112

2.8670

0.0329

0.0292

0.0875

0.0608

0.0843

0.0375

0.0204

0.1859

0.4671

7.75

0.1024

0.0240

0.0219

0.0119

2.8690

0.0349

0.0292

0.0925

0.0643

0.0867

0.0399

0.0209

0.1935

0.4861

7.50

0.1029

0.0263

0.0228

0.0134

2.8730

0.0395

0.0294

0.1043

0.0724

0.0889

0.0448

0.0214

0.2042

0.5129

7.25

0.1037

0.0314

0.0227

0.0164

2.8790

0.0483

0.0296

0.1287

0.0894

0.0882

0.0533

0.0213

0.2100

0.5275

7.00

0.1052

0.0415

0.0207

0.0210

2.8880

0.0618

0.0300

0.1725

0.1197

0.0836

0.0633

0.0202

0.2018

0.5070

6.75

0.1072

0.0585

0.0171

0.0257

2.8980

0.0755

0.0306

0.2402

0.1667

0.0757

0.0678

0.0183

0.1798

0.4517

6.50

0.1096

0.0840

0.0130

0.0279

2.9070

0.0822

0.0313

0.3332

0.2311

0.0651

0.0622

0.0157

0.1494

0.3752

0.2Z

;κ=

50

8.50

0.1010

0.0171

0.0177

0.0091

2.9000

0.0267

0.0287

0.0715

0.0496

0.0729

0.0302

0.0176

0.1600

0.4030

8.25

0.1010

0.0173

0.0178

0.0092

2.9000

0.0270

0.0287

0.0722

0.0501

0.0735

0.0305

0.0177

0.1620

0.4070

8.00

0.1010

0.0176

0.0182

0.0095

2.9000

0.0278

0.0287

0.0740

0.0514

0.0748

0.0314

0.0180

0.1650

0.4150

7.75

0.1010

0.0183

0.0189

0.0101

2.9000

0.0296

0.0288

0.0786

0.0546

0.0768

0.0335

0.0185

0.1720

0.4330

7.50

0.1010

0.0202

0.0194

0.0115

2.9100

0.0338

0.0289

0.0894

0.0621

0.0782

0.0377

0.0189

0.1810

0.4550

7.25

0.1025

0.0245

0.0189

0.0141

2.9180

0.0416

0.0293

0.1117

0.0776

0.0764

0.0447

0.0184

0.1836

0.4613

7.00

0.1043

0.0326

0.0165

0.0180

2.9310

0.0530

0.0298

0.1505

0.1045

0.0708

0.0519

0.0171

0.1723

0.4329

6.75

0.1067

0.0462

0.0131

0.0215

2.9440

0.0633

0.0305

0.2088

0.1448

0.0624

0.0531

0.0151

0.1490

0.3744

6.50

0.1096

0.0657

0.0095

0.0226

2.9580

0.0666

0.0313

0.2857

0.1980

0.0520

0.0461

0.0126

0.1198

0.3008

0.2Z

;κ=

20

8.50

0.0981

0.0109

0.0140

0.0069

2.9500

0.0203

0.0280

0.0541

0.0376

0.0599

0.0230

0.0145

0.1320

0.3330

8.25

0.0981

0.0110

0.0141

0.0070

2.9500

0.0206

0.0280

0.0547

0.0380

0.0604

0.0233

0.0146

0.1340

0.3360

8.00

0.0982

0.0112

0.0144

0.0072

2.9600

0.0212

0.0280

0.0563

0.0391

0.0615

0.0240

0.0148

0.1370

0.3430

7.75

0.0986

0.0118

0.0149

0.0077

2.9600

0.0228

0.0281

0.0603

0.0418

0.0629

0.0257

0.0152

0.1420

0.3580

7.50

0.0994

0.0132

0.0150

0.0089

2.9700

0.0262

0.0284

0.0697

0.0484

0.0631

0.0291

0.0152

0.1490

0.3730

7.25

0.1010

0.0162

0.0139

0.0111

2.9900

0.0326

0.0288

0.0886

0.0615

0.0599

0.0341

0.0145

0.1470

0.3680

7.00

0.1030

0.0220

0.0114

0.0139

3.0100

0.0410

0.0295

0.1200

0.0832

0.0534

0.0377

0.0129

0.1320

0.3310

6.75

0.1070

0.0310

0.0084

0.0159

3.0300

0.0468

0.0304

0.1640

0.1140

0.0448

0.0357

0.0108

0.1080

0.2710

6.50

0.1100

0.0432

0.0056

0.0157

3.0500

0.0463

0.0315

0.2180

0.1510

0.0353

0.0284

0.0085

0.0819

0.2060

0.2Z

;κ=

10

8.50

0.0942

0.0059

0.0094

0.0042

3.0400

0.0125

0.0269

0.0352

0.0244

0.0421

0.0149

0.0101

0.0936

0.2350

Page 94: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 94 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

8.25

0.0943

0.0060

0.0095

0.0043

3.0400

0.0127

0.0269

0.0356

0.0247

0.0424

0.0151

0.0102

0.0946

0.2380

8.00

0.0945

0.0061

0.0097

0.0045

3.0500

0.0131

0.0270

0.0369

0.0256

0.0431

0.0157

0.0104

0.0969

0.2440

7.75

0.0951

0.0065

0.0100

0.0049

3.0540

0.0143

0.0272

0.0402

0.0279

0.0437

0.0170

0.0105

0.1008

0.2531

7.50

0.0965

0.0076

0.0095

0.0057

3.0700

0.0169

0.0276

0.0481

0.0334

0.0422

0.0192

0.0102

0.1020

0.2570

7.25

0.0990

0.0098

0.0080

0.0072

3.0900

0.0212

0.0283

0.0628

0.0436

0.0374

0.0216

0.0090

0.0943

0.2370

7.00

0.1030

0.0138

0.0057

0.0086

3.1100

0.0254

0.0293

0.0853

0.0592

0.0306

0.0217

0.0074

0.0771

0.1940

6.75

0.1070

0.0196

0.0036

0.0090

3.1200

0.0263

0.0306

0.1140

0.0791

0.0235

0.0179

0.0057

0.0572

0.1440

6.50

0.1110

0.0273

0.0021

0.0081

3.1100

0.0237

0.0319

0.1470

0.1020

0.0168

0.0127

0.0041

0.0394

0.0989

0.1Z

;κ=∞

8.50

0.0981

0.0140

0.0124

0.0043

2.9000

0.0125

0.0280

0.0496

0.0345

0.0454

0.0215

0.0110

0.0974

0.2450

8.25

0.0981

0.0141

0.0125

0.0043

2.9000

0.0126

0.0280

0.0499

0.0347

0.0456

0.0216

0.0110

0.0979

0.2460

8.00

0.0982

0.0142

0.0126

0.0043

2.9000

0.0128

0.0280

0.0506

0.0352

0.0462

0.0220

0.0111

0.0993

0.2500

7.75

0.0984

0.0147

0.0130

0.0045

2.9000

0.0133

0.0281

0.0526

0.0365

0.0473

0.0229

0.0114

0.1030

0.2580

7.50

0.0989

0.0158

0.0135

0.0050

2.9000

0.0147

0.0282

0.0576

0.0400

0.0486

0.0251

0.0117

0.1080

0.2710

7.25

0.1000

0.0184

0.0135

0.0060

2.9100

0.0176

0.0285

0.0692

0.0481

0.0484

0.0294

0.0117

0.1120

0.2820

7.00

0.1020

0.0238

0.0121

0.0077

2.9100

0.0225

0.0291

0.0911

0.0633

0.0457

0.0349

0.0110

0.1090

0.2730

6.75

0.1050

0.0334

0.0099

0.0095

2.9200

0.0280

0.0298

0.1260

0.0874

0.0411

0.0379

0.0099

0.0965

0.2430

6.50

0.1080

0.0478

0.0074

0.0106

2.9300

0.0311

0.0308

0.1750

0.1210

0.0354

0.0350

0.0085

0.0799

0.2010

0.1Z

;κ=

50

8.50

0.0966

0.0105

0.0104

0.0035

2.9300

0.0104

0.0276

0.0412

0.0286

0.0397

0.0173

0.0096

0.0853

0.2140

8.25

0.0966

0.0106

0.0105

0.0036

2.9300

0.0104

0.0276

0.0415

0.0288

0.0399

0.0174

0.0096

0.0858

0.2160

8.00

0.0967

0.0107

0.0106

0.0036

2.9300

0.0106

0.0276

0.0421

0.0293

0.0404

0.0177

0.0098

0.0871

0.2190

7.75

0.0970

0.0110

0.0109

0.0038

2.9400

0.0111

0.0277

0.0440

0.0305

0.0415

0.0185

0.0100

0.0901

0.2260

7.50

0.0977

0.0119

0.0112

0.0042

2.9400

0.0124

0.0279

0.0487

0.0338

0.0424

0.0204

0.0102

0.0949

0.2390

7.25

0.0990

0.0141

0.0110

0.0051

2.9500

0.0150

0.0283

0.0594

0.0412

0.0416

0.0239

0.0100

0.0976

0.2450

7.00

0.1010

0.0186

0.0095

0.0065

2.9600

0.0192

0.0289

0.0790

0.0548

0.0384

0.0280

0.0093

0.0921

0.2310

6.75

0.1040

0.0261

0.0074

0.0080

2.9700

0.0234

0.0298

0.1090

0.0756

0.0337

0.0291

0.0081

0.0795

0.2000

6.50

0.1080

0.0371

0.0053

0.0085

2.9800

0.0251

0.0308

0.1490

0.1030

0.0281

0.0254

0.0068

0.0637

0.1600

0.1Z

;κ=

20

8.50

0.0945

0.0066

0.0079

0.0026

2.9900

0.0077

0.0270

0.0306

0.0213

0.0321

0.0126

0.0078

0.0692

0.1740

8.25

0.0945

0.0066

0.0080

0.0027

2.9900

0.0078

0.0270

0.0308

0.0214

0.0323

0.0127

0.0078

0.0697

0.1750

8.00

0.0946

0.0067

0.0081

0.0027

2.9900

0.0080

0.0270

0.0314

0.0218

0.0327

0.0129

0.0079

0.0709

0.1780

7.75

0.0950

0.0070

0.0083

0.0029

3.0000

0.0084

0.0271

0.0330

0.0229

0.0335

0.0136

0.0081

0.0735

0.1850

7.50

0.0959

0.0076

0.0085

0.0032

3.0100

0.0095

0.0274

0.0373

0.0259

0.0339

0.0151

0.0082

0.0772

0.1940

Page 95: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 95 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

7.25

0.0977

0.0092

0.0079

0.0040

3.0200

0.0117

0.0279

0.0465

0.0323

0.0323

0.0176

0.0078

0.0773

0.1940

7.00

0.1010

0.0124

0.0064

0.0050

3.0400

0.0148

0.0288

0.0624

0.0433

0.0287

0.0198

0.0069

0.0698

0.1750

6.75

0.1040

0.0174

0.0046

0.0059

3.0500

0.0173

0.0299

0.0853

0.0591

0.0240

0.0191

0.0058

0.0571

0.1440

6.50

0.1090

0.0242

0.0030

0.0059

3.0700

0.0174

0.0311

0.1140

0.0786

0.0190

0.0153

0.0046

0.0433

0.1090

0.1Z

;κ=

10

8.50

0.0911

0.0035

0.0051

0.0016

3.0800

0.0046

0.0260

0.0194

0.0135

0.0221

0.0077

0.0053

0.0480

0.1210

8.25

0.0911

0.0035

0.0052

0.0016

3.0800

0.0047

0.0260

0.0196

0.0136

0.0222

0.0078

0.0054

0.0484

0.1220

8.00

0.0913

0.0036

0.0052

0.0016

3.0800

0.0048

0.0261

0.0201

0.0139

0.0226

0.0080

0.0055

0.0493

0.1240

7.75

0.0920

0.0037

0.0053

0.0018

3.0870

0.0052

0.0263

0.0215

0.0149

0.0230

0.0085

0.0056

0.0513

0.1289

7.50

0.0935

0.0043

0.0052

0.0020

3.1000

0.0060

0.0267

0.0251

0.0175

0.0225

0.0095

0.0054

0.0529

0.1330

7.25

0.0963

0.0054

0.0044

0.0026

3.1200

0.0075

0.0275

0.0326

0.0226

0.0200

0.0108

0.0048

0.0495

0.1240

7.00

0.1010

0.0076

0.0031

0.0031

3.1300

0.0092

0.0287

0.0441

0.0306

0.0163

0.0111

0.0039

0.0405

0.1020

6.75

0.1060

0.0108

0.0020

0.0033

3.1400

0.0097

0.0302

0.0590

0.0409

0.0125

0.0093

0.0030

0.0300

0.0753

6.50

0.1110

0.0151

0.0011

0.0030

3.1200

0.0089

0.0318

0.0761

0.0527

0.0090

0.0067

0.0022

0.0206

0.0518

0.05Z

;κ=∞

8.50

0.0964

0.0077

0.0068

0.0018

2.9180

0.0054

0.0275

0.0266

0.0185

0.0237

0.0117

0.0057

0.0507

0.1273

8.25

0.0964

0.0077

0.0068

0.0019

2.9180

0.0055

0.0275

0.0267

0.0186

0.0238

0.0118

0.0057

0.0509

0.1278

8.00

0.0965

0.0078

0.0069

0.0019

2.9200

0.0055

0.0275

0.0270

0.0188

0.0241

0.0119

0.0058

0.0514

0.1290

7.75

0.0967

0.0079

0.0070

0.0020

2.9200

0.0057

0.0276

0.0279

0.0194

0.0246

0.0123

0.0059

0.0528

0.1330

7.50

0.0972

0.0085

0.0072

0.0021

2.9200

0.0062

0.0277

0.0302

0.0210

0.0253

0.0134

0.0061

0.0554

0.1390

7.25

0.0984

0.0098

0.0072

0.0025

2.9300

0.0074

0.0281

0.0358

0.0248

0.0252

0.0155

0.0061

0.0578

0.1450

7.00

0.1000

0.0126

0.0065

0.0032

2.9300

0.0094

0.0286

0.0467

0.0324

0.0238

0.0183

0.0057

0.0561

0.1410

6.75

0.1030

0.0176

0.0053

0.0040

2.9300

0.0118

0.0295

0.0645

0.0447

0.0213

0.0200

0.0000

0.0498

0.1250

6.50

0.1070

0.0252

0.0039

0.0045

2.9400

0.0132

0.0305

0.0894

0.0620

0.0183

0.0185

0.0044

0.0411

0.1030

0.05Z

;κ=

50

8.50

0.0950

0.0057

0.0056

0.0015

2.9540

0.0045

0.0271

0.0220

0.0153

0.0207

0.0093

0.0050

0.0442

0.1109

8.25

0.0950

0.0057

0.0056

0.0015

2.9540

0.0045

0.0271

0.0221

0.0153

0.0208

0.0093

0.0050

0.0443

0.1113

8.00

0.0951

0.0058

0.0057

0.0016

2.9550

0.0046

0.0271

0.0223

0.0155

0.0210

0.0095

0.0051

0.0448

0.1126

7.75

0.0953

0.0059

0.0058

0.0016

2.9570

0.0048

0.0272

0.0231

0.0161

0.0214

0.0098

0.0052

0.0462

0.1159

7.50

0.0960

0.0064

0.0060

0.0018

2.9610

0.0052

0.0274

0.0253

0.0176

0.0219

0.0107

0.0053

0.0485

0.1219

7.25

0.0975

0.0075

0.0059

0.0021

2.9660

0.0063

0.0278

0.0305

0.0212

0.0216

0.0125

0.0052

0.0501

0.1259

7.00

0.0998

0.0098

0.0051

0.0027

2.9720

0.0080

0.0285

0.0404

0.0280

0.0199

0.0146

0.0048

0.0475

0.1193

6.75

0.1031

0.0137

0.0039

0.0034

2.9810

0.0099

0.0295

0.0557

0.0386

0.0174

0.0152

0.0042

0.0409

0.1028

6.50

0.1070

0.0195

0.0028

0.0036

2.9890

0.0106

0.0306

0.0763

0.0529

0.0145

0.0133

0.0035

0.0327

0.0822

Page 96: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 96 –

Tab

le5—

Con

tinued

HeI

[OI]

[SIII]

[NII]

[NII]

HeI

[SII]

[SII]

[ArIII]

[OII]

[ArIII]

[SIII]

[SIII]

log(q)

5875

6300

6312

6548

6563

6584

6678

6717

6731

7136

7318,30

7751

9068

9532

0.05Z

;κ=

20

8.50

0.0929

0.0035

0.0042

0.0011

3.0130

0.0033

0.0265

0.0162

0.0113

0.0166

0.0067

0.0040

0.0356

0.0894

8.25

0.0930

0.0036

0.0043

0.0011

3.0140

0.0033

0.0265

0.0163

0.0113

0.0167

0.0067

0.0040

0.0358

0.0898

8.00

0.0931

0.0036

0.0043

0.0012

3.0160

0.0034

0.0266

0.0165

0.0115

0.0169

0.0068

0.0041

0.0362

0.0910

7.75

0.0934

0.0037

0.0044

0.0012

3.0190

0.0036

0.0267

0.0172

0.0120

0.0173

0.0071

0.0042

0.0374

0.0941

7.50

0.0944

0.0040

0.0045

0.0014

3.0250

0.0040

0.0269

0.0192

0.0133

0.0175

0.0078

0.0042

0.0394

0.0988

7.25

0.0963

0.0049

0.0042

0.0017

3.0360

0.0049

0.0275

0.0238

0.0165

0.0167

0.0091

0.0040

0.0397

0.0996

7.00

0.0993

0.0065

0.0034

0.0021

3.0500

0.0062

0.0284

0.0318

0.0221

0.0148

0.0102

0.0036

0.0359

0.0901

6.75

0.1034

0.0091

0.0024

0.0025

3.0660

0.0073

0.0296

0.0435

0.0301

0.0124

0.0099

0.0030

0.0293

0.0736

6.50

0.1081

0.0127

0.0016

0.0025

3.0840

0.0074

0.0309

0.0579

0.0401

0.0098

0.0079

0.0024

0.0222

0.0557

0.05Z

;κ=

10

8.50

0.0897

0.0019

0.0027

0.0007

3.0950

0.0020

0.0256

0.0102

0.0071

0.0114

0.0040

0.0027

0.0245

0.0615

8.25

0.0898

0.0019

0.0027

0.0007

3.0960

0.0020

0.0256

0.0102

0.0071

0.0114

0.0040

0.0028

0.0246

0.0619

8.00

0.0900

0.0019

0.0027

0.0007

3.0990

0.0020

0.0257

0.0104

0.0073

0.0116

0.0041

0.0028

0.0250

0.0629

7.75

0.0906

0.0020

0.0028

0.0007

3.1050

0.0022

0.0259

0.0111

0.0077

0.0118

0.0043

0.0028

0.0260

0.0653

7.50

0.0922

0.0022

0.0027

0.0008

3.1160

0.0025

0.0263

0.0129

0.0089

0.0116

0.0048

0.0028

0.0269

0.0676

7.25

0.0951

0.0028

0.0023

0.0011

3.1320

0.0031

0.0272

0.0166

0.0115

0.0103

0.0055

0.0025

0.0254

0.0637

7.00

0.0995

0.0040

0.0016

0.0013

3.1450

0.0038

0.0285

0.0224

0.0156

0.0084

0.0057

0.0020

0.0208

0.0522

6.75

0.1048

0.0057

0.0010

0.0014

3.1460

0.0041

0.0300

0.0301

0.0208

0.0064

0.0048

0.0015

0.0153

0.0385

6.50

0.1107

0.0079

0.0006

0.0013

3.1300

0.0037

0.0317

0.0389

0.0269

0.0046

0.0034

0.0011

0.0105

0.0264

Page 97: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 97 –

Table 6. The recombination and forbidden line temperatures of the

MAPPINGS 4 models.

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

5.0Z ; κ =∞8.50 2706 2506 – – 3814 3721 3953 3599

8.25 2729 2562 – – 3586 3508 3720 3423

8.00 2799 2682 – – 3407 3359 3538 3279

7.75 2889 2824 – – 3266 3007 3397 3168

7.50 2950 2928 – – 3133 2987 3248 3052

7.25 2918 2932 – – 2977 – 3051 2898

7.00 2756 2807 – – 2804 – 2833 2717

6.75 2481 2561 – – – – – 2574

6.50 2026 2117 – – – – – 2373

5.0Z ; κ = 50

8.50 2666 2472 4613 4256 4247 4499 4540 3945

8.25 2689 2529 – – 4021 4286 4306 3773

8.00 2759 2645 – – 3847 4128 4127 3637

7.75 2847 2785 – – 3714 4006 3986 3531

7.50 2905 2886 – – 3597 5878 3845 3425

7.25 2873 2892 – – 3466 3701 3672 3290

7.00 2721 2770 – – 3315 3420 3481 3131

6.75 2453 2531 – – 3165 – 3316 2989

6.50 2021 2110 – – – – 3077 2795

5.0Z ; κ = 20

8.50 2603 2429 5729 5030 4875 5674 5396 4434

8.25 2621 2472 5509 4823 4660 5469 5168 4274

8.00 2691 2585 5347 4685 4499 5317 4995 4151

7.75 2774 2716 5240 4598 4384 5200 4860 4056

7.50 2829 2812 5221 4546 4295 5090 4738 3968

7.25 2818 2838 5237 4513 4218 4974 4619 3873

7.00 2671 2721 – 4422 4086 4832 4454 3737

6.75 2400 2476 – – 3916 4688 4267 3586

6.50 1989 2075 – – 3671 4443 4021 3399

5.0Z ; κ = 10

8.50 2464 2315 7115 6218 5874 7658 6772 5194

8.25 2484 2357 6776 6038 5697 7455 6561 5061

8.00 2553 2462 6492 5939 5580 7279 6403 4962

7.75 2627 2578 6297 5935 5506 7117 6298 4888

7.50 2672 2661 6192 5965 5460 6984 6220 4826

7.25 2660 2681 6175 5964 5418 6933 6139 4760

7.00 2530 2578 5783 5894 5312 6437 6005 4656

6.75 2297 2357 – 5757 5148 5115 5811 4523

6.50 1916 1994 – – 4897 3995 5425 4344

3.0Z ; κ =∞8.50 4570 4552 5955 5971 5855 5992 6441 5370

8.25 4708 4687 5830 5848 5749 5867 6294 5276

8.00 4899 4874 5685 5714 5644 5725 6128 5174

7.75 5101 5075 5538 5581 5548 5555 5940 5060

Page 98: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 98 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

7.50 5263 5239 5433 5465 5465 5355 5739 4936

7.25 5341 5323 5405 5373 5387 5152 5548 4802

7.00 5313 5307 5412 5296 5296 4974 5379 4661

6.75 5196 5203 5390 5212 5181 4822 5219 4519

6.50 5010 5030 5312 5105 5036 4679 5054 4377

3.0Z ; κ = 50

8.50 4453 4437 6557 6343 6142 6608 6866 5573

8.25 4584 4563 6437 6228 6046 6485 6723 5484

8.00 4538 4517 7284 6703 6419 7261 7187 5684

7.75 4951 4927 6201 6006 5883 6185 6386 5287

7.50 5101 5079 6151 5921 5825 6008 6207 5179

7.25 5170 5154 6163 5856 5767 5837 6043 5060

7.00 5142 5135 6188 5796 5690 5688 5894 4934

6.75 5028 5034 6170 5718 5581 5549 5745 4802

6.50 4847 4867 6089 5611 5438 5408 5582 4666

3.0Z ; κ = 20

8.50 4261 4246 7474 6886 6559 7508 7469 5842

8.25 4378 4359 7372 6790 6481 7391 7335 5765

8.00 4538 4517 7284 6703 6419 7261 7187 5684

7.75 4707 4685 7239 6640 6379 7124 7036 5601

7.50 4836 4817 7250 6594 6350 6984 6887 5515

7.25 4892 4879 7300 6559 6314 6859 6758 5420

7.00 4861 4856 7334 6514 6253 6744 6636 5316

6.75 4753 4759 7313 6441 6152 6624 6503 5201

6.50 4587 4604 7231 6337 6015 6490 6350 5078

3.0Z ; κ = 10

8.50 3902 3890 9061 7799 7270 9014 8440 6272

8.25 4001 3985 9040 7748 7230 8925 8338 6223

8.00 4134 4117 9034 7717 7215 8831 8230 6171

7.75 4272 4254 9067 7710 7222 8745 8127 6125

7.50 4378 4364 9137 7717 7234 8672 8039 6077

7.25 4425 4413 9210 7716 7231 8610 7964 6021

7.00 4395 4392 9243 7687 7188 8537 7879 5946

6.75 4300 4306 9222 7624 7102 8440 7767 5854

6.50 4149 4163 – 7523 6971 8317 7622 5743

2.0Z ; κ =∞8.50 6107 6125 6881 7012 6890 7228 7832 6308

8.25 6174 6188 6813 6949 6826 7112 7698 6228

8.00 6297 6307 6745 6889 6782 6961 7529 6128

7.75 6462 6467 6707 6843 6770 6780 7335 6021

7.50 6633 6632 6731 6815 6783 6594 7147 5915

7.25 6760 6755 6821 6804 6805 6446 7000 5817

7.00 6805 6807 6926 6793 6806 6343 6898 5720

6.75 6758 6753 6975 6753 6759 6250 6799 5619

6.50 6631 6631 6945 6673 6655 6135 6668 5501

Page 99: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 99 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

2.0Z ; κ = 50

8.50 5907 5923 7474 7335 7145 7727 8139 6396

8.25 5969 5982 7422 7284 7092 7623 8020 6329

8.00 6084 6092 7379 7240 7058 7485 7864 6246

7.75 6237 6241 7373 7216 7060 7326 7692 6158

7.50 6395 6394 7426 7212 7087 7176 7533 6074

7.25 6511 6506 7531 7217 7116 7060 7411 5994

7.00 6565 6541 7633 7209 7117 6977 7322 5911

6.75 6496 6492 7674 7171 7071 6895 7230 5819

6.50 6373 6373 7639 7091 6969 6785 7105 5711

2.0Z ; κ = 20

8.50 5581 5591 8396 7800 7505 8446 8543 6479

8.25 5634 5643 8363 7762 7460 8350 8436 6428

8.00 5733 5738 8353 7743 7444 8236 8308 6367

7.75 5865 5865 8382 7742 7458 8113 8167 6305

7.50 5997 5994 8460 7761 7495 8008 8046 6249

7.25 6083 6078 8570 7779 7526 7931 7954 6191

7.00 6093 6088 8657 7772 7521 7869 7880 6125

6.75 6021 6019 8671 7721 7460 7789 7788 6042

6.50 5885 5885 8607 7628 7345 7675 7657 5940

2.0Z ; κ = 10

8.50 4993 4997 10009 8586 8101 9677 9196 6674

8.25 5031 5034 10001 8568 8070 9605 9115 6642

8.00 5102 5103 10022 8567 8066 9526 9022 6607

7.75 5190 5188 10077 8584 8088 9450 8929 6573

7.50 5264 5261 10161 8610 8118 9394 8851 6540

7.25 5296 5292 10246 8626 8135 9358 8798 6508

7.00 5272 5269 10283 8613 8117 9322 8751 6472

6.75 5191 5189 10243 8549 8044 9250 8669 6413

6.50 5074 5072 10150 8453 7932 9150 8556 6339

1.0Z ; κ =∞8.50 8332 8337 8582 8598 8619 8531 9334 7202

8.25 8330 8340 8554 8571 8585 8476 9273 7173

8.00 8357 8368 8551 8555 8559 8396 9187 7135

7.75 8428 8438 8590 8571 8567 8299 9079 7081

7.50 8548 8553 8686 8631 8629 8210 8977 7033

7.25 8685 8684 8839 8717 8725 8159 8911 6995

7.00 8781 8771 9003 8785 8805 8139 8878 6956

6.75 8785 8766 9103 8792 8814 8104 8831 6896

6.50 8691 8664 9092 8721 8738 8018 8731 6807

1.0Z ; κ = 50

8.50 8064 8028 9222 8882 8817 8921 9484 7144

8.25 8008 8010 9197 8857 8787 8874 9434 7121

8.00 8030 8033 9197 8845 8764 8806 9360 7090

7.75 8089 8100 9235 8861 8771 8726 9270 7054

Page 100: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 100 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

7.50 8187 8183 9328 8915 8825 8658 9188 7020

7.25 7614 7590 10330 9318 9095 9277 9409 6971

7.00 8340 8322 9598 9029 8950 8601 9097 6954

6.75 8292 8264 9646 9000 8917 8544 9026 6887

6.50 8145 8111 9576 8888 8791 8422 8887 6786

1.0Z ; κ = 20

8.50 7496 7482 10163 9283 9083 9514 9693 7076

8.25 7488 7478 10139 9263 9058 9475 9651 7063

8.00 7497 7488 10138 9249 9036 9421 9594 7046

7.75 7530 7519 10169 9259 9036 9363 9527 7023

7.50 7581 7565 10239 9289 9065 9312 9462 7000

7.25 7614 7590 10330 9318 9095 9277 9409 6971

7.00 7571 7539 10382 9295 9069 9224 9338 6916

6.75 7421 7381 10321 9182 8945 9106 9202 6822

6.50 7179 7132 10133 8981 8724 8907 8984 6686

1.0Z ; κ = 20

8.50 6580 6554 11695 9939 9503 10585 10088 7097

8.25 6559 6537 11668 9915 9480 10557 10061 7093

8.00 6537 6516 11648 9891 9452 10518 10022 7086

7.75 6510 6488 11639 9864 9421 10472 9969 7073

7.50 6462 6435 11634 9826 9379 10413 9904 7045

7.25 6357 6326 11596 9742 9293 10330 9809 6992

7.00 6165 6130 11472 9581 9120 10183 9650 6898

6.75 5894 5857 11223 9333 8852 9951 9405 6766

6.50 5594 5558 10872 9030 8524 9664 9104 6614

0.5Z ; κ =∞8.50 10500 10450 10924 10496 10536 9822 10685 7812

8.25 10480 10450 10894 10496 10529 9810 10669 7808

8.00 10470 10440 10863 10492 10522 9786 10645 7802

7.75 10460 10440 10850 10487 10517 9752 10610 7793

7.50 10480 10450 10869 10493 10522 9713 10566 7784

7.25 10490 10460 10920 10502 10533 9675 10519 7762

7.00 10460 10420 10968 10486 10517 9629 10459 7720

6.75 10330 10270 10931 10383 10411 9528 10341 7640

6.50 10080 10020 10753 10177 10195 9333 10128 7515

0.5Z ; κ = 50

8.50 10030 9972 11481 10673 10609 10115 10690 7671

8.25 10010 9962 11450 10671 10606 10105 10679 7669

8.00 9981 9943 11414 10665 10597 10087 10661 7668

7.75 9962 9923 11384 10650 10585 10059 10632 7665

7.50 9933 9894 11371 10626 10563 10022 10589 7658

7.25 9875 9836 11364 10581 10522 9968 10529 7631

7.00 9758 9700 11325 10488 10426 9881 10430 7572

6.75 9532 9466 11181 10299 10232 9716 10253 7466

6.50 9211 9134 10897 10016 9931 9452 9970 7310

Page 101: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 101 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

0.5Z ; κ = 20

8.50 9269 9196 12269 10902 10686 10576 10710 7508

8.25 9244 9180 12232 10903 10681 10568 10702 7509

8.00 9201 9146 12179 10887 10670 10556 10690 7512

7.75 9137 9086 12114 10845 10638 10527 10665 7515

7.50 9036 8984 12034 10765 10564 10476 10613 7504

7.25 8878 8817 11926 10629 10434 10384 10520 7464

7.00 8634 8562 11749 10417 10219 10221 10354 7369

6.75 8280 8207 11452 10109 9899 9958 10082 7218

6.50 7878 7782 11039 9732 9495 9607 9711 7022

0.5Z ; κ = 10

8.50 7965 7874 13503 11265 10797 11440 10849 7394

8.25 7919 7840 13445 11257 10791 11433 10845 7397

8.00 7837 7768 13347 11218 10763 11417 10833 7403

7.75 7698 7634 13198 11114 10678 11372 10799 7406

7.50 7477 7411 12988 10917 10498 11268 10709 7378

7.25 7165 7095 12699 10627 10211 11078 10534 7295

7.00 6769 6696 12319 10251 9824 10788 10253 7145

6.75 6326 6251 11840 9817 9365 10407 9865 6951

6.50 5894 5823 11316 9374 8885 9990 9433 6746

0.3Z ; κ =∞8.50 12010 11900 12740 11881 11865 10716 11537 8127

8.25 11980 11890 12714 11888 11865 10714 11535 8127

8.00 11940 11860 12662 11886 11864 10709 11530 8130

7.75 11870 11810 12582 11866 11852 10695 11518 8134

7.50 11770 11710 12476 11797 11800 10663 11486 8134

7.25 11610 11550 12342 11658 11681 10589 11415 8114

7.00 11390 11320 12161 11451 11482 10452 11280 8048

6.75 11070 10990 11890 11161 11193 10226 11050 7927

6.50 10670 10580 11508 10797 10816 9901 10716 7758

0.3Z ; κ = 50

8.50 11359 11233 13149 11903 11793 10909 6949 7927

8.25 11330 11223 13116 11907 11784 10902 11416 7934

8.00 11271 11184 13048 11902 11780 10896 11413 7935

7.75 11184 11107 12937 11868 11757 10883 11402 7944

7.50 11029 10961 12781 11755 11671 10839 11363 7945

7.25 10806 10728 12571 11553 11492 10737 11269 7917

7.00 10495 10408 12298 11267 11214 10550 11089 7830

6.75 10098 10000 11930 10899 10841 10263 10803 7681

6.50 9643 9536 11466 10474 10399 9881 10408 7486

0.3Z ; κ = 20

8.50 10360 10221 13723 11929 11655 11229 11289 7710

8.25 10323 10203 13677 11931 11657 11228 11289 7713

8.00 10249 10147 13581 11918 11648 11224 11286 7718

7.75 10110 10018 13417 11846 11599 11201 11271 7726

Page 102: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 102 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

7.50 9888 9805 13177 11668 11455 11131 11214 7724

7.25 9574 9481 12855 11370 11181 10970 11076 7674

7.00 9153 9054 12458 10977 10793 10708 10827 7551

6.75 8667 8555 11968 10516 10319 10336 10457 7362

6.50 8152 8028 11411 10026 9803 9889 9996 7131

0.3Z ; κ = 10

8.50 8755 8602 14657 12029 11511 11921 11253 7523

8.25 8697 8560 14585 12025 11505 11920 11253 7526

8.00 8585 8465 14429 11986 11480 11908 11247 7533

7.75 8372 8270 14162 11844 11380 11857 11215 7540

7.50 8035 7940 13778 11541 11121 11720 11108 7517

7.25 7578 7482 13290 11094 10691 11455 10880 7418

7.00 7047 6949 12724 10566 10153 11068 10520 7238

6.75 6504 6407 12107 10016 9578 10598 10054 7013

6.50 6009 5617 11486 9499 9022 10115 9558 6785

0.2Z ; κ =∞8.50 12970 12830 13976 12776 12698 11264 12029 8276

8.25 12930 12810 13943 12779 12696 11264 12029 8278

8.00 12870 12770 13866 12775 12695 11262 12029 8281

7.75 12770 12670 13727 12738 12670 11252 12022 8287

7.50 12580 12490 13509 12611 12576 11213 11991 8293

7.25 12290 12210 13210 12359 12364 11104 11898 8274

7.00 11910 11820 12840 12002 12032 10901 11709 8199

6.75 11460 11360 12401 11573 11610 10591 11408 8055

6.50 10970 10850 11891 11104 11131 10190 11004 7865

0.2Z ; κ = 50

8.50 12174 12018 14241 12663 12516 11373 11829 8054

8.25 12135 11999 14185 12662 12471 11359 11827 8052

8.00 12067 11950 14106 12653 12497 11360 11821 8057

7.75 11931 11824 13927 12604 12472 11356 11819 8064

7.50 11698 11601 13644 12432 12312 11290 11764 8069

7.25 11349 11252 13281 12123 12056 11156 11655 8040

7.00 10903 10796 12838 11699 11652 10907 11426 7941

6.75 10398 10282 12324 11212 11166 10544 11075 7776

6.50 9865 9729 11754 10701 10637 10098 10625 7563

0.2Z ; κ = 20

8.50 11017 10841 14637 12534 12246 11597 11594 7794

8.25 10971 10813 14572 12536 12197 11599 11581 7797

8.00 10869 10739 14443 12514 12190 11583 11596 7796

7.75 10693 10582 14210 12434 12179 11562 11562 7815

7.50 10397 10286 13850 12198 11928 11485 11520 7811

7.25 9962 9851 13382 11792 11567 11293 11365 7758

7.00 9435 9315 12845 11280 11080 10953 11065 7629

6.75 8865 8731 12235 10732 10544 10526 10643 7404

6.50 8294 8146 11588 10180 9957 10029 10139 7186

Page 103: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 103 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

0.2Z ; κ = 10

8.50 9214 9027 15341 12447 11901 12151 11437 7567

8.25 9146 8985 15249 12454 11895 12138 11419 7577

8.00 9019 8874 15051 12419 11870 12153 11446 7575

7.75 8764 8636 14731 12252 11818 12106 11424 7584

7.50 8356 8240 14222 11895 11482 11954 11294 7566

7.25 7808 7693 13622 11352 10958 11624 11038 7468

7.00 7197 7079 12931 10728 10334 11213 10645 7274

6.75 6598 6481 12249 10116 9691 10706 10154 7039

6.50 6069 5961 11571 9564 9096 10169 9621 6787

0.1Z ; κ =∞8.50 13980 13810 15367 13676 13505 11795 12464 8389

8.25 13940 13790 15316 13678 13527 11779 12457 8393

8.00 13860 13720 15197 13664 13480 11788 12445 8396

7.75 13700 13570 14983 13619 13440 11759 12476 8402

7.50 13420 13300 14623 13449 13367 11715 12433 8412

7.25 12990 12870 14119 13084 13102 11603 12332 8397

7.00 12440 12320 13564 12553 12538 11325 12108 8312

6.75 11850 11710 12908 11972 12017 10935 11742 8166

6.50 11250 11100 12252 11387 11429 10459 11264 7944

0.1Z ; κ = 50

8.50 13037 12862 15471 13424 13184 11813 12160 8146

8.25 12988 12823 15398 13416 13211 11804 12212 8139

8.00 12901 12746 15263 13419 13171 11790 12201 8134

7.75 12717 12581 15003 13340 13128 11763 12200 8156

7.50 12397 12271 14582 13134 12953 11705 12119 8165

7.25 11912 11795 14011 12715 12639 11549 12017 8139

7.00 11320 11194 13392 12143 12100 11259 11748 8032

6.75 10689 10544 12724 11519 11487 10817 11341 7855

6.50 10078 9913 12028 10913 10864 10298 10822 7652

0.1Z ; κ = 20

8.50 11701 11507 15669 13136 12759 11949 11861 7846

8.25 11646 11470 15562 13128 12753 11951 11852 7842

8.00 11535 12300 15382 13111 12738 11905 11841 7846

7.75 11313 11165 15044 13020 12684 11894 11837 7860

7.50 10924 10795 14597 12746 12477 11795 11796 7859

7.25 10379 10240 13958 12233 12049 11567 11588 7826

7.00 9731 9582 13231 11585 11431 11191 11282 7686

6.75 9062 8901 12502 10919 10765 10703 10822 7469

6.50 8430 8257 11787 10309 10107 10158 10263 7216

0.1Z ; κ = 10

8.50 9699 9495 16141 12879 12270 12393 11593 7578

8.25 9631 9444 16055 12874 12266 12387 11599 7575

8.00 9478 9316 15760 12811 12248 12378 11600 7592

7.75 9180 9036 15323 12665 12118 12324 11581 7609

Page 104: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

– 104 –

Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

7.50 8696 8560 14694 12249 11810 12155 11470 7577

7.25 8050 7912 13943 11617 11230 11808 11195 7505

7.00 7349 7208 13148 10903 10522 11342 10770 7293

6.75 6691 6552 12375 10205 9807 10786 10214 7059

6.50 6128 6001 11667 9615 9178 10241 9661 6815

0.05Z ; κ =∞8.50 14450 14270 16081 14070 13886 12008 12655 8441

8.25 14410 14240 16014 14069 13882 12008 12655 8442

8.00 14320 14160 15888 14059 13873 12000 12641 8436

7.75 14130 13990 15613 14012 13831 11980 12653 8434

7.50 13810 13680 15170 13815 13706 11981 12615 8441

7.25 13320 13190 14561 13418 13383 11840 12528 8451

7.00 12690 12560 13849 12799 12846 11511 12289 8367

6.75 12020 11880 13146 12161 12208 11103 11889 8202

6.50 11380 11220 12422 11523 11572 10593 11385 7985

0.05Z ; κ = 50

8.50 13444 13250 16091 13764 13496 11993 12331 8176

8.25 13396 13221 16017 13762 13492 11993 12332 8177

8.00 13289 13134 15845 13750 13481 11992 12332 8179

7.75 13085 12940 15531 13687 13438 11977 12328 8186

7.50 12726 12591 15043 13466 13285 11915 12292 8195

7.25 12183 12047 14398 12999 12905 11744 12163 8176

7.00 11524 11378 13662 12354 12311 11412 11882 8073

6.75 10835 10680 12908 11666 11637 10943 11449 7883

6.50 10175 10001 12169 11016 10974 10401 10917 7647

0.05Z ; κ = 20

8.50 12034 11822 16195 13407 13008 12084 11972 7875

8.25 11979 11785 16105 13405 13004 12083 11972 7877

8.00 11849 11683 15891 13387 12991 12077 11972 7879

7.75 11609 11452 15513 13297 12933 12053 11963 7888

7.50 11193 11045 14944 13008 12727 11960 11906 7896

7.25 10582 10434 14219 12453 12257 11727 11729 7857

7.00 9870 9713 13427 11745 11586 11325 11385 7715

6.75 9155 8984 12637 11028 10868 10803 10896 7489

6.50 8493 8310 11876 10370 10182 10233 10327 7227

0.05Z ; κ = 10

8.50 9937 9721 16577 13071 12451 12506 11679 7596

8.25 9869 9673 16447 13066 12447 12504 11679 7598

8.00 9707 9537 16157 13032 12425 12491 11676 7602

7.75 9393 9231 15658 12876 12324 12437 11651 7611

7.50 8866 8721 14952 12447 11993 12267 11539 7606

7.25 8170 8022 14117 11756 11367 11916 11263 7515

7.00 7423 7272 13261 10981 10601 11408 10819 7312

6.75 6735 6588 12444 10259 9855 10834 10266 7060

6.50 6154 6021 11705 9642 9195 10272 9701 6815

Page 105: arXiv:1307.5950v1 [astro-ph.CO] 23 Jul 2013

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Table 6—Continued

log(q) TH THe T[OIII] T[ArIII] T[SIII] T[OII] T[NII] T[SII]

Table 7: Line ratios diagnostics used with the pyqz Python module v0.2 and their associated

regions of validity in logZ =12+log(O/H) and log q space.

Line Ratios κ = 10 κ = 20 κ = 50 κ =∞logZ log q logZ log q logZ log q logZ log q

[NII]/[SII] vs. [OIII]/[SII] 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5

[NII]/[SII] vs. [OIII]/Hβ 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.25 7.39–9.39 6.5–8.5

[NII]/[SII] vs. [OIII]/[OII] 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–8.99 6.5–8.5

[NII]/[OII] vs. [OIII]/[SII] 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5 7.39–9.39 6.5–8.5

[NII]/[OII] vs. [OIII]/Hβ 7.39–9.39 6.5–7.5 7.39–9.39 6.5–7.5 7.39–9.39 6.5–7.5 7.39–9.39 6.5–7.5

[NII]/[OII] vs. [OIII]/[OII] 7.39–9.39 6.5–8.25 7.39–9.39 6.5–8.0 7.39–9.39 6.5–7.75 7.39–9.39 6.5–7.75

[NII]/Hα vs. [OIII]/Hβ 7.39–8.69 6.5–8.5 7.39–8.39 6.5–8.5 7.39–8.39 6.5–8.25 7.39–8.39 6.5–8.5

[NII]/Hα vs. [OIII]/[OII] 7.39–8.69 6.5–8.5 7.39–8.39 6.5–8.5 7.39–8.17 6.5–8.25 7.39–7.99 6.5–8.5