Testing Coelho’s 2014 models with the MILES Library · 2018. 2. 15. · University of Groningen...

University of GroningenBachelor Thesis

Kapteyn Astronomical Institute

Testing Coelho’s 2014 models with the MILES Library

Author : Supervisor :R.W. Koet Prof. dr. R.F. Peletier

December 19, 2017

Abstract

In 2014, Coelho released a theoretical stellar library, containing stellar spectraover a large range of temperatures, log(g) and [Fe/H], for two different compositionsof [α/Fe]. In this Thesis, the spectral indices of the aforementioned theoretical libraryare compared to the MILES library, to test the validity of the models. This was doneby calculating several spectral indices for the Coelho library and the MILES library,and plotting these against one another. It was found that the models of Coelho libraryfit the Iron lines well. Also, the equivalent widths of the Balmer lines are overestimatedfor A-type giants. This is likely due to the non-LTE effects in which these lines arecreated, which are not taken into account during the calculation of these lines. Thiseffect also affected some of the C&N lines, which showed an increased amount ofemission. Further, the results were compared to Martins & Coelho (2007), whichcompares the previous version of the theoretical library with observed stellar libraries.One of the differences that is seen between the found results and the results in Martins& Coelho (2007) is that in Coelho (2014) the Balmer lines in some giants are muchmore overestimated than in Martins & Coelho (2007). As stated above, this alsoaffected the C&N lines, which was also not seen in Martins & Coelho. Furthermore,the models of the Iron lines have improved, especially for the colder stars.

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Contents1 Introduction 5

2 Theoretical Background 62.1 Stellar Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Continuum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Absorption lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.2 Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3 Stellar Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3.1 Empirical Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.3.2 Theoretical Libraries . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Library Compatibility 113.1 Atmospheric Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4 Calculation and Visualization of Indices 14

5 Results & Discussion 165.1 Balmer Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165.2 Iron Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185.3 C&N Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195.4 Alpha Element Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.5 Other Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

6 Summary & Conclusion 256.1 Differences with M&C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

References 28

A Resolution Calculation 30

B Measured Indices 31

C Balmer Line Plots 33C.2 HdA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33C.3 HdF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34C.4 HgF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34C.5 Hbeta p . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

D Iron Line Plots 36D.6 Fe4058 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36D.7 Fe4383 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36D.8 Fe4531 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37D.9 Fe4668 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38D.10 Fe4930 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39D.11 Fe5015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40D.12 Fe5270 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41D.13 Fe5406 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42D.14 Fe5709 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43D.15 Fe5782 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

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E C&N Line Plots 45E.16 CNO3862 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45E.17 CN1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46E.18 CNO4175 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47E.19 CO4685 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48E.20 CO5161 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

F Alpha Element Line Plots 49F.21 Cr3594 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49F.22 Ni3667 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50F.23 Ni3780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50F.24 Mg3835 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51F.25 CaHK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52F.26 Si4101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53F.27 Ca4227 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53F.28 Cr4264 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54F.29 Ni4292 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55F.30 Ti4296 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55F.31 Si4513 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56F.32 Ti4533 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56F.33 Mg4780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57F.34 Mg1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58F.35 Ni4910 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59F.36 Ni4976 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59F.37 Ti5000 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60F.38 Mgb5177 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60F.39 Cr5206 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61F.40 Ni5592 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61F.41 TiO1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

G Other Element Line Plots 63G.42 Sc3613 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63G.43 Co3701 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63G.44 Mn3794 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64G.45 Co3840 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65G.46 Co3876 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65G.47 Al3953 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66G.48 Eu3970 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66G.49 Mn4018 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67G.50 K4042 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67G.51 Mn4061 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68G.52 Sr4076 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68G.53 V4112 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69G.54 Sc4312 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69G.55 Ba4552 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70G.56 Eu4592 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70G.57 S4693 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71G.58 Zn4720 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71G.59 Mn4757 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72G.60 V4928 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72G.61 Ba4933 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73G.62 Cu5217 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

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G.63 Cu5780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74G.64 Ba6142 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74G.65 Sc6292 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75G.66 V6604 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

H Overview of phenomena in lines 76

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Chapter 1: IntroductionA lot of galaxies are so far away that we cannot resolve the stars in that galaxy. We stillwant to learn more about these galaxies; especially about how these galaxies are formed.This can be done by studying their chemical compositions and their star formation histo-ries. The information we get from the unresolved galaxies is the integrated light they emit,which is the light from all the different stars with their different temperatures, masses,ages, metallicities, and compositions.

A technique called Stellar Population Synthesis uses stellar populations to fit the inte-grated light from these galaxies. This method [Spinrad and Taylor, 1971][Tinsley, 1980]assumes an initial mass function, which is an assumption about how many stars exist forevery mass initially. It also assumes (several) single stellar populations, which are all thestars born at the same time - that is with a range of masses and temperatures, but thesame metallicity.

The single stellar population models are made up of two parts, the isochrones, and thestellar atmosphere. Isochrones are theoretical models that give the position of a groupof stars with the same chemical composition on the Hertzsprung-Russel diagram. Thepoint of isochrones is to model the main sequence and the evolutionary phases of thestars. Examples of isochrones are the BaSTI isochrones [Cassisi et al., 2005] or the Padovaisochrones [Bertelli et al., 1994]

The atmospheres come from a stellar library, which is a collection of stellar spectra,preferably with a good coverage of the parameter space (temperature, surface gravity, andmetallicity). There are two kinds of stellar libraries, empirical and theoretical libraries.An empirical stellar library is a collection of real, observed stars, whereas a theoretical (orsynthetic) stellar library is a collection of spectra that have been calculated on the basis ofour knowledge of stellar atmospheres. They each have their advantages and disadvantages,which will be discussed further in Section 2.3.

In this Thesis, one of these synthetic stellar libraries is tested by investigating atmo-spheric indices, to show where the models could be improved. The library that will betested is the library of Coelho, released in 2014 [Coelho, 2014]. The empirical library thatwill be used is the MILES library [Sanchez-Blazquez et al., 2006]. Improvement of thistheoretical library is beneficial for research that involves stellar populations since moreaccurate stellar libraries lead to more reliable results. In the second chapter, the basicconcepts about stellar atmospheres and stellar libraries are given, including more infor-mation about the two stellar libraries used in this Thesis. The third chapter covers themethods used to make the two libraries compatible with each other. The fourth chapterexplains how the indices are visualized in such a way that the indices from the modelscan be compared with the indices of the MILES stars. The fifth chapter demonstratesthese visualizations holds the discussion. Finally, the sixth and last chapter provides theconclusion.

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Chapter 2: Theoretical Background2.1 Stellar Spectra

Stars emit photons of almost every wavelength. These photons come from the pho-tosphere of the star. By observing the star, the number of photons per wave-length is measured. By plotting the number of photons observed per wavelengthagainst the wavelength, an absorption spectrum is seen. This absorption spectrumis a continuum with absorption lines, which contain the information (Figure 1).

Figure 1: Spectrum of MILES star s0020 with T=15276K, log(g)=4.10 and[Fe/H]=-0.20.

2.1.1 Continuum

The continuum emission of a star is radiation with wavelengths ranging from radio wavesto x-rays. This is due to thermal radiation, combined with the assumption of an opaquemedium under the atmosphere of the star. This radiation is that of a black body, of whichthe function is the Planck function [LeBlanc, 2011].

Bλ(T ) =2hc2

λ5

1

ehcλkT − 1

(1)

For stellar spectra, the Effective Temperature Teff is used to determine the black bodyof the continuum. This means that the continuum is mostly dependent on the physicaltemperature of the outer layers of the star, but also slightly on the metallicity of the star.

2.1.2 Absorption lines

Absorption lines take away flux from the continuum. The opposite is also possible;these are emission lines, which contribute more flux to the spectrum. The formation ofabsorption happens in the atmosphere of the star, which consists of (partially) ionizedatoms or even molecules for colder stars. The photons from the continuum emissioninteract with the electrons of these atoms and molecules, such that these photonsdisappear from the continuum, resulting in an absorption line.

The shape and depth of the absorption lines are determined by the composition ofthe atmosphere of the star and the atmospheric parameters. These atmospheric parame-ters are the temperature, surface gravity, and metallicity. As said above, the temperatureof the star determines the shape of the continuum emission. The temperature alsodetermines the ionization level of atoms in the atmosphere of the star and the possibility

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of the existence of molecules. The possibility of certain lines appearing in the spectrumare dependent on these properties. The surface gravity of the star determines the widthof the absorption lines by pressure broadening, which is the interaction between particles.A higher surface gravity leads to a higher pressure, which in turn leads to broaderabsorption lines.

2.2 Indices

Absorption lines give information about the stellar spectrum. A means of obtaining theinformation from absorption lines is by looking at indices. The way an index is calcu-lated is different for atomic lines and molecular bands. The molecular band indices areratios of magnitudes, whereas the atomic line indices are equivalent widths. (Equation 2)[Worthey et al., 1994]

I =

−2.5 log

[( 1

λ2 − λ1

)∫ λ2

λ1

FλFλc

dλ]

for molecular bands, in magnitudes.∫ λ2

λ1

(1− Fλ

Fc

)dλ for atomic lines, in A.

(2)

where I is the value of the index, Fc is the continuum flux and Fλ is theflux of the index. The sign of the index shows whether it is an absorptionline or an emission line, which have a plus or minus sign, respectively. Themagnitude of the index is due to the depth with respect to the continuum.

Figure 2: Example of how equivalent width is calculated. The area of the absorptionline under the continuum level is equal to the equivalent width times the height of thecontinuum.

2.3 Stellar Libraries

Stellar libraries are a collection of stellar spectra. A stellar library preferably has a goodcoverage of the different parameters: temperature, surface gravity, and metallicity. Itshould also have a large wavelength range and good resolution. Stellar libraries can beused for a plethora of things, for example, determination of atmospheric parameters instellar surveys, calibration of photometric indices or studying star formation histories ofgalaxies. There are two kinds of stellar libraries, namely empirical and theoretical stellarlibraries.

2.3.1 Empirical Libraries

An empirical stellar library is a collection of spectra of observed stars. One of theadvantages of empirical libraries is that they contain real stars. Consequently, thespectrum is a good representation of a star with the parameters that are measured.

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Another advantage of the empirical libraries is that there is no need for complicatedphysics of convection or stellar winds for any of the stars.

However, empirical stellar libraries also have drawbacks. A major drawback of em-pirical spectra is that they are limited by observations. The observed spectra have tobe corrected for atmospheric absorption and they have to be flux calibrated. Otherdrawbacks are that the wavelength range and resolution of the observed spectra areusually limited. The largest shortcoming of empirical libraries is most likely the coverageof the parameter space. This because some kinds of stars are not numerous near the Sun,for example very massive variable stars, or very massive, very metal-poor stars.

The final drawback is that the only stars that can be used are stars that can beresolved. This means that the stars that can be used, are in the vicinity of the Sun, andhave (approximately) the same chemical composition. This means that if an empiricallibrary is used to fit the spectrum of a galaxy with a different chemical composition,the outcome of used stars may be different than if a library was used with the correctchemical composition

As stated in Chapter 1, the empirical MILES library is used in this Thesis. TheMedium-resolution Isaac Newton Telescope Library of Empirical Spectra (MILES)consists of 985 stars, which cover the parameter range as shown in Figure 3. As the namealready states, the spectra are obtained by using the Isaac Newton Telescope, which islocated at La Palma, in Spain. The library has a resolution of R ≈ 2000, or a FWHM of2.5 A and a wavelength range of 3500 to 7429.4 A. [Sanchez-Blazquez et al., 2006]

Figure 3: Gravity-temperature diagram for the MILES library. The colours give the valueof the metallicity [Fe/H], as given in the legend.

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2.3.2 Theoretical Libraries

Theoretical (or synthetic) libraries are the modeled counterpart of empirical spectra.They are based on our understanding of the physics of stellar atmospheres, rather thanobservations. The theoretical libraries excel where empirical libraries fall short; they offera high resolution and a good coverage of the parameter space. An additional advantageis that they are not subject to observational limitations such as flux calibration andatmospheric absorption.

Although the advantages are great improvements on the empirical libraries, thereare a few drawbacks that do not necessarily make theoretical libraries superior toempirical libraries. One of these drawbacks is the information loss due to incompleteabsorption line lists. Since there are many transitions within atoms and even more withinmolecules, there are billions of lines that need to be calculated. Not all of these linesare in line libraries yet, which in turn leads to spectra in which some of the lines of anelement are missing.

Another drawback is that we do not yet know all of the physics behind stars andtheir atmospheres. Some of these process are known, but very computationally ex-pensive to model. Molecular bands is an example of this. Since molecules have manytransitions, it is hard to calculate all of them. Another example is convection, whichmakes some lines appear stronger and others weaker [Collet et al., 2007]. A final exampleis strong stellar winds, a phenomenon that happens in massive stars. Stellar windscan have their own spectral lines, which can contaminate the spectrum of the star.[Lamers and Cassinelli, 1999]

Figure 4: Gravity-temperature diagram for the Coelho library for solarmetallicity.[Coelho, 2014]

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The theoretical library used in this thesis is the HIGHRES library by Coelho, releasedin 2014. The parameters that the library covers are (3000K ≤ Teff ≤ 25000K),(−0.5 ≤ log(g) ≤ 5.5) and (−1.3 ≤ [Fe/H] ≤ 0.2). A visualization of the parametersat solar metallicity is given in Figure 4. There are a few additions in comparison withthe previous libraries by Coelho [Coelho et al., 2005] [Coelho et al., 2007]. One of theseadditions is that there is two α-enhanced mixtures for every solar mixture, rather thanone. One of these mixtures has fixed [Fe/H] and the other has fixed Z, where Z is themass fraction of metals. Previously, there was no mixture with fixed Z.

The effects of Predicted Lines (PLs) are also added into Coelho’s 2014 library.PLs are quantum mechanical calculations of certain absorption lines. However, these linesare not fit for high-resolution spectra [Munari et al., 2005]. The PLs were included inthe lower resolution SEDs, also published with Coelho (2014). To include the PLs in theHIGHRES models, the HIGHRES models were compared with the SED library. Usingthe differences found caused by PLs, the HIGHRES models were adjusted in such a waythat the high-resolution features were untouched, but the continuum emission includedthe effect of the PLs.

These models are calculated for a wavelength range of 2500-9000 A with an initialresolution of R = 300000, but the resolution was broadened using a Gaussian LSF withR = 20000 and then resampled to 0.02 A bins. [Coelho, 2014]

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Chapter 3: Library CompatibilityBefore it is possible to compare two libraries with each other, they need to be the at sameresolution and have the same atmospheric parameters, i.e. temperature, surface gravityand metallicity. This chapter describes the process of making the MILES library and theCoelho library compatible with each other.

3.1 Atmospheric Parameters

The Coelho library has spectra of stars with values of atmospheric parameters which siton a regular grid, as described in Chapter 1. For the MILES library, this is sadly notthe case. Since this library contains real, observed stars, it can be expected that thesestars do not have round values for the parameters. There are several ways to go aboutthis. One way is to choose the star that is closest to the model, like in Martins & Coelho(2007). Another way, however, is to use the observed stars with an interpolator to create anew spectrum with the desired parameters. This is the method that was used in this thesis.

The interpolator used was made by A. Vazdekis [Vazdekis et al., 2003]. This inter-polator creates 8 boxes around the desired parameter, each with one corner at this point.This is required as the stars in the library are not (necessarily) distributed on a regulargrid. Each box is then checked for content. If there are no stars found within a box, thebox grows until at least one star is found (up to a certain limit). After this process, thestars in each box are combined according to their weights. A closer match to the desiredparameters and a higher signal-to-noise ratio equals a higher weight. If the interpolatorcannot reach the desired parameters, it creates a spectrum that minimizes the distancebetween the desired parameters and the parameters from the solution star.

Before creating interpolated MILES spectra with the parameters of the Coelhomodels, I tested the interpolator by creating the stars from the MILES library, excludingthe star that was being recreated. After normalizing the spectra, I calculated the valueN, for different wavelength ranges:

N =1

λe − λ0

λe∑i=λ0

(Ii −Ri)2

Ri(3)

where I is the interpolated spectrum, R is the original MILES spectrum and λ0 andλe are the starting- and end points of the wavelength range, respectively. This meansthat N gives a dimensionless measure of the average error per wavelength. Each of thedifferent wavelength ranges had a visual representation as shown in Figure 5, which is therepresentation for the wavelength range 4500-7300 A.

A few things had to be taken into consideration for picking a wavelength range:the amount of stars that were to be removed and the length of the wavelength range. Ofcourse, as few stars as possible need to be eliminated, to keep a large sample available.Also, the desired wavelength range has to be as long as possible. Looking at differentwavelength ranges, I noticed that the blue part of the spectrum was recreated the worst.Because of this, I chose the wavelength range for the sample stars to be 4500-7300 A.Note that this does not imply that I will not be looking at indices at a wavelength lowerthan 4500 A, but these indices might not be as accurate as the ones within the safe limit.The more a line is in the shorter wavelength regime, the less trustworthy the line will be.

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The upper limit of deviation was chosen to be 10% per pixel on average. This correspondsto a value of N = 0.01, since N considers the normalized square of the difference betweenthe interpolated spectrum and the real spectrum. Figure 5 shows us that the stellarspectra that do not fall within this limit are mostly in the cold regime of the sample.The most likely cause for this is the presence of molecular bands, which are stronglyaffected by temperature (see Figure 13 in [Coelho et al., 2005]). In combination withthe factor that there is a low density of stars with a low temperature, this might leadto these stars being not recreated well enough. However, for the higher temperaturestars this cannot be the reason, as they do not have molecular bands. A likely reasonthat these spectra do not coincide, is because the parameters of the spectrum arenot properly determined. The stars with N-values higher than 0.01 were removedand another interpolation was done with the new sample. This showed that someother stars had an increased value for N, probably because they were affected by theremoved spectra. This procedure was done three times, after which no stars had an N-value of 0.01 or higher. In total, 55 out of 985 stars were removed from the MILES sample.

After cleaning the sample of stars that could not be recreated properly, the sameinterpolation was used to create stellar spectra that have the same atmospheric param-eters as the models of Coelho. Since the interpolator does not necessarily reach therequested parameters, it also returns the parameters of the created spectrum. I checkedthese returned parameters against the input parameters, to exclude any spectrum withparameters more than 10% deviation from the requested parameters. Note that this 10%deviation was taken in linear space, e.g. ≈ 0.05 in log-space. After purging the list ofvalues that did not fall within this 10% limit, there were 1734 spectra left. One morespectrum was thrown out since the model was flat in the desired wavelength range. Thisis probably an anomaly in the calculation of the model. Finally, 1733 stellar spectra wereremaining to work with.

3.2 Resolution

The resolution of the Coelho models is higher than that of the MILES library. Sinceindices are dependent on resolution, the resolution of the models and that of the MILESlibrary have to be equal. The resolution of the MILES library cannot be increased, so theresolution of the Coelho models should be decreased. First, I binned the models of Coelhoto the wavelength range of that of MILES, which was a wavelength range from 3500-7300A, with a spacing of 0.9A. The next step was a convolution with a Gaussian. This canbe used to decrease the resolution of a spectrum. The library of Coelho is calculated at aresolution of 300000, and then convolved with a line spread function with a resolution of20000. The FWHM of the MILES library is 2.5 A[Falcon-Barroso et al., 2011]. Using thisinformation, the standard deviation of the Gaussian was found to be 1.056 A. (AppendixA)

12

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13

Chapter 4: Calculation and Visual-ization of Indices

In the previous chapter, I discussed how to make the library by Coelho and the MILESlibrary compatible with each other. In this chapter I will talk about what I did to usethe model- and interpolated spectra to obtain a result. I used the REDUCEME package[Cardiel, 1999] to extract information from both sets of spectra. This package only workswith .fits files. Since I worked with ASCII files, I first had to transform the ASCII filesto .fits files using iraf, specifically by using the rspectext function. After convertingthe spectra to .fits format, the REDUCEME package could be used. The first step isto make the file comprehensible for REDUCEME by using the leefits function. A bash

script was used to do this for all .fits files.

The next step is to use the index function, which calculates the indices from thespectra. This function takes a list of defined indices (as defined in Appendix B)and a spectrum. The definition of this index gives a red and blue pseudocontin-uum bandpass and a central bandpass. As can be seen in Figure 6, a line is drawnfrom the average of the red bandpass to that of the blue bandpass. In the centralbandpass the index is calculated, taking this line as the continuum, as explainedin Section 2.2. The index function then returns a file with the information of thedefined lines that could be found within the given spectrum. I used a bash-script toiterate through all the files and applynig the leefits and index functions on them.

Figure 6: Visual of the index function, calculating the index of Hbeta.

14

To extract the data I need from the output files, I wrote a python script that iterates overall the output files and stores all the desired information in a table. Each row representsa spectrum, while each column represents a line in the spectrum. The values inside thetable represent the index for each line and spectrum. One table was made for the MILESspectra and one table was made for the Coelho spectra. The next thing to do was thevisualization of the data in the tables.

This was done by plotting the index of each model versus the index of their inter-polated companion. To investigate the lines with extra detail, I used rainbow colourschemes in the three parameters, as can be seen in Figure 7. I will show the results of theindex as shown in Figure 8, since this is clearer to look at. I adopted the categories oflines as stated in Martins & Coelho (2007). However, as they also state, these categoriesare rough, since lines usually do not depend on only one element. [Serven et al., 2005]The chosen categories are Balmer lines, Iron lines, C&N lines, Alpha element lines and”Other” lines.

During the visualization of the indices, a certain phenomenon occured. In abouthalf of the lines, there was a group of hot stars, marked in blue, with a temperature ofaround 10000K that moved away from the rest of the blue marked stars. This group hadsomething in common, namely having a high surface gravity, log(g) = 5 dex. In Figure7, this can also be seen. This is most likely an effect produced by the interpolator ofthe MILES library. The library tries to create this star, but in the process uses somevery hot, high gravity dwarfs, which may not have a representative spectrum for thattemperature range. Because of this, these stars are excluded from the results.

Figure 7: Visualization of index Ti4296, Alpha-enhanced version. The top-left plot hascolours and markers as described in Figure 8, while the others have a rainbow trend fromred (low) to blue (high) in the three parameters as can be seen in the subtitles. Encircledin red is the group of high gravity blue stars.

15

Chapter 5: Results & Discussion5.1 Balmer Lines

The first set of lines is the Balmer Line group. This group includes the indices HgA, HgF,HdA, HdF, Hbeta and Hbeta plus. For the indices HgA (Figure 8) and HdA (Figure 26;Appendix C), it can be seen that the equivalent widths of the red stars are underestimatedin the model, as shown in Figure 8 with an arrow. The colder the star is, the moreits equivalent width is underestimated by the model. This effect is less visible for HdF(Figure 28; Appendix C) and HgF (Figure 29; Appendix C), which have smaller continuumbandpasses, see Appendix B.

Figure 8: Empirical (MILES) versus model (Coelho) of index HgA. There are three groupsof temperatures; Blue is more than 10000K, red is 5000K or less and green is in between.Then we have open and closed symbols for giants (log(g) < 3) and dwarfs (log(g) ≥ 3).Circles: [M/H] > 0. Squares: -1 < [M/H] ≤ 0. Diamonds : [M/H] ≤ -1.

Figure 9: From Martins & Coelho, 2007. Comparison of the index HgA. There is a differentmarker scheme here. The blue colour is for temperatures of more than 7000K, red is for4500K or less and green is in between. The open and closed symbols mean the same as infigure 8.

16

For Hbeta (Figure 10) and Hbeta plus (Figure 30; Appendix C), this effect is not visible.One characteristic this group shares, is the overestimation of the equivalent width of thegreen giants. These are stars with a temperature between about 8000K and 10000K. Theyare most likely A-type giants, the Hydrogen lines in this group are strong. This is dueto too strong cores in the line [Coelho, 2014], which are caused by non-LTE conditionsin the chromosphere. This effect is most visible in the indices of Hbeta (Figure 10) andHbeta plus (Figure 30; Appendix C), as indicated with an arrow in the plot for Hbeta(Figure 10). Comparing Hbeta with Martins and Coelho, 2007 (from now on referred to asM&C) (Figure 11), such a large group of giants with overestimated indices in the models isnot present. In Martins’ models, there are two hot giants that are overestimated (encircledin Figure 11), but their index in MILES is around 2-4 A, while in the the current resultsof Hbeta (Figure 10) this value is 4-7 A. This means that this cannot be the same groupof stars.

Figure 10: Empirical (MILES) versus model (Coelho) of index Hbeta. The colours andshapes are the same as in 8.

Figure 11: From Martins & Coelho, 2007. Comparison of the index Hbeta. The colourscheme is the same as in Figure 9.

17

5.2 Iron Lines

For the Iron lines, I found that the models and the observations are in agreement for themost part. The clear exception to this is the line Fe4668 (Figure 35; Appendix D), whichhas a different slope than one. This might be a result of its strong Carbon sensitivity,which is why this line is also known as C24668 [Tripicco and Bell, 1995]. The lines thatkeep to the one-to-one relation very well are the lines Fe4531 (Figure 33), Fe5015 (Figure38), Fe5270 (Figure 40), Fe5406 (Figure 42), which can all be found in Appendix D, andFe5335, which can be found below (Figure 12). In Fe5335, it can be seen that there is adifference between the alpha-enhanced and non-enhanced models. In the non-enhancedcase, the scatter of the red stars is larger than the alpha-enhanced case. If Fe5335 iscompared with M&C (Figure 13), we see a difference in the red giants. In the right-mostsubplot of M&C, these giants are overestimated in the model (indicated with an arrow inFigure 13), while in the current results it can be seen that they are underestimated in themodel.

Figure 12: Empirical (MILES) versus model (Coelho) of index Fe5335. The colour schemeis the same as in Figure 8.

Figure 13: From Martins & Coelho, 2007. Comparison of the index Fe5335. The colourscheme is the same as Figure 9.

18

5.3 C&N Lines

The third group is the C&N lines group. Below, the index CN2 is shown (Figure 14).There is a clear distinction between the red stars in the alpha-enhanced and the non-enhanced case. In the non-enhanced case, the equivalent widths of red stars follow theone-to-one line, while in the alpha-enhanced case the colder stars are underestimated. Bylooking at M&C (Figure 15), it one can see that the red stars scatter widely around theone-to-one line.Another thing that can be seen in CN2 (Figure 14) is the deviation from the one-to-oneline of some higher temperature stars, as indicated with an arrow. This is not visible inM&C (Figure 15). This deviation from the one-to-one line is likely due to the fact that theblue bandpass overlaps with the central bandpass of HdA, which is overestimated by themodel (see the Balmer Lines). Because HdA is overestimated by the model, this lower thecontinuum for the blue bandpass of the CN2 line, which then leads to the overestimationof the emission line. The same thing happens in CN1 (Figure 50; Appendix E)

Figure 14: Empirical (MILES) versus model (Coelho) of index CN2. The colour schemeis the same as in Figure 8.

Figure 15: From Martins & Coelho, 2007. Comparison of the index CN2. The colourscheme is the same as Figure 9.

19

In Figure 16 we look at the index of G4300, which is the G-band as determined by Fraun-hofer, mostly dominated by the CH molecule [Newall et al., 1916]. The same phenomenonas in CN2 (Figure 14) can be observed. The index of stars with a temperature of around8000K are underestimated by the model. To be more precise, the emission is overestimated.This is due to to the overestimation of the index HgA (Figure 8). The red bandpass ofG4300 overlaps with the central bandpass of HgA (Appendix B). By looking at G4300from M&C (Figure 17), specifically at the models from Coelho (right-most subplot), it isnoticeable that the red stars are heavily overestimated by the model, as indicated with anarrow. In the current results of G4300 (Figure 16), this effect is less prominent; the redstars stay closer to the one-to-one line.

Figure 16: Empirical (MILES) versus model (Coelho) of index G4300. The colour schemeis the same as in Figure 8.

Figure 17: From Martins & Coelho, 2007. Comparison of the index G4300. The colourscheme is the same as Figure 9.

20

5.4 Alpha Element Lines

The fourth group is the group of Alpha Elements, which includes lines of the elementsMg, Si, S, Ca, Ti, Cr and Ni (see Appendix B). In this group, the differences betweenthe alpha-enhanced and the non-enhanced versions are best seen. For example, in Mg2(Figure 18) it can be seen that the slope of the green stars follows the one-to-one line inthe non-enhanced case. However, the alpha-enhanced case shows a slight overestimationof the index of these models. This is because the MILES stars are not alpha-enhanced,because they are from the solar neighborhood [Cenarro et al., 2007][Vazdekis et al., 2015].However, Mg1 (Figure 72; Appendix F) shows that the green stars follow the one-to-onerelation in the case of the alpha-enhanced models, while the non-enhanced models areslightly underestimating the index of green stars, which is a contradiction to the thoughtthat the MILES stars are not alpha-enhanced. Comparing Mg2 (Figure 18) with M&C(Figure 19), it can be seen that the fit of the red stars in the current result is worse thanin M&C. Another thing that can be seen is that the models of Martins and Munari inM&C (Figure 19; left and middle panel) both have the index of the green stars a bitoverestimated with respect to the one-to-one line, just like the enhanced case.

Figure 18: Empirical (MILES) versus model (Coelho) of index Mg2. The colour schemeis the same as in Figure 8.

Figure 19: From Martins & Coelho, 2007. Comparison of the index Mg2. The colourscheme is the same as Figure 9.

21

However, the models of Coelho in M&C (Figure 19; right panel) agree more with the non-enhanced case in Figure 18. This is likely due to distinct line lists used by the differentmodels in M&C. The current results of Mg2 (Figure 18) and M&C (Figure 19) agree thatthe models with the lowest temperature have overestimated magnitudes.TiO-bands are heavily dependent on temperature [Coelho et al., 2005] and have a large in-fluence on the spectrum of cold stars. It can be seen below, in Figure 20, that atmosphereswith a temperature above 5000K have little to no contribution of TiO2. The indices ofstars that do have contribution from TiO2 seem to be underestimated in the model in thenon-enhanced case. In the alpha-enhanced case it seems that the indices of the coldeststars with medium to high gravities are overestimated in the model, while the indices ofcold stars with the lowest gravities are underestimated in the model. The index of ”hot”red stars seems to be underestimated in the model. M&C (Figure 21) also shows scatterin the indices of the red stars. This is also seen in the alpha-enhanced case of the currentresults (Figure 20).

Figure 20: Empirical (MILES) versus model (Coelho) of index TiO2. The colour schemeis the same as in Figure 8.

Figure 21: From Martins & Coelho, 2007. Comparison of the index TiO2. The colourscheme is the same as Figure 9.

22

In Figure 22, the Calcium line Ca4455 is shown. Calcium is an alpha element usedto look at the metallicity of galaxies in the Local group, like in [Tolstoy et al., 2009].Even though Ca4455 is a line of an alpha element, the difference between the alpha-enhanced and the non-enhanced panels (Figure 22; left and right panel respectively) isnot apparent. Ca4455 is dominated by Fe and Cr contributions; being correlated toCr, but anticorrelated to Fe. This is why it is almost invariant to changes in [α/Fe][Tripicco and Bell, 1995][Thomas et al., 2003]. It can be seen (Figure 22) that the equiv-alent width of the Ca4455 is overestimated for the hottest stars. When looking at M&C(Figure 23; left and middle panel), we see that the equivalent widths of the hottest starsare underestimated, rather than overestimated, like in the current results. Comparing thered stars shows that the current results (Figure 22) have a better fit to the one-to-oneline than in M&C (Figure 23). In the results of M&C, it can be seen that the equivalentwidths of the cold stars are underestimated, as indicated with an arrow in Figure 23.

Figure 22: Empirical (MILES) versus model (Coelho) of index Ca4455. The colour schemeis the same as in Figure 8.

Figure 23: From Martins & Coelho, 2007. Comparison of the index Ca4455. The colourscheme is the same as Figure 9.

23

5.5 Other Lines

Finally we get to the fifth and last group of elements, the ”rest”-group. There is no cleargrouping within these elements. Below, Na5895 is shown (Figure 24). Na5895, also knownas NaD, is a line that is often found in K-star giants [Faber et al., 1985]. These red giantsmake up a large part of the spectrum of elliptical galaxies [Sparke and Gallagher III, 2007].The visualization of NaD (Figure 24) shows that the equivalent widths of most of the starsare underestimated by the model. Only the blue and green stars with the highest surfacegravities are on the one-to-one line. The lower the surface gravity, the more the equivalentwidth is underestimated by the model. This does not hold for the red stars, since someof the indices of giants are slightly overestimated by the model. In the models of Coelhofrom M&C (Figure 25; right panel) this behaviour can also be seen, where the green starsare just below the one-to-one line.

Figure 24: Empirical (MILES) versus model (Coelho) of index Na5895. The colour schemeis the same as in Figure 8.

Figure 25: From Martins & Coelho, 2007. Comparison of the index Na5895. The colourscheme is the same as Figure 9.

24

Chapter 6: Summary & Conclu-sion

In this Thesis, the theoretical library of Coelho, presented in 2014, was tested using theempirical MILES library, by looking at the spectral indices of several elements. First,the sample of MILES stars was tested by recreating them with the interpolator describedin Chapter 3. The stars that could not be recreated properly, were removed from thesample. Secondly, the remaining stars were used to create interpolated spectra with thesame atmospheric parameters as the models of Coelho. Interpolated spectra with morethan 10% offset were removed, as well as the spectra with a high surface gravity. Theresolution of the models of Coelho was lowered to match that of the MILES library, toa FWHM of 2.5A. Then, using the REDUCEME package, several spectral indices werecalculated for both the models and the interpolated spectra. Finally, these indices wereplotted against each other to visualize the results.

The most apparent effects of each group are shown in Table 1. Appendix H givesa short description the features seen in every line, rather than a summary of the group.We see that in for stars with a temperature of around 8000K, the Balmer lines wereoverestimated. This is due to the cores of the Balmer lines, which cannot be calculatedproperly without non-LTE calculations. The second phenomenon that can be seen inthe Balmer line group is the underestimation of the index of red stars. This effect is notapparent in Hbeta and Hbeta plus. The hottest stars and the green dwars perform well.The Iron line group performs well, with some of the best fits to the one-to-one line.A clear exception of this is Fe4668 (or C24668), this might be because it is stronglydependent on carbon.In the C&N group, the hottest stars perform best, the cold stars fit to the one-to-oneline well in the cases of CN1 and CN2. For the alpha-enhanced models, the equivalentwidths of the red stars are generally underestimated. In this group, contamination fromthe Balmer line group could be seen in the lines of CN1, CN2, and G4300.The group of alpha elements shows the clearest separation between the alpha-enhancedand the non-enhanced models. The alpha-enhanced model often has a higher index thanthe non-enhanced counterpart. This results in the alpha-enhanced models to generallybe more overestimated than the non-enhanced models, especially the red stars. This isbecause the MILES library itself is not alpha-enhanced.

It can be concluded that the hottest stars perform best in most of the lines. This is ofcourse not a surprise, considering that the hottest stars do not have a lot of absorptionlines, except in the blue part of the spectrum. The models of the cold stars seem to disagreemost often with the observations. Because the used sample of the MILES library couldbe recreated well by the interpolator, this is likely not a consequence of poor atmosphericparameters. The group of stars that stands out in this Thesis is the group of A-typegiants, whose equivalent widths are overestimated for the Balmer lines. Because thisoverestimation also leads to effects in lines like CN1, CN2 and G4300, it is of importanceto look into improvement of the models of these stars.

25

Group Observed phenomenon Indices (Figure Number)

Balmer Overestimation A-type giants All

Balmer Underestimation red stars HdA (26); HdF (28)HgA (8); HgF (29)

Iron Good fit Fe4531 (33); Fe5015 (38)Fe5270 (40); Fe5335 (12)Fe5406 (42)

C&N Group of hot stars (about8000K) with overestimated

emission

CN1 (50); CN2 (14)CNO4175 (52); G4300 (16)

AlphaElements

Overestimation of red stars Cr3594 (56); Mg3835 (60)CaHK (61); Ca4227 (64)Mg1 (72); Mg2 (18)Ni4976 (75); Cr5206 (78)

Other Overestimation red stars Sc3613 (82); Co3840 (86)Al3953 (88); Eu3970 (89)Mn4061 (92); Sr4076 (93)Ba6142 (105)

Other Underestimation red stars Co3701 83); Mn3794 (84)Mn04018 (90); V4112 (94)Ba4552 (96); Eu4592 (97)Ba4933 (102); V6604 (107)

Table 1: Overview of effects seen per group in the found results.

Group Observed phenomenon Indices (Figure Number;M&C Figure Number)

Balmer Green giants overestimated HdA (26; 27)HgA (8; 9)Hbeta (10; 11)

Iron Red stars closer to one-to-oneline

Fe5015 (38; 39)Fe5270 (40; 41)Fe5335 (12; 13)Fe5406 (42; 43)Fe5709 (44; 45)

C&N Red stars closer to one-to-oneline

CNO3862 (48; 49)CN1 (50; 51)CN2 (14; 15)G4300 (16; 17)

C&N Group of hot green stars withoverestimated emission

appeared

CN1 (50; 51)CN2 (14; 15)G4300 (16; 17)CNO4175 (52; 53)

Table 2: Overview of differences between found results and M&C

26

6.1 Differences with M&C

The clearest difference between the current results and M&C in the Balmer line group isthe position of the group of giants with a temperature of around 8000K. The equivalentwidths are overestimated in the current results, while this is not visible in the results ofM&C.

In the group of Iron lines it can be seen that the models improved. In the resultsof M&C, the cold stars were often not situated on the one-to-one line. In the currentresults, most of the Iron lines show a good fit to the one-to-one line, even in the caseof the cold stars. The clear exception for this is the line Fe4668 (Figure 35; Figure 36,Appendix D, current results and M&C respectively), also known as C24668.

In the C&N group, two changes are observed. The first change is in the coldstars; the index of the model and observations are closer together. In other words, thefit got better for the colder stars, as compared to M&C. The other change is that agroup of hot green and cold blue stars appeared that move away from the one-to-oneline, in the direction of underestimation (or overestimated emission). For CN1, CN2and G4300 this effect can be explained by looking at the definition of their indices andthe definitions of two Balmer lines; HgA and HdA. The pseudocontinua of the C&Nlines overlap with the central bandpasses of these Balmer lines. This means that theircontinuum will be lower than it would be if the Balmer lines were not overestimated.However, this effect does not play a role for CNO4175, because its pseudocontinua do notoverlap with any Balmer line. The reason why this effect appears in this line is not known.

Overall, we see improvement in Coelho’s 2014 library, compared to the libraryfrom 2005 (used in M&C). Especially the cold stars perform a lot better, which can beseen best in the Iron lines and C&N group. The effect that was most apparent in hotstars of the 2014 library, was the overestimation of Balmer lines. Because the Coelholibrary in 2005 did not have stars with T > 7000K, this could not be compared. However,Martins’ and Munari’s models did have hot stars, but did not show the effect of A-typegiants being overestimated.

27

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[Vazdekis et al., 2015] Vazdekis, A., Coelho, P., Cassisi, S., Ricciardelli, E., Falcon-Barroso, J., Sanchez-Blazquez, P., Barbera, F. L., Beasley, M., and Pietrinferni, A.(2015). Evolutionary stellar population synthesis with MILES–II. Scaled-solar and α-enhanced models. Monthly Notices of the Royal Astronomical Society, 449(2):1177–1214.

[Worthey et al., 1994] Worthey, G., Faber, S., Gonzalez, J. J., and Burstein, D. (1994).Old stellar populations. V Absorption feature indices for the complete LICK/IDS sampleof stars. The Astrophysical Journal Supplement Series, 94:687–722.

[Worthey and Ottaviani, 1997] Worthey, G. and Ottaviani, D. (1997). Hγ and hδ absorp-tion features in stars and stellar populations. The Astrophysical Journal SupplementSeries, 111(2):377.

29

Appendix A: Resolution Calculation In this

appendix, a detailed calculation of the σ of the Gaussian that the models have to beconvolved with will be given. Firstly, some basic formulae are given.

R =λ

∆λ=

λ

2.355σ⇐⇒ σ =

λ

2.355R(4)

where R is the resolution, λ is the wavelength, ∆λ is the FWHM of the resolution and σis the standard deviation of the Gaussian. Therefore, it can be said that

σ2Final = σ2

In + σ2LSF ⇐⇒

1

R2Final

=1

R2In

+1

R2LSF

(5)

where, on the left side, the different variances are the variances of the convolution product,the variance of the input function and the variance of the line spread function respectively.The right side of the equation is derivated from using the right side of Equation 4. Knowingthat the models of Coelho were calculated at a resolution R = 300000 and they wereconvolved with a line spread function with resolution R = 20000, Equation 5 can be used,after rewriting it in favor of RFinal.

RCoelho = (1

R2Calculated

+1

R2LSF

)−12 = 19955.7 (6)

To find the value of σGauss, which is the Gaussian that will be convolved with models, theleft side of Equation 5 will have to be rewritten in favor of σLSF .

σLSF = (σ2Final − σ2

In)12 ⇒ σGauss = (σ2

MILES − σ2Coelho)

12 (7)

The FWHM of the MILES spectra is known to be 2.5A[Falcon-Barroso et al., 2011]. Therelation that can be seen on the left side of Equation 4 can be used to fill in σMILES andthe right side of the same equation can be used to fill in σCoelho.

σGauss =

√(

2.5A

2.355)2 − (

λ

2.355RCoelho)2 (8)

The middle of the wavelength range is used as the value for λ = 3500+73002 = 5400A. Filling

this into Equation 8 yields a value for σGauss = 1.056A.

30

Appendix B: Measured Indices

Table 3: Absorption line index definitions

Index Blue Bandpass Central Bandpass Red Bandpass Source

Cr3594 3536.600-3560.500 3586.600-3602.400 3625.200-3641.500 Serven1

Sc3613 3539.700-3563.200 3604.900-3620.400 3676.800-3697.400 ServenNi3667 3630.400-3646.600 3655.100-3679.400 3685.400-3705.300 ServenCo3701 3656.000-3676.100 3695.000-3708.000 3712.400-3723.000 ServenNi3780 3749.400-3764.400 3766.100-3794.700 3800.100-3815.600 ServenMn3794 3744.900-3769.600 3780.900-3806.100 3847.900-3865.300 ServenMg3835 3754.700-3782.000 3823.400-3847.600 3850.000-3865.000 ServenCo3840 3772.700-3810.200 3831.400-3849.300 3850.400-3863.400 ServenCNO3862 3768.100-3812.300 3840.300-3883.400 3896.400-3916.200 ServenCo3876 3850.400-3863.400 3864.500-3887.000 3909.300-3934.400 ServenCaHK 3806.500-3833.800 3899.500-4003.500 4020.700-4052.400 ServenAl3953 3921.300-3935.500 3937.600-3967.400 3969.500-3987.000 ServenEu3970 3929.000-3945.800 3962.800-3976.700 3980.700-3993.900 ServenMn4018 3940.900-3962.300 3992.600-4044.400 4096.300-4121.500 ServenK4042 4014.900-4029.000 4035.900-4047.500 4054.700-4070.400 ServenFe4058 4009.000-4031.100 4037.900-4078.400 4107.600-4125.700 ServenHdA 4041.600-4079.750 4083.500-4122.250 4128.500-4161.000 Worthey & Ottaviani2

HdF 4057.250-4088.500 4091.000-4112.250 4114.750-4137.250 Worthey & OttavianiSr4076 4038.400-4055.600 4069.000-4082.200 4105.300-4126.800 ServenCN1 4080.125-4117.625 4142.125-4177.125 4244.125-4284.125 Lick3

CN2 4083.875-4096.375 4142.125-4177.125 4244.125-4284.125 LickV4112 4057.100-4074.300 4086.400-4138.500 4145.000-4160.500 ServenSi4101 4057.900-4075.300 4093.300-4107.800 4111.500-4131.000 ServenCNO4175 4082.500-4123.300 4129.400-4219.800 4243.300-4284.200 ServenCa4227 4211.000-4219.750 4222.250-4234.750 4241.000-4251.000 LickCr4264 4179.300-4195.600 4246.800-4281.300 4310.700-4334.700 ServenG4300 4266.375-4282.625 4281.375-4316.375 4318.875-4335.125 LickNi4292 4260.900-4275.300 4279.600-4305.400 4307.400-4323.600 ServenHgA 4283.500-4319.750 4319.750-4363.500 4367.250-4419.750 Worthey & OttavianiHgF 4283.500-4319.750 4331.250-4352.250 4354.750-4384.750 Worthey & OttavianiTi4296 4253.800-4274.400 4283.600-4308.200 4324.500-4343.000 ServenSc4312 4286.100-4300.600 4303.000-4320.700 4335.800-4354.400 ServenFe4383 4359.125-4370.375 4369.125-4420.375 4442.875-4455.375 LickMn4061 4386.800-4406.900 4443.300-4477.700 4506.100-4530.300 ServenCa4455 4445.875-4454.625 4452.125-4474.625 4477.125-4492.125 LickSi4513 4448.700-4487.600 4490.800-4534.600 4541.100-4572.700 ServenFe4531 4504.250-4514.250 4514.250-4559.250 4560.500-4579.250 LickTi4533 4486.300-4506.200 4525.300-4541.100 4548.700-4561.300 ServenBa4552 4522.200-4535.000 4545.400-4558.500 4559.500-4578.800 ServenFe4668 4611.500-4630.250 4634.000-4720.250 4742.750-4756.500 Lick

31

CO4685 4557.300-4589.500 4626.400-4743.300 4805.100-4835.300 ServenS4693 4652.200-4677.300 4680.600-4704.400 4717.600-4737.700 ServenZn4720 4652.700-4670.000 4708.700-4731.500 4755.400-4775.500 ServenMn4757 4715.600-4737.800 4741.500-4773.400 4792.400-4812.100 ServenMg4780 4738.900-4757.300 4760.800-4798.800 4819.800-4835.500 ServenHbeta 4827.875-4847.875 4847.875-4876.625 4876.625-4891.625 LickHbeta p 4815.000-4845.000 4851.320-4871.320 4880.000-4930.000 Gonzalez4

Eu4592 4533.500-4550.800 4584.800-4598.800 4626.300-4645.700 ServenMg1 4895.125-4957.625 5069.125-5134.125 5301.125-5366.125 LickMg2 4895.125-4957.625 5154.125-5196.625 5301.125-5366.125 LickNi4910 4879.300-4895.800 4897.400-4922.100 4953.200-4969.400 ServenFe4930 4894.500-4907.000 4907.000-4943.800 4943.800-4954.500 ServenV4928 4899.800-4914.800 4919.600-4937.400 4951.800-4965.200 ServenBa4933 4902.700-4916.100 4922.800-4943.300 4967.200-4992.700 ServenFe5015 4946.500-4977.750 4977.750-5054.000 5054.000-5065.250 LickNi4976 4951.500-4964.400 4966.000-4986.300 5016.800-5028.900 ServenTi5000 4930.600-4959.400 4973.100-5026.100 5035.400-5052.500 ServenMgb5177 5142.625-5161.375 5160.125-5192.625 5191.375-5206.375 LickCO5161 5108.400-5138.800 5154.300-5167.300 5188.400-5202.000 ServenCr5206 5130.000-5149.200 5198.900-5213.600 5240.300-5257.000 ServenCu5217 5160.900-5186.900 5209.100-5225.300 5247.500-5275.800 ServenFe5270 5233.150-5248.150 5245.650-5285.650 5285.650-5318.150 LickFe5335 5304.625-5315.875 5312.125-5352.125 5353.375-5363.375 LickFe5406 5376.250-5387.500 5387.500-5415.000 5415.000-5425.000 LickNi5592 5521.100-5542.700 5578.300-5605.400 5612.600-5632.600 ServenFe5709 5672.875-5696.625 5696.625-5720.375 5722.875-5736.625 LickFe5782 5765.375-5775.375 5776.625-5796.625 5797.875-5811.625 LickCu5780 5720.100-5753.200 5772.300-5787.300 5808.000-5830.800 ServenNa5895 5860.625-5875.625 5876.875-5909.375 5922.125-5948.125 LickTiO1 5816.625-5849.125 5936.625-5994.125 6038.625-6103.625 LickTiO2 6066.625-6141.625 6189.625-6272.125 6372.625-6415.125 LickBa6142 6105.800-6128.200 6130.700-6152.600 6176.300-6209.600 ServenSc6292 6199.200-6231.100 6265.100-6318.800 6320.900-6366.500 ServenV6604 6516.500-6549.700 6592.200-6615.400 6655.800-6693.800 Serven

1 [Serven et al., 2005]2 [Worthey and Ottaviani, 1997]

3 [Worthey et al., 1994]4 [Gonzalez, 1993]

32

Appendix C: Balmer Line Plots

C.2 HdA

Figure 26: Empirical (MILES) versus model (Coelho) of index HdA. The colour schemeis the same as in Figure 8.

Figure 27: From Martins & Coelho, 2007. Comparison of the index HdA. The colourscheme is the same as Figure 9.

33

C.3 HdF

Figure 28: Empirical (MILES) versus model (Coelho) of index HdF. The colour scheme isthe same as in Figure 8.

C.4 HgF

Figure 29: Empirical (MILES) versus model (Coelho) of index HgF. The colour scheme isthe same as in Figure 8.

34

C.5 Hbeta p

Figure 30: Empirical (MILES) versus model (Coelho) of index Hbeta p. The colour schemeis the same as in Figure 8.

35

Appendix D: Iron Line Plots

D.6 Fe4058


D.7 Fe4383


36

D.8 Fe4531



37

D.9 Fe4668



38

D.10 Fe4930


39

D.11 Fe5015



40

D.12 Fe5270



41

D.13 Fe5406



42

D.14 Fe5709



43

D.15 Fe5782



44

Appendix E: C&N Line Plots

E.16 CNO3862

Figure 48: Empirical (MILES) versus model (Coelho) of index CNO3862. The colourscheme is the same as in Figure 8.

Figure 49: From Martins & Coelho, 2007. Comparison of the index CNO3862. The colourscheme is the same as Figure 9.

45

E.17 CN1

Figure 50: Empirical (MILES) versus model (Coelho) of index CN1. The colour schemeis the same as in Figure 8.

Figure 51: From Martins & Coelho, 2007. Comparison of the index CN1. The colourscheme is the same as Figure 9.

46

E.18 CNO4175

Figure 52: Empirical (MILES) versus model (Coelho) of index CNO4175. The colourscheme is the same as in Figure 8.

Figure 53: From Martins & Coelho, 2007. Comparison of the index CNO4175. The colourscheme is the same as Figure 9.

47

E.19 CO4685

Figure 54: Empirical (MILES) versus model (Coelho) of index CO4685. The colour schemeis the same as in Figure 8.

E.20 CO5161

Figure 55: Empirical (MILES) versus model (Coelho) of index CO5161. The colour schemeis the same as in Figure 8.

48

Appendix F: Alpha Element Line Plots

F.21 Cr3594

Figure 56: Empirical (MILES) versus model (Coelho) of index Cr3594. The colour schemeis the same as in Figure 8.

Figure 57: From Martins & Coelho, 2007. Comparison of the index Cr3594. The colourscheme is the same as Figure 9.

49

F.22 Ni3667

Figure 58: Empirical (MILES) versus model (Coelho) of index Ni3667. The colour schemeis the same as in Figure 8.

F.23 Ni3780


50

F.24 Mg3835


51

F.25 CaHK

Figure 61: Empirical (MILES) versus model (Coelho) of index CaHK. The colour schemeis the same as in Figure 8.

Figure 62: From Martins & Coelho, 2007. Comparison of the index CaHK. The colourscheme is the same as Figure 9.

52

F.26 Si4101

Figure 63: Empirical (MILES) versus model (Coelho) of index Si4101. The colour schemeis the same as in Figure 8.

F.27 Ca4227

Figure 64: Empirical (MILES) versus model (Coelho) of index Ca4227. The colour schemeis the same as in Figure 8.

53

F.28 Cr4264


Figure 66: From Martins & Coelho, 2007. Comparison of the index Cr4264. The colourscheme is the same as Figure 9.

54

F.29 Ni4292


F.30 Ti4296

Figure 68: Empirical (MILES) versus model (Coelho) of index Ti4296. The colour schemeis the same as in Figure 8.

55

F.31 Si4513

Figure 69: Empirical (MILES) versus model (Coelho) of index Si4513. The colour schemeis the same as in Figure 8.

F.32 Ti4533


56

F.33 Mg4780


57

F.34 Mg1


Figure 73: From Martins & Coelho, 2007. Comparison of the index Mg1. The colourscheme is the same as Figure 9.

58

F.35 Ni4910


F.36 Ni4976


59

F.37 Ti5000


F.38 Mgb5177

Figure 77: Empirical (MILES) versus model (Coelho) of index Mgb5177. The colourscheme is the same as in Figure 8.

60

F.39 Cr5206


F.40 Ni5592


61

F.41 TiO1

Figure 80: Empirical (MILES) versus model (Coelho) of index TiO1. The colour schemeis the same as in Figure 8.

Figure 81: From Martins & Coelho, 2007. Comparison of the index TiO1. The colourscheme is the same as Figure 9.

62

Appendix G: Other Element Line Plots

G.42 Sc3613

Figure 82: Empirical (MILES) versus model (Coelho) of index Sc3613. The colour schemeis the same as in Figure 8.

G.43 Co3701

Figure 83: Empirical (MILES) versus model (Coelho) of index Co3701. The colour schemeis the same as in Figure 8.

63

G.44 Mn3794

Figure 84: Empirical (MILES) versus model (Coelho) of index Mn3794. The colour schemeis the same as in Figure 8.

Figure 85: From Martins & Coelho, 2007. Comparison of the index Mn3794. The colourscheme is the same as Figure 9.

64

G.45 Co3840


G.46 Co3876


65

G.47 Al3953

Figure 88: Empirical (MILES) versus model (Coelho) of index Al3953. The colour schemeis the same as in Figure 8.

G.48 Eu3970

Figure 89: Empirical (MILES) versus model (Coelho) of index Eu3970. The colour schemeis the same as in Figure 8.

66

G.49 Mn4018


G.50 K4042

Figure 91: Empirical (MILES) versus model (Coelho) of index K4042. The colour schemeis the same as in Figure 8.

67

G.51 Mn4061


G.52 Sr4076

Figure 93: Empirical (MILES) versus model (Coelho) of index Sr4076. The colour schemeis the same as in Figure 8.

68

G.53 V4112

Figure 94: Empirical (MILES) versus model (Coelho) of index V4112. The colour schemeis the same as in Figure 8.

G.54 Sc4312


69

G.55 Ba4552

Figure 96: Empirical (MILES) versus model (Coelho) of index Ba4552. The colour schemeis the same as in Figure 8.

G.56 Eu4592

Figure 97: Empirical (MILES) versus model (Coelho) of index Eu4592. The colour schemeis the same as in Figure 8.

70

G.57 S4693

Figure 98: Empirical (MILES) versus model (Coelho) of index S4693. The colour schemeis the same as in Figure 8.

G.58 Zn4720

Figure 99: Empirical (MILES) versus model (Coelho) of index Zn4720. The colour schemeis the same as in Figure 8.

71

G.59 Mn4757

Figure 100: Empirical (MILES) versus model (Coelho) of index Mn4757. The colourscheme is the same as in Figure 8.

G.60 V4928


72

G.61 Ba4933

Figure 102: Empirical (MILES) versus model (Coelho) of index Ba4933. The colourscheme is the same as in Figure 8.

G.62 Cu5217

Figure 103: Empirical (MILES) versus model (Coelho) of index Cu5217. The colourscheme is the same as in Figure 8.

73

G.63 Cu5780

Figure 104: Empirical (MILES) versus model (Coelho) of index Cu5780. The colourscheme is the same as in Figure 8.

G.64 Ba6142

Figure 105: Empirical (MILES) versus model (Coelho) of index Ba6142. The colourscheme is the same as in Figure 8.

74

G.65 Sc6292


G.66 V6604


75

Appendix H: Overview of phenomena inlines

In this Appendix, an overview is given for all lines that were calculated. For eachof the temperature ranges, a short comment is given. Note that ”Underestimated” and”Overestimated” here mean the under- and overestimation for the equivalent widths of agroup of stars.

Index Red Stars Green Stars Blue Stars Extra Comments

HdAFigure 26

Underestimated;more and morefor colder stars

A-type giantsoverestimated

- Blue part of thespectrum

HdFFigure 28

Underestimated A-type giantsoverestimated

- Blue part of thespectrum

HgAFigure 8


A-type giantsoverestimated

- -

HgFFigure 29

Underestimated A-type giantsoverestimated

- -

HbetaFigure 10

- A-type giantsoverestimated

- -

Hbeta plusFigure 30

- A-type giantsoverestimated

- -

Table 4: Overiew of Balmer Lines


Fe4058Figure 31

Overestimatedmode and morefor colder stars

- - Blue part of thespectrum

Fe4383Figure 32

Overestimated;more for

non-enhancedcase

- - -

Fe4531Figure 33

- - - Good fit

Fe4668Figure 35

Underestimated Underestimated Underestimated Slope of the lineseems to be lessthan one. Also

known as C24668

Fe4930Figure 37

Coldest giantsslightly

underestimated

- - -

Fe5015Figure 38

- - - Good fit

Fe5270Figure 40

- - - Good fit

Fe5335Figure 12

- - - Good fit

76

Fe5406Figure 42

- - - Good fit

Fe5709Figure 44

- - - Slightlyoverestimated

Fe5782Figure 46

- Large scatter forlow value of index

Remains aboutzero for model,but ranges from0-0.4 for MILES

-

Table 5: Overview of Iron Lines


CNO3862Figure 48

Large scatter Large scatter - Blue part of thespectrum

CN1Figure 50

Alpha-enhancedcase: red giantsunderestimated

- - Tail of hot starswith

overestimatedemission; due to

overlap withHdA. Molecular

band

CN2Figure 14




overlap withHdA. Molecular

band

CNO4175Figure 52




overlap with HdA

G4300Figure 16

Slightlyoverestimated for

coldest stars



overlap with HgA

CO4685Figure 54

Underestimated Underestimated - -

CO5161Figure 55

Large scatter.non-enhancedcase: dwarfs

underestimated

- - Not a good fit

Table 6: Overview of C&N Lines

77


Cr3594Figure 56

Overestimated - - Blue part ofspectrum

Ni3667Figure 58

Underestimated Slightlyunderestimated

- Blue part ofspectrum

Ni3780Figure 59

Underestimated Slightlyunderestimated


Mg3835Figure 60

Overestimated Mostlyoverestimated


CaHKFigure 61

Overestimated;more and morefor higher index

value

Overestimated;more and morefor higher index

value


Si4101Figure 63

Slightlyunderestimated

Giants:Overestimated

- Samecharacteristics as

a Balmer line

Ca4227Figure 64

Enhanced:Overestimated;more and morefor higher value

of index.Non-enhanced:

Slightlyoverestimated

Enhanced:Overestimated;more and morefor higher value

of index

- -

Cr4264Figure 65


Tail of A-typestars like in

G4300

- -

Ni4292Figure 67


- - -

Ti4296Figure 68


- - -

Ca4455Figure 22

- - Hottest starsoverestimated

-

Si4513Figure 69

Underestimated Colder dwarvesunderestimated

- -

Ti4533Figure 70

Slightlyoverestimated for

colder stars

- - -

Mg4780Figure 71

Enhanced:Coldest starsoverestimated

- - -

Mg1Figure 72

Overestimated Non-enhanced:slope smaller

than 1

- Molecular band

Mg2Figure 18

Overestimated Enhanced: slopelarger than 1

- Molecular band

Ni4910Figure 74

Coldest starsunderestimated

- - -

Ni4976Figure 74

Overestimated Overestimated - -

78

Ti5000Figure 76

Enhanced:coldest stars

overestimated

Scatter aroundone-to-one line

Invariant inmodel, slighlychanging in

MILES

-

Mgb5177Figure 77

Enhanced:Overestimated

- - Non-enhanced isreasonable fit

Cr5206Figure 78

Overestimated - - -

Ni5592Figure 79

Enhanced:Slightly

overestimated

Enhanced:Slightly

Overestimated

Invariant inmodel, slightly

changing inMILES

TiO1Figure 80

Enhanced: Largescatter.

Non-enhanced:underestimated

- - Molecular band

TiO2Figure 20

Enhanced: Largescatter.

Non-enhanced:underestimated

- - Molecular band

Table 7: Overview of Alpha Element Lines


Sc3613Figure 82

Overestimated Giants:Underestimated


Co3701Figure 83

Underestimated Overestimated Colder starsOverestimated

Blue part ofspectrum

Mn3794Figure 84


- - Blue part ofspectrum

Co3840Figure 86

Overestimated Overestimated - Blue part ofspectrum

Co3876Figure 87

Enhanced:Underestimated.Non-enhanced:Broad scatter

aroundone-to-one line

- - Blue part ofspectrum

Al3953Figure 88

Overestimated Enhanced: broadscatter around

one-to one.Non-enhanced:

Giantsunderestimated


Eu3970Figure 89

Overestimated Giantsoverestimated.Dwarfs large

scatter


79

Mn4018Figure 90

Underestimated More and moreunderestimatedfor lower gravity

- -

K4042Figure 91

Enhanced:Giants

overestimated.Non-enhanced:Both giants and

dwarvesoverestimated


- Broader scatterin enhanced case

Mn4061Figure 92

Overestimated Colder starsoverestimated

- -

Sr4076Figure 93

Overestimated Colder starsoverestimated

- -

V4112Figure 94

Enhanced:Slightly

underestimatedfor coldest stars.Non-enhanced:

Moreunderestimatedfor coldest stars

- - -

Sc4312Figure 95

Dwarves:Underestimated.

Giants:Overestimated


- -

Ba4552Figure 96

Underestimated Underestimatedby model

Large scatteraround

one-to-one-line

-

Eu4592Figure 97

More and moreunderestimatedfor colder stars

Underestimated Underestimated,except for thehottest stars.

S4693Figure 98

Non-enhanced:Underestimated

Slope lowerthan 1

Hottest starsinvariant, colder

stars scatteraround

one-to-one

-

Zn4720Figure 99

Enhanced:Coldest stars

slightlyunderestimated

Giants slightlyoverestimated

Overestimated inthe model

-

Mn4757Figure 100

- Underestimated Underestimated -

V4928Figure 101

Coldest giantsunderestimated

- - Reasonable fit

Ba4933Figure 102

Underestimated Underestimated - -

80

Cu5217Figure 103

Enhanced:coldest dwarves

slightlyunderestimated

Non-enhanced:good fit.

Cu5780Figure 104

- Large scatter forhotter stars

Invariant inmodel, slightly

changing inMILES

-

Na5895Figure 24

- Slightlyunderestimated;more and more

for lower gravity


-

Ba6142Figure 105

Overestimated - - -

Sc6292Figure 106

No clearstructure

Hotter starsbehave the sameas blue. Colderstars show noclear structure

Almost invariantin model,

depending onmetallicity.

Non-enhancedversion is more

invariant inmodel.

V6604Figure 107

- - - Almost all indicesare

underestimatedby model

Table 8: Overview of Other Lines

81

Testing Coelho’s 2014 models with the MILES Library · 2018. 2. 15. · University of Groningen...

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