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Mon. Not. R. Astron. Soc. 000, 1–23 (2010) Printed 23 October 2018 (MN LATEX style file v2.2)

Keck Spectroscopy of Faint 3 < z < 7 Lyman Break

Galaxies: - I. New constraints on cosmic reionisation from

the luminosity and redshift-dependent fraction of Lyman-α

emission

Daniel P. Stark1⋆, Richard S. Ellis2, Kuenley Chiu2, Masami Ouchi3,4, Andrew Bunker51 Kavli Institute of Cosmology & Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK2 California Institute of Technology, 1200 E. Calfornia Blvd. Pasadena, CA 91125, USA3 Observatories of the Carnegie Institution of Washington, 813 Santa Barbara Street Pasadena, CA 91101 USA4 Carnegie Fellow5 Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK

Accepted ... ; Received ... ; in original form ...

ABSTRACT

We present the first results of a new Keck spectroscopic survey of UV faint Ly-man break galaxies in the redshift range 3 < z < 7. Combined with earlier Keck andpublished ESO VLT data, our spectroscopic sample contains more than 600 dropoutsoffering new insight into the nature of sub-L∗ sources typical of those likely to dom-inate the cosmic reionisation process. In this first paper in a series discussing theseobservations, we characterise the fraction of strong Lyα emitters within the continuum-selected dropout population. By quantifying how the “Lyα fraction” varies with red-shift, we seek to constrain changes in Lyα transmission associated with reionisation. Inorder to distinguish the effects of reionisation from other factors which affect the Lyαfraction (e.g. dust, ISM kinematics), we study the luminosity and redshift-dependenceof the Lyα fraction over 3

∼< z

∼< 6, when the IGM is known to be ionised. These results

reveal that low luminosity galaxies show strong Lyα emission much more frequentlythan luminous systems, and that at fixed luminosity, the prevalence of strong Lyman-αemission increases moderately with redshift over 3 < z < 6. Based on the striking cor-relation between blue UV slopes and strong Lyα emitting galaxies in our dataset, weargue that the Lyα fraction trends are governed by redshift and luminosity-dependentvariations in the dust obscuration, with likely additional contributions from trends inthe kinematics and covering fraction of neutral hydrogen. We find a tentative decreasein the Lyα fraction at z ≃ 7 based on the limited IR spectroscopic data for candidatez ≃ 7 galaxies, a result which, if confirmed with future surveys, would suggest anincrease in the neutral fraction by this epoch. Given the abundant supply of z andY-drops now available from deep Hubble WFC3/IR surveys, we show it will soon bepossible to significantly improve estimates of the Lyα fraction using optical and near-infrared multi-object spectrographs, thereby extending the study conducted in thispaper to 7

∼< z

∼< 8.

Key words: cosmology: observations - galaxies: evolution - galaxies: formation -galaxies: high-redshift

1 INTRODUCTION

Considerable observational progress has been achieved in re-cent years in the study of star-forming galaxies seen beyond

⋆ dps@ast.cam.ac.uk

z ≃ 3, a period corresponding to ≃ 2 Gyr after the BigBang. It is now clear that this is a period of rapid galaxyevolution and a number of key results have emerged fromrecent multi-wavelength surveys.

For the colour-selected z > 3 Lyman break galaxies(LBGs), it is now established from various independent sur-

c© 2010 RAS

http://arxiv.org/abs/1003.5244v1

2 Stark et al.

veys that the star formation density, deduced from rest-frame UV luminosities, declines monotonically with red-shift (e.g. Stanway et al. 2003; Bunker et al. 2004) largelyas a result of a corresponding fading of the characteristicUV luminosity (e.g., Ouchi et al. 2004; Yoshida et al. 2006;Bouwens et al. 2006, 2007; McLure et al. 2010) The associ-ated stellar mass density in Lyman break galaxies, deducedfrom near-infrared Spitzer photometry, increases by ≃1 dexfrom z ≃ 6 to 4 (Eyles et al. 2007; Stark et al. 2009). As therate of change of stellar mass is governed by ongoing starformation, it is useful to relate the two measures and such acomparison indicates a rapid duty-cycle of star formation ac-tivity at this time, unlike the more continuous modes seen forequivalent sources at z ≃ 2− 3 (Stark et al. 2009). By con-trast, the redshift-dependent luminosity function of narrow-band selected Lyman alpha emitters, shows no equivalentdecline with redshift over 3 < z < 6 (Ouchi et al. 2008),suggesting an increasing fraction of line emitters amongstthe star forming population at early times. Moreover, de-tailed studies of the slope of the UV continuum in z > 3Lyman break galaxies indicates a decreasing dust content atearlier times (e.g. Stanway et al. 2005; Bouwens et al. 2006,2009b) as well as a luminosity dependence at z ≃ 3 (e.g.Reddy & Steidel 2009). Conceivably the combination of areduced dust content and a shift to more intense, shorter-term star formation at high redshift, can explain these var-ious redshift-dependent trends.

Notwithstanding this considerable progress, a majorconcern is that the above conclusions rest largely on de-ductions made with photometric data, particularly for theLyman break population. Quite apart from the possibilityof low redshift interlopers lying within the photometric sam-ples (a problem that increases for drop-out selected sam-ples at redder wavelengths), the wanted physical measuresof the star formation rate, dust content and stellar massare all rendered uncertain by the absence of precise spectro-scopic redshifts. While considerable effort has been investedin the spectroscopic study of z ≃ 3 Lyman break galaxies(e.g. Shapley et al. 2003; Steidel et al. 2003; Quider et al.2010), comparably little spectroscopy has been achieved forhigher redshift samples. Steidel et al. (1999) obtained spec-troscopic redshifts for nearly 50 bright (I < 25) z ≃ 4LBGs. Most surveys of z ≃ 5 − 6 V and i′-drops have gen-erally involved relatively small samples, typically compris-ing fewer than 10 sources (e.g. Stanway et al. 2004, 2007;Ando et al. 2007; Dow-Hygelund et al. 2007). Recent deepHST ACS Grism observations of the Hubble Ultra DeepField have allowed the spectra of faint z ≃ 5 LBGs to becharacterised (Rhoads et al. 2009), albeit at very low spec-tral resolution, resulting in 39 redshift confirmations. Thelargest spectroscopic sample of 4 < z < 6 LBGs thus farpublished is the VLT/FORS2 survey of the Chandra DeepField South (Vanzella et al. 2002, 2005, 2006, 2008, 2009).This survey represents a major step forward, targetting 195B, V and i′-drop galaxies and securing high redshifts for 99of them. In addition, a recent campaign with the VIMOSspectrograph on the VLT has also targeted bright z ∼

> 3.5

LBGs (i′775 < 25) in the Chandra Deep Field South, con-firming redshifts for 20 bright sources at 3.5 < z < 5.5(Balestra et al. 2010).

We build on these strides in this paper, the first in a se-ries presenting the results of a new Keck survey of 3 < z < 7

LBGs selected photometrically in the GOODS fields. Theoverall goal is to improve our understanding of the evolutionof star-forming galaxies during the first 2 Gyr of cosmic his-tory. Fully exploiting the 10 metre Keck aperture, we havedesigned our survey to target intrinsically fainter sourcesthan those reached in the VLT/FORS2 survey, thereby com-plementing that effort. Spectroscopy spanning a wide rangeof intrinsic luminosities is very important if we seek to under-stand earlier examples of the luminosity-dependent trendsseen at z ≃ 3 (Reddy & Steidel 2009). As discussed below,it is equally important to target and study sub-luminousstar forming sources at early times, as these may be typ-ical of those galaxies responsible for cosmic reionisation(Bouwens et al. 2007; Ouchi et al. 2009; Bunker et al. 2010;Oesch et al. 2010; McLure et al. 2010).

Understanding evolution in the demographic trends ofstar-forming galaxies over 3 < z < 7 is vital if we are to usegalaxies as tracers of cosmic reionisation, a cosmic eventwhich is now a frontier of observational cosmology. Knowl-edge of when reionisation occurred is crucial to our under-standing of the nature of the earliest UV-emitting sourcesas well as the discrepancy between the observed number ofdwarf galaxies and those expected from cosmological sim-ulations (e.g. Salvadori & Ferrara 2009). Current observa-tional constraints are limited. WMAP measurements indi-cate that the universe may have been partially ionised asearly as z ≃ 11 (Dunkley et al. 2009; Larson et al. 2010),while observations of transmission in the spectra of quasarsreveal that intergalactic hydrogen must be highly ionisedbelow z

∼< 6. While the discovery of an accelerated decline

and increased variance in the mean transmitted flux fromquasars initially led many to suggest that the intergalacticmedium (IGM) is still partially neutral at z ≃ 6.2 (Fan et al.2006), recent work has demonstated that these results donot necessarily require a sudden change in the ionisationstate of the IGM (Becker et al. 2007). Given the difficultyin locating quasars at z > 7, it seems unlikely that quasarspectroscopy will constrain the epoch when the bulk of theIGM was reionised in the near future.

Lyα emitting galaxies offer a valuable additionalprobe of the IGM (e.g., Rhoads & Malhotra 2001;Malhotra & Rhoads 2004; Kashikawa et al. 2006). In prin-ciple, the test is straightforward to apply. Young galax-ies emit copious amounts of Lyα photons, which areresonantly scattered by neutral hydrogen. Hence as weprobe the regime when the IGM becomes significantly neu-tral, the fraction of star-forming galaxies showing strongLyα emission should decrease (e.g. Haiman & Spaans 1999;Santos 2004; Furlanetto et al. 2006; McQuinn et al. 2007;Mesinger & Furlanetto 2008; Iliev et al. 2008; Dayal et al.2010). Recent measurements of the luminosity function ofLyα emitters (LAEs) selected via narrowband imaging haverevealed a tantalising decline between z = 5.7 and z = 7.0(e.g. Kashikawa et al. 2006; Iye et al. 2006; Ota et al. 2008),offering possible evidence that the ionisation state of theIGM evolves over 6 < z < 7.

Regardless of the validity of claims for an increasingfraction of neutral hydrogen over 6 < z < 7, in prac-tice the interpretation of the Lyα test is more complex.While the ionisation state of the IGM affects the Lyα LF,so does evolution of a multitude of other properties in-trinsic to the sampled population (e.g., Verhamme et al.

c© 2010 RAS, MNRAS 000, 1–23

Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 3

2006, 2008; Atek et al. 2008). Evolution in the dust content(Bouwens et al. 2009b), the column density, kinematics, andgeometrical distribution (generally described as the “cov-ering fraction”) of neutral hydrogen (Shapley et al. 2003;Quider et al. 2009, 2010; Steidel et al. 2010) can each playa key role. Also important for the transmission of Lyα pho-tons is the density of the IGM, which evolves continuouslywith redshift, and the stellar initial mass function of galax-ies, for which few robust constraints exist at high-redshift.

The existence of these complicating factors highlightsthe importance of understanding how the prevalence of Lyα-emitting galaxies varies just after reionisation in addition tocharacterising the decline that may occur during reionisa-tion itself. With this goal in mind, we seek to construct anindependent measure of the redshift evolution of Lyα emit-ting galaxies over a large redshift baseline, complementaryto past efforts (e.g. Ota et al. 2008). Here we introduce themethod of measuring the fraction of strong Lyα emitters(hereafter the “Lyα fraction”) within the LBG population.Applying the Lyα fraction test to a large sample of LBGshas many advantages. Firstly, the LBG samples are alreadyin place over 4 < z < 8 owing to deep surveys with HST(e.g. McLure et al. 2010; Bunker et al. 2010; Bouwens et al.2010b); hence the only time investment required is follow-upspectroscopy. This spectroscopy not only provides a sampleof Lyα emitters with known spectroscopic redshifts, but italso provides information on the kinematics of the ISM (e.g.Shapley et al. 2003; Vanzella et al. 2009; Steidel et al. 2010)for individual bright sources (and for faint systems via com-posite spectra) and improves estimates of dust obscurationvia UV colors, both of which are key factors governing thetransmission of Lyα photons. By improving our understand-ing of how these properties change with time, we can beginto isolate the effect of reionization on the evolution in theLyα fraction. Additionally, the Lyα fraction is insensitiveto the declining number density of star-forming galaxies,in contrast to the Lyα luminosity function test (which re-quires comparison to the UV luminosity function to accountfor this degeneracy). Naturally, the Lyα fraction test hasits own complications, but we show that these can be cor-rected for (see §3.3 and 3.4), and we thus argue that thistest will provide valuable constraints on reionization as new7 < z < 10 LBGs emerge in the next several years.

Our goal is therefore to obtain a robust measure of theluminosity and redshift dependence of the Lyα fraction whenthe IGM is highly-ionised (z ≃ 3− 6) and to compare it tothe Lyα fraction at progressively earlier times. If the IGMionisation state evolves significantly at z

∼> 6 as possibly im-

plied by the narrowband Lyα results, we would expect themeasured fraction of LBGs with strong Lyα emission to belower at z ≃ 6 − 8 than expected from extrapolating thetrends seen over 3 < z < 6. By placing the evolution of theLyα fraction at 3 < z < 6 in the context of the evolutionof the well-characterised LBG parent population (e.g. vari-ation of dust extinction with redshift and luminosity), wewill calibrate the relative importance of factors other thanreionisation on the transmission of Lyα photons.

Our Lyα fraction test is ideally suited to our large spec-troscopic sample of continuum-selected LBGs spanning theredshift range 3 ∼

< z ∼< 7. The current Keck sample (includ-

ing a sample of archival i′-drops to be presented in Bunker etal. 2010, in preparation) consists of 455 B, V, i′, and z-drops

(photometrically-selected to lie at 3.5 < z < 7.0) spanninga wide range in UV luminosity (to MUV ≃ −18). We com-bine this sample with a more luminous publically-availableFORS2 dataset of 195 sources satisfying photometric crite-ria similar to those adopted for the Keck surveys. Using thislarge spectroscopic database, we address the primary goal ofthis first paper in our series - to compute the Lyα fractionas a function of luminosity and redshift. This will enable usto identify the principal factors governing its evolution over3∼< z

∼< 6, prior to extending the test to 6

∼< z

∼< 8, where

we can probe changes in the IGM.The plan of the paper is as follows. In §2, we describe the

target selection and spectroscopic observations, and presentthe rest-frame UV properties of our current sample. In §3,we describe the construction of the Lyα catalog, discuss themethod used to measure Lyα equivalent widths, and com-pute the completeness of Lyα detection as a function of lu-minosity and redshift. In §4, we discuss the luminosity de-pendence of Lyα emission in the context of earlier studiesat z ≃ 3. We then turn to the redshift-dependence of Lyαemission and discuss the important implications of our find-ings. Finally, in §5, we examine the extant data on the rateof occurrence of Lyα emission for candidate sources thoughtto lie beyond z ≃ 6. We use this to test the practicality ofusing our test as a valuable probe of cosmic reionisation. Wesummarise the conclusions of our study in §6.

Throughout the paper, we adopt a Λ-dominated,flat universe with ΩΛ = 0.7, ΩM = 0.3 and H0 =70h70 kms

−1 Mpc−1. All magnitudes in this paper arequoted in the AB system (Oke & Gunn 1983).

2 OBSERVATIONS

We present the results of a new and ongoing Keck spec-troscopic survey of photometrically-selected B, V and i′-band ‘dropouts’ in the northern and southern GOODS fields(Giavalisco et al. 2004b). The GOODS fields were selectedfor this survey on account of the depth and precision of theirunique multi-color photometric data useful for selecting tar-gets, as well as the availability of associated Spitzer andChandra data which provided valuable stellar masses andAGN-related properties (Eyles et al. 2005; Yan et al. 2006;Eyles et al. 2007; Stark et al. 2007a, 2009; González et al.2010; Labbé et al. 2009).

2.1 The Keck/DEIMOS Survey in GOODS-N andGOODS-S

The majority of spectra discussed in this paper were ob-tained from an ongoing survey undertaken with the DEepImaging Multi-Object Spectrograph (DEIMOS) at the Nas-myth focus of the 10 m Keck II telescope (Faber et al. 2003).DEIMOS is comprised of eight 2k x 4k CCDs spanningroughly half of the ACS GOODS field of view (≃ 16.′7×5.′0)on the sky. Our first observations have primarily focused ontargeting the B and V -drop populations. Although futureDEIMOS observations will expand coverage of higher red-shift i′ and z-band dropouts, we include early data taken inthis territory, some of which is described independently inBunker et al (2010, in preparation).

The recently-studied target list is primarily selected

c© 2010 RAS, MNRAS 000, 1–23

4 Stark et al.

from the B, V and i′ dropout samples discussed inStark et al. (2009). To this we will add earlier Keck data oni′ drops discussed in §2.2 (Bunker et al. 2003; Stanway et al.2004, Bunker et al. 2010, in preparation) as well as newly-discovered z-drops from the recent WFC3/IR UDF cam-paign (see below). Optical magnitudes range from relativelybright systems (z850 ≃ 23.5) to the faintest dropouts ob-served in GOODS (z850 ≃ 27.5). Although the ACS pho-tometry in Stark et al. (2009) was based upon the GOODSversion r1.1 ACS multi-band source catalogs, for this anal-ysis we have updated the photometry to the recently re-leased GOODS version 2.0 catalogs. These new catalogs con-tain significantly deeper z850-band imaging. The 5σ limitingmagnitudes vary across the different frames, but are typi-cally 28.0 in F435W (B435), 28.2 in F606W (V606), 27.9 inF775W (i′775), and 27.8 in F850LP (z850) when measured in0.5 arcsecond diameter apertures. At the median redshiftsexpected for these populations (z = 3.8 for B-drops, z = 5.0for V-drops, and z = 5.9 for i′-drops, e.g., Bouwens et al.2007), these limits correspond to absolute magnitude limitsof MUV ≃ −18.2, -18.8 , and -19.1 for B, V, and i

′-drops.

A summary of the various observing campaigns is givenin Table 1. Apart from the i′-drop exploratory survey dis-cussed by Bunker et al. 2010, (in preparation), in ourcampaigns during 2004-2007 targets were selected to fillempty regions on slitmasks designed for other purposes,e.g., studying the kinematics of disk galaxies at z ≃ 1(MacArthur et al. 2008). For these observing runs, we usedthe Gold 1200 line mm−1 grating which provided coveragebetween 5570 and 8210 Å (allowing Lyα to be detected inthe redshift range z = 3.6 to 5.8), with a spectral pixel sizeof 0.3 Å pixel−1. The spectral resolution measured fromskylines was 1.4 Å.

The main survey began in earnest in 2008, when westarted a dedicated programme geared at obtaining spec-tra of z > 3 dropouts. Most spectra were obtained from5 slitmasks observed in April 2008 and March 2009 (Ta-ble 1). These slitmasks utilised the 600 line mm−1 grat-ing on DEIMOS, providing spectroscopic coverage between4850 Åand 10150 Å (allowing Lyα to be detected betweenz ≃ 3.0 and 7.3) with a spectral pixel scale of 0.7 Å pixel−1.These spectra provided a resolution (measured from sky-lines) of ≃ 3.5 Å. This setup allowed us to efficently follow-up B and V-band dropouts simultaneously. Each individualmask was observed for ≃ 5 − 7 hours and contained ≃ 80-110 dropouts. Seeing was typically 0.′′8, ranging between 0.′′5and 1.′′0.

We observed a final slitmask toward GOODS-S on 19-20 October 2009. For this run, we prioritised i′-drops andnewly-discovered z-drops (Oesch et al. 2010; McLure et al.2010; Bunker et al. 2010; Wilkins et al. 2010a) and there-fore opted for the higher resolution 830 line mm−1 gratingblazed at 8640 Å with order blocking filter OG550. Withthis set-up, the spectra generally provide coverage between6800 and 10100 Å (allowing Lyα to in principle be detectedbetween z=4.5 and 7.3), with each spectral pixel spanning0.46 Å. Skylines are measured to have a FWHM of ≃ 2.4 Å, asignificant improvement upon the resolution obtained withthe 600 line grating. However, poor seeing (average of 1.3arcseconds) and fog made redshift confirmation particularlydifficult.

All data were reduced using the spec2d IDL pipeline de-

veloped for the DEEP2 Survey. The final reduction providestwo-dimensional (2D) spectra and variance arrays, alongwith a one-dimensional (1D) extraction at the expected po-sition of the dropout. Wavelength calibration was typicallyobtained from Ne+Xe+Cd+HG+Zn reference arc lamps. Ingeneral, the final wavelength solution is accurate to within≃ 0.1 Å. Examples of reduced 1D-spectra are presented inFigure 1.

We flux calibrated the spectra using spectroscopic stan-dard stars observed in the 24-26 March 2009 observing run.We tested the flux calibration derived from these standardsusing spectra of alignment stars included on the slitmask(observed in 2 arcsec × 2 arcsec boxes). We compute opti-cal broadband magnitudes for the alignment stars from theflux-calibrated spectra using the appropriate filter transmis-sion functions. The magnitudes measured from the spectramatch those from the ACS images to within a factor of ≃ 2.We bootstrapped a flux calibration on spectra from observ-ing runs for which spectroscopic flux standards were nottaken (03-05 April 2008) using the measured flux in align-ment stars that are in common between the 2008 and 2009observing runs.

Using the flux calibrations, we compute our typical 1σflux sensitivity across the DEIMOS spectra for the 600 linegrating. These measurements predict that we should detectcontinuum at the 1σ level for sources with V ≃ 25.5 (perspectral resolution element in 1D spectra which have beenextracted over ≃ 1′′) across much of the wavelength regimecovered by the 600 line spectra. This prediction is consis-tent with expectations based on the optical magnitudes ofsources that show continuum traces in the spectra. The av-erage 10σ limiting line flux is 1-1.5×10−17 erg cm−2 s−1 be-tween 6500Å and 9300Å, although sky lines become muchmore common toward the red side of the spectra. In a latersection, we present more detailed simulations that reveal thecompleteness for emission lines of a given flux and redshift.

For the most recent run (October 2009), the limitingsensitivity was significantly worse than in previous runs dueto the seeing and fog. Based on the signal obtained fromthe bright alignment stars on the mask (each of which hasknown broadband magnitudes) and the signal from our spec-troscopic standard stars, we estimate that our continuum 1σsensitivity (computed per resolution element with a spatialextraction width of ≃ 1.5′′) was ≃ 3.5−4.0×10−19 erg cm−2

s−1 Å−1 in between sky lines (corresponding to a continuummagnitude of i′ ≃ 24.25). Assuming typical line widths, thislimit translates into a 10σ line flux limit of 2.5-4.0×10−17

erg cm−2 s−1 for Lyα. As most of the sources targeted inthis run were faint (z850 > 26 for the i

′-drops), this meansthat we are only sensitive to very strong emission lines (the10σ rest-frame equivalent width limit is ≃ 75-100 Å forsources with z850 ≃ 26.5). For fainter sources (e.g. the ma-jority of WFC3 z-drops in the UDF), the equivalent widthlimits are too large to enable detection of Lyα.

To summarise the current status of our DEIMOS ob-servations, we have obtained 549 spectra of B, V, i′, andz-drops. To boost the S/N of our spectra, many dropoutswere observed on multiple masks; hence, each spectra doesnot correspond to a unique sources. Accounting for this, weobserved a total of 268 B-drops, 95 V-drops, 19 i′-drops,and 17 z-drops. We combine this sample with archival Keckand VLT spectra in the following two subsections, and in

c© 2010 RAS, MNRAS 000, 1–23

Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 5

Number Field Mask ID Date texp (ksec) NB NV Ni NZ Grating

1 GOODS-S GS031 08-09 January 2003 19.8 0 0 3 0 12002 GOODS-N GN031 02-06 April 2003 37.8 0 0 5 0 12003 GOODS-S GS041 11 December 2004 21.9 0 0 20 0 12004 GOODS-S GS051 31 October, 01-02 November 2005 8.4 0 0 17 0 12005 GOODS-S GS071 10-11 November 2007 18.0 7 7 0 0 12006 GOODS-N GN081 03-05 April 2008 21.6 85 9 0 0 6007 GOODS-N GN082 03-05 April 2008 21.6 95 12 0 0 6008 GOODS-N GN083 03-05 April 2008 20.4 86 14 0 0 6009 GOODS-N GN094 24-26 March 2009 18.0 45 63 0 0 60010 GOODS-N GN095 24-26 March 2009 25.2 43 36 0 0 60011 GOODS-S GS091 19 October 2009 19.2 0 0 19 17 830

Total Unique Keck/DEIMOS Sample 268 95 64 17 −Total Unique VLT/FORS2 Sample 83 56 56 0 −

Combined Unique Sample 351 151 108 17

Table 1. Summary of observations with Keck/DEIMOS and VLT/FORS2. NB, NV, Ni, Nz denote the number of B, V, i′, and z-drops

observed on each mask. To maximise S/N, many sources were observed on multiple DEIMOS masks; we account for such duplicationwhen computing the total Keck sample size. The i′-drops in the first two rows were originally published in Bunker et al. (2003) andStanway et al. (2004), and the i′-drops presented in rows 3 and 4 are from Bunker et al. (2010, in preparation). The VLT FORS2 sampleis take from observations presented in Vanzella et al. (2009). The combined total sample in the last row includes all unique dropouts inthe Keck and VLT surveys.

§2.4, we present the absolute magnitude distribution of thecombined VLT and Keck spectroscopic samples.

2.2 Archival Keck Spectroscopy in GOODS-N/S

Additional i′-drops were observed with Keck/DEIMOS be-tween 2003 and 2005 (Table 1). Early observations were pre-sented by Bunker et al. (2003) and Stanway et al (2004), andan updated discussion, including additional DEIMOS obser-vations from 2003-2005, is given by Bunker et al. (2010).These sources were observed with the 1200 line mm−1 (de-scribed above) with seeing of 0.′′7 - 1.′′0.

In total, 45 i′-drops were observed in the two GOODSfields on 4 separate slitmasks. Of the 45 sources observed,12 were included in the Vanzella et al. (2009) VLT/FORSobservations discussed below. Integration times ranged be-tween 2.3 and 10.5 hrs. The z850-band magnitudes of thesources ranged between 24.7 and 28.3. Given the consider-able range of exposure times, we take care to estimate theequivalent width completeness for sources of different mag-nitudes on the various masks that were observed.

2.3 Archival VLT/FORS Spectroscopy inGOODS-S

Two programmes aimed at following up high-redshiftdropouts in GOODS-S have been conducted with the VLT.The first of these used the FORS2 multi-object spectrograph(Vanzella et al. 2005, 2006, 2008, 2009), and the secondused the VIMOS multi-object spectrograph Balestra et al.(2010). Both teams have released their datasets to the pub-lic. In this paper, we focus on the FORS2 survey, as its sur-vey characteristics (resolution, spectral coverage) are closestto the DEIMOS survey. We discuss the basic FORS2 surveydetails below.

Between September 2002 and October 2006, the VLTFORS2 multi-object spectrograph was used to observe

sources identified in the GOODS imaging of CDF-S. In to-tal, 38 FORS2 masks were obtained using the 300I grismwithout an order-separating filter. Each mask was observedfor roughly 4-6 hours. In general, the spectra provide cover-age between 6000 Å and 10000 Å, with a spectral resolvingpower of R=660 which provides resolution of ≃ 13 Å at8600 Å.

The FORS2 database provides redshift classificationsand quality grades (ranging from A to C) for the en-tire spectroscopic sample. The colour criteria used to se-lect the dropouts in the FORS2 sample are discussed inGiavalisco et al. (2004a); however, for the B-drops, a slightvariation in the colour-selection was adopted (for details seeVanzella et al. 2009).

In general, these criteria are very similar to those wehave adopted for our DEIMOS survey. Using the coordi-nates provided in the public FORS2 database, we query theversion 2.0 ACS catalogs for GOODS-S and measure opti-cal magnitudes in an identical fashion as described in §2.1.Adopting the selection criteria used for the DEIMOS sam-ple (see Stark et al. 2009), we find 83 B-drops, 56 V-drops,and 56 i′-drops that were observed with FORS2. Redshiftswere obtained for 48 B-drops (46 with z > 3), 37 V-drops(32 with z > 4), and 26 i′-drops (21 with z > 5).

The magnitude distribution of the FORS2 sample isgenerally weighted toward brighter sources, with few B andV-drops with magnitudes fainter than z850 ≃ 26. Given theinherent faintness of i′-drop samples, the magnitude distri-bution is significantly fainter than for the lower redshiftdropout samples, with z850 ≃ 25 − 27. In Figure 2, weplot a comparison of the absolute magnitude distributionof the FORS2 and DEIMOS dropout samples. The currentDEIMOS sample contributes 76% of the B-drops and 63%of the V-drops and crucially extends the spectroscopic cov-erage to lower luminosities.

c© 2010 RAS, MNRAS 000, 1–23

6 Stark et al.

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Figure 1. Montage of DEIMOS 1D spectra from our survey arranged according to redshift and luminosity. B-drops are shown in the leftcolumn, and V-drops appear in the right column. Each panel contains a label indicating the apparent magnitude of the continuum andredshift. Spectra are smoothed to a spectral pixel size of ≃ 3 Å. Where present, dashed vertical lines denote Lyα, Si II 1260, OI+SiII1303, and CII 1334 lines.

2.4 Final Spectroscopic Sample

When combined, the FORS2 and DEIMOS surveys containa total of 627 spectra of unique high-redshift dropouts (351B-drops, 151 V-drops, 108 i′-drops, and 17 z-drops). In Fig-ure 3, we present colour-colour diagrams of the entire B

and V-drop spectroscopic sample, indicating the selectioncriteria. The i′-drops were selected using the standard sin-gle i′ − z > 1.3 colour criterion (see Figure 4). Comparingthe distribution of selected targets on these figures with thelarger sample of sources in the Stark et al. (2009) photomet-ric catalog, we demonstrate that the colours of our targets

c© 2010 RAS, MNRAS 000, 1–23

Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 7

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5(V606 - z850)

0

2

4

6

(B43

5 -

V60

6)

-0.5 0.0 0.5 1.0 1.5 2.0(i775 - z850)

0

2

4

6

(V60

6 -

i 775

)

Figure 3. Colour-colour diagrams for the B-drops (left) and V-drops in combined VLT and Keck spectroscopic surveys. Objects withLyα in emission are denoted with a second red circle. The dotted lines show the Lyman break selection criteria adopted in this paper.The small grey circles show the distribution of colours for the parent population of LBGs from Stark et al. (2009).

−23 −22 −21 −20 −19 −18 −17MUV

0

20

40

60

80

100

120

N(M

UV)

DEIMOS BViFORS2

Figure 2. Absolute magnitude distribution of FORS andDEIMOS spectroscopic samples. The new DEIMOS B, V, andi′-drops are shown in shaded blue, and below the FORS2 observa-tions (Vanzella et al. 2009) are shown in light red. The DEIMOSdatasets comprise the majority of the spectra considered in ouranalysis.

with spectroscopic coverage span nearly the full range of theparent LBG population.

Figure 5 also shows the apparent magnitude distribu-tions of the various dropout samples. While previous surveyshave focused on sources with apparent magnitudes brighterthan m ≃ 26, a major achievement of our survey is that wehave been able to push significantly below this limit withDEIMOS. Our primary motivation for doing so is that thecharacteristic UV luminosity shifts to lower values at higherredshifts (e.g., Bouwens et al 2007), so to compare sourceproperties over 3 ∼

< z ∼< 7 in a meaningful manner, probing

deep becomes a necessity. To demonstrate our survey hasachieved this over 3 < z < 6, in Figure 6, we compare theabsolute magnitude distribution of our various dropout sam-ples. Current estimates of the characteristic absolute mag-nitude at z ≃ 7 are MUV ≃ −19.9 (Bouwens et al. 2009a;Ouchi et al. 2009; Oesch et al. 2010). As objects more lumi-

25 26 27 28 29z850

0

2

4

6

(i77

5−z 8

50)

Figure 4. i′ − z colour versus magnitude for i′-drops with spec-troscopic observations with the dashed line showing the selec-tion cut. Points surrounded by a red open circle indicates sourceswith Lyα seen in emission, and the small grey circles indicate thecolours and magnitudes of i′-drops from the parent LBG samples(Stark et al. 2009).

nous than this are exceedingly rare at z ∼> 6−7, if we are to

make consistent Lyα fraction comparisons, we must probeto at least this depth over 4 < z < 6.

Redshifts were determined via visual examination of thespectra (see Figure 7 for a redshift distribution). For UVfaint sources, the continuum is too faint for identification ofthe Lyman break or absorption lines, so we can only measurespectroscopic redshifts for those sources with Lyα in emis-sion. For UV bright sources, redshift identification is per-formed via a combination of the Lyman break, interstellarabsorption lines, and/or Lyα emission. We classify all red-shifts according to their quality, ranging from A (definite),B (secure), C (possible/likely). Nearly all Lyα emitters fallinto the first two categories owing to the combination of lineprofile, lack of other emission lines, and strong continuumbreak (in spectra and/or imaging), but some of the absorp-tion line detections are much more tenuous owing to skyline residuals and noise. As the results of this paper are in-

c© 2010 RAS, MNRAS 000, 1–23

8 Stark et al.

23 24 25 26 27 28i775

0

20

40

60

80

100

N(i

775)

B−drops

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0

10

20

30

40

N(z

850)

V−drops

23 24 25 26 27 28z850

0

10

20

30

40

N(z

850)

i−drops

Figure 5. Distribution of apparent magnitudes of B-drops (top),V-drops (middle), and i′-drops (bottom) in combined Keck andVLT spectroscopic survey.

-23 -22 -21 -20 -19 -18 -17MUV

0

50

100

150

200

N(M

UV)

TotalB-dropV-dropi-drop

Figure 6. Distribution of absolute magnitudes of sources in thecombined DEIMOS and FORS2 spectroscopic survey (shadedblue). The shaded light red, green, and grey denote the mag-nitude distribution of the B, V, and i′-drop samples.

0

10

20

30

40

50

60

70

N(z

)

Keck/DEIMOS+VLT/FORS2

VLT/FORS2

3 4 5 6 7redshift

0.00.20.40.60.81.0

p(z

)

B V i

Figure 7. Redshift distribution of B, V, and i′-drops with spec-troscopic confirmation in GOODS-N and GOODS-S (dark blue).This sample includes absorption line systems in addition to theLyα emitters discussed in this paper. The total sample contains179 galaxies with redshifts in the range 3

∼< z

∼< 4.5, 87 galaxies

with redshifts over 4.5∼< z

∼< 5.5, and 44 galaxies with redshifts

over 5.5∼< z

∼< 6.5. For reference, we display the redshift distri-

bution of the VLT/FORS2 survey (Vanzella et al. 2009) in lightred.

dependent of the absorption line sample, we delay furtherdiscussion of the absorption line catalog until a subsequentpaper (Stark et al. 2010, in preparation), while details of theLyα selection are described in the following section. How-ever, we note that, in total, the FORS2+DEIMOS samplecontains 179 redshifts over 3 ∼

< z ∼< 4.5, 87 redshifts over

4.5 ∼< z ∼

< 5.5, and 44 redshifts over 5.5 ∼< z ∼

< 6.5.

3 EMISSION LINE MEASUREMENTS

3.1 Constructing the Lyα catalog

Emission lines were initially identified visually in thetwo-dimensional DEIMOS spectra and later in the one-dimension extractions at the position of the dropouts. Wetook care to distinguish Lyα from other emission features

c© 2010 RAS, MNRAS 000, 1–23

Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 9

−50

0

50

100

Flu

x

zLyα=6.44

9020 9040 9060 9080 9100Wavelength(Å)

0255075

100

Noi

se

Figure 8. Spectra of a J125 ≃ 27.3 z-drop showing tentative Lyαemission at 9044 Å. Top panel: The 2D spectrum shows a sig-nificant emission feature detected at the 7σ level (black corre-

sponds to positive flux in the image) in between two sky linesand centered exactly at the position of z-drop ’3’ in Wilkins et al.(2010a). Bottom panel: The 1d spectrum of the galaxy and asso-ciated noise. The spectrum and noise are not smoothed to avoidblending with skylines at 9038 Å and 9048 Å. The emissionline between these features lies in a region of low noise, spanning≃ 10 Å in width.

(e.g. [OII] which is resolved by DEIMOS) which correspondto lower-redshift galaxies. Lyα emission is detected in 152of the DEIMOS dropouts.

For the VLT/FORS dataset, the redshifts were deter-mined in Vanzella et al. (2009). As discussed in §2.3, to en-sure a uniform selection across the Keck and VLT samples,we performed our own photometric selection. With the re-sulting subset of 193 galaxies, we identified those objectsshowing Lyα in emission in their one-dimensional spectra.

We defined Lyα redshifts (zLyα) for each object as thewavelength at which the Lyα line is at its peak flux value.As Lyα is generally redshifted by at least ≃ 300 km s−1

from the frame of rest of the galaxy (e.g. Shapley et al.2003; Vanzella et al. 2009), we note that this redshift isnot necessarily equivalent to the systemic redshift of thegalaxy. Across both surveys, we identified Lyα emissionin 108 B-drops, 63 V-drops, and 28 i′-drops. The relativecolour distribution of these sources in relation to the largerspectroscopically-targetted sample is shown in Figures 3 and4.

In addition to the B, V, and i′-drops, we present tenta-tive spectroscopic confirmation for one of the z-drops thatwas studied in poor conditions in the October 2009 DEIMOSrun (Table 1). The only z-drop to show a clear emissionfeature at the expected object location was source 3 inWilkins et al. (2010a). This object, identified in the GOODSERS WFC3 imaging of CDF-S (PI: O’Connell), is reason-ably faint (J125 ≃ 27.3) but is brighter than most of thez ∼> 6 sources detected in the UDF (e.g. Oesch et al. 2010;

Bunker et al. 2010; McLure et al. 2010). The DEIMOS spec-

0.6 0.8 1.0 1.2 1.4 1.6 1.8λobs (µm)

10-32

10-31

10-30

f ν (e

rg c

m-2

s-1

Hz-

1 )

z=zLyα=6.44MUV=-19.5SFR∼ 3 MO • yr

-1

Figure 9. Spectral energy distribution of z-drop ’3’ fromWilkins et al. (2010a). The datapoints show detections and up-per limits from ACS and WFC3 imaging of CDF-S. Overplottedis a Bruzual-Charlot population synthesis model with a redshiftfixed at z = 6.44, the spectroscopic redshift inferred from theemission line detected in Figure 8. The broadband imaging datashow a prominent break where the Lyman break is predicted anda significant excess of flux in the medium-band Y098 filter (rela-tive to the J125-band), as expected in the presence of strong Lyαemission.

trum illustrates a significant 7σ emission line in betweensky lines and centered at 9044 Å (Figure 8). The S/N andnearby sky line do not enable a robust measure of the asym-metry of the line. The broadband SED is well fit by a sourcez ≃ 6.44 with strong Lyα contaminating the medium-bandY098 filter (Figure 9). If this emission feature is Lyα, it wouldlie at z = 6.44, consistent with the photometric redshift pre-dictions. Our flux calibration suggests a flux of 1.5 × 10−17

erg cm−2 s−1 and hence an equivalent width (rest-frame) of83 Å. We will confirm the redshift of this source in futurecampaigns of CDF-S.

3.2 Computation of Lyα properties

Next we compute the flux (FLyα) and equivalent width(WLyα) for each Lyα emitter in our spectroscopic sample.Previous attempts to constrain evolution in the prevalenceof Lyα emitters have focused on measuring evolution in theluminosity function of Lyα emitters (selected via narrow-band filters). For our Lyα fraction test described in §1, weare interested in determining the percentage of LBGs of agiven luminosity with Lyα emission much stronger than thecontinuum flux. This test thus relies on accurate measure-ments of the Lyα equivalent widths (WLyα).

In principle, WLyα provides a more robust constraintthan FLyα as it does not rely on an absolute flux calibra-tion. However since the majority of spectra in our samplehave broadband continuum magnitudes fainter than the 1σcontinuum flux limit of our survey (m ≃ 25 − 26, §2.1), wecan only place an upper limit on the continuum flux mea-sured in this subset of our spectra, thus producing a lowerlimit to the observed WLyα. We can obtain a better es-timate of the equivalent width by adopting the continuumflux measured from broadband imaging, taking care to avoidfilters that are contaminated by Lyα. We detail the specificprocedure used to measure WLyα below.

c© 2010 RAS, MNRAS 000, 1–23

10 Stark et al.

For each spectrum, we compute the line flux, FLyα, bysumming emission in excess of the continuum between 1213and 1221 Å, taking care to avoid contribution from nearbysky lines or artifacts and ensuring that the spatial extractionbox covers the entire spatial width of the line emission.

The measurement of the continuum flux depends onwhether or not continuum is detected. For those objectswith continuum detections, we compute the average contin-uum level redward of Lyα, cred, by averaging the flux in re-gions between OH sky lines between 1225 Å and 1255 Å inthe rest-frame of the galaxy. As discussed in Kornei et al.(2009), this should minimize contribution from nearby ab-sorption features. The observed-frame WLyα is then com-puted by taking the ratio of FLyα and cred.

For those objects without continuum detections, wecompute equivalent widths using the continuum level justredward of Lyα with the broadband photometry discussedin the previous section and taking care not to include thecontribution of Lyα to the continuum. For the B-drops andV-drops, we use the i′775 and z850-band fluxes, respectively.These measurements provide the luminosity at rest-frame≃ 1500 Å, rather than just redward of Lyα. The vast ma-jority of sources are very blue (and hence nearly flat in fν),requiring no correction between the flux at 1500 Å andthat at 1240 Å (the central value in the wavelength-regionsummed for continuum measurements above). For those fewsources with very red UV slopes (measured from the broad-band SEDs presented in Stark et al. 2009), we apply asmall adjustment to correct for the change in flux between1500 Å and 1240 Å.

For galaxies with redshifts above z ≃ 5.7, the z850-bandfilter is contaminated by both Lyα emission, if emission ispresent, as well as Lyα forest absorption shortward of rest1216 Å. Accurate continuum determinations must accountfor this. If sources contain Y or J-band detections via WFC3or ISAAC, then we use these measures for the UV continuumHowever, at the moment, the majority of UV-faint i′-dropsare not detected with significance in the near-IR, so we mustuse z850 detections for these sources. For galaxies with no de-tected Lyα emission, we must only correct for the Lyα forestabsorption, which we do assuming the redshift is identicalto its value inferred from BPZ and that its SED is flat in fν .Corrections range from ≃ 0.2 mag at z = 6 to 0.7 mag atz ≃ 6.4. But for z > 5.7 objects with strong Lyα emission,we also subtract off the line contribution when computingthe continuum flux. Typical line contributions are ≃ 0.1-0.3mag.

To test the reliability of the above method, we examinethe subset of galaxies with bright UV-continua, comparingthe continuum flux determined from broadband-imaging tothat extracted from the spectra. We find that the medianfractional error using the estimate from broadband imagingis ≃ 20% (Figure 10). We add this error in quadrature to thephotometric error on each equivalent width measurement.

3.3 Completeness of Lyα detection

In order to properly assess the fraction of Lyα emitters in oursample as a function of UV luminosity and redshift, we mustconsider how completeness varies with apparent magnitudeand wavelength of the Lyα emission line. We estimate thetypical completeness by adding fake Lyα emission to random

10 100 1000WLyα with cred from spectrum (Å)

10

100

1000

WL

yα w

ith

cre

d f

rom

ph

otom

etry

(Å)

Figure 10. Reliability of WLyα measurements. The x-axis showsequivalent widths (observed-frame) determined directly fromspectra for sources bright enough for a continuum measurement.The y-axis shows the equivalent widths measured for the samesources using the continuum flux from the broadband photome-try. The dashed lines demarcate values 0.5× and 2× the WLyαmeasured directly from the spectrum. The median fractional er-ror from using equivalent widths derived using the continuum fluxfrom broadband imaging is ≃ 20%.

positions across the DEIMOS and FORS2 spectra. In eachcase, we measure the line properties (WLyα, FLyα, S/N) ofthe fake emission feature. We ran enough trials (using alarge number of spectra from each mask) to obtain reliableestimates of the completeness of the Lyα recovery.

Our goal is to identify a lower flux threshold abovewhich Lyα is highly complete for most objects in our samplein order to minimize the necessary completeness corrections.We illustrate the results of the completeness simulations forthe 600 line mm−1 grating on DEIMOS in Figure 11. Themasks on this grating included B and V-drops which spanthe redshift range 3.5 ∼

< z ∼< 5.5. The simulations reveal that

sources with mAB ≃ 27.0 and with rest-frame Lyα equiva-lent widths (WLyα,0) in excess of 50 Å are generally re-covered over nearly the entire redshift range probed by ourdropouts (see Figure 11). The high completeness for verystrong Lyα emitters amongst bright sources (m

∼< 26) arises

as these bright emission features correspond to fluxes thatare in excess of 10-20σ and are recovered even when they lieon top of sky lines. The WLyα,0 > 50 Å emission line com-pleteness begins to decline for very faint sources (i′ ≃ 27.5)at the high-z tail of the V-drop redshift distribution. For theFORS2 data, the spectra show similarly high completenessfor B and V-drops with WLyα,0 > 50 Å. These simulationssuggest that the measured Lyα fraction of sources in theredshift range 3.5

∼< z

∼< 5.5 should not suffer from signifi-

cant incompleteness for B and V-drops more luminous thanMUV ≃ −19.

For the i′-drops, the completeness in the deep DEIMOSand FORS2 spectra remains high for strong (e.g. WLyα,0 >

c© 2010 RAS, MNRAS 000, 1–23

Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 11

3 4 5 6 7Redshift

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Com

ple

ten

ess

m=26.0, WLyα,0=50Å (rest−frame)m=26.5, WLyα,0=50Å (rest−frame)m=27.0, WLyα,0=50Å (rest−frame)m=27.5, WLyα,0=50Å (rest−frame)

Figure 11. Emission line recovery completeness. The complete-ness is determined via simulations placing fake lines in spectraand testing the rate at which sources about the equivalent widththreshold are recovered. From top to bottom, the figure showscompleteness versus redshift for WLyα,0 sources with continuummagnitudes (longward of the Lyman break) of 26.0, 26.5, 27.0,and 27.5.

50 Å ) Lyα lines. However, it is clear from Figure 11 that in-completeness is not negligible, particularly for faint (z850 >27.0) sources at z ∼

> 5.8 which are less than 80% complete.

We thus adopt this as our i′-drop magnitude threshold forinclusion into the Lyα fraction test, limiting us to sourcesmore luminous than MUV ≃ −19.7. We also do not includethe 17 i′-drops on the mask GS051 (see Table 1) from Bunkeret al. 2010 (in preparation) owing to its reduced integrationtime of 2.3 hours.

3.4 Contamination in spectroscopic samples

Although foreground emission line sources (e.g. [O II] emit-ters can be readily distinguished from those revealing Lyα(§3.1), our Lyα fraction test requires that we have a reliablesample of LBGs for which no emission line is seen.

While the Lyman break selection criteria are chosento minimize the inclusion of low-redshift and stellar con-taminants, it is clear that interlopers still populate dropoutsamples. For our purposes, it is important that we considerthe luminosity and redshift dependence of contaminants, asthese could create artificial trends in our derived Lyα frac-tions. We expect low-z contamination to increase toward thefainter end of our sample. This is primarily due to photo-metric scatter; since faint sources are detected with lowerS/N and have less dynamic range available to constrain thebreak, it is more likely that a faint low-z source will be scat-tered into the LBG selection window. However, if the typ-ical contamination is fairly low in all luminosity bins (e.g.

∼< 10%), then this would only require a minor correction tothe luminosity dependence of the Lyα fraction.

To investigate this in more detail, we compute pho-tometric redshift probability distributions for the spectro-scopic sample using the observed photometric cataloguescompiled in Stark et al. (2009), updated to include v2GOODS ACS photometry, and the BPZ software (Benitezet al. 2000). Details of the photometric redshift methodol-ogy is discussed in Stark et al. (2009). Using the probabilitydistributions derived from BPZ, we compute the probability

that each object lies outside the redshift range constrainedby our spectroscopic observations (typically z ∼

< 3.4). Wethen place those galaxies without spectroscopic redshifts inbins of UV luminosity and compute the total contamina-tion fraction as a function of UV luminosity. As expected,the results show that the contamination fraction increasestoward lower luminosities. We find negligible contamina-tion for bright sources (−22 ∼

< MUV ∼< −20) with SEDs con-

strained by high S/N photometry. In the two faintest abso-lute magnitude bins considered (MUV = −19 and -18), thepredicted contamination increases to ≃ 10%. This suggeststhat, owing to low-z contamination, the true Lyα fractionsin the two faintest bins should be 1.11× greater than de-rived. We consider the effects of this in our discussion of theLyα fraction in §4.1.

We now examine whether the SEDs predict contam-ination should vary strongly with redshift. As above, wemeasure the contamination fraction (of objects that arenot Lyα emitters) implied for B, V, and i′-drop samplesfrom the photometric probability distributions. As above,we find negligible contamination at the brighter magni-tudes. Combining sources with UV luminosities spanning−20 ∼

< MUV ∼< −18, we find that the contamination fraction

increases from 2% for V and i′-drops to 5% for B-drops. Thissuggests that in this luminosity regime, the B-drop Lyα frac-tion will be underestimated by a factor of 1.05, while the Vand i′-drop Lyα fraction will be underestimated by a factorof 1.02. Hence low-z contamination will cause the positiveevolution in the Lyα fraction with redshift to be overesti-mated by a factor of 1.03 in this luminosity range. As wewill show in §4.2, while the redshift-dependent trends in theLyα fraction are small in their amplitude, this contamina-tion effect contributes little to the observed variation withredshift.

4 ANALYSIS

We now turn to the key questions posed in §1. Armed witha large sample of LBGs for which some fraction, xLyα, showLyα emission, we discuss what can be learned about the de-mographics of line emission in the star-forming populationand how such trends might affect our ability to use Lyαas a tracer of reionization. In this analysis section, first wepresent the results, both in terms of the fraction of LBGsshowing line emission as a function of luminosity and red-shift. We then discuss the physical factors that might explainthese trends prior to the use of Lyα emission statistics as apossible probe of reionisation.

4.1 The Luminosity-Dependence of Lyα emissionat high-redshift

First, we discuss the relationship between Lyα emissionand luminosity in our spectroscopic sample of Lyα emit-ters between 3 ∼

< z ∼< 6. If the Lyα fraction varies strongly

with luminosity, as may be expected given recent claimsof luminosity-dependent dust obscuration at high-redshift(Reddy & Steidel 2009; Bouwens et al. 2009b), then caremust be taken to compare only galaxies of similar luminos-ity when searching for evolution in the Lyα fraction with

c© 2010 RAS, MNRAS 000, 1–23

12 Stark et al.

redshift. As our survey probes to considerably lower lu-minosities than past spectroscopic LBG samples at z ∼

> 3(MUV ≃ −18, Figure 6), our sample is well-suited to inves-tigating such a relationship.

There have been a number of previous studies which ex-amine how Lyα line strength varies with luminosity. Manyof these studies have reported a correlation between Lyαequivalent width and UV luminosity. Shapley et al. (2003)binned their sample of z ≃ 3 galaxies with WLyα,0 > 20 Å inthree groups of apparent UV luminosity and found that themean of theWLyα,0 distribution increased toward fainter UVluminosity. Others have examined Lyα equivalent widths asa function of UV continuum luminosity, revealing a deficitin large equivalent width Lyα lines in the most luminouscontinuum sources (Ando et al. 2006; Ouchi et al. 2008;Pentericci et al. 2009; Vanzella et al. 2009; Balestra et al.2010). Additionally, by comparing the UV luminosity func-tion of LBGs with that of narrowband-selected LAEs,Ouchi et al. (2008) has shown that Lyα emitters are likely tobe more prevalent at the faint-end of the luminosity func-tion. As we discussed earlier, these results are consistentwith simple theoretical expectations in which low luminos-ity galaxies are less obscured by dust (due to lower metal-licities) and perhaps have lower column densities (or cover-ing fraction) of HI surrounding them (e.g. Verhamme et al.2006, 2008; Schaerer & Verhamme 2008). Perhaps of equalor greater importance is the bulk velocity field of the HI(Shapley et al. 2003; Steidel et al. 2010), which we discussfurther in §4.3.

However, others have found the evidence for a corre-lation between luminosity and Lyα equivalent width to beless convincing (e.g. Steidel et al. 2000; Nilsson et al. 2009).In particular, Nilsson et al. (2009) demonstrated that thedearth of luminous galaxies with extreme Lyα emissionin magnitude or flux-limited surveys does not require theequivalent width distribution to be luminosity-dependent.The lack of such extreme emitters is actually expected ina magnitude or flux limited survey, as the most luminousand the most extreme emitters are both rare, causing thisportion of parameter space to poorly represented unlessvery large volumes are covered. This is an important re-alisation but only considers LBGs with continuum lumi-nosities brighter than MUV ≃ −20, significantly more lu-minous than the feeble sources probed in our survey. Like-wise, Kornei et al. (2009) found only marginal evidence fora correlation between WLyα and UV continuum luminosityin a large sample of z ≃ 3 LBGs, but concluded that thismay result from the limited dynamic range in UV luminosityprobed by their sample.

Figure 12 shows the distribution of rest-frame equiva-lent width, WLyα,0 for Lyα emitters in our survey as a func-tion of rest-frame UV luminosity, MUV. In considering thisfigure we must choose a sufficiently bright WLyα,0 thresholdto avoid incompleteness in the faintest sources. As demon-strated in §3.3 and Figure 11, sources with WLyα,0 in excessof 50 Å are detected with high completeness (> 90%) acrossour spectra, so we adopt this value as our equivalent widththreshold. The data show an apparent lack of strong lineemission among the most luminous dropouts, as has beenfound elsewhere (Ando et al. 2006; Pentericci et al. 2009;Vanzella et al. 2009), yet as demonstrated in Nilsson et al.(2009), this does not necessarily imply that Lyα emission is

−22 −21 −20 −19 −18MUV

0

100

200

300

WL

yα,0(Å

)

Lyα Emitter sample

Figure 12. Rest-frame Lyα equivalent width (WLyα,0) as a func-tion of rest-frame absolute magnitude, MUV for Lyα emitters inour spectroscopic sample. The sample is nearly complete at allMUV for sources with WLyα,0 > 50 Å (dotted line).

less common in luminous galaxies. However, when Figure 12is viewed in concert with the absolute magnitude histogramof our spectroscopic sample (Figure 6), it becomes clear thatstrong line emission must be more common in low lumi-nosity dropouts, for the number of low luminosity galaxies(MUV > −19.5) targeted in our campaign is as low as themost luminous sources (MUV < −21.5), but the number ofstrong line emitters is far greater among the feeble sources.We emphasize that owing to our equivalent width thresholdof WLyα,0 ≃ 50 Å, the Lyα emitters amongst low luminositysources are secure and robust (S/N > 10) detections (simi-lar to those at the top of Figure 1); hence this result is notdriven by noisy features.

In order to most clearly quantify the luminosity-dependence of Lyα emission, we must compute the frac-tion of LBGs in our spectroscopic sample that show strong

Lyα emission, xLyα, as a function of emerging UV luminos-ity. Given that the majority of our spectroscopic sample isfainter than our continuum flux sensitivity (Figure 5), it isnot possible to measure redshifts for faint sources withoutemission. Hence if we were to compute xLyα based soley onsources with confirmed redshifts (as has been done previ-ously for brighter samples), we would artificially increasexLyα toward lower luminosities. To avoid this bias, we de-fine xLyα as the number of Lyα emitters above some WLyα,0threshold divided by the total number of dropouts placed onour slitmasks.

The error on xLyα is computed as follows. We first de-rive the Poisson error from the number of sources consideredin each luminosity or redshift bin. In addition to the Pois-son error, each measurement is subject to additional errorowing to uncertainty in the equivalent width measurements.We thus conduct Monte Carlo simulations, randomly vary-ing the equivalent width of each galaxy assuming a normaldistribution with mean and standard deviation correspond-ing to the measured WLyα,0 and σW . For each realization,we compute the luminosity-dependent Lyα fraction. Con-sidering all the trials, we compute the standard deviationin the xLyα distribution. We then combine this error termin quadrature with the random error derived above. In do-ing these simulations, we also consider whether equivalent

c© 2010 RAS, MNRAS 000, 1–23

Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 13

width error may artifically scatter a net flux of feeble galax-ies above our equivalent width threshold, introducing theobserved trend. However the simulations demonstrate thatthis is not the case, as the trend is readily apparent in eachrealisation.

In constructing the Lyα fraction, we must also recog-nize that the wavelength coverage of some spectra is suchthat Lyα would not be recovered across the full redshiftrange over which those dropouts might be selected. Thisapplies mostly to FORS2 spectra of B-drops which can onlydetect Lyα for sources with z ∼

> 3.9. Given that B-dropsare expected to span the redshift range 3.5 ∼

< z ∼< 4.5, this

suggests that a large number of B-drops would not be re-covered in the FORS2 spectra even if they showed Lyα inemission. We therefore limit our study of B-drops to thosewith spectra that allow Lyα to be detected over the entireredshift range expected. This is a particular advantage ofthe DEIMOS component of our survey where the numer-ous B-drops taken with the 600 line mm−1 grating are fullysampled.

Following this procedure, we compute the luminosity-dependence of our entire spectroscopic sample. We find thatxLyα is considerably larger in low luminosity galaxies (Figure13), increasing from 10-20% for luminous sources (MUV ≃−21) to 60-70% for feeble galaxies (MUV ≃ −18−19). A sim-ilar trend is seen if we adopt larger equivalent width thresh-olds. The Lyα fraction rises slowly with decreasing luminos-ity over −22.0 ∼

< MUV ∼< −20.5 but then begins to increase

more rapidly at lower luminosities( −20.5 ∼< MUV ∼

< −18.5).We thus fit first order polynomials over each of these lumi-nosity ranges, finding xLyα = 1.09 + 0.047 MUV at the lu-minous end and xLyα = 5.46 + 0.26 MUV for the lower lumi-nosity sources. Given that the Lyα fraction increases slowlyfor luminous sources, it is perhaps no surprise that previousstudies which were limited to this luminosity regime foundonly moderate evidence for luminosty dependent trends(Nilsson et al. 2009; Kornei et al. 2009); it is only by prob-ing lower luminosity galaxies that we start to see a cleartrend in the prevalence of Lyα with luminosity.

Intriguingly, the “break” in the luminosity-dependenceof the Lyα fraction in Figure 13 occurs at very similar lumi-nosities to the characteristic UV luminosity of the rest-frameUV 4 < z < 6 luminosity function (e.g., Bouwens et al.2007). At luminosities greater than L⋆UV , the Lyα fractionis low and increases slowly, but below this luminosity, theLyα fraction increases to much larger values. While perhapscoincidence, this may suggest that whatever process modu-lates the knee of the luminosity function at z > 4 may playa role in the escape of Lyα photons.

In order to put these results in context, it is interest-ing to estimate the escape fraction of Lyα photons that isimplied by these large equivalent widths. In particular, weare interested in the Lyα escape fraction that is implied bythe WLyα,0 ≃ 50 Å threshold we have adopted. Assuminga Salpeter IMF with Mupper=120 M⊙, case B recombina-tion, constant star formation, and metallicity ranging be-tween Z=1/20 Z⊙ and Z⊙, Lyα equivalent widths can beas high as ≃ 200 − 300 Å in the first few Myr of the starformation episode, asymptoting to ≃ 100 Å after 10 Myr(Malhotra & Rhoads 2002; Schaerer 2003). Hence our equiv-alent width threshold corresponds to a Lyα escape fractionof 15-50%. Of course, this assumes that all ionising photons

are absorbed; if there is significant Lyman continuum leak-age, then the predicted equivalent widths would decrease,increasing the inferred Lyα escape fraction. Alternatively, ifdust is confined to cold neutral clouds, then the maximumLyα equivalent widths may be larger than quoted above(Neufeld 1991; Hansen & Oh 2006; Finkelstein et al. 2008),decreasing the implied Lyα escape fraction.

These results provide clear evidence that Lyα emissionbecomes continuously more prevalent among lower luminos-ity star forming galaxies. Indeed, it appears that the major-ity of feeble (MUV < −19) sources are strong Lyα emitters.These results appear to indicate that the escape fraction ofLyα photons (relative to that of far-UV continuum photons)is strongly luminosity-dependent and at very low continuumluminosities may commonly exceed the 5% robustly derived(at z ≃ 2) via Lyα and Hα surveys (Hayes et al. 2010).In the following section, we examine whether similar trendsare seen with redshift, while in §4.3 we examine the physi-cal mechanism is that are likely to be governing the escapefraction of Lyα photons at z ∼

> 3.

4.2 Variation in the Lyα fraction in the redshiftrange 3 ∼

< z ∼< 6

We now examine the redshift evolution of the prevalence ofLyα emitters in the Lyman break galaxy population over3 < z < 6. Since the IGM appears to be highly ionisedover this redshift range, this measurement provides the op-portunity to understand the extent to which factors otherthan IGM attenuation affect the Lyα fraction. By calibrat-ing these effects over this redshift interval, we can more ac-curately detect the signal of reionisation on the Lyα fraction.

We consider luminosity-dependent samples in two sep-arate redshift bins, 3.0 < z < 4.5 and 4.5 < z < 6.0 (Fig-ure 13). Sources without spectroscopic redshifts are placedinto one bin or the other based on their photometric red-shift (see Stark et al. 2009 for discussion of photometric red-shifts). In each UV luminosity bin, the fraction xLyα in-creases with redshift. The two bins with the lowest errorand incompleteness (MUV ≃ −21 and -20) show increasesof 60% and 40%, respectively. Our equivalent width thresh-old and redshift binning ensures that this result is not biasedby redshift-dependent incompleteness. To determine the dif-ferential growth, we compute the average change in Lyαfraction, ∆xLyα, across all luminosity bins (weighted by theinverse variance of each bin) and compute ∆z using the me-dian redshift in each of the two bins. With this approach, wefind that the Lyα fraction increases with redshift followingdxLyα/dz ≃ 0.05. As we mentioned in §3.4, low-z contami-nation appears to decrease very slightly with redshift. How-ever, we find that this effect introduces such small changes inthe Lyα fractions (∼

< 1%) in each redshift bin, such that theweighted Lyα fraction redshift evolution remains as quotedabove. Hence Lyα fractions grow by nearly ∆xLyα ≃ 0.1 atfixed MUV between z ≃ 4 and z ≃ 6.

We emphasize that this trend is not driven by biasesassociated with LBG selection. It is well-established thatthe presence of strong Lyα can affect the broadband coloursused for dropout selection (Stanway et al. 2007, 2008). Lineemission can either boost the dropout color (if the redshiftis at the high end of the distribution with Lyα in the red-der filter) or it can dilute the color (if the redshift is at

c© 2010 RAS, MNRAS 000, 1–23

14 Stark et al.

−22 −21 −20 −19 −18MUV

0.0

0.2

0.4

0.6

0.8

1.0

XLy

α

3.0 < z < 6.2WLyα,0 > 50 Å

-23 -22 -21 -20 -19 -18MUV

0.0

0.2

0.4

0.6

XL

yα

3.5 < z < 4.54.5 < z < 6.0

Figure 13. (Left:) Fraction of spectroscopic dropout sample showing strong Lyα emission (WLyα,0 > 50 Å) as a function of UVluminosity. The dashed lines corresponds to first order polynomial fits to the Lyα fractions in the range −22.0

∼< MUV ∼

< −20.5 and

−20.0∼< MUV ∼

< −18.5. (Right:) Fraction of spectroscopic dropout sample showing strong Lyα emission (WLyα > 50 Å) as a functionof UV luminosity for samples with 3.5 < z < 4.5 (blue circles) and 4.5 < z < 6.0 (red circles). Vertical lines correspond to ≃ 90%completeness limits for B and V-drop samples. For the i′-drops, the completeness limits are ≃ 0.7 mags brighter. Any incompletenesswould serve to increase the Lyα fractions further.

the low end with Lyα in the bluer filter). In principle, thiscould lead to Lyα being preferentially recovered at higherredshifts. But we minimize these biases by simultaneouslytargeting the B, V, and i′-dropout population. For example,sources with very strong Lyα emission at 5.5 < z < 5.7 (suchthat the line falls in the i′775-band) may be scattered out ofthe i′-drop selection but would instead appear in V-drop se-lections. Thus, in this case, by conducting spectroscopy ofV-drops, we can account for this diffusion of Lyα sources.Similarly, our B-drop sample will contain the small num-ber of sources at 4.5 < z < 4.8 with very high strong Lyαcontaminating the V606-band filter (which would otherwisehave little flux). While we don’t target U-drops, Lyα emis-sion from galaxies at 3.5 < z < 3.8 does not contaminatethe B435-band filter, so our B-drop sample should not haveredshift-dependent biases.

The redshift dependence of xLyα is affected not onlyby evolution in the internal properties of galaxies but alsoby the increase in the density of the IGM with redshift.At z ≃ 6, the IGM provides a significantly greater opticaldepth to Lyα photons than that at z ≃ 4, resulting in a sec-ond order affect on the Lyα fraction. In the absence of IGMdensity evolution, we would thus expect the redshift evolu-tion of the Lyα fraction to be slightly greater than derivedabove. We can attempt to estimate the variation in xLyαthat is intrinsic to galaxy evolution (e.g. dust, ISM kinemat-ics) by subtracting the differential evolution expected fromchanges in IGM density. Deconvolving the effects of the IGMon Lyα radiative transfer requires careful modeling of the lo-cal density, velocity, and ionisation field (e.g. Santos 2004;Dijkstra et al. 2007a,b; Zheng et al. 2009). We delay sucha treatment to subsequent works, and instead we follow avery simple approach adopted in Ouchi et al. (2008) whichyields a very rough estimate on the intrinsic redshift evo-lution of the Lyα fraction. We compute the percentage ofphotons absorbed by the IGM assuming that the blue side

of the Lyα line is attenuated by exp[τα(z)], where τα(z) isthe optical depth for Lyα photons as computed in Meiksin(2006). With this approach, we find that the IGM absorbs28, 42, and 49% of the Lyα line flux at z ≃ 4, 5, and 6.In a more sophisticated and realistic treatment, the den-sity and ionising background surrounding Lyα emitters islikely to be greater than the mean, and infalling gas wouldalso erase a fraction of the Lyα line redward of rest-frame1216 Å; the combination of these effects can cause the red-shift evolution in the transmission of Lyα photons through areionised IGM to be considerably different than implied byour model above (e.g., Santos 2004; Dijkstra et al. 2007b).We will model this effect in greater detail in the future. Forthe sake of clarity, here we define the intrinsic WLyα,0,int asthe rest-frame equivalent width that would have been ob-served if not for IGM attenuation, where the IGM absorp-tion is taken to follow the numbers derived above. Adoptinga fixed intrinsic WLyα,0,int, we derive Lyα fractions as aboveand find that the differential redshift evolution in xLyα in-creases to dxLyα/dz ≃ 0.12. In the next section, we attemptto understand the factors likely to be creating this redshifttrend and the luminosity trend presented in the previoussection.

4.3 The factors governing the Lyα escape fraction

Earlier we demonstrated that prevalence of strong Lyα emis-sion increases toward lower luminosities and higher redshifts.Here we discuss the factors that are likely governing the ob-served trends prior to exploring the use of higher redshiftgalaxies and their line emission as a probe of cosmic reion-isation. In §4.3.1, we examine whether trends in dust ob-scuration could potentially drive the observed Lyα fractionrelations. In §4.3.2 and §4.3.3, we discuss how the geomet-ric distribution and kinematics of the surrounding ISM mayimpact the Lyα fraction trends we observe and discuss fu-

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Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 15

−2.5

−2.0

−1.5

−1.0

−0.5

< β

>

B−drops with WLyα,0>50 ÅB−drops with WLyα,0 50 Å) are denoted by red triangles, while theaverage UV slopes rest of the B-drop sample is denoted by pur-ple circles. For reference, we overplot the average UV slope as afunction of MUV for the entire photometric sample of B-drops inGOODS-N and GOODS-S from Stark et al. (2009) as filled yel-low squares. The average UV slope from B-drops in the HubbleUDF is shown as open blue squares. Typical uncertainties in theUV slopes of individual galaxies are shown as error bars on thebottom of the plot; uncertainties in the mean take both this errorand the number of sources in each bin into account.

ture spectroscopic work in progress to provide further insightinto the ISM of feeble high-z galaxies. Finally in §4.3.4 and§4.3.5, we close our discussion with a variety of factors possi-bly affecting Lyα that are more difficult to directly constrainobservationally.

4.3.1 Impact of dust extinction

Previous observations have demonstrated that, among lu-minous LBGs, those objects showing Lyα in emission tendto display bluer UV continuum slopes than those with Lyαabsorption (Shapley et al. 2001, 2003; Vanzella et al. 2009;Pentericci et al. 2009; Kornei et al. 2009). While the pres-ence of dust may enhance Lyα relative to the continuum(Neufeld 1991; Hansen & Oh 2006; Finkelstein et al. 2008),the results in Figure 14 suggest that most often, the presenceof significant quantities of dust generally leads to increasedabsorption of Lyα photons relative to the continuum.

Here, we examine whether similar trends are seen atlower luminosities. In order not to bias the UV colors, wedetermine the slopes using filters that are not contaminatedwith Lyα emission or IGM absorption. Obtaining accurateUV slopes requires very accurate color measurements, thuswe choose to focus on the B-drops, as the UV colors can bedetermined entirely from deep i′ and z-band imaging withACS. We translate the UV colors into UV slopes using therelation presented in Bouwens et al. (2009b): β=5.30(i775 −z850) - 2.04. We have verified that this relation holds for avariety of star formation histories and age combinations thatare appropriate for the z ≃ 4− 6 population.

Given the relationship between UV color and β, it is

important to note that even a small photometric colour er-ror translates into substantial uncertainty in the derived UVslope. We thus estimate the luminosity limit at which theGOODS data become unreliable for estimating UV slopesby comparing the average UV slopes of B-drops in GOODSwith UV slope measurements from higher S/N data in theUDF, using the photometric catalogs of Coe et al. (2006)for our UDF sample. These results indicate that UV slopesmeasured from the GOODS dataset differ significantly fromthose determined from the high S/N UDF sample for B-drops with luminosities fainter than MUV ≃ −20.5. There-fore, we cannot derive robust UV slopes for sources in ourGOODS spectroscopic sample that are fainter than thislimit.

Concentrating on the brighter subset of objects, we ex-amine the UV slopes of our B-drop spectroscopic sample asa function of UV luminosity (Figure 14). The data show thatgalaxies with strong Lyα in emission (WLyα,0 > 50 Å) arebluer than those systems without strong Lyα emission, andare generally fit with β = −2.0 across the entire luminosityrange covered. Following Meurer et al. (1999), this value isconsistent with very little dust obscuration (A1600 ≃ 0.5),assuming a Calzetti extinction curve and normal stellar pop-ulations. The UV slopes of the overall population of B-drops are significantly redder than the Lyα emitters, butwhen viewed as a function of luminosity, they grow steadilybluer toward low luminosities, ranging from β ≃ −1.5 (atMUV ≃ −21.5) to β ≃ −1.7 (at MUV ≃ −20.5). The cor-relation between UV slope and emerging UV luminosity atthese redshifts was first demonstrated in a large photomet-ric sample in Bouwens et al. (2009b); here we confirm thistrend with a spectroscopic sample of dropouts. As arguedin Bouwens et al. (2009b), the trend most likely arises as aresult of lower luminosity galaxies having less dust obscura-tion. Given that strong Lyα emitters tend to arise in galaxieswith little dust extinction, it is perhaps no surprise that wesee a larger Lyα fraction in low luminosity galaxies. Similarreasoning can also explain the observed redshift-dependenceof the Lyα fraction, as UV slopes are found to grow steadilybluer with redshift over 3

∼< z

∼< 6 (Bouwens et al. 2009b).

If we attribute the luminosity-dependence of the Lyαfraction to the variation in dust obscuration, we can de-rive a relationship between mean UV slope and Lyα frac-tion. From Figure 14, we find that dβ/dMUV ≃ −0.23 over−21.5 < MUV < −20.0. This is similar, but slightly steeper,than the value derived in Bouwens et al. (2009b). Over thissame luminosity range, we derive dxLyα/dMUV = 0.29. As-suming that dust extinction drives the evolution in the Lyαfraction, we derive dxLyα/dβ = −1.2. While this result wasderived from the luminosity-dependence of xLyα, it shouldalso apply to the redshift evolution if dust obscuration wereto dominate the redshift-dependent trends. Measurements ofsimilarly luminous z ≃ 6 LBGs (Bouwens et al. 2009b) sug-gest that the average UV slopes grow bluer by ∆β ≃ −0.6from z ≃ 4 to z ≃ 6. If dust evolution dominates the redshift-dependence of the Lyα fraction and the evolution in UVslopes, the above relationship suggests that xLyα should in-crease by ∆xLyα = 0.84. The fact that the actual redshiftevolution is significantly less rapid (∆xLyα = 0.24 afterroughly accounting for IGM absorption) can be explainedby several factors. For example, it is likely that the lumi-nosity dependence of xLyα is driven by more than just dust

c© 2010 RAS, MNRAS 000, 1–23

16 Stark et al.

obscuration (see the following sections for a discussion). Ad-ditionally as UV slopes grow bluer than β = −2.0, the varia-tion in the UV slope is possibly driven by factors other thandust obscuration (e.g., Stanway et al. 2005; Bouwens et al.2010a). Secondly, given that xLyα cannot be larger than 1.0,the differential growth must slow down as xLyα increases;hence any extrapolation of the xLyα relations below our com-pleteness limits is highly uncertain. Finally, as emphasizedin §4.2, our simple treatment of IGM absorption may in-correctly estimate the evolution in the Lyα fraction that isintrinsic to galaxy processes.

In summary, these results indicate that the variationin dust extinction with luminosity and redshift likely playsan important role in governing the observed evolution andluminosity-dependence in the Lyα fractions. But, not sur-prisingly, it seems likely that additional factors play a rolein governing xLyα as well. We discuss these in more detailbelow.

4.3.2 The hydrogen covering fraction

After Lyα photons escape the H II regions where they werecreated, they must diffuse through neutral gas and dustat larger radii. This could include gas that is participat-ing in outflows surrounding the galaxy in addition to gasthat is being accreted onto the galaxies. Rest-UV spectra ofhigh-redshift star-forming galaxies reveal low-ionisation ab-sorption lines that are generally blue-shifted by ∆v ≃ −200km s−1 (Shapley et al. 2003; Steidel et al. 2010) relative tothe centre of rest, indicating that outflowing neutral gasis nearly always present, while accreting gas appears lessprevalent. The geometrical distribution and kinematics ofthis outflowing material plays a crucial role in governing theescape of Lyα photons. This is clearly evidenced by the factthat Lyα photons are typically observed to be redshiftedby ≃ 400 − 500 km s−1 with respect to the centre of rest(Steidel et al. 2010). This result implies that the majorityof Lyα photons to escape through the absorbing materialalong the line of sight are those that achieve a sufficient (red-shifted) velocity such that they can travel through the inter-vening material without resonantly scattering. This is mosteasily accomplished in a model in which the Lyα photonsthat are observed are those that have been “backscattered”off of the ouflowing material on the far side of the galaxy(e.g., Shapley et al. 2003; Steidel et al. 2010). Hence, it islikely that the increased prevalence of Lyα emitters amonglow luminosity galaxies tells us something about the distri-bution and/or kinematics of the ISM of feeble sources. Inthis section, we discuss the relationship of the ISM distribu-tion, dust obscuration, and Lyα emission in luminous LBGsas found in previous work, and then consider whether a sim-ilar picture is likely to hold for low luminosity galaxies; inthe following section, we focus on the kinematics of the ISM.

Even for luminous sources, observational constraints onthe distribution of the blueshifted neutral absorbing gas inthe immediate vicinity of high redshift galaxies are lim-ited. The spectroscopic study of z ≃ 3 LBGs conducted inShapley et al. (2003) revealed a strong correlation betweenthe equivalent width of low-ionisation interstellar absorptionlines (WLIS) and that of Lyα, in the sense that the strongestLyα emitters tend to have the least absorption by the low-ionisation interstellar medium. As the absorption lines are

highly saturated, Shapley et al. (2003) note that the trendin WLIS is due either to variations in the velocity width orthe covering fraction of absorbing gas, with the latter arguedto be the dominant factor, such that sources showing strongLyα emission, on average, have the patchiest distribution ofabsorbing gas covering the continuum source (at least alongthe line of sight). Galaxies also show a strong correlationbetween WLIS and E(B-V), which Shapley et al. (2003) ar-gue implies a significant fraction of the dust which reddensthe stellar continuum (and absorbs Lyα photons) is locatedwithin the outflowing neutral gas. As noted in Steidel et al.(2010), from a theoretical standpoint, the exact effect of anon-uniform covering fraction on the observed Lyα flux isnot obvious. But regardless, these observations thus suggesta scenario in which strong Lyα emission is generally coupledwith low dust extinction and a low hydrogen covering frac-tion, a picture supported by recent observations of strongly-lensed LBGs at z ≃ 3 (Quider et al. 2009, 2010) for whichdirect measures of the covering fractions of various ions areavailable.

If similar trends are present in low luminosity galaxies,then the fact that Lyα is much more common in feeble galax-ies may imply that these sources typically have lower cov-ering fractions of absorbing gas than more luminous LBGs.Addressing whether this is indeed the case requires deepspectroscopy of UV-faint systems, and thus is perhaps onlyfeasible via studies of gravitationally-lensed galaxies. Someprogress can be made with current field samples however.In particular, we can determine whether the coupling be-tween strong Lyα emitters and weak ISM absorption is alsopresent for feeble galaxies by creating composite spectra ofLyα emitters binned by MUV. We will present the resultsof this analysis in a subsequent paper (Stark et al. 2010,in preparation). Some indication that the correlation is inplace at low intrinsic luminosities is already apparent fromthe i′-drop composite spectra presented in Vanzella et al.(2009). As all the i′-drops in their sample are UV faint(< MUV >≃ −20), this spectrum provides insight into theproperties of feeble sources. Owing to the faintness of the i′-drops, the composite is dominated by strong Lyα emittersand shows very weak interstellar absorption lines. HigherS/N spectra are required to ensure that the absorption linesare saturated and to quantify the absorption line equivalentwidths.

Finally, while admittedly speculative, we note brieflythat if a low hydrogen covering fraction is more commonfor low luminosity galaxies, it may also enable Lyman con-tinuum photons to more easily escape from feeble systems.Naively, this statement seems contradictory since the pres-ence of Lyα photons stems from the absorption of ionisingphotons. However high-redshift galaxies are clearly not per-fect H II regions. In practice, a significant fraction of ionisingphotons are absorbed in the ionised regions surrounding themassive stars, leading to the production of Lyα photons.Both Lyα photons as well as any escaping ionising photonswill then approach the surrounding neutral ISM, much ofwhich is likely moving at great speeds with respect to thestars. Clearly, those systems with significant holes in theirsurrounding distribution of hydrogen will leak a larger frac-tion of ionising radiation. Indeed, the combination of strongLyα and significant ionising photon escape fractions are seenin observations at z ≃ 2 (Shapley et al. 2006). Intriguingly,

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Cosmic Reionisation and the Lyα Emitting Fraction at High Redshift 17

recent results reveal a possible trend toward greater Lymancontinuum leakage in sources with low UV continuum lu-minosities (Steidel et al. 2010, in preparation). While muchwork is still required to verify the luminosity-dependence inthe hydrogen covering fraction and the Lyman continuum es-cape fraction, these results strongly motivate detailed studyof the physical properties of low luminosity galaxies.

4.3.3 Kinematics of ISM

As we discussed above, Lyα is affected not only by the geom-etry and column density of the dust and hydrogen aroundit but also by the velocity distribution of the surroundingneutral HI. Recently, Steidel et al. (2010) has compared thekinematics of the absorbing gas (extracted from the proper-ties of rest-UV absorption lines) and the properties of Lyαas a function of total baryon mass for a sam