On the redshift-evolution of the Lyman-alpha escape fraction and the dust content of galaxies

0.39 MB·English

by  Matthew Hayes

Accepted by the Astrophysical Journal
PreprinttypesetusingLATEXstyleemulateapjv.2/16/10
ON THE REDSHIFT-EVOLUTION OF THE LYMAN-ALPHA ESCAPE FRACTION AND THE DUST
CONTENT OF GALAXIES
Matthew Hayes1, Daniel Schaerer1,2, Go¨ran O¨stlin3, J. Miguel Mas-Hesse4, Hakim Atek5, Daniel Kunth6
Accepted by the Astrophysical Journal
ABSTRACT
The Lyα emission line has been proven a powerful tool by which to study evolving galaxies at the
1 highest redshifts. However, in order to use Lyα as a physical probe of galaxies, it becomes vital to
1 know the Lyα escape fraction (fLyα). Unfortunately, due to the resonant nature of Lyα, fLyα may
esc esc
0 vary unpredictably and requires empirical measurement. Here we compile Lyα luminosity functions
2 between redshift z=0 and 8 and, combined with Hα and ultraviolet data, assess how fLyα evolves
esc
n withredshift. We finda strongupwardsevolutioninfeLsycα overthe rangez =0.3−6,whichis well-fit
a by the power-lawfLyα∝(1+z)ξ with ξ =(2.57+0.19). This predicts that fLyα should reach unity at
esc −0.12 esc
J z = 11.1. By comparing fLyα and E in individual galaxies we derive an empirical relationship
esc B−V
5 between fLyα and E , which includes resonance scattering and can explain the redshift evolution
esc B−V
of fLyα between z = 0 and 6 purely as a function of the evolution in the dust content of galaxies.
] esc
O Beyondz ≈6.5, fLyα dropsmoresubstantially;aneffectattributedtoeitherionizingphotonleakage,
esc
or an increase in the neutral gas fraction of the intergalactic medium. While distinguishing between
C
those two scenarios may be extremely challenging, by framing the problem this way we remove the
.
h uncertainty of the halo mass from Lyα-based tests of reionization. We finally derive a new method
p by which to estimate the dust content of galaxies based purely upon the observed Lyα and UV LFs.
- These data are characterizedby an exponential with an e-folding redshift of ≈3.5.
o
Subject headings: Galaxies: evolution — Galaxies: high-redshift — Galaxies: luminosity function,
r
t mass function — Galaxies: star formation— dark ages, reionization, first stars
s
a
[
1. INTRODUCTION oftheLyαlinemeansitsradiationtransportbecomesan

2 involvedanddetailedproblem(Osterbrock1962;Adams
SurveystargetingtheLyman-alphaemissionline(Lyα)
v 1972; Harrington 1973; Neufeld 1990; Ahn et al. 2003;
show unique profitability for examining the formation
6 Verhamme et al. 2006; Tasitsiomi 2006; Laursen et al.
and evolution of the galaxy population between redshift
9 2009). This further implies that the escaping fraction of
z ≈ 2 and & 7. Lyα has been exploited by many teams
47 and the combined catalogues would currently include photons (feLsycα) may not be assumed, is liable to evolve
over two thousand entries (e.g. Venemans et al. 2002; strongly with an evolving galaxy population, and must
.
0 Hu et al. 2004; van Breukelen et al. 2005; Wang et al. be measured empirically. Pursuing this line of inquiry,
1 2005; Shimasaku et al. 2006; Gronwall et al. 2007; theevolutionoffeLsycα canthereforeprovideuswithinde-
0 Ouchi et al.2008;Nilsson et al.2009;Guaita et al.2010; pendentestimatesofhowvariouspropertiesofthegalaxy
1 Cassata et al. 2010; Hayes et al. 2010a). Wherever such population evolve over cosmic time.
v: large samples are available, the temptation is strong to Since Lyα photons scatter in neutral hydrogen (Hi)
i use their statistical power to examine as many physical until they either escape or are absorbed by dust grains,
X properties of the galaxy population as possible. This, most fundamentally the radiation transport depends
r however, requires that the numbers one has at hand are upon the Hi content, its geometry and kinematics, and
a in some way a physical reflection of those underlying thedustcontentanddistribution. Regrettably,withcur-
properties; to first order the luminosity (and/or equiv- rentobservationalfacilities,theonlyoneofthesequanti-
alent width for emission lines) must be related to its tiesthatcaneasilybeestimatedforlargesamplesofhigh-
intrinsic value. For surveys that target the restframe redshift galaxies is the dust attenuation, which is typi-
ultravioletcontinuum(UV)thisissimplyamatterofap- cally derived from the stellar continuum. Consequently
plying a dust correction. However, the resonant nature theamalgamatedeffectsoftheremainingquantities,and
howtheyaffectfLyα,canonlybeassessedonastatistical
esc
[email protected] basis.
1ObservatoryofGeneva,UniversityofGeneva,51chemindes Lyαsurveyshavebeenfruitfuloverthelastdecade,but
Maillettes,1290Versoix,Switzerland it is only very recently that robust fLyα measurements
2Laboratoired’AstrophysiquedeToulouse-Tarbes,Universit´e esc
have been made on statistically meaningful samples
deToulouse,CNRS,14AvenueE.Belin,31400Toulouse,France
3Oskar Klein Centre, Department of Astronomy, AlbaNova (Verhamme et al. 2008; Atek et al. 2009; Kornei et al.
UniversityCenter,StockholmUniversity,10691Stockholm,Swe- 2010; Hayes et al. 2010a). However at the current junc-
den ture,allofthesestudiesestimatefLyα bydifferentmeth-
4Centro de Astrobiolog´ıa (CSIC-INTA), PO Box 78, 28691 esc
VillanuevadelaCan˜ada,Madrid,Spain ods, andare derivedamong samples compiled atvarious
5SpitzerScienceCenter,Caltech, Pasadena,CA91125,USA redshifts and filtered through differing selection func-
6Institut d’Astrophysique de Paris (IAP), 98 bis boulevard tions. Thus synthesis of the results remains somewhat
Arago,75014Paris,France
2 Matthew Hayes et al.
difficult. Furthermore, there is no self-consistent study whereE mustbethe dustattenuationcomputedfor
B−V
inthecurrentliteratureofhowfLyαevolveswithredshift the Hα emitting sample, and k the extinction coeffi-
esc 6563
and it is this point that we take the first steps towards cientatthe wavelengthofHα. SuperscriptsIntandObs
rectifying with the current article. We begin by com- refer to the intrinsic and observed quantities.
piling various Lyα, Hα, and UV datasets in § 2, which At z & 2.3 we are unable to obtain Hα LFs in or-
we use to estimate the redshift evolution of fLyα. We der to use line ratios to estimate fLyα and instead the
esc esc
discuss the general trends and draw comparisons with estimate is derived from the UV continuum. This is a
other observational and theoretical methods in § 3. In less elegant method since the conversion between UV
§ 4 we investigate the effect of the one quantity that is and Lyα requires the assumption of a metallicity, initial
relatively easy to measure – the dust content – and dis- mass function (IMF), and evolutionary stage. However,
cusshowitaffectsfLyα. In§5wediscussthetrendswith in light of the fact that higher-redshift Hα studies will
esc
redshift in more detail and synthesize information from remain impossible until the arrival of the James Webb
§ 3 and § 4 in order to make more detailed inferences Space Telescope, this is the only way to proceed. It is
about the evolution of the properties of the interstel- fortunatethatthereisnoevidencethatIMFsshoulddif-
lar medium (ISM) of galaxies, the intergalactic medium ferbetweenLyα-andUVselectedpopulations,although
(IGM), and the overall dust content. In § 6 we present metallicitieshavebeenshowntobearound0.2dexlower
a final summary. All data are scaled to a cosmology of (e.g.Cowie et al.2010)whichtranslatesintoadifference
(H ,Ω ,Ω )=(70 km s−1 Mpc−1,0.3,0.7). of.20%inthe intrinsicLyα/UVratio(Leitherer et al.
0 M Λ
1999). For “normal”metallicities andIMFs, andassum-
ing that on average star-formation is ongoing at equi-
2. METHOD:THELyαESCAPEFRACTION librium, this method is the same as taking the ratio of
MEASUREMENTS Lyα/UV star-formation rate densities (ρ˙⋆):
2.1. Escape fraction calculations ρ˙Obs ρ˙Obs
asWaefunnocwtiopnroocfereeddsthoifcto,mbuptilefirvsatrwioeuspreessteimntattheseofofrfmeLsayclα- feLsycα(z >2.3)= ⋆ρ˙,I⋆Lnytα = 100.4EB−⋆V,kLUyVα·ρ˙O⋆,bUsV, (3)
ism. WecontinuewiththeHayes et al.(2010a)definition wherenowE mustbetheextinctionseenbytheUV-
B−V
of feLsycα: the sample-averaged,“volumetric” escape frac- selected population and kUV is the extinction coefficient
tion. This quantity is defined as the ratio of observedto in the UV.
intrinsic Lyα luminosity densities (ρ ), derived by inte- The UV is of course not the only wavelength we can
L
grationoverluminosityfunctions(LF),asinEquation1: use for this experiment, but we choose to work exclu-
sivelywithUVLFssincethey(a)aresoabundantinthe
ρObs ∞ Φ(L)Obs ·L·dL literature,(b) have reasonablywell-understoodselection
fLyα = L,Lyα = Llo Lyα (1)
esc ρILn,tLyα RL∞loΦ(L)ILnytα·L·dL fruednschtiioftn.s,Waendad(ocp)tspUaVnmaneaaspupreromperniatstealyt rlaerdgsehirftasngmeoisnt
whereΦ(L)arethestandardRluminosityfunctions7. Thus appropriatetoourcompiledLyαdataanddustattenua-
tionsderivedfromthesesamplesthemselves. We further
fLyαisnotsimplyare-scalingoftheLFbyL(constantly
esc adopt the dust attenuation law of Calzetti et al. (2000),
scaling the escape fraction of all galaxies) or by Φ (the
and the SFR calibrations of Kennicutt (1998). These
dutycycle;seeNagamine et al.2008forexamplesofboth
calibrations assume a stabilized star formation episode
of these methods). Instead, since fLyα is simply defined
esc at a constant rate for longer than around 100 Myr, with
as the ratio of luminosity densities, it can be thought
aSalpeterInitialMassfunction(masslimitsbetween0.1
of as the fraction of Lyα photons that escape from the
and 100 M ), and a complete ionization efficiency (no
survey volume, regardless of whether all galaxies show ⊙
leaking and no destruction of ionizing photons by dust).
low fLyα, or whether only a fraction of galaxies are in
esc In general we assume that ‘UV’ refers to the restframe
the Lyα emitting phase with high fLyα (see arguments
esc wavelength of 1500 ˚A, where the extinction coefficient
in Tilvi et al. 2009). By definition fLyα also includes
esc computed from the relationship of Calzetti et al. (2000)
any possible effect that the IGM may have on the Lyα
is 10.3. We want to emphasize that the definition of
emissionfromgalaxies. However,itisclearthatthebulk fLyα we are using for highredshift galaxiesincludes any
oftheevolutionoffLyα withredshiftfoundinthisarticle esc
esc effect that would decrease the number of observed Lyα
can clearly not be attributed to variations of the IGM
photons with respect to the number expected from the
transmission.
starformationratederivedfromtheUVcontinuumlevel.
Where possible (i.e. z < 2.3) we make a direct com-
The leaking of ionizing photons, as we will discuss later,
parisonbetweenLyαandHα. Weapplythemostappro- would therefore imply an fLyα value below unity, even
priate dust correctionto Hα and multiply by the case B esc
if 100% of the Lyα photons effectively produced in the
recombinationratioofLyα/Hα=8.7(Brocklehurst1971)
galaxy are able to escape without being affected by res-
in order to obtain the intrinsic Lyα. I.e.
onant trapping or destruction by dust.
fLyα(z <2.3)= ρOL,bLsyα = ρOL,bLsyα , 2.2. Limits of integration
esc 8.7·ρILn,tHα 8.7·100.4EB−Vk6563 ·ρOL,bHsα The goal of this study is to determine the total, vol-
(2) umetric escape fraction of a given volume, and ideally
would include the very faintest systems. In practice this
7 LFsaretypicallyparameterizedbytheSchechter (1976)func- wouldrequireintegrationoftheLFsdowntozero,which
tion: Φ(L)·dL=φ⋆·(L/L⋆)α·exp(L/L⋆)·dL/L⋆. depending on the observational limits of a given survey
On the redshift evolution of the Lyman-alpha escape fraction 3
andtheredshift-dependentvaluesofbothL andα,may linetobesystematicallyweakened,applyingacutatthe
⋆
include large extrapolations (or may even be divergent). correspondingSFRtothatofHαortheUVwouldcause
It is vital therefore, that our study employs lower in- us to miss much of this light. The best way to proceed,
tegration limits that are: (a) self-consistent between the therefore,is to adoptthe same philosophyas above,and
populations;(b)includeasufficientlymeaningfulfraction adopt0.04Lz=3 . ByselectingtheLFofGronwall et al.
⋆,Lyα
of ρL, and (c) are not dominated by over-extrapolation (2007), we obtain a lower limit of 1.75×1041 erg s−1.
and uncertainties in the faint-end slope. ShouldfLyα=1,thiswouldcorrespondtoanSFRofjust
At z =2,3 and >4, several studies of the ρ have esc
L,UV 0.15M yr−1. However, in Hayes et al. (2010a) we de-
been published, andhere we adopt those of Reddy et al. ⊙
termined a volumetric fLyα of just 5 %, and scaling this
(2008) and Bouwens et al. (2009a), respectively. Both esc
performintegrationsdownto0.04Lz=3 andintegrateto SFRupbyafactorof20bringsitto2.9M⊙ yr−1,almost
⋆,UV perfectly into line with the UV-derived 2.6M yr−1 dis-
thesamenumericallowerlimitatallredshifts. Thelower ⊙
cussed above. Naturally, this integration from 0.04L
limitis,ofcourse,somewhatarbitrarybutisdesignedto ⋆
again includes ≈ 70% of the total luminosity density
findareasonablemediumbetweenincludingalargefrac-
(compared with integrating from zero).
tionofthetotalluminosity/SFRdensity,andpreventing
In summary, selecting the optimal integration limits
(possible over-) extrapolation by integrating to zero. In
is a non-trivial process, yet we argue that by adopting
this sense, it reflects the observational limits of the UV
theselimitsweshouldbeselectingverysimilarsamplesof
surveys.
galaxies, at least with respect to their unobscured SFR.
Admitting thatthisnumber issomewhatarbitrary,we
Thelowerlimitsare4.36×1027ergs−1 Hz−1 (UV),4.6×
adopt the same approach and use 0.04Lz=3−∞ as the
⋆ 1041 erg s−1 (Hα), and 1.75×1041 erg s−1 (Lyα). We
range for all of integrations of the UV LF. For Mz=3 =
⋆ have insured that these limits include the bulk of the
−21.0 (AB), the corresponding lower luminosity limit is
luminosity density but arenot dominatedin uncertainty
4.36×1027ergs−1Hz−1 (unobscuredSFR=0.6M yr−1).
⊙ by extrapolationin the faint end, although we have also
By adopting this limit, our results can easily be cross-
confirmed that integration to zero in fact has only very
checkedagainsttheavailableliterature. Atredshift3for minor effects on the final measurements of fLyα.
the UV LF of Reddy et al. (2008), this range incorpo- esc
rates 70% of an infinite integration under the LF. 2.3. Compilation of the samples
Deciding upon a lower limit for the Hα LF is more
All of the assembled data and the derived fLyα mea-
tricky, since it is difficult to know if we are extract- esc
surementsare summarizedin Table 1 andFigure 1. The
ing comparable samples of galaxies. There is no avail-
measurementsofE relevanttoeachoftheHαorUV
able z = 3 Hα LF, but if we adopt that compiled at B−V
measurementsarederivedfromdatainthesamepublica-
z = 2.2 in Hayes et al. (2010b), and set the lower limit
tion as the Hα or UV LF data themselves (with one ex-
to 0.04L , we obtain a luminosity of 4.6×1041 erg s−1.
⋆ ception, which is discussed in the following paragraph).
This corresponds to much higher unobscured SFR than
In this subsection we provide the necessary motivation
the lower UV limit at 3.5M yr−1. However, the UV
⊙ for our choices and comments on the various samples.
and Hα-selection functions naturally recover galaxies of
NoinstrumentationcanperformaLyα-selectedsurvey
different dust contents; if we translate these limits to
in the very nearby universe so we begin at z ≈0.2−0.4
“true”SFRs for the respectivesamples, we obtainlimits
with the Lyα LFs presented in both Deharveng et al.
of 2.6 and 6.0M yr−1 for the UV and Hα, respectively.
⊙ (2008) and Cowie et al. (2010). At these redshifts Hα
These limits differ by a factor of over 2 in SFR, but still
LFs are available, and therefore we proceed using Equa-
are not able to account for the differing populations of
tion 2. We adopt the Hα LF of Tresse & Maddox
galaxies that survive the respective selection functions –
(1998), and correct it for dust attenuation by applying
were the dustier galaxies that are selected by Hα able
the 1 magnitude of extinction that is representative of
to enter the UV-selected catalogues, the increased av-
local Hα-selected galaxies (Kennicutt 1992). For secu-
erage dust content would bring these values even closer
rity and consistency with higher redshift measurements,
together. We also argue that to some extent, the over-
we also examine the z = 0.3 UV LFs of Arnouts et al.
all shape of the UV and Hα LFs must be governed by
(2005), which we correct for dust using the method
the same physical processes and, regardless of the exact
of Meurer et al. (1999) and the β slope measured by
dust content, selecting galaxies brighter than a certain
Schiminovich et al. (2005) in the same sample, finding
fraction of the characteristic luminosity should recover
extremely consistent numbers.
objects with similar underlying SFRs. Ultimately this
Beyondtheverynearbyuniverse,nofurtherLyαinfor-
argumentisbackedupin§2.3whenwefindverysimilar
mationisavailablebeforez =2,whereweadoptourown
UV- and Hα-derived SFRs in the local universe, and by
measurementof fLyα=5.3±3.8 % (Hayes et al. 2010a),
theverysimilarSFRdensitiesderivedbythetwotracers esc
based upon Hα and individually estimated E .
in Reddy et al. (2008) and Hayes et al. (2010b). Natu- B−V
It is already at this juncture in redshift that we lose
rally by cutting both LFs at the same fraction of L , we
⋆ the possibility to use Hα, and therefore we proceed us-
recover similar fractions of the luminosity density com-
ing published UV LFs and Equation 3. Our next step is
pared with integration to zero (70 %).
to take the Lyα LF of Cassata et al. (2010, hzi = 2.5)
For Lyα, the situation is more complicated still: cut-
which we contrast against the dust-corrected ρ of
ting at the same intrinsic SFR would mean that we do L,UV
Reddy et al. (2008, hzi = 2.3). For this, and all sub-
not include Lyα emission at lower luminosities. This is
sequent points from Cassata et al. (2010), we adopt the
now not simply a matter of dust attenuation but also
values of L that are uncorrected for IGM attenuation.
includes radiation transporteffects. Since we expect the ⋆
It is reassuring that the measurements at z = 2.2 and
4 Matthew Hayes et al.
z ≈2.5(whicharebaseduponHαandUV,respectively) 2.4. Consistency (and inconsistency) between groups
giveveryconsistentnumbers. Furthermore,inaveryre-
Itshould alwaysbe borne in mind that we arecompil-
cent submission (Blanc et al. 2010) an additional Lyα
ing results from different survey teams, who may adopt
LF has been presented at 1.9 < z < 2.8, the integrated
different techniques for data reduction and photome-
Lyα luminosity density from which differs from our own
try, derivation of the luminosity functions, and incom-
result by ≈25 %.
pleteness corrections. For example, Malhotra & Rhoads
We then continue with the Reddy et al. (2008) UV
(2004) find reasonable agreement at z ≈ 5.7 between
data at hzi = 3.05, which we use to compute feLsycα for thenarrowband-selectedLyαLFsofRhoads & Malhotra
the z = 3.1 Lyα samples of Gronwall et al. (2007) and (2001); Ajiki et al. (2004) and the lensing-based sur-
Ouchi et al. (2008). vey of Santos et al. (2004). However, the z = 5.7
At z ∼4 we have available Lyα LFs from Ouchi et al. LF of Shimasaku et al. (2006), on which the study of
(2008, z = 3.7) and Cassata et al. (2010, z = 3.9), Kashikawa et al.(2006)isbased(see§5.2),findastrong
and UV LFs from Bouwens et al. (2007, hzi = 3.8). disagreementatthe faintend betweentheir ownLF and
We also use the z = 4.5 and 4.86 Lyα LF points from the compilation of Malhotra & Rhoads (2004). As com-
Dawson et al. (2007) and Shioya et al. (2009), which we mented by Shimasaku et al. (2006) the likely cause for
normalize by the dust-corrected UV point at z = 4.7 this discrepancy lies in (a) the lack of incompleteness
from Ouchi et al. (2004). corrections, which are unmentioned in any of the 2004
The next redshift to examine is the popular z ≈ 5.7 articles,(b) the differences in equivalent-widthbased se-
Lyα window. Here we adopt the UV datapointfrom the lection criteria, and (c) the large cosmic variance which
i−dropout sample of Bouwens et al. (2007, hzi = 5.9), Ouchi et al.(2008)notedcanbeoffactorsof≈2infields
and the Lyα LF Ouchi et al. (2008, hzi=5.7), which is as large as 1 square degree. Our results are sensitive to
ingoodagreementwiththoseofShimasaku et al.(2006), all of these considerations.
Ajiki et al. (2006), and Tapken et al. (2006). We also It is only now that sufficiently large samples of Lyα-
add the highest redshift LF from Cassata et al. (2010) emitting galaxies are presented in the literature for this
at hzi=5.65. study to be undertaken, and we are now fortunate that
Finallyweassembleafewz >6samples. Weadoptthe a good fraction of our data must contain internal self-
z =6.5pointfromOuchi et al.(2010,whichincludesthe consistency. For example, three of our data-points at
sample of Kashikawa et al. 2006), and the measurement (at z = 3.1, 3.7, 5.7) are drawn from a single paper
of Iye et al. (2006) at z =7.0, which has also been com- (Ouchi et al. 2008) in which the methodologies must be
piledin Ota et al.(2008). Here we adoptBouwens et al. internally consistent, and the basic trend can be seen
(2010) UV measurement at hzi=6.8 for comparison. It in these data alone. A fourth point at z = 6.6 comes
should be noted that at this redshift the dust-corrected from Ouchi et al. (2010) where similar self-consistency
and uncorrected measurements of Bouwens et al. (2010) is to be expected. In the same fashion, three further
converge. We adopt the most optimistic estimate at z = points are taken from Cassata et al. (2010) where inter-
7.7fromHibon et al.(2010),forwhichweinterpolatebe- nally the same methodology must have been adopted at
tweentheBouwens et al.(2010)z =6.8and8.2UVdat- each redshift. It is certainly encouraging that, for ex-
apoints. Hibon et al. (2010) present Schechter parame- ample at z = 5.7 the measurements of fLyα based upon
esc
ters for four Lyα LFs, based upon various assumptions Cassata et al. (2010) and Ouchi et al. (2008) are prac-
about the rate of contaminationby lower redshift galax- tically indistinguishable, despite the fact that they are
ies. By assuming all of their candidates are real (their based upon completely different methods: blind spec-
samplea)wefindaLyαescapefractionof(33.5+50.6)%. troscopy and narrowband imaging, respectively. The
−33.5
Wealsobrieflyexaminetheirsubsampleb,inwhichonly z = 2.2 and 2.5 points of Cassata et al. (2010) and
four of the seven objects are real. For all of their sub- Hayes et al. (2010a) are similarly indistinguishable, as
samples,thenumbersareinsufficienttoprovidemeaning- (and also robust against the same fundamental method-
ful errorsonthe luminosity density and by our standard ological difference of blind spectroscopy vs narrowband
errorprocedure we derivefLyα=(22.2+1707) %. Further, imaging), are the z = 3.1 points of Ouchi et al. (2008)
esc −22.2
itshouldbenotedthatintheHibon et al.(2010)sample, and Gronwall et al. (2007) (both narrowbandimaging).
the lower limits obtained on the Lyα equivalent width Anystudyofthegalaxypopulationbenefits bytarget-
are in the range 6–15˚A, with their continuum-detected ing spatially disconnected, independent pointings in or-
object showing W =13˚A. Thus, at an acceptable con- dertobeatdowncosmicvariance. Byadoptingthestud-
Lyα ies of various authors pointed all over the extra-galactic
fidence limit, none of their seven objects would actually
sky, this study is able to benefit from the inclusion of a
survive the canonical W cut of 20˚A that is typically
Lyα large number of independent fields.
employedinnarrowbandsurveys. Includingthesedatais
thereforenotstraightforward,but inordertotreatthem
asconsistentlyaspossiblewiththe lowerredshiftpoints, 3. GENERALRESULTS
we have to set the z ≈ 7.7 Lyα escape fraction to zero,
3.1. The evolution of fLyα
but adopted a characteristic error of 50.6 % as derived esc
from their most optimistic sample. We note that this Figure1revealsageneralandsignificanttrendforfLyα
esc
limit is likely extremely high. to increase with increasing redshift. Beginning in the
All of our measurements of fLyα are listed in Table 1 verylocaluniverseweseefLyα∼0.01orlowerfornearby
esc esc
and shown graphically in Figure 1, which is the main star-formingobjects. Thisincreasestoaround≈5−10%
result of this paper. by redshift of ≈ 3 − 4, and further to ≈ 30 − 40 %
by redshift 6. In order to quantify this trend we fit
On the redshift evolution of the Lyman-alpha escape fraction 5
TABLE 1
Lyman-alphaescape fractionswith redshift
Lyαquantities Intrinsicquantities Derivedresults
z Ref ρ˙⋆ z Ref EB−V ρ˙⋆ feLsycα[%] Comment
(1) (2) (3) (4) (5) (6) (7) (8) (9)
EstimatesbaseduponLyαandHαluminosityfunctions..........
0.2–0.35 De08 (3.79±1.69)×10−4 0.2–0.35 TM98 0.33 (0.0303±0.017) (1.25±0.90) 1magatHα
0.2–0.4 Co10 (8.33±2.60)×10−5 0.2–0.35 TM98 0.33 (0.0303±0.017) (0.275±0.18) 1magatHα
2.2 Ha10 ··· 2.2 Ha10 0.22 ··· (5.3±3.8) MultidimensionalM.C.
EstimatesbaseduponLyαandUVluminosityfunctions..........
2.5 Ca10 (7.08±0.81)×10−3 h2.3i Re08 0.15 (0.201±0.022) (3.51±0.56)
3.1 Gr07 (8.50±5.32)×10−3 h3.05i Re08 0.14 (0.116±0.017) (7.33±4.71)
3.1 Ou08 (5.54±2.91)×10−3 h3.05i Re08 0.14 (0.116±0.017) (4.78±2.61)
3.7 Ou08 (4.78±1.14)×10−3 h3.8i Bo09 0.14 (0.089±0.011) (5.36±1.43)
3.8 Ca10 (8.71±1.00)×10−3 h3.8i Bo09 0.14 (0.089±0.011) (9.77±1.64)
4.5 Da07 (3.22±1.25)×10−3 h4.7i Ou04 0.075 (0.025±0.011) (12.6±7.17)
4.86 Sh09 (2.35±3.17)×10−3 h4.7i Ou04 0.075 (0.025±0.011) (9.24±13.0)
5.65 Ca10 (8.53±3.44)×10−3 h5.9i Bo09 0.029 (0.022±0.005) (38.1±17.2)
5.7 Ou08 (6.76±4.77)×10−3 h5.9i Bo09 0.029 (0.022±0.005) (30.2±22.2)
6.6 Ou10 (4.73±1.24)×10−3 6.5 Bo07 0.012 (0.016±0.008) (30.0±17.8) UVInterpolated
7.0 Iy06 (1.07±1.16)×10−3 7.0 Bo09 0.010 (0.012±0.008) (8.96±11.5) UVInterpolated
7.7 Hi10 (0−+808.5)×10−3 7.7 Bo10 0.0 (0.005±0.002) (0−+500.6) UVInterpolated
Note. — For the Hα-based estimates, we use the integrated luminosity densities directly; SFRD measurements are presented just
for homogeneity with the UV estimates. ρ˙⋆ units of are M⊙ yr−1 Mpc−3 and EB−V is in magnitudes. The references are ex-
panded as: Bo 09=Bouwensetal. (2009a); Ca 10=Cassataetal. (2010); Co 10=Cowieetal. (2010); Da 07=Dawsonetal. (2007);
De 08=Deharvengetal. (2008); Gr 07=Gronwalletal. (2007); Ha 10=Hayesetal. (2010a); Hi 09=Hibonetal. (2010); Iy 08=Iyeetal.
(2006); Ou04=Ouchietal.(2004); Ou08=Ouchietal.(2008); Ou10=Ouchietal.(2010); Sh09=Shioyaetal.(2009); Re08=Reddyetal.
(2008); TM 98=Tresse&Maddox (1998). Referencesfor EB−V measurementsare the same as for the intrinsicstar-formation rate density
(I.e. thatlistedinthe5thcolumn)withtheexceptionofthehzi=0.3pointsinwhichEB−V isadoptedfromKennicutt(1992).
an analytical function to these data-points, choosing a 2009).
power-lawofthe formfLyα(z)=C·(1+z)ξ –weobtain
coefficients of C = (1.6e7sc+0.53)×10−3;ξ = (2.57+0.19). 3.2. Comparison with the literature
−0.24 −0.12
Note that we do not include any z > 6 points in our Naturally this is not the first time that fLyα has been
esc
fit since previous studies suggest that it is around this estimated and several other studies based on a wide ar-
redshift that an appreciable fraction of the intergalac- ray of methods have attempted to pin down the same
tic hydrogen becomes neutral, and may in principle af- quantity at different redshifts.
fect the Lyα LF. For more discussion on this see § 5.2. For example, at redshifts of 5.7 and 6.5, we compute
To insure that the fit is not biased by the presence of fLyα of around 40 % and 30 %, respectively. Based
esc
two z ≈ 0.3 points that lie around 8 Gyr from z ≈ 2, upon the fitting of spectral energy distributions (SED)
we repeat the fit after excluding these points, finding to stacked broadband fluxes, Ono et al. (2010) estimate
C = (4.79+5.68)×10−4;ξ = (3.38+0.10). Clearly the fit fLyα=(36+68) % and (4+180) at the same redshifts. Al-
−0.69 −0.37 esc −35 −3.8
is affected by these points, but their exclusion actually though derived from an interesting approach,the uncer-
results in a more rapid evolution with redshift. taintiesarestilltoolargetoprovideausefulcomparison.
Beyond redshift 6 the apparent trend begins to break Like us, Nagamine et al. (2008) compared observed
but it is initially very slow. Over the redshift interval Lyα LFs (Ouchi et al. 2008, in this case, which we also
of 5.7 to 6.5, fLyα stabilizes, but decreases again to just use) with intrinsic estimates, having derived this intrin-
esc
≈ 10 % at z = 7. The redshift 7 point from Iye et al. sic LF from smoothed particle hydrodynamical (SPH)
(2006) is confirmed, whereas none of the sample of red- models of galaxy formation. They adopt two methods
shift7.7candidatesfromHibon et al.(2010)haveconfir- of scaling the intrinsic to the observed LFs, the first of
mations by spectroscopy, and this upper errorbar must which they call ‘escape fraction’, which is a scaling to
be regarded as an optimistic upper limit. the datapoints along the luminosity axis, and assumes
Finally,weperformasimpleexperimentwiththebest- all galaxies have the same fLyα. This method finds
fit relationship to the feLsycα−z trend, and extrapolate to feLsycα=10 % at z = 3, which isesccertainly consistent with
estimate the redshift at which fLyα reaches unity. This ourestimatesbasedonthe z =3.1 LFofGronwall et al.
esc
would carry the implication that the ISM of the aver- (2007) and similar to, but slightly higher than our esti-
age galaxy has become effectively devoid of dust, and mate based on Ouchi et al. (2008). At z = 6 however,
since dust is a byproduct of the star-formation process, Nagamine et al.(2008) requireanescape fractionofjust
mustalsocorrespondtoatimeofapproximatelyprimeval 15%whichislowerthanourestimatesof30−40%,and
star formation. It is interesting, therefore, that we find discrepant with our estimates at around the 2σ level.
fLyα=1 at z = 11.1+0.8, which is consistent with the Nagamine et al. (2008) also test a ‘duty-cycle’ scenario
esc −0.6
redshiftoftheinstantaneousreionizationoftheUniverse (an LF scaling along the Φ axis) in which only a frac-
based upon W-MAP data (z = 11±1.4; Dunkley et al. tion of the SPH galaxies are ‘on’ as Lyα-emitters but
emit100%oftheirLyαphotons. Notethatinthesetwo
6 Matthew Hayes et al.
100
De08
Co10
α) 10−1 Ha10
y
L Ca10
( Gr07
c
s
e Ou08
f
10−2 Da07
Sh09
Iy06
Ou10
Hi10
10−3
0 1 2 3 4 5 6 7 8 9 10 11 12
redshift
Fig.1.— The redshift evolution of feLsycα. Publication codes are listed in the footnote to Table 1. z = 3.1 and 5.7 points have been
artificially shifted by ∆z = 0.08 for clarity. The point from (Hibonetal. 2010) takes, according to our definition, a value of zero. It is
thereforedisplayedatavalueof0.002topermitvisualizationonaloggedaxis. Thesolidredlineshowsthebestfittingpower-lawtopoints
between redshift 0 and 6, which takes an index of ξ = 2.6 and is clearly a good representation of the observed points over this redshift
range. ItintersectswiththefeLsycα=1line(dotted) atredshift11.1.
extreme scenarios, there is no requirement for the inte- clustering properties of Lyα emitters (Orsi et al. 2008).
graloverthescaledLFtobeequivalent. Nagamine et al. Thisisatthelowerendofbeingconsistentwithourz =3
(2008)presentdutycyclesof0.07and0.2atz =3and6, measurements,andshouldthesameescapefractionhold
respectively. However, before they compute these scal- at z = 0.3, would also be consistent with our estimates
ings the observed LFs are shifted along the luminosity in the nearby universe. However, the Le Delliou et al.
axisbyIGMattenuationfactorsof0.82(z =3)and0.52 (2005) escape fractionis highly inconsistentwith our es-
(z = 6), which also need to be applied for a compari- timatesathigherredshift. Thesesemi-analyticalmodels,
son with our estimate. Thus in the duty cycle scenario, usingtheprescriptionofBaugh et al.(2005),categorized
thevolumetricescapefractionsthatonewouldinferfrom star-formation as occurring in two discrete modes, with
thestudyofNagamine et al.(2008)are6%atz =3and a normal Salpeter IMF (α = −1.35) assigned to quies-
10%atz =6. Againthisagreesverywellwithourmea- cent star-formation and a flat IMF (α = 0) for bursting
surement at z ≈ 3 but compared with our estimates at systems. This flat IMF increases the ionizing photon
z =6isanunderestimateofaroundthesamemagnitude production at a given SFR by a factor of ten and was
as their escape fraction method. implemented as a requirement in order to reproduce the
In contrast, using similar SPH galaxy formation mod- population of sub-mm selected galaxies at z > 2. How-
els but modified prescriptions for Lyα production and ever as noted by Le Delliou et al. (2006), the fraction of
transmission, as well as a different reionization history, total star-formationthat occurs in bursts increases from
Dayal et al. (2009) find Lyα escape fractions of 30 % at 5 % at z = 0 to over 80 % at z = 6, and thus their
bothz =5.7and6.5,whichcorrespondsexactlywithour model implies that by the z = 5.7 points, effectively
measurements. Similar values of fLyα ∼ 23–33% have allstars are formedin environments where ionizing pho-
esc
also been obtained in the follow-up work of Dayal et al. tons are greatly over-produced compared to the present
(2010), although they include also an IGM transmission day. However,shouldthisrequirementoftheflatIMFbe
of T =0.48. Throughoutthis paper we have made sure removed and Salpeter applied throughout, the intrinsic
α
not to apply any IGM correction, since the value of T rateofproductionofionizingphotonswouldbedecreased
α
remainspoorlyconstrained,eventheoretically,andfrom by a factor of 3 at z = 3.1 where the star-formation is
an observational perspective there is no strong evidence shared evenly between bursting and quiescent systems.
for exactly how close the IGM comes to a narrow Lyα This would bring the fLyα estimate to 11 % at this red-
esc
line. As with the Madau (1995) prescription, it is likely shift. Atz =6, fLyα=16%wouldbe foundbyreplacing
esc
that this IGM transmission is too low when considering the flat IMF with Salpeter. These numbers are indeed
lines that are systematically redshifted by the kinemat- verysimilartotheSPHmodelsofNagamine et al.(2008)
ics of the ISM, which would drive up these theoretical butinconsistentwiththoseofDayal et al.(2009)andour
estimates of the Lyα escape fraction. own estimates based upon observation. It is interesting
AdoptingasimilarmethodofLFscalingbyluminosity, to point out, however, that the IMF assumption has lit-
Le Delliou et al. (2005) found that an escape fraction of tleeffectonthez ≈0.3pointswhere,intheirmodel,the
2%wassufficienttomatchobservedLyαLFswiththeir quiescent mode of star-formation dominates.
predictions based upon semi-analytical models between
z =2and6,withthesamemachineryabletopredictthe
On the redshift evolution of the Lyman-alpha escape fraction 7
3.3. Possible physical explanations 101
The evolution in measured fLyα is substantial, cov- Ko10 Calzetti(2000)
esc Ha10Com 1Dfit(Ha10a)
ering approximately two orders of magnitude, and no Ha10Lyα 2Dfit(thiswork)
doubt holds vital information about the physical nature Ha10Hα
100
of galaxies at various cosmic epochs. As we will show in
§ 5, the most likely explanation for this evolution is the
decreaseoftheaveragedustcontentofgalaxies. However α)
from a physical perspective many effects may enter. For Ly10−1
(
example, galaxies may also contain less neutral hydro- esc
gen to scatter photons, show faster outflows, or become f
more clumpy. The inferred increase may alternatively
be mimicked by galaxies becoming younger on average, 10−2
having low and decreasing metallicities, or forming stars
with IMFs that become more biased in favor of mas-
sive, ionizing stars. On the other hand, the scattering of
10−3
Lyα photons by a neutral IGM, and the general leakage 0.0 0.1 0.2 0.3 0.4
of ionizing photons (LyC) are expected to increase with EB−V [mag]
increasing redshift, and would both serve to lower the
perceivedLyαescapefraction(althoughthe“true”fLyα Fig.2.—LiteraturecompilationoffeLsycα vsEB−V. Thecodings
esc inthelegendare: Ha10=Hayesetal.(2010a);Ko10=Korneietal.
of galaxies, i.e. before the IGM, would not be affected).
(2010). Solid circles from Hayesetal. (2010a) are six objects for
Regrettably we are not able to measure any of these
whichwehavedetectionsinbothLyαandHα. Caretdownmarkers
quantities directly from this compilation of data. We areHαemittersthatwereundetectedinLyαandhencepresented
have, however, assembled data that show a number of asupperlimits,whilecaretupmarkersareLyαgalaxiesforwhich
Hαliesbelowthedetectionlimitandarehencepresentedaslower
trends with redshift: the Lyα and UV luminosity densi-
limits. Errorbars are removed from the plot to aid readability,
ties and the dust contents. These we have combined to buttheaverageerrorsfromthecommondetectionsofHayesetal.
showhowfLyα evolves,yetinordertoextractthe maxi- (2010a)areshownbythesingularblackpointwitherrorbars. For
esc
mum of information from these, we need to examine an- furtherinformationthereaderisreferredtoFigure3ofHayesetal.
otherpossibletrend: howfLyα correlateswithdustcon- (2010a). The red lines show various conversions between the ob-
tent. Thus we delay a detaielsecd discussion of what drives servedstellarEB−V andfeLsycα. Thedottedlineshowsthestandard
Calzettietal.(2000)prescription,thedashed lineshows the1di-
the feLsycα–z trend until § 5 and now proceed to discuss mensional fit to the data from Hayes etal. (2010a) and the solid
the effects of radiation transport and dust absorption. linea2dimensionalfitdescribedinthetext.
(2009) computed fLyα and nebular reddenings based
esc
4. THELyαESCAPEFRACTIONANDITSDEPENDENCIES upon purely nebular physics in a sample of nearby
ThatLyαphotonsundergoa complexradiationtrans- Lyα-selected galaxies. Were Hα and Hβ observations
port, in which a large number of parameters enter, is available in the distant universe, this method would
well-knownbutpoorlyunderstoodfromanempiricalan- be the ideal one by which to proceed. More recently,
gle. Transport is thought to be affected by dust content Kornei et al. (2010) performed a similar experiment in
(Atek et al. 2008, 2009; Hayes et al. 2010a), dust geom- a sample of redshift ∼ 3 Lyα-emitting LBGs, in which
etry (Scarlata et al. 2009), Hi content and kinematics dust attenuation and intrinsic Lyα luminosities were es-
(Kunth et al.1998;Mas-Hesse et al.2003;Shapley et al. timatedfrommodellingofthe SED.Finally insampleof
2003;Tapken et al.2007),andgeometry/neutral–ionized redshift 2 Lyα- and Hα-selected galaxies, we also used
gas topology (Neufeld 1991; Giavalisco et al. 1996; SED modeling to estimate EB−V but estimated the in-
Hansen & Oh 2006; Finkelstein et al. 2008, 2009). Un- trinsicLyαproductionfromthedust-correctedHαlumi-
fortunately, Hi masses remain impossible to measure di- nosity (Hayes et al. 2010a).
rectly beyond the very local universe. Kinematic mea- In Figure 2 we show a compilation of the fLyα and
esc
surements of the neutral ISM can be obtained at high- EB−V points from Kornei et al. (2010) and Hayes et al.
redshift, but require deep absorption line spectroscopy (2010a). Here we adopt only these two data-sets since
against the vanishing continuum of Lyα-selected galax- they involve similar computations of EB−V but include
iesandthusareprohibitivelyexpensiveforlargesamples Lyα, Hα, and UV selection and should be broadly rep-
of individual galaxies. We are therefore effectively lim- resentative of the generalgalaxy populations under con-
ited, when targeting statistically meaningful samples, to sideration in this paper. These two studies both per-
examining Lyα emission against the dust content, and form full SED fits, but use them in different ways, with
havetoinfer informationaboutthe remainingquantities Kornei et al. (2010) requiring the intrinsic ionizing pho-
by secondary analysis. ton budget to estimate fLyα and Hayes et al. (2010a)
esc
Significant anti-correlations between fLyα and E usingonlytheE estimatetocorrectHαforthedust
esc B−V B−V
have been presented in four recent papers, all of which attenuation. Thus the Kornei et al. (2010) points are in
invoke different selection functions and employ differ- principle expected to be more sensitive to the standard
entmethodsofanalysis. Firstly,Verhamme et al.(2008) set of assumptions in population synthesis (IMF, stellar
usedradiationtransportmodellingofspectrallyresolved atmosphere models, etc). However a substantial overlap
Lyα features in a sample of LBGs between redshift betweenthetwopopulationsisclearinFigure2,withthe
2.8 and 5 to estimate both dust attenuation and fLyα. two populations occupying a very similar region of the
esc
Based upon the Balmer line ratio (Hα/Hβ), Atek et al. fLyα–E plane (the fact that we find more galaxies
esc B−V
8 Matthew Hayes et al.
at higher E is due to the fact we find redder galax- which fLyα is scaled down. As in Hayes et al. (2010a)
B−V esc
ies by Hα selection than is possible using the UV-biased we use Schmidt’s binned linear regression algorithm
Lyman-break criterion). (Isobe et al. 1986), since it permits the combination of
The dotted line shows the dust attenuation prescrip- data-points and limits in both directions. For k we
Lyα
tion of Calzetti et al. (2000) which should be valid in obtain a value of 13.8, which is much more similar to
the case of no Lyα scattering and a simple dust screen. the value of 12.0 obtained from Calzetti et al. (2000)
ThislineisdescribedbyfLyα =10−0.4·EB−V·k1216,where at the wavelength of Lyα. However, we also obtain
esc
k = 12. Very few points lie above this line and all C =0.445, indicating we expect fLyα to be around
1216 Lyα esc
arelikelyplacedthere bystatisticalscatter. Indeed, this 50%,evenwhenthereisnomeasurabledustattenuation
line sets an approximate upper limit to the datapoints, onthestellarcontinuum. Thisisinfactamoreplausible
whichextendsinthedirectionoflowerfLyαduetoradia- scenariosincetheeffectofscatteringbyneutralhydrogen
esc
tiontransporteffectsincreasingtheeffectivedustoptical isnotexpectedtodependonthedustcontentitself. This
depth seen by Lyα. fit is shown by the solid red line in Figure 2. Again the
Inattemptstoquantifytheeffectsofresonancescatter- points of Kornei et al. (2010) and Hayes et al. (2010a)
ing and dust absorption, the studies of Verhamme et al. are subject to different assumptions that enter the pop-
(2008),Atek et al.(2009),andHayes et al.(2010a)allfit ulationsynthesis. However,forthe reasonsoutlined pre-
linear relationships to the datapoints on the log(fLyα)– viouslyin this subsectionandthe similarity between the
esc
E plane, assuming no a priori information about distributions, we do not expect these quantities to be
B−V
the dust. These studies all used a functional form of strongly subject to these assumptions.
feLsycα =10−0.4·EB−V·kLyα, where kLyα (the single free pa- It is not necessarily straightforward to define a
rameterofthefit)isaneffectiveextinctionco-efficientfor goodness-of-fit measurement to compare the quality of
Lyα, and thus includes both scattering and absorption. thethreefits,giventhelargenumberofupper-andlower-
Both at high-z, the studies of Verhamme et al. (2008) limitsinthisdataset. Thuswedefineourownnormalized
andHayes et al.(2010a)foundeffectivelythesamevalue r.m.s. statistic (rmsn), as:
of k =17.8, which runs significantly steeper than the
Lyα
Calzetti et al. (2000) relationship as Lyα photons are 1 N fmeas−fEBV 2
preferentially attenuated. This is shown by the dashed rmsn =vN i fmeasi (5)
line in Figure 2. u i (cid:18) i (cid:19)
u X
These formalisms force the fits to conform to fLyα=1 t
esc where fmeas is the ith measured Lyα escape fraction,
atEB−V=0,andtechnically it is true that ifthere is ex- i
actlyzerodust,Lyαphotonscannotbeabsorbedbydust. fiEBV is the ith Lyα escape fraction predicted from
However, the very presence of Lyα photons implies that EB−V, and N is the number of data-points. However
star-formationmustbeoccurringand,afterjust∼3Myr in order to treat the limits, we permit a point to con-
ofstar-formation,dustproducedinsupernovaewouldbe tribute to the summation only if that limit is violated.
returnedtotheISMandtheopticalcolorexcessceasesto We appreciate that this is a non-standard statistic, but
be a goodproxy for dust. It is well-knownthat Lyα can itdoesenableaquantitativemeasureofthegoodness-of-
be strongly suppressed even when miniscule amounts of fitthatis philosophicallynottoo farremovedfrommore
dustarepresent(e.g.Hartmann et al.1984;Kunth et al. commonplace statistics. Adopting the feLsycα–EB−V rela-
1994; Thuan & Izotov 1997; O¨stlin et al. 2009) and as tions derivedfromCalzetti et al.(2000), the one param-
eter fit fromHayes et al. (2010a) andthe two parameter
Figure 2 shows some galaxies have fLyα=10% with no
esc fit from this work, we compute rms = 1.85, 1.02, and
measurable UV attenuation. Indeed, many star-forming n
0.66, respectively.
galaxies show little or no attenuation in front of their
We have now assembled information about three
ionizing clusters but substantially attenuated nebular
trends: the observed redshift evolution of fLyα; the ob-
regions. This is the origin of the factor of 2.2 differ- esc
served redshift evolution of the dust content of galaxies;
encebetweenstellarandnebularmeasurementsofE
B−V and the observed relationship between fLyα and dust
(Calzetti et al. 2000), but at a very low UV stellar at- esc
content. We will next show that we are able to syn-
tenuation of E ≈ 0 applying a factor of two is not
B−V thesize these points to infer some general trends in the
meaningful and nebular lines in general – and Lyα in
evolution of galaxies.
particular – may be heavily attenuated. It is unfortu-
nate that at high-z the UV continuum is our only proxy 5. ONTHEEVOLUTIONOFfeLsycα
for the dust contentas we indeedexpect to be surveying
5.1. Redshifts 0–6: the upwardly evolving escape
redshifts at which the stellar attenuation indeed falls to
fraction and the properties of galaxies
∼0 (e.g. Bouwens et al. 2009a).
To account for these factors we now proceed to 5.1.1. The evolving dust content of galaxies
relax the requirement of the fit passing through We showed in the previous section that fLyα of in-
(E ,fLyα)=(0,1) and re-fit the combined datasets of esc
B−V esc dividual galaxies is anti-correlated with the measured
Kornei et al. (2010) and Hayes et al. (2010a) using the
E (Figure 2). Given that the typical E evolves
following expression B−V B−V
withredshift (see Table 1), we mayindeed expect apos-
feLsycα =CLyα·10−0.4·EB−V·kLyα. (4) iatcivtleycworhraetlatFioignurbeet1wesehnowfesLs,ycαwhaenrderietdsishicftl.eaTrhtihsaits tehxe-
This expression takes the same form as the standard Lyα escape fraction increases smoothly and monotoni-
dust-screen prescription, with coefficient k , but adds cally out to z ∼6. Thus it appears that this increase in
Lyα
the additional free parameter of C , the factor by fLyα is the resultofthe dustcontentofthe star-forming
Lyα esc
On the redshift evolution of the Lyman-alpha escape fraction 9
within the errorbars, between redshift 0 and 6.6. We
Calzetti+2000 should point out that it is not clear that the use of the
100
1-D(thiswork) average E for a sample should by necessity repro-
B−V
2-D(thiswork) ducethevolumetricescapefraction. Duetovariationsof
thedustcontentsandISMofindividualgalaxies,andthe
associatedimpactuponthetransferofLyαandtheselec-
α)10−1 tionofgalaxies,itispossiblethattheaveragefLyα could
y esc
L havebeenskewedsubstantiallyfromthedata-points. In-
(
fesc deed, close examination of the feLsycα–EB−V relationship
(C =1; k =17.8) from Hayes et al. (2010a) reveals
10−2 thaLtyαitdoesLnyoαtperfectlyintersectthecenterofthefLyα
esc
datapoint(z =2.2pointin Figure3) fromthe same sur-
vey, despite fLyα, average E , and the coefficients of
esc B−V
the fLyα–E relationship all having been derived en-
10−3 esc B−V
0 1 2 3 4 5 6 7 8 tirelyfromthisonedataset. Thismostlikelyresultsfrom
redshift
theweightingacrossthepopulationfromwhichtheaver-
age E is computed (the representative E is not
Fig.3.—SameasFigure1,butzoomedontotherelevantregion. B−V B−V
The red lines show the Lyα escape fractions that would be pre- anaverageweightedbytheintrinsicLyαluminosity),ex-
dictedbaseduponthevaluesofEB−V thathavebeenmeasuredin actly the effect under discussion. However,the fact that
therespectiveHαandUVsamples(listedinTable1),andusingthe such tight agreement is seen between the observational
variousconversions between measuredEB−V andfeLsycα described estimates and those derived from our fit suggests that
inthetext. Thedottedlinerepresentsthedustattenuationlawof
such a bias in the selection of the populations is not at
Calzettietal.(2000), the dashedlinethe1dimensional empirical
fit to the data of Hayes etal. (2010a), and the solid line a 2 di- play here.
mensionalfittothedatadescribedin§4. Usingthe2dimensional Again we stress that the relationship we derived be-
fit,aremarkablygoodagreementisseenbetweenobservationsand tween fLyα and E in § 4 includes the effects of res-
predictionbetween redshifts0and6.5. esc B−V
onance scattering, and thus in some manner the neu-
tralgascontent, its kinematics andrelativegeometryall
galaxypopulationdecreasingwithredshift. Wenowtake
enter the relationship, which holds even when the mea-
the measured values of E from the various samples
B−V
suredopticalcolorexcessonthestellarcontinuumiszero.
(listed in Table 1), and use them to compute the fLyα
esc There is no reason to assume that these quantities are
that would be expected, from the three conversions be-
constant with redshift and we could, for example, envis-
tween E and fLyα discussed in the previous section
B−V esc agesituationswherethegascontent,feedbackproperties,
[Calzetti et al. (2000), an empirical fit with one free pa-
or clumpiness evolve and thereby change k or C .
rameter (Hayes et al. 2010a), and an empirical fit with Lyα Lyα
HoweverthetightagreementbetweenourobservedfLyα
twofreeparameters]. Weshowthemeasuredescapefrac- esc
tions together with these predictions in Figure 3. values and those computed from the feLsycα-EB−V rela-
We first discuss the predictions based upon the tionship provides no evidence for the evolution of these
Calzetti et al. (2000, red dotted line), which is clearly properties(atleastifthegascontentdoeschangeitdoes
discrepant with the observations at around the 3σ level not take part in the Lyα scatteringprocess). The evolu-
at every redshift. Obviously this is to be expected since tionoffLyα acrossalmostthe entireobservableuniverse
esc
Lyα photons resonantly scatter and it is unlikely that can be explained cleanly within the confines of this sim-
the dust is distributed in a uniform screen. The one di- ple model, as mainly due to a dust content that evolves
mensionalfitfromHayes et al.(2010a)offerssubstantial with redshift.
improvementandisabletodescribetheobservationsbe-
5.1.2. Other effects
tween redshifts 0 and 4. This reasoning is circular for
the redshift 2 points where the fLyα–E relationship We need to interpret an increase in the global fLyα
esc B−V esc
was derived, but we stress the tautology is present only of galaxies by a factor of ∼ 4 between z = 2 and 6, and
at this redshift. This relationship is not able to explain naturallyifsomethingweretoaltertheintrinsicLyα/UV
any of the datapoints at redshift above 4, where it sys- ratio of galaxies by this factor, the evolution in fLyα
esc
tematically over-predicts the Lyα escape fraction. could be mimicked.
As redshift increases the dust content of galaxies is Forexample,thereisevidencethatthe W distribu-
Lyα
clearly shown to change and, could we plot Figure 2 at tion of galaxies changes with increasing redshift: high-
redshiftshigher than3,we couldexpectgalaxiesto clus- W objects become relatively more abundant (e.g.
Lyα
ter successively further towards the upper left corner of Gronwall et al. 2007 c.f. Shimasaku et al. 2006; also
theplot. SincetheHayes et al.(2010a)fLyα–E fitis Ouchi et al. 2008), and thus pure selection may explain
esc B−V
forcedthroughthe(EB−V,feLsycα)=(0,1)coordinateanda thetrend. However,theWLyα distributionsatz =2and
highvalueofk isfound,thepredictedescapefraction 3 suggest a maximum of ∼20 % of the total luminosity
Lyα
evolves very quickly with redshift. Indeed, these predic- densitywillbe lostbynon-selectionof0<W <20˚A
Lyα
tions evolvemuchfaster thanthe data, asfLyα is forced galaxies, and such a selection bias can certainly not ex-
esc
for unphysical reasons towards unity. plain the magnitude of the trend observed here.
When we introduce the new fLyα–E fit with two Itmayalsobearguedthatlowermetallicitiesoraflat-
esc B−V
free parameters and allow C 6= 1, the agreement be- tening of the IMF may explain the trend. However,
Lyα
tween the measured and observed Lyα escape fractions between solar and 1/50 solar metallicity the increase
is striking: it agrees with essentially every datapoint, of W for constant SFR, a measure of the relative
Lyα
10 Matthew Hayes et al.
Lyα/UV output, is less than 50 % (Raiter et al. 2010), several times larger than the FWHM of the Lyα emis-
insufficient to explain the observed increase of fLyα. To sion and several studies apply the same method at sev-
esc
explain an increase by a factor ∼ 4 would require a de- eral redshifts (e.g. between z ∼ 3 and 6, Ouchi et al.
crease of the average metallicity from solar down to less 2008). Second, several independent measurements using
than 10−3 solar (Raiter et al. 2010), which seems highly both imaging and spectroscopy reveal the same trend
unlikely. between z ∼ 2 and 6 (Ouchi et al. 2008; Cassata et al.
One would also assume that a relatively higher frac- 2010; Stark et al. 2010a), and also over a smaller red-
tion of genuine primeval galaxieswould be discoveredas shift range (Reddy et al. 2008). Third, it is well-known
redshift increases, and a substantial (∼3-fold) enhance- that in individual Lyα-selected systems at redshifts 2–3,
ment of Lyα/UV may arise from preferential selection the SFRinferredby comparingLyαandUV radiationis
of extremely young systems (e.g. Charlot & Fall 1993; frequently found to be comparable (Guaita et al. 2010;
Schaerer2003). Togetthiskindofenhancementagalaxy Nilsson et al. 2009; Ouchi et al. 2008). Finally, some of
must either be observed at an age below ∼ 10 Myr or, thebrightestLyα-emittingobjectsonthesky–wherethe
should an episode of star-formation occur superimposed order-of-magnitude fainter low surface brightness scat-
atopanagedstellarpopulation,sufficienttimemusthave teredemissionshouldbecomeapparent–alsoseemtobe
elapsed for that population to fade in the UV. For this spatiallycompact(e.g.Westra et al.2006). Theseobser-
UVfading to occur,punctuatedburstsofstar-formation vational lines of evidence all argue against an important
would need to be separated by around the UV equilib- loss of Lyα photons related to its spatial extension.
rium timescale of ∼ 100Myr. At z = 6 the Universe At z ∼ 0.2−0.3 the Lyα emitting samples have been
has an age of 1 Gyr and even if all star-formation were carefully constructed from surveys using GALEX slit-
to occur in individual bursts, the chance of catching an less spectroscopy of NUV continuum selected objects
individual galaxy at this time would be around 10 %. (Deharveng et al.2008;Cowie et al.2010). Givenitsrel-
Thus, integrated over the entire galaxy population the atively low spatial resolution (∼ 5′′) the Lyα flux mea-
application of such a sampling bias also seems quite im- surementof individual sourcesshould not be affected by
plausible. possible differences in the spatial extension. Further-
We may expect at some point over this cosmic evolu- more, blending affects only 10% of the sources, accord-
tion, that galaxies start to leak a substantial fraction of ing to Cowie et al. (2010). Finally, comparing number
their ionizing photons (fLyC). Indeed as we approach counts of GALEX sources with/without Lyα emission
esc
the middle of the epoch of reionization, the reionization these authors have also shown that the Lyα emitters
processes itself dictates that this must be true, and we represent only ∼ 5 % of the NUV-selected continuum
may expect at lower redshifts (e.g. 4–6) that a substan- sources, a fraction significantly lower than the 20–25%
tialpopulationofgalaxiesmayremainwithanISMthat derived for z ∼ 3 LBGs by Shapley et al. (2003). In
permitshighfLyC. Inaddition,acrossapproximatelythe other words, a low escape fraction at low-z is not only
esc
sameredshiftdomainwemayexpectthethickeningneu- obtained from the ratio of the UV and Lyα luminosity
tral phase of the IGM to start to suppress Lyα. Both of density, but also from direct inspection of NUV contin-
theseeffectswouldacttolowertheperceivedLyαescape uum selected objects.
fractionbyeitherdrainingionizingphotonsorscattering Finally,as discussedin§ 2.2, ourassumedlimits ofin-
Lyα. Although we are not able to tell whether these tegrationmayintroduceanoverallbiasintothedata. For
effects become significant at z ∼ 4−6, if they do be- both the Lyα- and UV-selected populations, the char-
come important then the intrinsic Lyα escape fractions acteristic luminosity of the LF (L⋆) is known to evolve
of these galaxies will be still higher than we measure8. withredshift. Thusselectingaconstantlowerlimitatall
It may be argued that the measured Lyα fluxes (and redshifts may result in an artificial evolution. Firstly it
hence the Lyα luminosity density) could be underesti- should again be noted that our fixed lower limits apply
mated due to the spatial extension of Lyα, and that to both the numerator and denominator (Lyα and UV
some of the observed redshift trend could be due to LFs; in Equation 1) and to first order will cancel. Sec-
this (e.g. Loeb & Rybicki 1999; Zheng et al. 2010). Al- ondly, the evolution of both Lyα and UV LFs follows a
thoughasomewhatlargerspatialextensionofLyα com- similar pattern, starting low in the nearby universe and
pared to the UV continuum has been noted in some increasing rapidly to z = 2 or 3, from where they be-
surveys(e.g.Nilsson et al.2009;Finkelstein et al.2010), gin to decline in the direction of the highest redshifts
stacking analysis in other Hubble Space Telescope im- (with the Lyα LF declining slower than that of the UV
ages reveals the Lyα emission to be spatially compact, inthisrange). Thuswerethiseffecttobesignificant,and
with only a small fraction of the integrated luminos- also not to cancel as just suggested, we would expect a
ity lost to aperture effects (Bond et al. 2010). There- strong upwards evolution from z ≈ 0 to 2 which we do
fore it seems very unlikely that this could lead to a see, followed by a slow decline to higher redshift, which
significant underestimate of the Lyα flux, which would is certainly not reflected in the data.
mimic the apparenttrend of increasing Lyα escape frac- In short, the various methods and arguments all point
tion with redshift. The main reasons are the follow- clearly towards a significant evolution of the Lyα space
ing. First, the photometric apertures typically used fraction with redshift. The main uncertainty affecting
for the narrowband images taken from the ground are the precise absolute value of fLyα is probably due to
esc
statisticaluncertainties in the LFs and to the simple ex-
8 Forexample,assumingthathalfoftheLyαfluxislostdueto tinction correctionapplied to derive it, not possible Lyα
scatteringintheIGMthe“intrinsic”valueoffeLsycα outofgalaxies losses due to apertures.
wouldbehigherbyafactor1.22(1.92)atz∼3(6),assumingthe
averageIGMopacityofMadau(1995).