The Rest-Frame Optical Spectroscopic Properties of Ly α -Emitters at z∼2.5 : The Physical Origins of Strong Ly α Emission
Ryan F. Trainor, Allison L. Strom, Charles C. Steidel, Gwen C. Rudie
DDraft version September 26, 2016
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE REST-FRAME OPTICAL SPECTROSCOPIC PROPERTIES OF LY α -EMITTERS AT Z ∼ .
5: THEPHYSICAL ORIGINS OF STRONG Ly α EMISSION Ryan F. Trainor Department of Astronomy, University of California, Berkeley, 501 Campbell Hall, Berkeley, CA 94720; [email protected]
Allison L. Strom and Charles C. Steidel
Cahill Center for Astrophysics, MC 249-17, 1200 E California Blvd, Pasadena, CA 91125 andGwen C. Rudie
Carnegie Observatories, 813 Santa Barbara Street, Pasadena, CA 91101
Draft version September 26, 2016
ABSTRACTWe present the rest-frame optical spectroscopic properties of 60 faint ( R AB ∼ L ∼ . L ∗ ) Ly α -selected galaxies (LAEs) at z ≈ .
56. These LAEs also have rest-UV spectra of their Ly α emissionline morphologies, which trace the effects of interstellar and circumgalactic gas on the escape of Ly α photons. We find that the LAEs have diverse rest-optical spectra, but their average spectroscopicproperties are broadly consistent with the extreme low-metallicity end of the populations of continuum-selected galaxies selected at z ≈ −
3. In particular, the LAEs have extremely high [O
III ] λ β ratios (log([O III ]/H β ) ∼ II ] λ α ratios (log([N II ]/H α ) < . III ] λ T e ≈ . × K), low oxygenabundances (12 + log(O/H) ≈ Z neb ≈ . Z (cid:12) ), and high excitations with respect to their moreluminous continuum-selected analogs. Several of our faintest LAEs have line ratios consistent witheven lower metallicities, including six with 12 + log(O/H) ≈ − Z neb ≈ . − . Z (cid:12) ). Weinterpret these observations in light of new models of stellar evolution (including binary interactions)that have been shown to produce long-lived populations of hot, massive stars at low metallicities. Wefind that strong, hard ionizing continua are required to reproduce our observed line ratios, suggestingthat faint galaxies are efficient producers of ionizing photons and important analogs of reionization-era galaxies. Furthermore, we investigate the physical trends accompanying Ly α emission across thelargest current sample of combined Ly α and rest-optical galaxy spectroscopy, including both the 60KBSS-Ly α LAEs and 368 more luminous galaxies at similar redshifts. We find that the net Ly α emissivity (parameterized by the Ly α equivalent width) is strongly correlated with nebular excitationand ionization properties and weakly correlated with dust attenuation, suggesting that metallicityplays a strong role in determining the observed properties of these galaxies by modulating their stellarspectra, nebular excitation, and dust content. Subject headings: galaxies: formation — galaxies: high-redshift — galaxies: dwarf INTRODUCTION
The optical emission lines of galaxies can provide awealth of information regarding the properties of youngstars and the regions in which they form. The histori-cal accessibility of optical wavelengths has enabled largespectroscopic surveys to measure these lines in local star-forming regions and thereby identify and calibrate theirrelationships with the physical properties of galaxies.These properties include star-formation rates, elementalabundances, gas temperatures and densities, ionizationstates, and the nature of sources of ionizing radiationwithin galaxies and gaseous clouds. In particular, theBaldwin et al. (1981) line ratios (including the N2-BPT Based on data obtained at the W.M. Keck Observatory,which is operated as a scientific partnership among the Cali-fornia Institute of Technology, the University of California, andNASA, and was made possible by the generous financial supportof the W.M. Keck Foundation. Miller Fellow. ratios [N II ]/H α and [O III ]/H β ) are frequently used todiscriminate between ionization by star formation and/oractive galactic nuclei (AGN), and these same line ratiosprovide a measure of gas-phase metallicity among star-forming galaxies (Dopita et al. 2000).At z (cid:38)
1, however, these well-studied transitions shiftinto infrared bands, where efficient, multiplexed spec-trocopic survey instruments have only recently becomeavailable (e.g.,
Keck /MOSFIRE [McLean et al. 2012];
VLT /KMOS [Sharples et al. 2013]). In the last few years,these spectrometers have enabled the collection of thefirst statistical samples of galaxies at z ≈ − a r X i v : . [ a s t r o - ph . GA ] S e p R. F. Trainor et al.eter space with respect to typical low-redshift galaxies(e.g., from the Sloan Digital Sky Survey; SDSS). Ear-lier limited rest-optical spectroscopy had hinted at thistrend (Shapley et al. 2005; Erb et al. 2006; Liu et al.2008; Brinchmann et al. 2008), but the KBSS and MOS-DEF surveys have demonstrated that the population ofbright continuum-selected galaxies (LBGs; L ∼ L ∗ ) isshifted toward high [O III ]/H β ratios at fixed [N II ]/H α (or equivalently, high [N II ]/H α at fixed [O III ]/H β ) withrespect to the SDSS star-forming galaxy locus (Steidelet al. 2014, 2016; Shapley et al. 2015; Sanders et al. 2015;Strom et al. 2016).While this trend has been firmly established for LBGs,its physical origins remain under debate. Several studieshave suggested that this “BPT offset” may be explainedby high N/O ratios at z ≈ − II ]/H α . However, Strom et al. (2016)present detailed rest-optical spectroscopy of ∼
250 LBGsover a wide range of stellar masses and star-formationrates (SFRs), finding behavior consistent with the low-redshift N/O vs. O/H relation. Rather, Strom et al.(2016) (along with Steidel et al. 2014, 2016) suggest thatthe N2-BPT offset corresponds primarily to a change inthe excitation state of nebular gas, which can be ex-plained by the presence of stars with hotter, harder spec-tra than typical of stars in the local Universe.At the same time, new studies of massive stars haveindicated that the rotation and binarity of stars playimportant roles in shaping their evolution and emis-sion (e.g., Eldridge & Stanway 2009; Brott et al. 2011;Levesque et al. 2012). These effects can cause stars toexhibit longer lifetimes and higher-temperature spectralshapes than their single or slowly-rotating counterparts.Furthermore, these effects may naturally be more pro-nounced at high redshifts, where low photospheric metal-licities produce weaker winds and less associated lossof angular momentum. Similarly, lower-metallicity starsproduce harder spectra regardless of their rotation rate,and metallicity may influence stellar binarity through thecooling and fragmentation of star-forming clouds.In light of these trends, Steidel et al. (2016) used ex-tremely deep composite LBG spectra in the rest-UV andrest-optical to measure a suite of emission lines and theirratios, finding that stellar spectra from the Binary Pop-ulation and Spectral Synthesis (BPASSv2; Eldridge &Stanway 2016; Stanway et al. 2016) models are able toreproduce the full set of measured values. Conversely,the softer spectra of single-star models, including non-binary BPASSv2 models and those from the Starburst99model suite (Leitherer et al. 2014), do not fulfill theseconstraints irrespective of the assumed N/O ratio.In addition to these observational constraints, modelspectra similar to those produced by binary evolutionmodels are preferred by other observations as well astheoretical grounds. Most obvious is that approximately70% of local massive stars are expected to experiencemass transfer in binary systems (e.g., Sana et al. 2012),so single star models are unlikely to provide an accuratedescription of their evolution. Secondly, simulations ofionizing photon production have extreme difficulty gen-erating the large escape fractions needed to reionize theUniverse, in part because the stars remain buried in theiroptically thick birth clouds for longer than the (cid:46) −
10 Myr (including the aformentioned binary models)continue to produce ionizing photons after their birthclouds have been cleared away by stellar feedback, whichallows the photons to escape to large radii. Ma et al.(2016) demonstrate that simulations from the FeedbackIn Realistic Environments (FIRE; Hopkins et al. 2014)project that include the BPASSv2 stellar models are ableto reproduce the high escape fractions of ionizing pho-tons required by other constraints on reionization (e.g.,Robertson et al. 2015). Modeling the epoch of reioniza-tion (EoR) therefore requires further understanding ofthe stellar populations of these galaxies.The specific galaxies that dominated the EoR, how-ever, were less luminous and less mature than those se-lected as LBGs at z ≈ −
3. One method of identifyinggalaxies with properties more analgous to the EoR pop-ulation is by selecting on the basis of Ly α line emission.As this technique does not require a detection in the stel-lar continuum, it naturally selects fainter, younger, andlower-mass galaxies than typical samples of LBGs (e.g.,Gawiser et al. 2006). We have also shown through theKBSS-Ly α survey (Trainor et al. 2015) that these Ly α -emitting galaxies (LAEs) have lower covering fractionsof interstellar and/or circumgalactic gas, which allows ahigher fraction of their UV photons to escape. Further-more, there is evidence from radiative-transfer simula-tions that the physical conditions which facilitate Ly α emission are also conducive to ionizing photon escape(Dijkstra et al. 2016, but cf. Yajima et al. 2014).LAEs comprise an increasing proportion of galaxies asredshift increases up to the EoR at z ≈ α absorption and scattering by the neutral inter-galatic medium (Pentericci et al. 2011; Schenker et al.2012; Ono et al. 2012). However, the intrinsic Ly α emis-sivity of galaxies (divorced from their intergalactic andcircumgalactic attenuation) likely continues to increasetoward the earliest cosmic times, given the trends of Ly α equivalent width with galaxy luminosity and UV spectralslope (e.g., Schenker et al. 2014). For all of these reasons,LAEs at z ≈ − α -emitting galaxies have affirmed thisinterpretation: McLinden et al. (2011) measured strong[O III ] emission in two LAEs at z ≈ .
1, Finkelstein et al.(2011) found strong [O
III ]/H β and weak [N II ]/H α intwo LAEs at z ≈ .
4, and Nakajima et al. (2013) mea-sured high [O
III ]/[O II ] ratios in two LAEs and in acomposite spectrum of four additional LAEs at z ≈ . α -Emitters 3Furthermore, the LAEs in these studies have luminosi-ties similar to those of typical LBG samples ( ∼ × thatof the KBSS-Ly α LAEs), which eliminates many of theadvantages of continuum-faint LAEs for selecting EoRanalogs.Galaxy selections based on emission lines other thanLy α have also yielded similar populations. Hagen et al.(2016) find that optical-emission-line-selected galaxiesexhibit a wide range of properties consistent with LAEs(although cf. Oteo et al. 2015, who find that H α -selectedgalaxies are more massive and redder than LAEs).Maseda et al. (2014) present 22 Extreme Emission-Line Galaxies (EELGs) selected by H α or [O III ] emis-sion in grism spectroscopy, which show high excitations(log([O
III ]/H β ) ≈ .
7) and low metallicities ( Z neb =0 . − . Z (cid:12) ). Masters et al. (2014) present a similargrism-selected sample of 26 galaxies with a compara-ble N2-BPT offset to the LBG samples discussed above.Both of these EELG samples lie at slightly lower red-shifts ( z ≈ . − .
3) than the KBSS, KBSS-Ly α , andMOSDEF galaxies. The EELGs also have atypically highspecific star-formation rates (sSFR), with stellar and dy-namical masses similar or slightly higher than those ofKBSS-Ly α LAEs ( M dyn ∼ M (cid:12) ) and SFRs 3 − × higher, similar to typical LBGs (SFR ∼
30 M (cid:12) yr − ).Most of these EELGs also do not have Ly α measure-ments (being observationally difficult at z (cid:46) α production and escape.This paper, therefore, has two primary objectives: 1)to extend our understanding of the nebular properties ofgalaxies toward low stellar masses and faint luminositiesby measuring the rest-frame optical spectra of typical LAEs; and 2) to determine how the Ly α emissivities ofgalaxies are related to the physical properties of theirstellar populations and star-forming regions. Toward thisaim, we present deep nebular emission line spectra of 60LAEs from the KBSS-Ly α sample presented in Trainoret al. (2015), as well as a comparison sample of 368 LBGspectra from the KBSS (Steidel et al. 2014; Strom et al.2016), and rest-UV spectra covering the Ly α transitionof each galaxy.In Sec. 2, we describe the rest-optical LAE spectra pre-sented in this paper, as well as the LBG spectra and rest-UV LAE spectra originally presented in previous work.Sec. 3 describes our emission line measurements from theindividual object spectra and the creation and fitting ofcomposite LAE spectra. In Sec. 4, we present diagnos-tic line ratios including the N2-BPT diagram in orderto compare the nebular LAE properties to those of theLBG sample. In Sec. 5, we discuss the variation of Ly α equivalent width across the combined sample of LAEsand LBGs to infer the relationship between Ly α emission(and absorption) and physical galaxy properties includ-ing dust content and nebular excitation. Sec. 6 includesour photoionization modeling of the rest-optical line ra-tios and the resulting constraints on the properties of thegas and stellar populations (including binary star mod-els) in the LAE star-forming regions. Finally, we provideadditional physical interpretation of our results in com-parison with previous work in Sec. 7 and a summary andconclusions in Sec. 8. Because the majority of our ob-served properties are line ratios, our results have little dependence on the assumed cosmology, but we assume aΛCDM universe with (Ω m , Ω Λ , H ) = (0.3, 0.7, 70 kms − Mpc − ) when necessary. OBSERVATIONS
LAE sample
LAEs were selected from the KBSS-Ly α (Trainor et al.2015; hereafter T15) sample of LAEs. The KBSS-Ly α is a survey for Ly α -emitting objects in the Keck Bary-onic Structure Survey (KBSS; Rudie et al. 2012; Steidelet al. 2014; Strom et al. 2016) fields, which are centeredon hyperluminous QSOs at z ∼ −
3. The spectro-scopic properties of the KBSS-Ly α LAE sample are de-scribed in detail in T15 and Trainor & Steidel (2013),and the full photometric parent sample of objects willbe described in an upcoming paper (R. Trainor et al., inprep.). Briefly, the LAEs are selected via imaging in nar-rowband filters selecting Ly α emission near the redshiftof the QSO in each KBSS field. These narrowband im-ages are combined with deep continuum images to isolateobjects with strong Ly α emission, typically defined as arest-frame photometric equivalent width W Ly α > The selected objects have a limiting narrowband magni-tude m NB,AB = 26 .
5, corresponding to an integrated Ly α line flux F Ly α > − erg s − cm − for a continuum-free source, or F Ly α (cid:38) × − erg s − cm − for atypical LAE with W Ly α ≈ R AB (6930˚A) ≈
27, correspond-ing to L ∼ . L ∗ at z ∼ . α line and sur-rounding wavelengths) are low-redshift [O II ] emitters orintermediate-redshift AGN with high equivalent widthC IV λλ II λ z QSO = 2 . z QSO =2 . ∼ α fields, resulting ina limiting Ly α luminosity ∼
60% higher, but the proper-ties of the Q1603 LAEs appear to be otherwise consistentwith the remainder of the KBSS-Ly α sample.As discussed in T15, the KBSS-Ly α LAEs have typical As in T15, we note that this definition is useful both for con-sistency with previous samples and to rule out low-redshift [O II ]emitters, which rarely exhibit W [O II ],obs (cid:38) < W Ly α < α -emitting galaxies at z ≈ . R. F. Trainor et al.dynamical masses (cid:104) M dyn (cid:105) ≈ × M (cid:12) , and our mea-surements of stacked LAE spectral energy distributions(SEDs; R. Trainor et al., in prep.) imply stellar masses M ∗ ∼ − M (cid:12) . Rest-optical spectroscopic observations
Rest-frame optical spectra of the KBSS-Ly α LAEswere obtained using the Multi-Object Spectrometer ForInfraRed Exploration (MOSFIRE; McLean et al. 2010,2012) on the Keck 1 telescope. Initial observations (in-cluding all of the K -band spectroscopy presented here)were obtained over the course of the KBSS-MOSFIREsurvey (Steidel et al. 2014). The data were reduced usingthe spectroscopic reduction pipeline provided by the in-strument team, and the details of the observing strategiesand reduction are described in Steidel et al. (2014). Allspectra were observed using 0 . (cid:48)(cid:48) R ≈ σ inst ≈
35 km s − .A total of 28 LAEs were detected in the K -bandover the course of the KBSS-MOSFIRE observations,all in the Q2343 field (this sample was described inT15). As these LAEs are selected at z ≈ .
56, the ob-served K -band spectra cover the range 5380˚A (cid:46) λ rest (cid:46) α λ II ] λλ K -band spectra have 4.9 hourintegrations, while our shallowest have 1 hour integra-tions. The average exposure time is 2.7 hours, for a totalof 83 object-hours of integration.Limited H -band spectroscopy was also obtained dur-ing KBSS-MOSFIRE observations (12 LAEs, 36 object-hours of integration; T15). The majority of the H -bandspectra presented here were obtained on 15-16 Septem-ber 2015 in clear weather. These observations included40 LAEs (7 of which had been previously observed) inthe Q2343 field with a typical exposure time of 4 hoursper object and a total of 173.4 object-hours of exposure.Another 8 LAEs in the Q1603 field have measurements ofat least one nebular line from a single mask observed for1 hour on 16 September 2015, producing a final sampleof 55 LAEs with nebular line detections in the H -bandand a total of 218.4 object-hours of integration.At z ≈ .
56, the MOSFIRE H -band covers 4100˚A (cid:46) λ rest (cid:46) γ and H β transitions of hydrogen, the [O III ] λ III ] λλ β and [O III ] λλ z QSO ≈ .
56, the [O
III ] λ H -band filter, which lowers the accu-racy of our flux calibration with respect to bluer wave-lengths. In addition, some LAEs in the Q2343 field haveslightly higher redshifts than the QSO, such that their[O III ] λ III ] λ III ] λ f /f = 3. Whilethis issue affects only 5 individual LAEs at a significantlevel (Table 1), it is particularly clear in our composite H -band spectrum (Fig. 3; Table 3), where the apparent line ratio f /f = 2 . III ] λ ≡ log([O III ] λ β ); Table 2) are computed fromthe corrected [O III ] λ f ≡ × f .For both H -band and K -band spectra, slit correctionsare estimated for each mask according to the proceduredeveloped for KBSS-MOSFIRE (Strom et al. 2016). Themajority of LAE spectra included here were observedon masks which include a bright star, for which the in-tegrated stellar flux in each band is compared to thephotometric magnitude to determine the flux correctionfor point sources on the mask. Given that the typi-cal KBSS-Ly α LAEs are spatially unresolved, their slitlosses are well-approximated by this factor. For masksobserved without a calibration star, mask correction fac-tors are estimated by comparing the relative fluxes ofobjects observed on several different masks. The opti-mal set of mask-specific correction factors are calculatedvia an MCMC procedure that adjusts each correctionfactor to achieve the maximum degree of internal consis-tency among all flux measurements of objects appearingon multiple masks (using the observations of calibrationstars to set the overall normalization of slit corrections).When there are not enough data to reliably estimate theslit correction for a single object, we adopt a correctionfactor of 2, the median of those observed. Slit correc-tions for all the LAE spectra included in this samplerange from 1.53 to 2.34. Ly α spectroscopic observations Rest-UV spectroscopy of the KBSS-Ly α LAEs and acomparison sample of KBSS LBGs is described in detailin T15. In Sec. 5, we use the same comparison sampleof T15, but with the addition of LBGs displaying Ly α absorption (the T15 comparison sample was restricted tothose spectra displaying detectable Ly α emission). Eachof the LAE and LBG rest-UV spectra in the T15 sam-ple were obtained with LRIS-B (Oke et al. 1995; Steidelet al. 2004) using the 600 lines/mm grism, yielding a res-olution R ≈ R ≈ α line and rest-optical spectra covering several emis-sion lines in the MOSFIRE H and K bands (describedin detail in Sec. 5.1).The Ly α emission or absorption profiles in the LAEand LBG spectra are identified using the line-detectionalgorithm described in T15, and spectroscopic Ly α equivalent widths (in emission or absorption) are cal-culated comparing the directly-integrated line profile tothe local continuum level on the red side of the Ly α line(1222˚A < λ rest < α line, the integrated Ly α equivalent width is in-sensitive to the spectral resolution, which allows us to usethe larger sample of low-resolution KBSS LBG rest-UVspectra.As discussed in T15, the spectroscopic Ly α equivalentwidths ( W Ly α ,spec ) measured for individual or stackedrest-UV spectra are not directly comparable to photo-metric Ly α equivalent width measurements ( W Ly α ,phot )est-Frame Optical Spectroscopy of Ly α -Emitters 5 TABLE 1MOSFIRE LAE Properties
Object Name z sys a RA Dec R W Ly α b Bands [O
III ] λ c H β c Q1603-NB1036 2.5412 16:04:43.35 +38:11:16.47 > ± ± ± ± > ± < ± ± ± ± ± ± ± ± ± < ± ± ± ± > ± d ± ± d ± ± d ± ± d < > ± ± > ± < > ± ± ± ± > ± ± > ± ± > ± ± ± < ± ± ± ± > ± ± > ± < ± < > ± ± ± ± − − Q2343-NB1585 2.5648 23:46:35.59 +12:47:28.53 > ± ± > ± ± ± ± ± ± ± ± ± ± > ± ± − − Q2343-NB1828 2.5727 23:46:25.25 +12:48:08.61 25.8 26.7 H+K 21.7 ± ± ± < > ± < > ± ± > ± ± > ± < > − − Q2343-NB2807 2.5446 23:46:40.22 +12:48:27.64 23.4 24.6 H 143.4 ± d ± > ± ± ± < > − − Q2343-NB2835 2.5738 23:46:33.80 +12:49:10.63 > ± ± > ± ± ± ± > ± ± ± ± ± ± ± ± > ± ± > ± ± ± ± > − − a Systemic redshift measured from the H or K nebular line spectrum. b Rest-frame Ly α equivalent width in ˚A measured from the narrowband and broadband photometry. c Observed line flux in 10 − erg s − cm − . d [O III ] λ III ] λ R. F. Trainor et al.
TABLE 2Emission Line Ratios
Ratio DefinitionO3 log([O
III ] λ β )N2 log([N II ] λ α )O3N2 O3 − N2O32 log([O
III ] λλ II ] λλ III ] λλ II ] λλ β )R O3 log([O III ] λ III ] λλ Note . — The λλ notation refers to the sum of both lines. measured from narrowband and broadband photometry.This difference arises in part from the scattering of Ly α photons in the ISM and CGM of their host galaxies,leading to larger inferred physical sizes in the Ly α linewith respect to the continuum (Steidel et al. 2011; Mo-mose et al. 2014) and therefore a relative underestimateof Ly α flux in slit spectroscopy. In T15, we find thatthis differential slit loss leads to an overall underesti-mate of the Ly α equivalent width in LAE spectra, suchthat W Ly α ,phot ≈ W Ly α ,spec (with substantial scatterbased on the size of the source). Similarly, Steidel et al.(2011) find a differential slit loss of 3 − × for LBGs.In general, W Ly α ,phot has the advantage of including allthe Ly α flux, as well as being more easily measured forfaint sources (for which the continuum flux is typicallynot detected in individual spectra), but it also cannotbe measured for the majority of LBGs that do not fallwithin the narrowband-selected redshift range. As such,we use W Ly α ,spec to compare the LAE and LBG sam-ples, but W Ly α ,phot is used to select individual high- W Ly α LAEs, and we denote the choice of measurement explic-itly where values are presented. In either case, the valuesof W Ly α always correspond to a measurement of the Ly α equivalent width in the rest-frame of the galaxy. EMISSION LINE MEASUREMENTS
Individual object spectra
Rest-frame optical spectra for individual LAEs were fitusing the IDL program MOSPEC (Strom et al. 2016), asdescribed in T15. For H -band spectra, the H β , [O III ] λ III ] λ z neb,H ) and velocity width ( σ v, H ), and the[O III ] λ III ] λ Sky lines are masked in the fitting pro-cess using the error vector extracted by MOSPEC, anduncertainties are measured from the χ -minimization foreach of the free parameters in the fit (i.e., H β flux, com-bined [O III ] λλ K -band spectra are fit similarly,with a simultaneous fit to the H α and [N II ] λλ α flux, combined [N II ] λλ z neb,K ), and velocity width ( σ v, K ). For each LAE,the H -band and K -band line flux measurements are cor-rected by the mask-specific correction factor(s) of thespectra contributing to the line measurement. In total, As noted in Sec. 2.2, the [O
III ] λ λ β lines are fit. SFR ( M fl yr − ) N u m b e r Observed H α sampleFull sample (incl . scaled Ly α ) H α flux (10 − erg s − cm − ) Fig. 1.—
The distribution of star-formation rates for the 60 LAEspresented in this paper. Red histogram gives the distribution ofmeasured H α fluxes and dust-corrected H α star-formation rates(SFR). The hatched histogram includes estimates for LAEs withno current K -band measurements; for these objects, the H α fluxis estimated from the measured Ly α flux and the median Ly α /H α ratio among the objects with measured H α fluxes. The H α fluxand SFR from the full LAE composite spectrum (Fig. 4) is shownby the dashed line.
27 spectra have > σ detections of H α while 27 (55, 50)have > σ detections of H β ([O III ] λ III ] λ II ] λλ σ upper limits on the ratio N2 ( ≡ log([N II ] λ α ); Table 2) range from − − α measurements using the Kennicutt (1998)relation, as displayed in Fig. 1. We apply a uniformdust-correction based on the average nebular reddeningestimated in Sec. 4.4 ( E ( B − V ) = 0 .
06; Eq. 7) and aCardelli et al. (1989) extinction curve, which produces a15% increase in the estimated star-formation rates. Forthe LAEs without current H α flux measurements, we es-timate SFRs based on the narrowband Ly α flux, scaledby the median Ly α /H α flux ratio from the objects withdirect H α measurements ( (cid:104) f Ly α /f H α (cid:105) = 3 . α - and Ly α -derived SFRs are statisticallyindistiguishable, as shown in Fig. 1. The median LAEH α SFR = 5.3 M (cid:12) yr − , which is consistent with thevalue estimated from the composite K -band spectrum(5.7 ± (cid:12) yr − ) and significantly lower than the H α -derived SFRs typical of the KBSS LBG sample we con-sider here (median SFR = 27 M (cid:12) yr − ; Strom et al.2016).Fig. 2 displays the O3 ratio for each of the 27 LAEswith > σ detections of both H β and at least one of [O III ] λ III ] λ ≈ .
5. An exception to this trendoccurs for the LAEs with the faintest continuum lumi-nosities ( M AB (1900˚A) (cid:38) − L (cid:46) . L ∗ from Reddyet al. 2008), which have lower O3 ratios than the averageLAEs or even the typical LBG values. These faintestLAEs are undetected in our R band images, and fourof them have no detection in deep, 8000 second im-ages from HST /WFC3 in the F160W filter, setting a(point source) limiting magnitude m AB (1 . µ m) > . α -Emitters 7
23 24 25 26 27 28 m AB (6800 ) l og ( [ O III ] / H β ) LBG median(Strom +16)LAE stack
22 21 20 19 18 M AB (1900 ) Fig. 2.—
The ratio O3 ≡ log([O III ] λ β ) vs. R -bandmagnitude for 27 LAEs with > σ detections of both H β and [O III ] λ R magnitudes,while triangles denote LAEs fainter than the 3 σ limit R > . σ depth m AB,F160W > . > σ detections of both H β and[O III ] λ (cid:28) Z neb (cid:28) . Z (cid:12) ) as discussed in Sec. 6.3. (3 σ ). The low O3 ratios of these sources suggest thatthe faintest LAEs have either lower excitation states thantypical galaxies at these redshifts or very low metallici-ties ( Z neb < . Z (cid:12) ). These objects are discussed in moredetail in Sec. 6.3. Measurements from composite spectra
Creation of composite spectra
In addition to our measurements of emission lines fromindividual LAEs, we construct composite LAE spectra toobtain high-S/N measurements typical of the populationof LAEs and various sub-populations.The H -band composite spectra are constructed as fol-lows. Before the individual spectra are combined, theyare resampled to the same rest-frame wavelength scaleof 0.45 ˚A pix − (equivalent to MOSFIRE’s native H -band pixel scale of 1.63 ˚A pix − in the observed frameshifted to z ≈ .
56) spanning the wavelengths 4200˚A < λ rest < H passband. In order to account for OHsky-line contamination, we resample the error vector out-put by the MOSFIRE reduction pipeline to the samewavelength scale as the science spectrum. The H -banderror vector is extremely flat across the band betweenthe sky lines, so we identify sky lines as those regionsof the error spectrum that exceed twice the median errorvalue. The exposure mask is then set to zero for these re-gions, such that contaminated pixels receive zero weightin the final stack. Typically, 19 ±
1% of pixels in eachspectrum are removed by this algorithm. In addition,some of our objects have particularly high background noise at λ rest (cid:46) H band). Wetherefore set the exposure mask to zero in any regions ofa given spectrum that lie at λ rest < > × the median noise level of the other H -band spectra at the same rest-frame wavelengths.Because the rest-optical continuum is not detected inany individual LAE spectrum, we do not scale the spec-tra by continuum magnitude before stacking. The final H composite spectrum for a given set of LAEs is then themean of all their H -band spectra, scaled by their mask-correction factors and weighted by their correspondingexposure masks (which reflect both the relative differ-ences in exposure time per object and the removal ofcontaminated or unobserved regions of each spectrum).Our H -band spectra have very little difference in expo-sure times, so each LAE receives approximately equalweight in the final H -band composite. The compositespectrum of all 55 LAEs with H -band spectroscopy isgiven in Fig. 3.Our K -band composite spectrum is constructed in asimilar manner: the individual object spectra are resam-pled to a constant pixel scale of 0.6 ˚A pix − for 5400˚A < λ rest < K pixel scale is2.17 ˚A pix − in the observed frame). The K -band er-ror spectrum has less sky-line contamination than the H band, but it also has a strong wavelength dependence at λ obs (cid:38) . µ m, where the uncertainty is dominated bythermal noise. In order to remove sky-line-contaminatedregions of the spectra before combining, we constructa smoothed noise spectrum for each object using a 25-pixel boxcar kernel and median averaging within the ker-nel. This process produces a good approximation to thethermal noise profile with minimal contributions fromsky lines. Pixels where the error spectrum is greaterthan 2.5 × this local smoothed noise spectrum are thenidentified as sky-line-contaminated regions and do notcontribute to the composite spectrum. Only 5 ±
1% ofpixels are removed from each K -band spectrum via thisprocess. The composite spectrum of all 28 LAEs with K -band spectroscopy is given in Fig. 4.We estimate uncertainties in the H and K compositespectra by means of a bootstrap procedure. For eachsample of N obj LAE spectra used to construct a com-posite spectrum, a bootstrap spectrum is generated byconstructing a bootstrap sample of size N = N obj (wherespectra are drawn randomly with replacement) averag-ing them into a bootstrap composite spectrum using thesame weighting and masking procedures described above.This process is repeated 300 times to construct an arrayof bootstrap composite spectra, and the uncertainty ateach pixel is estimated from the standard deviation ofbootstrap composite values at that pixel. In this way,the bootstrap uncertainties represent the combinationof measurement uncertainties and the true variation ofLAE spectra within each sample. These uncertaintiesare shown in Figs. 3 & 4 as a grey shaded region beloweach spectrum.In Sec. 5, we discuss composite spectra for high- W Ly α and low- W Ly α subgroups of our LAE sample. Thesecomposites are constructed in a manner identical to the R. F. Trainor et al. Rest wavelength ( ) f λ ( − e r g s − c m − − ) Fig . Fig. 3.—
Full composite H band spectrum of 60 LAEs (218 object-hours). Red line is the fit to the composite spectrum as described inSec. 3.2.2, and grey shaded region shows the 1 σ bootstrap errors on the composite spectrum, offset for clarity. Blue dashed lines correspondto the rest-wavelengths of H γ and H β , while green dot-dashed lines denote the wavelengths of [O III ] λ III ] λλ Rest wavelength ( ) f λ ( − e r g s − c m − − ) Fig. 4.—
Composite K band spectrum of 28 LAEs (83 object-hours), as in Fig. 3. Red line is the fit to the composite spectrumincluding the 2 σ upper limit on the total [N II ] λλ α . above, including the creation of their boostrap uncer-tainty vectors. The groups are split at the median pho-tometric Ly α equivalent width of our sample; LAEs with W Ly α > W Ly α compositespectrum (30 H -band spectra, 12 K -band), while theLAEs with W Ly α < W Ly α composite spectrum (25 H -band, 16 K -band). Fitting composite spectra
The composite spectra were fit using a set of gaussianline profiles and a linearly-varying continuum. For the H -band composite, five emission lines are fit simultane-ously: H γ , [O III ] λ β , [O III ] λ III ] λ λ rest of the associ-ated transition (see Table 3), and all lines are constrainedto have the same velocity width, but the amplitude ofeach emission line is fit independently. With a linearcontinuum component, there are a total of 8 free param-eters in the fit. The results of the fit are displayed inFig. 3, and the fit line fluxes are given in Table 3.The K -band composite is fit in a similar manner, butwith only 3 fit emission lines: [N II ] λ α , and[N II ] λ TABLE 3Emission Line Measurements
Transition λ rest (˚A) a Flux (10 − cgs) b H γ ± III ] λ ± β ± III ] λ ± III ] λ ± c [O III ] λ ± d [N II ] λ < e,f H α ± e [N II ] λ < e,fa Rest-frame vacuum wavelength of transition. b Best-fit line flux (10 − erg s − cm − ) in compositespectrum with 68% confidence intervals from bootstrapanalysis (Sec. 3.2). c Raw [O
III ] λ d Corrected [O
III ] λ III ] λ e The H α and [N II ] λλ K -band spectrum, which in-cludes an overlapping but smaller sample of LAEs com-pared to the H -band composite measurements. f [N II ] λλ σ limit assuming a 1:3 doubletratio. The results of this fit are also given in Fig. 4 and Table 3.Line flux uncertainties are estimated from the samplesof bootstrap spectra. For each bootstrap spectrum, theemission lines and continuum level are fit as describedabove, where each free parameter in the full compos-ite fit is allowed to vary for each bootstrap spectrum aswell. For each bootstrap spectrum, the line fluxes andbest-fit velocity width are measured. The 1 σ uncertaintyin the measurement of these parameters in the compos-ite spectrum is then estimated from the distribution ofvalues from the 300 bootstrap spectra; specifically, fromthe central interval including 68% of corresponding pa-rameter values among the bootstrap spectra (Table 3).Note that the actual uncertainty in our measurement ofa given emission line in the composite spectrum is of-ten significantly smaller than this value, but we presentthese uncertainties to reflect the range of values associ-ated with a “typical” sample of similarly-selected LAEs.In the same way, the uncertainty in the line ratioswithin a band (e.g., N2, O3; Table 4) are estimated bycomputing the corresponding line ratio for each boot-strap spectrum and measuring the size of the intervalest-Frame Optical Spectroscopy of Ly α -Emitters 9 log([NII] / H α ) l og ( [ O III ] / H β ) Fig. 5.—
N2-BPT diagram (Baldwin et al. 1981) with SDSS z ∼ σ limits; cross in lower left shows typicalerrors). Yellow bar is the O3 measurement for the LAE H -bandcomposite spectrum (Fig. 3), and pink region is current 2 σ limiton N2 from the K -band composite (Fig. 4). Black hatches denotethe combined constraints from both measurements, which showthat the LAEs are consistent with the extreme high-ionization,low-metallicity tail of the LBG population . For comparison, theblack line shows the “maximum starburst” curve from Kewley et al.(2001). encompassing 68% of the bootstrap line ratio measure-ments. Line fluxes and ratios are calculated in the samemanner for the low- W Ly α and high- W Ly α composite spec-tra. Note that this this strategy must differ for cross-band line ratios (e.g., H α /H β ), where a different numberof individual spectra contribute to the bootstrap com-posite for each emission line (see Sec. 4.4 below).In Sec. 4 below, we discuss the constraints inferredfrom the emission line ratio measurements and limits inthese composite LAE spectra. MEASUREMENTS FROM OPTICAL LINE RATIOS
N2-BPT constraints
The Baldwin et al. (1981) “BPT” diagrams provide asimple means of classifying the sources of ionizing radia-tion and physical gas properties in galaxies. In particu-lar, the N2-BPT diagram compares the ratio log([O
III ] λ β ) (hereafter, O3) to log([N II ] λ α )(hereafter, N2), which separate into two clear tracks forlow-redshift galaxies. These emission lines also have theadvantage of lying close to one another in wavelength,such that neither ratio is strongly affected by dust atten-uation or cross-band calibration errors. Fig. 5 displaysthe N2-BPT diagram for local galaxies from the SloanDigital Sky Survey (SDSS DR7; Abazajian et al. 2009)along with high-redshift measurements described below.In the N2-BPT diagram, star-forming galaxies occupythe locus of objects at low N2, while AGN-dominated andcomposite objects form a “fan” that extends toward highO3 and N2. The star-forming locus is extremely tight,with 90% of star-forming galaxies falling within ± . II regions exhibiting high O3 and low N2 (the upperleft of the N2-BPT), while those with high metallicitiesoccupy the lower right of the diagram.As described in Sec. 1, however, recent surveys athigher redshifts indicate that typical galaxies at z ≈ − σ upper limits on N2, andthe cross in the lower left shows the median uncertaintyof the points with detections. While measurement uncer-tainties contribute significantly to the observed scatter,the KBSS LBGs appear to roughly span the region be-tween the SDSS locus and the black solid line, which de-notes the “maximum starburst” limit from Kewley et al.(2001).The measurements from the LAE composite spectraare displayed as colored bands in the plot. The hori-zontal dashed line is the best-fit O3 measurement fromthe composite H -band spectrum in Fig. 3, and the yel-low region encompasses the 68% confidence interval onthis value (accounting for the scatter among the com-bined spectra through the bootstrap procedure describedin Sec. 3.2.1). The red band corresponds to the 2 σ upperlimit and confidence interval on N2 from the composite K -band spectrum in Fig. 4. The average N2-BPT lineratios of our LAEs are thus localized to the far upper leftcorner of the plot, where the two regions overlap (the val-ues of the line ratios and their uncertainties are given inTable 4).Given the correspondence between the N2-BPT locusand nebular metallicity, typical LAEs appear to be sim-ilar to the lowest-metallicity LBGs in the KBSS sample.In fact, Erb et al. (2016) isolate the most extreme 5%of LBGs in the upper left of the N2-BPT plane (effec-tively constructing a metallicity-selected sample of galax-ies) and find that they occupy almost exactly the sameregion as that defined by our composite LAE constraints:O3 ≥ .
75 and N2 ≤ − .
1. These “extreme” LBGs arefound to have similar physical and spectroscopic prop-erties to the low-redshift population of rare, compact,high-excitation galaxies known as “Green Peas” (Carda-mone et al. 2009; Amor´ın et al. 2012; Jaskot & Oey 2013),including high Ly α equivalent widths, Ly α escape frac-tions, and ionization states (O32; Table 2 & Sec. 5.2.2).In T15, we also showed that these Green Peas (as pre-sented by Henry et al. 2015) show similar Ly α and kine-matic properties to the KBSS-Ly α LAEs. Given that a Three of these “extreme” LBGs were previously described bySteidel et al. (2014).
Rest wavelength ( ) f λ ( − e r g s − c m − − ) Fig. 6.—
Zoomed-in version of the composite H -band spectrumfrom Fig. 3 at the location of the H γ (blue dashed line) and [O III ] λ simple selection based on Ly α emission and continuumfaintness apparently isolates the most extreme subset ofobjects with respect to z ≈ z ≈ − α emission and nebular properties of thesegalaxies are related; we discuss this topic in depth inSec. 5. [O III ] auroral line and gas temperature
The [O
III ] λ III gas . As this temperature is set in part by metal-line-dominated cooling in the ionized nebular regions, theauroral and nebular line measurements can also be con-verted into an estimate of the gas-phase metallicity , of-ten described as the “direct method” metallicity mea-surement.The region of the H -band composite spectrum nearthe [O III ] λ H -band spectrum are fit simultaneously (alongwith the continuum) and constrained to have the samevelocity width and redshift. These constraints signifi-cantly improve our ability to determine the [O III ] λ γ emission line providesa valuable cross-check of the wavelength and flux cali-brations at these wavelengths, which lie near the blueedge of the MOSFIRE H band. Notably, the H γ line More precisely, this measurement provides the electron tem-perature T in the region of the nebula where O III is the dominantionization state of oxygen. Specifically, the abundance of oxygen, which dominates thecooling of gas at the temperatures, densities, and metallicities typ-ical of star-forming regions. As discussed in Sec. 3.2.1, we mask out high-noise regions ofthe H band spectra at λ rest < is detected with high significance, the emission is cen-tered at the proper rest-wavelength, and the measuredflux is consistent with the expected H γ /H β ratio undercase-B recombination and E ( B − V ) ≈
0, as discussedin Sec. 4.4 below. For these reasons, we expect that thederived [O
III ] λ σ ) detection of the peak.The [O III ] line fluxes are given in Table 3. As de-scribed above, we use the λ III ] λ H band.The ratio of auroral to nebular O III line flux R O3 ≡ [O III ] ( λ λλ III ] ( λ × λ R O3 = 2 . ± . III electron temperature T ,finding a converged value T = 1 . ± . × K, wherethe uncertainty reflects the 1 σ range of R O3 ratios mea-sured in our bootstrap spectra. Gas-phase metallicity estimates
Given a measurement of the electron temperature,ionic abundances (and the “direct method” oxygen abun-dance) can be estimated via the ratios of additionalmetal-ion and hydrogen emission lines, as further dis-cussed by Izotov et al. (2006). Using the formulae fit inthat paper, we calculate the ionic O
III abundance 12 +log(O ++ /H + ) = 7 . ± .
16. The estimation of the ele-mental O/H abundance requires an ionization correctionthat can only be measured with the addition of emissionline measurements from other oxygen ions, which are notcurrently measured for the LAE sample presented here.However, there is a close relationship between O32 andO3 among the KBSS LBG galaxies (see further discus-sion in Sec. 5.2.2), such that the LBGs with O3 ≈ . ≈ . − . III ] emission5 − × stronger than that of [O II ]; Strom et al. 2016).For this reason, the contribution of O II to the total oxy-gen abundance is likely to be small among the highly-excited LAEs, and we calculate an ionization correctionbased on a likely value of O32 = 0 .
7. The temperatureof the O II zone of the H II region is typically lowerthan that of the O III zone, and the difference in tem-perature (the “ T − T ” relation) is typically found to be T ≈ . × T − T in H II regions of local star-forming galaxies(Brown et al. 2014; Berg et al. 2015).Under these assumptions, the inferred ionic O II abun-dance is 12 + log(O + /H + ) = 7 . ± .
19, where the un-certainty includes only the range of T consistent withour bootstrap spectra. If the true O32 ratio for ourLAE spectra is greater than the assumed value of 0.7,or if the O II temperature is higher than that predictedby our assumed T − T relation, then the contributionof O II to the total oxygen abundance is even smaller.Conversely, Andrews & Martini (2013) suggest that the improves the quality of our H γ and [O III ] λ See also discussion in Steidel et al. (2014), wherein we present T e measurements for three KBSS LBGs. est-Frame Optical Spectroscopy of Ly α -Emitters 11formula above overestimates T by ∆ T ≈ + /H + ) to 7.28.Assuming that O III and O II are the dominant statesof oxygen in the nebular regions (and likewise that theneutral fraction of hydrogen is negligible in these re-gions), the inferred “direct” oxygen abundance is thusthe sum of the above ionic abundances, and we estimatea total oxygen abundance 12 + log(O/H) dir = 7.80 ± Z neb ≈ . Z (cid:12) ). As above, the uncertainty correspondsto the statistical uncertainty from our bootstrap mea-surements; for comparison, assuming O32 = 1.0 or usingthe Andrews & Martini (2013) T calibration would shiftour inferred oxygen abundance by − III lines discussed above to over-estimate the volume-averaged electron temperature of acloud. This effect may occur due to the temperaturesensitivity of the emissivity of CELs, which causes anyluminosity-weighted T e measurement to be biased towardthe highest-temperature regions of the nebula. Such abias may cause metallicity estimates from CELs to un-derestimate the metallicity relative to that inferred fromrecombination lines (RELs) and stellar spectra. Thiseffect is seen in the detailed spectroscopic LBG studydescribed by Steidel et al. (2016), who find an offsetbetween the nebular O/H abundance inferred from the[O III ] “direct” method and that obtained through com-prehensive modeling of the nebular and stellar spectra.Steidel et al. find an offset consistent with that mea-sured from CELs and RELs in local low-metallicity dwarfgalaxies by Esteban et al. (2014):log(O / H) REL − log(O / H) CEL = 0 . ± .
02 dex (1)In constrast, Bresolin et al. (2016) find a low-metallicity REL-CEL offset of similar magnitude, butthey suggest that CELs are more accurate than RELsby comparing both estimators to stellar metallicities col-lected from the literature. Given that the results of Stei-del et al. (2016) appear to corraborate the Esteban et al.(2014) offset at z ≈ −
3, we apply a +0.24 dex correctionto our “direct” abundance measurement described abovein order to determine our final estimate of the nebulargas-phase metallicity:12 + log(O / H) = 8 . ± .
19 (2) Z neb = 0 . +0 . − . Z (cid:12) (3)where the uncertainty reflects both the statistical uncer-tainties from our bootstrap analysis and the statisticaluncertainty in the Esteban et al. (2014) calibration, butit does not include the systematic uncertainty in the ap-plication of the REL-CEL offset, nor those associatedwith the O II abundance discussed above.As described in Sec. 4.1, the O3 and N2 ratios arealso often used as gas-phase metallicity indicators (the“strong-line” metallicity indicators N2 and O3N2, Ta-ble 2) through local calibrations to T e -based measure-ments. As discussed by Steidel et al. (2014, 2016), thesestrong-line indicators are based on the adherence of star- forming galaxies to their locus in the local N2-BPT plane,and thus require recalibration at high redshift, where thislocus is offset toward higher values of nebular excita-tion. Lacking a direct calibration of these relationshipsat z ≈
2, we use the recent calibration of O3N2 by Stromet al. (2016), which is based on a local set of extragalacticH II regions from Pilyugin et al. (2012). Using this rela-tion, our best-fit measurement of O3, and our 2 σ upperlimit on N2, we obtain the following limit:12 + log(O / H) O3N2,Strom16 < .
17 (4)which is consistent with the corrected direct estimate inEq. 2. For comparison, the widely-used N2 and O3N2abundance calibrations by Pettini & Pagel (2004) alsoproduce estimates consistent with our direct-method de-termination:12 + log(O / H) O3N2,PP04 < .
10 (5)12 + log(O / H) N2,PP04 < . . (6) Balmer decrement and extinction measurements
The above inferences are based on line ratios (O3, N2,R O3 ) that fall within a single MOSFIRE band. However,not all the LAEs in our sample have both H and K banddetections, which means that cross-band line ratios (suchas the Balmer decrement, H α /H β ) cannot be measuredfor the full sample of spectra. Eleven LAEs in our samplehave > σ detections of both H α and H β . Among thesespectra, the average ratio is H α /H β = 2.92 ± σ error on the average estimated viaa modified bootstrap technique similar to that describedin Sec. 3.2.1 above, but modified so that the same ran-domized set LAEs contribute to each bootstrap sampleof both H α (in the K band) and H β (in the H band).We estimate the average extinction from the Balmerdecrement assuming a Cardelli et al. (1989) Milky-Wayextinction curve and the tabulated intrinsic H α /H β ra-tios from Brocklehurst (1971). Typically, extinction mea-surements for high-redshift galaxies assume an electrontemperature T e ≈ K, corresponding to an intrinsicratio H α /H β = 2.89 . However, our measurement ofthe [O III ] λ T e ≈ . × K, so we adopt the Balmer decrement valuefor T e = 2 × K from Brocklehurst (1971): H α /H β =2.74. Choosing the higher intrinsic ratio would decreaseour inferred extinction by a small amount, as discussedbelow.Under these assumptions, our Balmer decrement mea-surements correspond to a reddening, V -band extinction,and H α extinction as follows:E( B − V ) = 0 . ± .
12 (7) A V = 0 . ± . A H α = 0 . ± . . Choosing an intrinsic ratio H α /H β = 2.89 would im-ply E ( B − V ) = 0 . ± .
12, consistent with the above Some references prefer the value of 2.86 from Osterbrock &Ferland (2006), but this difference makes a negligible change in ourinferred extinction. H and K stacks usingthe uncorrected H α and H β values from Table 3 (de-spite corresponding to different samples of LAEs). Fromthese values, we calculate a Balmer decrement H α /H β =3.37, or E( B − V ) = 0 . α and H β lines, likely re-flecting the fact that our current K -band spectra areshallower on average than those in the H band, suchthat bright H α lines are over-represented in the full K stack. We therefore take the extinction inferred from thematched sample (Eq. 7) to best represent our full LAEpopulation, and the dust-corrections used to derive LAEstar-formation rates in Fig. 1 are based on this value. THE NEBULAR ORIGINS OF Ly α EMISSION
In order to determine the physical properties of LAEs,it is important to understand the physical drivers of theirmost salient characteristic: strong Ly α emission. Towardthis end, we here consider the relationship between thenebular properties described above and the Ly α emis-sion of our LAE sample, as well as that of a compari-son sample of LBGs from the KBSS (Steidel et al. 2014,2016; Strom et al. 2016). The KBSS and KBSS-Ly α rep-resent the richest current sample of combined Ly α andrest-optical spectroscopy for star-forming galaxies at anyredshift , so these surveys are a powerful tool for dissect-ing the physical differences between galaxies selected byLy α emission and those selected by continuum bright-ness, while also establishing the variation in net Ly α emissivity with galaxy properties across the combinedpopulation of LAEs and LBGs. The BPT-Ly α relation As discussed above in Sec. 4.1, the N2-BPT diagramprovides a useful discriminant of the physical propertiesof ionized regions within a galaxy, which constrains themetallicity of both the gas itself and the sources of ion-izing radiation, including properties of the stellar popu-lations.Fig. 7 displays the N2-BPT line ratios of 336 KBSSgalaxies with > σ ( > σ , > σ ) detections of H α (H β ,[O III ] λ α equivalent widths, W Ly α ,spec . While there is consid-erable scatter in the nebular line ratios at a given valueof W Ly α ,spec , there is also a clear trend such that Ly α -emitting LBGs ( W Ly α ,spec >
0, blue points) have highvalues of O3 and low values of N2 (i.e., they lie in theupper-left region of the N2-BPT space), whereas Ly α absorbers ( W Ly α ,spec <
0, red points) preferentially oc-cupy the opposite corner of parameter space. Objectswith spectra indicating AGN activity (e.g., broad nebu-lar emission lines and/or strong C IV or He II UV emis-sion) are denoted by diamonds in the plot; these objectsshow high ratios of both O3 and N2 similar to the spectraof low-redshift AGN.The region of the N2-BPT parameter space consistentwith our composite LAE spectra (as in Fig. 5) is dis-played as the hatched region in Fig. 7. The nebular lineproperties of the composite LAE spectra are generally The central 68% confidence interval in O3 and the 2 σ upperlimit on N2 from our bootstrap analysis. consistent with those of the KBSS LBGs with the high-est values of W Ly α .Fig. 8 compares the composite LAE line ratios to anal-ogous stacked measurements of subsamples of the KBSSLBGs, which are described in Table 4. The KBSS sub-samples are divided on the basis of W Ly α : Ly α -absorbers( W Ly α ,spec < α -emitters (0 < W Ly α ,spec < α -emitters ( W Ly α ,spec > H and K spectra cover the rest-wavelengthsof all 4 of the N2-BPT diagnostic lines: H β , [O III ] λ α , and [N II ] λ H and K composites while maximiz-ing their S/N, both spectra for each object are weightedby the inverse-variance at the wavelength of the [N II ] λ σ upper limit of N2, witherror bars reflecting the 68% confidence interval on O3and the 2 σ upper limit of N2. The value of W Ly α ,spec ismeasured for each LAE and LBG sample directly fromthe corresponding composite UV spectrum by compar-ing the measured Ly α line flux (without correcting forLy α slit losses) to the UV continuum flux on the redside of the Ly α line, as is described for measurements ofindividual LBG spectra in Sec. 2.3.As in Fig. 7, Fig. 8 shows a clear trend between thevalue of W Ly α for a given subsample and its position inthe N2-BPT plane. The composite measurements paral-lel the locus of SDSS N2-BPT measurements, albeit withan offset consistent with previous studies of high-redshiftstar-forming galaxies, as discussed above. Notably, ourcurrent limits on the typical properties of faint LAEsappear consistent with the trend seen in the LBG com-posites; the “BPT offset” of the full LAE composite mea-surement may be slightly greater than that of the KBSScomposites, but the LAE measurement may actually be more consistent with the SDSS locus depending on the(currently unmeasured) typical LAE N2 ratio. Ratherthan investigating the source of this offset, we thereforeconsider what physical galaxy properties are changing along the locus of z ≈ − α emissivity.The highest- W Ly α objects and composite spectra inour sample are those that lie nearest to the low-metallicity end of the SDSS galaxy locus (see discussionin Sec. 4.1). Given the correlation between gas-phasemetallicity and dust content, this may suggest that ourobserved trend is a signature of the previously-studiedtendency of LAEs to exhibit lower dust attenuation withrespect to continuum-selected galaxies. In such a sce-nario, the variation in net Ly α emissivity along the N2-BPT locus (as parameterized by W Ly α ) is primarily avariation in the physics of Ly α escape , which is expectedto depend sensitively on the distribution of gas and dustwithin the interstellar medium of the host galaxies.However, Steidel et al. (2014) demonstrate that gas-est-Frame Optical Spectroscopy of Ly α -Emitters 13 TABLE 4LAE and LBG Subsamples
Sample Subsample N obj (cid:104) W Ly α (cid:105) a SFR b N2 O3 H α /H β c E( B − V ) d all 60 56.2˚A 7.7 ± < − ± ± ± W Ly α ,phot > ± < − ± ± < − < W Ly α ,phot ≤ ± < − ± ± ± W Ly α ,spec > ± − ± ± ± ± ≤ W Ly α ,spec ≤ ± − ± ± ± ± W Ly α ,spec < − ± − ± ± ± ± a Composite spectroscopic rest-frame Ly α equivalent width. W Ly α > W Ly α < b Dust-corrected H α star-formation rate in M (cid:12) yr − . For the LAEs, only objects with K -band spectra are included (Table1). c The Balmer decrement H α /H β is measured only for the subset of objects with > σ detections of both H α and H β in theirindividual spectra (11 LAEs, of which 5 are in the low- W Ly α group and 8 are in the low- W Ly α group). d Color excess is estimated using a Cardelli et al. (1989) extinction curve ( R V = 3 . α /H β = 2 .
74 ( T e ≈ × K) is assumed for the LAEs, whereas H α /H β = 2 .
89 ( T e ≈ K) is assumed for the LBGs as describedin Sec. 4.4. log([NII] / H α ) l og ( [ O III ] / H β ) ± ± ± W L y α , s p ec Fig. 7.—
N2-BPT diagram as in Fig. 5, but with KBSS LBGs color-coded by Ly α equivalent width ( W Ly α ). Blue points show Ly α inemission, while red points show Ly α in absorption. The sizes of the points correspond to the absolute value of W Ly α . Error bars in lowerleft correspond to the median 1 σ uncertainties on the detected KBSS points. Blue diamonds in the upper right corner correspond to KBSSobjects with spectroscopically-identified AGN emission (Steidel et al. 2014). The black hatched region shows the confidence interval forthe LAE stacks. Solid black line denotes the “maximum starburst” curve from Kewley et al. (2001), while the dashed black line shows theStrom et al. (2016) KBSS locus. There is a general trend for high- W Ly α galaxies to occupy the upper left of the diagram (near the LAEsample), whereas low- W Ly α objects occupy the lower right. The physical origins of this trend are analyzed throughout Sec. 5. LAEsLBGs log([NII] / H α ) l og ( [ O III ] / H β ) W L y α , s p ec Fig. 8.—
N2-BPT diagram as in Figs. 5 & 7, but with KBSSpoints stacked in three subsamples according to their value of W Ly α (Table 4). Error bars correspond to the 1 σ uncertaintiesfrom bootstrap resampling. In analogy to the other points, theLAE stacks are presented with a point at the best fit value of O3and the 1 σ limit on N2, with error bars indicating the 1 σ uncer-tainty on O3 and the 2 σ upper limit on N2. The solid black linedenotes the “maximum starburst” curve from Kewley et al. (2001),while the dashed black line shows the Strom et al. (2016) KBSSlocus. A strong trend is visible as W Ly α increases toward the low-metallicity end of the N2-BPT locus. phase metallicity has more minor effects on the positionof individual galaxies within the locus of star-forminggalaxies at z ≈ − z ≈
0. Rather, theprimary determinants of the N2-BPT line ratios in LBGsgalaxies appear to be the relative hardness of the inci-dent radiation field and the effective ionization parameter n γ /n H , the dimensionless ratio of hydrogen-ionizing pho-tons to hydrogen atoms within the ionized star-formingregions. This ionization parameter may also be expressedas the factor U ≡ Φ H /n H c , where n H is the numberdensity of hydrogen atoms (including ionized, neutral,and molecular) in the star-forming regions and Φ H isthe surface flux of H-ionizing photons incident on theilluminated face of the H II region, as defined by Oster-brock & Ferland (2006). A recent, thorough discussionof the ionization parameter, its various definitions, andits observational constraints in the star-forming regionsof z ≈ − U in the sectionsthat follow in order to compare our measurements topredictions from the Cloudy photoionization code (Fer-land et al. 2013), which explicitly defines U as describedabove, but we note that the physical interpretation ofthis ratio can become ambiguous when divorced fromthe specific plane-parallel or spherical ionization geome-tries assumed by photoionization models (as discussed bySteidel et al. 2014).Crucially, the dependence of a galaxy’s nebular lineratios on U and the radiation field hardness means thatthese ratios are strongly determined by the overall nor-malization and shape of the stellar radiation field at pho-ton energies 1 Ryd < E γ (cid:46) II regions as to the intrinsic properties of the ionizedgas. Specifically, Steidel et al. (2014) argue that the neb- E( B − V ) neb W L y α Spearman correlation ρ = − . p =5 . e − Fig. 9.—
The spectroscopic equivalent width of Ly α ( W Ly α ) vs.the nebular reddening E( B − V ) inferred from the Balmer decre-ment measurement for individual KBSS LBGs (grey points) andKBSS-Ly α LAE composite spectra (large black square indicatesthe full sample, while smaller squares denote the low- W Ly α andhigh- W Ly α subsamples). Circled points are those with S/N > α /H β , the limit proposed by Strom et al. (2016) for secure mea-surements of E( B − V ). The horizontal dashed line demarcates theboundary between Ly α -absorbers ( W Ly α <
0) and Ly α -emittingLBGs ( W Ly α > W Ly α has only modest dependence on the in-ferred reddening and attenuation by dust. The LAEs have muchhigher values of W Ly α than reddening-matched LBGs. ular line spectra of z ≈ − (cid:29) Myr) timescales as described inSec. 1.In the section below, we consider two possible modesby which the nebular spectra of these galaxies may betied to Ly α emissivity: variation in the extinction ofLy α photons by interstellar dust (which may also ap-pear as reddening in the nebular spectra), or variationin the Ly α production rate via recombination in ionizedstar-forming regions (which may produce changes in theobserved nebular excitation). Origin of the BPT-Ly α relation Ly α emission vs. dust attenuation We investigate the modulation of Ly α emissivity bydust by comparing the relationship between W Ly α andthe nebular reddening E( B − V ) estimated from theBalmer decrement (as described in Sec. 4.4) for each ofthe KBSS LBG spectra and the LAE composites (includ-ing the low- W Ly α , high- W Ly α , and combined subsam-ples). The inferred nebular reddening and Ly α equiva-lent width for each LBG (from the set of 336 objects withfull N2-BPT and Ly α line coverage) and LAE compositeis shown in Fig. 9. An association of high- W Ly α LBGswith low values of E( B − V ) is visible, although thereare several LBGs with high values of both W Ly α andE( B − V ). A non-parametric Spearman rank-correlationtest finds a weak negative correlation ( ρ = − .
15) be-est-Frame Optical Spectroscopy of Ly α -Emitters 15tween W Ly α and E( B − V ) for the LBG sample withmoderate significance ( p = 5 × − ). Strom et al. (2016)find that some KBSS LBGs exhibit unphysical dust-corrected line ratios (e.g., in the R23-O32 plane) whencorrections are applied based on low-S/N measurementsof E( B − V ) neb , suggesting a limit of H α /H β > σ for reli-able estimates of the dust attenuation. The 200 LBGsin the sample that meet this cut (including the uncer-tainty in the cross-band calibration) are circled in Fig. 9;they occupy a very similar distribution to the lower-S/Nobservations, with a comparable correlation ( ρ = − . p = 3 × − ). The LAE compositespectra (black squares) appear to show a much strongerrelationship with E( B − V ), but we have insufficient datato quantify this trend among the LAEs alone. Notably,however, the LAE W Ly α measurements are clearly incon-sistent with the distribution of LBG points at similar val-ues of E( B − V ): at fixed reddening, the LAE compositeshave significantly higher values of W Ly α than the LBGpoints. It appears, therefore, that a difference in dustattenuation is insufficient to explain either the variationof W Ly α among the KBSS LBG sample or the differencesbetween the LAE and LBG populations.Although it is expected that absorption by dust is theprimary mechanism for the destruction of Ly α photonsin galaxies, there have been previous observational indi-cations that dust and Ly α emission can co-exist. Whileno previous sample of z ≈ − W Ly α and nebular E( B − V ) in detail, studies of thebroadband spectral energy distributions of LAEs havefound galaxies exhibiting both strong Ly α emission andlarge inferred stellar E( B − V ) (Kornei et al. 2010; Ha-gen et al. 2014; Matthee et al. 2016), including objectswith E ( B − V ) stars (cid:38) .
4. The 14 “extreme” LBGsin the Erb et al. (2016) sample have higher W Ly α andlower E( B − V ) neb than average KBSS LBGs, but in-clude individual objects with inferred reddening as highas E ( B − V ) neb ≈ .
34 in the sample of objects withH α /H β S/N >
10 (or as high as E ( B − V ) neb ≈ . W Ly α > E ( B − V ) neb = 1 .
2, evenwith the Strom et al. (2016) cut on S/N. Conversely,there is a substantial population of LBGs with low val-ues of E( B − V ) and low or no net Ly α emission: theaverage LBG with E( B − V ) neb consistent with our fullLAE composite ( E ( B − V ) neb (cid:46) .
06, approximately thelowest quartile in the LBG E( B − V ) neb distribution)is actually a net absorber of Ly α photons in slit spec-troscopy (median W Ly α ,spec = − . .While neither E( B − V ) stars nor E( B − V ) neb is a per-fect proxy for the attenuation of Ly α photons by dust, Specifically, Strom et al. (2016) find that some low-S/N ob-jects are scattered toward unphysically low O32 and high R23 val-ues. In addition, there is a subset of objects with robust line de-tections for which the H α /H β appears to overestimate E( B − V ),likely indicating cases where the Cardelli et al. (1989) extinctioncurve is inappropriate. Note, however, that the escape of scattered Ly α photons atlarge galacto-centric radii can cause galaxies with net (spatially-integrated) Ly α emission to show net absorption in slit spec-troscopy (Steidel et al. 2011). O32 W L y α Spearman correlation ρ =0 . p =2 . e − Fig. 10.—
The spectroscopic equivalent width of Ly α ( W Ly α )vs. the dust-corrected O32 ratio for individual KBSS LBGs (greypoints). Circled points are those with more secure dust corrections,as in Fig. 9. Despite substantial scatter, there is a stronger trendthan is seen for W Ly α vs. E( B − V ). log([OIII] / H β ) W L y α Spearman correlation ρ =0 . p =1 . e − Fig. 11.—
The spectroscopic equivalent width of Ly α ( W Ly α )vs. the [O III ]/H β ratio–a measure of nebular excitation–for in-dividual KBSS LBGs (grey points) and LAE composites (largeblack square indicates the full sample, while smaller squares de-note the low- W Ly α and high- W Ly α subsamples), as in Fig. 9. Astrong trend is present, with the LAE stacks displaying similarexcitation-matched W Ly α values to the LBGs, indicating that theobserved W Ly α is strongly modulated by the physics governing Ly α production within H II regions. E( B − V ) neb has the advantage of tracing the attenua-tion of photons from the same star-forming regions whereLy α photons are expected to originate (rather than thediffuse interstellar dust distribution traversed by photonsfrom spatially-extended populations of stars). We sug-gest, therefore, that our observations are the strongestevidence yet that low dust content, while associated withLy α escape, is neither necessary nor sufficient for pro-ducing strong Ly α emission in galaxy spectra. The trendin W Ly α with position on the N2-BPT diagram is there- While E( B − V ) neb is seen to be greater than E( B − V ) stars intypical galaxies samples, Price et al. (2014) demonstrate that thisdiscrepancy is minimized in high sSFR galaxies similar to thosediscussed here. Ly α emission vs. nebular excitation We now consider the second mode by which the nebularspectra of galaxies may be linked to their Ly α emission:the ionization and recombination processes within theirstar-forming regions. There are multiple reasons why theionization and excitation states of gas in H II regions maybe associated with Ly α emission. Stronger sources of ion-izing photons (e.g., hotter populations of massive stars)will both increase the typical ionization state of theirsurrounding gas and result in a larger production rate ofLy α photons (as well as other products of recombinationemission). Secondly, density-bounded H II regions (thosein which the star-forming cloud becomes completely ion-ized) will be more transparent to escaping Ly α photonsthan those that are surrounded by thick shells of neutralgas. Similarly, such density-bounded H II regions mayexhibit high average ionization ratios (e.g., O32; Table2), as discussed in Sec. 7We have not obtained measurements of the [O II ] λλ J band at z ≈ . − .
6) for our LAE sample,but we can investigate the trend between O32 and W Ly α in our comparison sample of KBSS spectra. Fig. 10 showsthe O32 ratio for the subset of the N2-BPT LBG samplethat also have a > σ detection of [O II ] λλ B − V ) neb measurements described aboveand a Cardelli et al. (1989) extinction curve. As in Fig. 9,circled points are those meeting a 5 σ cut on the H α /H β dust correction and MOSFIRE J - H cross-calibration.Substantial scatter is present among the valuesof W Ly α at fixed O32, although a Spearman rank-correlation test shows a much stronger trend ( ρ = 0 . p = 2 × − ) than is seen in the W Ly α -E( B − V ) rela-tionship. The objects with the most secure dust correc-tions and cross-band flux calibrations (175 objects) showa still stronger correlation ( ρ = 0 . p = 3 × − ).The median W Ly α measurement among LBGs in the up-per quartile of O32 (O32 > .
46) is W Ly α = 8 . α emitters (unlikethe lowest quartile of LBGs in E( B − V )). Among theKBSS-LBG sample, it therefore appears that O32 is abetter predictor of strong Ly α emission than E( B − V ).While we cannot directly measure O32 for the LAEsamples presented here, the O3 ratio is a related mea-sure of the nebular excitation properties of galaxies. Al-though O3 is sensitive to the gas-phase oxygen abun-dance at very low metallicities ( Z (cid:46) . Z (cid:12) , Sec. 6),it is much more sensitive to the ionization parameterand hardness of the incident spectrum at more interme-diate sub-solar metallicities typical of the KBSS LBGs(0 . Z (cid:12) (cid:46) Z (cid:46) . Z (cid:12) ; Steidel et al. 2014, 2016; Stromet al. 2016). Furthermore, the O32 and O3 ratios areclosely correlated; the Spearman rank correlation be-tween both values is ρ = 0 .
74 for the 175 KBSS LBGswith the highest-confidence dust-corrected O32 values.The O3 ratio also has the advantage of requiring no dustcorrection or cross-band calibration, as both lines lie neareach other in the MOSFIRE H band at z ≈ − .
6. The O3 ratio is therefore a useful discriminant for com-paring the excitation properties of the LBG and LAEsamples and their variation with W Ly α , as is shown inFig. 11. A Spearman test among the 336 LBGs in theN2-BPT sample yields ρ = 0 .
39 and p = 10 − forthe O3- W Ly α correlation, approximately as strong as theO32- W Ly α correlation. Furthermore, the KBSS galax-ies with O3 > .
82, consistent with the full LAE com-posite measurement, are typically strong Ly α emitters(median W Ly α = 14 . In general, the LAEs havequite similar values of W Ly α to excitation-matched sam-ples of KBSS LBGs, in contrast to the distribution ofattenuation-matched LBGs in Fig. 9 . Similarly, thereare very few Ly α -emitting KBSS LBGs with low O3values, including only two objects with O3 < . W Ly α > W Ly α at fixed excitation isnot surprising, given the multiplicity of factors that gov-ern Ly α escape. Nevertheless, it appears that the netLy α emission that escapes star-forming galaxies at smallgalactic radii (that is, the Ly α emission to which slitspectroscopy is most sensitive) remains closely coupledto the properties of their ionized birthplaces despite thesubsequent interactions of these photons with the sur-rounding interstellar and circumgalactic media. PHOTOIONIZATION MODEL COMPARISON
Model parameters
The nebular spectra of star-forming galaxies are sen-sitive to a broad range of physical parameters, includ-ing the electron density n e , ionization parameter U , gas-phase metallicity and elemental abundance patterns; thestellar metallicity and abundance patterns, ages, initial-mass function (IMF), and evolutionary properties of theembedded stars; as well as the foreground extinction.Many of these properties can produce degenerate effectson galaxy spectra, particularly when only a few nebularlines are observed. Given that our current measurementsare limited to the brightest lines in the H and K atmo-spheric windows, we use the trends established amongthe brighter LBG samples in Sec. 5.2 and the more de-tailed modeling presented by Steidel et al. (2016, here-after S16) and Strom et al. (2016) to constrain the rangeof physically-motivated model parameters.With this in mind, we run a grid of Cloudy (Fer-land et al. 2013) photoionization models over a rangeof physical gas parameters and sources of incident radi-ation consistent with these previous studies. We varythe ionization parameter U over the range − ≤ log U ≤ − .
5, where log U is varied in steps of ∆log U =0 .
1. The gas-phase metallicity is varied over the range0 . ≤ Z neb /Z (cid:12) ≤ . Z = 0 .
1, as well as0 . ≤ Z neb /Z (cid:12) ≤ . Z = 0 .
01. TheCloudy models assume a solar abundance pattern fromAsplund et al. (2009), but we scale the output nitrogen-based line ratios according to the relation between N/Oand O/H suggested by Strom et al. (2016):log(N/O) = − .
48 + 1 . × [12 + log(O/H)] . (8) We use Cloudy v13.02 for consistency with the modeling ofKBSS LBGs by Steidel et al. (2016) and Strom et al. (2016). est-Frame Optical Spectroscopy of Ly α -Emitters 17However, this relationship is not intended to be appliedat the lowest metallicities, where many surveys of locallow-metallicity galaxies and H II regions have found thatthe N/O vs. O/H relation becomes flat, with log(N/O) ≈− . − .
5, which applies at all inferred oxygenabundances less than 12 + log(O/H) = 8.26 ( Z neb =0 . Z ).We fix the electron density n e = 300 cm − as in S16,consistent with the measured electron densities from theKBSS and MOSDEF surveys ( n e ≈ −
360 cm − ; Stei-del et al. 2014, 2016; Sanders et al. 2016; Strom et al.2016). While individual galaxy spectra in these surveysexhibit a wide range of n e , Strom et al. (2016) demon-strate that there is no trend between inferred n e andoffset from the low-redshift N2-BPT locus, and we like-wise find no correlation between inferred n e and stellarmass or Ly α equivalent width.We perform our photoionization modeling using inci-dent stellar radiation fields from the latest version of twospectral-synthesis codes: Starburst99 (Leitherer et al.2014) and BPASSv2 (Eldridge & Stanway 2016; Stan-way et al. 2016), the latter of which includes explicitmodelling of the effects of binary interactions on stel-lar evolution. Several models from each model suite aredescribed in detail in S16. In that paper, deep rest-UV and rest-optical spectra are modeled simultaneouslyto constrain the properties of the stellar populations inKBSS LBGs, finding that the composite spectra require Z ∗ (cid:28) .
008 and are best fit by Z ∗ = 0 . − . Z ∗ /Z (cid:12) = 0 . − . Z ∗ ) from thegas-phase metallicity input to the photoionization code( Z neb ); the physical rationale for this choice is dicussedbelow.We adopt the best-fit Z ∗ = 0 . Z (cid:12) BPASSv2 modelfrom S16 as our fiducial stellar population, which isdenoted as BPASSv2-z001-300bin in that paper. Themodel assumes a Salpeter (1955) IMF (power law indexof − .
35) and a stellar mass range of 0 . ≤ M ∗ ≤ (power law index of − .
30) anda stellar mass range of 0 . ≤ M ∗ ≤ Z ∗ = 0 .
002 ( Z ∗ = 0 . Z (cid:12) ) that areotherwise identical to the Z ∗ = 0 .
001 models. All ourstellar models assume a continuous star-formation his-tory of 100 Myr. As noted in S16, these models do notchange appreciably in the far-UV after a few × years,which is approximately the central dynamical time of theKBSS-Ly α LAEs and thus the shortest likely timescalefor galaxy-scale bursts of star formation in these systems.As shown in S16, small differences in the IMF power-law index do not significantly affect the output nebularline ratios: increasing (flattening) the slope of the Star-burst99 IMF from − . − . − . Note that the low-mass behavior of the IMF causes signifi-cant differences in the total stellar masses and star-formation ratesinferred for Salpeter (1955) and Kroupa (2001) IMFs, but has anegligible effect on the predicted UV spectrum of a stellar popula-tion. These models are denoted BPASSv2-z002-300bin and S99-v00-z002 in S16.
LBG composite spectrum by S16. Changing the upper-mass cutoff of the IMF (i.e., from 100 M (cid:12) to 300 M (cid:12) )does harden the EUV spectrum, although to a lesser ex-tent than the inclusion of massive stellar binaries. Eventhe Starburst99 models from Leitherer et al. (2014) thatinclude rapid stellar rotation do not produce the signifi-cant changes to the EUV spectral shape that are requiredto explain the nebular line ratios of the KBSS LBGs. Inaddition, models which exclude binary interactions (e.g.,both the Starburst99 models and the BPASS non-binarymodels) do not generate He II λ > Modeling the composite spectra
The Cloudy predictions for both the S99-v00-z***models (hereafter “the S99 models”) and the BPASSv2-z***-300bin models (hereafter “the BPASS models”) inthe N2-BPT plane are given in the top panels of Fig. 12for a range of gas-phase metallicities and ionization pa-rameters. Values of Z neb between grid points are interpo-lated using a cubic spline. For both stellar metallicitiesconsidered, the BPASS model produces higher averageexcitation (O3) values at fixed Z neb and U . Note thatO3 increases with Z neb at low Z neb for all models up toa maximum at Z neb ≈ . Z neb isincreased further. N2, however, increases monotonicallywith increasing Z neb .The constraints on the typical LAE excitation are plot-ted as the shaded box in each panel (as above, we usethe 68% confidence interval in O3 and the 2 σ upper limiton N2). For the S99 models, only the highest ioniza-tion parameters are able to reproduce the best-fit LAEline ratios (particularly for Z ∗ = 0 . Z (cid:12) models), whilethe BPASS stellar models are relatively insensitive to Z ∗ and are able to reproduce the LAE measurements over arange of values of Z ∗ , Z neb , and U .The bottom panels of Fig. 12 show these constraintsexplicitly. In each panel, the red shaded region corre-sponds to the values of ( U , Z neb ) that produce N2 andO3 ratios consistent with the LAE composite measure-ments using the BPASS stellar models. Similarly, theblue region corresponds to the range of allowed parame-ters assuming the S99 input stellar spectra. The blue andred dashed curves correspond to the values ( U , Z neb ) thatproduce the best-fit value of O3 = 0 .
82 (Table 4) and areconsistent with the upper limit on N2. As in the top pan-els, values are interpolated in between grid points using acubic spline. Formally, values of Z neb (cid:38) Z (cid:12) are allowedfor both of the Z ∗ = 0 . Z (cid:12) stellar models, although theBPASS model cannot reproduce the best-fit observed O3ratio and N2 limit with Z neb > .
7. Stronger constraintson the N2 ratio are needed to cross-check the typicalgas-phase metallicity ( Z neb ≈ . Z (cid:12) ) inferred from the[O III ] λ Z neb less than ∼ U (cid:38) − . log([NII] / H α ) l og ( [ O III ] / H β ) Z n e b / Z fl . . l og U − . − . Z ∗ =0 . Z fl BPASSS99LBG locusLAE stack log([NII] / H α ) l og ( [ O III ] / H β ) LBG locus Z ∗ =0 . Z fl BPASSS99LAE stack log( U ) Z n e b / Z fl Z ∗ =0 . Z fl LAE
BPASS constraintsLAE
S99 constraintsLBG
BPASS (S16)LBG
S99 (S16)LAE best est .Z neb = Z ∗ Z neb = Z dir log( U ) Z n e b / Z fl Z ∗ =0 . Z fl LAE
BPASS constraintsLAE
S99 constraintsLBG
BPASS (S16)LBG
S99 (S16) Z neb = Z ∗ Z neb = Z dir Fig. 12.— ( Top ) N2-BPT predictions for the Cloudy photoionization models given an input spectrum from BPASS (red) or S99 (blue)stellar populations. The left panel uses a Z ∗ = 0 . Z (cid:12) ( Z ∗ = 0 . Z ∗ = 0 . Z (cid:12) ( Z ∗ = 0 . σ limit on N2 from the full LAE composite spectra (Figs. 3 & 4). Photoionizationmodels are plotted as a function of Z neb for each value of U , with − ≤ log U ≤ − . U increasing from the bottom to the top ofthe panel) and 0 . ≤ Z neb /Z (cid:12) ≤ .
0. Marker size increases with increasing metallicity, and Z neb < . Bottom ) Constraints on the gas-phase metallicity Z neb and ionization parameter U from the LAE composite spectra and the Cloudymodels presented in the top panels. Red regions correspond to the parameters consistent with the LAE N2-BPT limits assuming a BPASSstellar population (with stellar metallicity as above), while the blue regions correspond to parameter constraints assuming a S99 stellarpopulation. Dashed curves correspond to parameters that reproduce the best-fit measurement of O3 from the LAE composite spectrum.The horizontal dot-dash line corresponds to the gas-phase metallicity estimated via the auroral [O III ] transition (Sec. 4.2), and the blackbox represents our best estimate of the LAE nebular and stellar parameters: ( Z ∗ , Z neb , log U ) = (0.07, 0.022, -2.1). The dashed linerepresents the gas-phase metallicity equal to the input stellar metallicity in each panel: it is evident that the two metallicities are difficultto reconcile assuming solar abundance patterns. Red circles (blue squares) represent the best-fit values of Z neb inferred for the LBGcomposite spectra by Steidel et al. (2016) using the same stellar BPASS (S99) model spectra, although the S99 models fail to reproduceother nebular ratios discussed in that paper. The LAE spectra require significantly enhanced ionization parameters with respect to theLBG samples. est-Frame Optical Spectroscopy of Ly α -Emitters 19Given that the galaxies in the LBG sample have lumi-nosities and masses ∼ × larger than the typical LAEs,we find it likely that the LAEs have average stellar metal-licities at least as low as the metallicity favored for theLBGs in S16 ( Z ∗ = 0 . Z (cid:12) ). Under this assumption,our LAE observations strongly favor values of Z neb sig-nificantly higher than the modeled stellar metallicities,similar to the effect seen in the S16 and Strom et al.(2016) LBG samples. As described in those works, thisapparent discrepancy is likely a manifestation of the samenon-solar abundance ratios in both the stars and gas.The shape of the model stellar spectrum is most stronglydependent on those elements that dominate the opacityof the stellar photosphere (i.e., iron), which are producedby Type Ia SNe at late times. Conversely, the nebularmetallicity constraints are most sensitive to the specieswhich dominate the cooling of the ∼ K gas, domi-nated by oxygen that is released in the comparativelyprompt Type II SNe. S16 and Strom et al. (2016) there-fore argue that the apparent Z neb /Z ∗ ratio should be in-terpreted as a non-solar O/Fe abundance ratio, and thesediscrepancies signify the α -enhancement of young galax-ies and star-forming regions at high redshift. Our LAEmeasurements are consistent with this interpretation.The ionization parameter of the gas has even strongerconstraints from our LAE compsite spectra. Using theBPASS models, the best-fit O3 ratio can only be repro-duced with log U > − . U > − .
3) for Z ∗ = 0 . Z (cid:12) ( Z ∗ = 0 . Z (cid:12) ). The dependence of the minimum valueof U on stellar metallicity reflects the fact that the samenebular excitation can be achieved with a lower valueof U (that is, fewer photons per hydrogen atom) fora harder incident spectrum. This effect is seen morestrongly for the S99 models, which have significantlysofter EUV spectra: the Z ∗ = 0 . Z (cid:12) S99 model re-quires log
U > − . Z neb , and the Z ∗ = 0 . Z (cid:12) S99 model re-quires log
U > − .
65. If Z neb = 0 . Z (cid:12) is assumed,log U (cid:29) − . U and Z neb fromtheir LBG composite spectra, and these values are alsoplotted on the bottom panels of Fig. 12. The best-fitvalues ( U , Z neb ) are shown as calculated using the sameBPASS and S99 model spectra used for the LAE con-straints in each plot. As described above, the S99 mod-els provide a poor match for full set of line ratios in theS16 spectrum, but we note that the required ionizationparameter for the LAE composite measured here is sig-nificantly higher than the best-fit value for the S16 LBGcomposite even if we remain agnostic as to the choice ofstellar population model.In Fig. 13, we display similar constraints for the high- W Ly α and low- W Ly α LAE samples. Only the Z ∗ =0 . Z (cid:12) models are displayed, since the BPASS predic-tions change only slightly with Z ∗ and the S99 modelswith Z ∗ = 0 . Z (cid:12) struggle to reproduce the measure-ments from the full composite spectrum. The models inthe left panel of Fig. 13 are the same as those presentedin the first panel of Fig. 12, but the hatched regions cor-respond to the constraints on N2 and O3 from the high- W Ly α and low- W Ly α LAE composite spectra (Table 4).The low- W Ly α LAE subsample (green region in the leftpanel of Fig. 13) has lower average excitation, such thatit can be reproduced by both BPASS and S99 stellar models with intermediate values of U . The constraintson Z neb and U for this sample are displayed in the centerpanel of Fig. 13. The allowed range of ionization param-eters shifts closer to the LBG values from S16 (the redcircle and blue square in the same panel) compared tothe values estimated from the full LAE stack.Similarly, the allowed range of U shifts even farther from the S16 measurements for the high- W Ly α sample.Only the most extreme S99 models are able to repro-duce O3 line ratios consistent with the high- W Ly α con-straints (yellow region in the left panel), and none of theS99 models reproduce the best-fit value for that sample.Even the BPASS models require extremely high ioniza-tion parameters (log U ≈ − .
0) to reproduce the best-fit value of O3 at W Ly α > U ≈ − . W Ly α and full sampleof LAEs, the constraints indicate that the characteristicnebular ionization parameter for a population of galaxiesgrows with the typical Ly α equivalent width among thatpopulation.This trend can be seen more clearly in Fig. 14. Here,we show the minimum value of the ionization param-eter U consistent with the best-fit O3 ratio for eachof the LAE samples (marginalizing over the gas-phasemetallicity) as a function of the median Ly α equivalentwidth W Ly α of that sample. For comparison, we alsoinclude the best-fit value of U from S16 with the mea-sured value of W Ly α from the composite UV LBG spec-trum. The minimum U inferred from both the BPASSand S99 Z ∗ = 0 . Z (cid:12) models are shown as solid curves.We also include the variation in U assuming the neb-ular metallicity inferred from the REL-corrected directmethod (Sec. 4.2) as dashed curves (although the truemetallicity is likely to vary among the W Ly α subsam-ples). As in Figs. 12 & 13, the increase in U with W Ly α is clearly visible, as is the fact that the softer S99 mod-els require higher values of U to reproduce the obser-vational constraints. In fact, the deviation between thetwo stellar population models grows with W Ly α , indicat-ing that Ly α -emitting populations may be particularlyadvantageous galaxy samples for discriminating amongthese stellar models. If the high- W Ly α LAEs have loweroxygen abundances than the intermediate and low- W Ly α samples, as might be expected from the BPT- W Ly α re-lation seen in the LBG sample (Fig. 7), the slope of the U - W Ly α relation may be even steeper than displayed inFig. 14, which has necessarily marginalized over this vari-ation. Conversely, harder stellar spectra resulting fromlower iron abundances among high- W Ly α LAEs could re-duce the necessary value of U . Future observations thatprobe the ionization state of the gas with less depen-dence on metallicity (i.e., via O32 or [Ne III ]/[O II ]) andfurther cross-checks of the gas-phase oxygen abundance(e.g., from N2) will therefore provide more powerful testsof the physical properties of stars and their surroundinggaseous regions. Low metallicity objects
As shown in Figs. 12 & 13, the relationship between Z neb and O3 is double-valued, and its shape at 0 . (cid:46) Z neb (cid:46) . log([NII] / H α ) l og ( [ O III ] / H β ) Z ∗ =0 . Z fl BPASSS99 W Ly α > stack W Ly α < stack log( U ) Z n e b / Z fl W Ly α > Z ∗ =0 . Z fl modelsBPASSS99 Z neb = Z ∗ Z neb = Z dir log( U ) Z n e b / Z fl 07 as in the left panelsof Fig. 12 ( Center ) Constraints on Z neb and U for the high- W Ly α sample corresponding to the green region in the left panel. Annotationmatches the bottom panels of Fig. 12. ( Right ) Constraints on Z neb and U for the low- W Ly α sample (yellow region in the left panel). phase oxygen abundance from O3 measurements alone.However, at low values of Z neb , the relationship becomesmuch steeper, and the abundances of objects that can beassumed to occupy the low- Z neb or high- Z neb branchesmay be constrained much more easily.Fig. 2 shows that the O3 ratios of our individual LAEsexhibit a marked downturn at the lowest continuum lu-minosities. Based on the photoionization models dis- W Ly α l og ( U ) S99BPASS Z neb = Z ( U min ) Z neb = Z dir Fig. 14.— The ionization parameter U inferred from the compos-ite spectrum of a given galaxy sample vs. the stacked spectroscopicequivalent width W Ly α ,spec of that sample. Black points refer tothe LBG measurements of Steidel et al. (2016), while colored pointscorrespond to the full, low- W Ly α , and high- W Ly α LAE samplespresented in this paper. Circles and solid red lines indicate theminimum value of U (for any metallicity 0 . ≤ Z neb /Z (cid:12) ≤ . U > − . 5. Dashed lines reflect theassumption of Z neb = 0 . Z (cid:12) for each LAE sample. In general,the differences between the S99 and BPASS models become moreapparent as W Ly α increases. 12 +log(O / H) l og ( [ O III ] / H β ) m AB > . ( R )m AB > . (F160W) Z neb /Z fl Fig. 15.— Inferred oxygen abundances for the faintest LAEs inour sample. Red and black arrows on the left side are the measuredO3 ratios for the continuum-undetected LAEs in Fig. 2. These val-ues are converted to abundances (shown as triangles on the top andbottom axes) assuming the log U = − . U curve willyield a lower (higher) inferred oxygen abundance at fixed O3. cussed above, these lower values of O3 could be explainedby the faintest LAEs having 1) significantly higher stel-lar metallicities, 2) lower ionization parameters, and/or3) lower gas-phase metallicities (i.e., oxygen abundance)compared to the typical LAEs in our sample.Given the fact that the LAEs exhibit higher ioniza-tion parameters than the continuum-bright LBGs andseem to require similar (or lower) stellar metallicities,we suggest that the observed downturn is caused by lowoxygen abundances among the faintest LAEs. This inter-pretation is supported by other arguments as well: Ly α -emitting galaxies that are faint at λ rest ≈ − α -Emitters 21star-formation rates, both qualities that correlate withlow oxygen abundances in other galaxy samples. Finally,the shape of the Z neb − O3 relation would predict a sharpdownturn, as O3 is fairly flat at Z neb (cid:38) . Z neb (cid:46) . 2. As the typical inferred gas-phasemetallicity of our LAE sample is Z neb ≈ . Z (cid:12) , wewould expect LAEs with below-average oxygen abun-dances to exhibit significantly lower values of O3.We therefore interpret the O3 values of the faintestLAEs according to the following assumptions: they haveionization parameters at least as high as that inferred forthe typical LAEs in our sample (log U ≈ − . 1) and havestellar populations similar to the BPASS Z ∗ = 0 . Z (cid:12) models that match the LAE and LBG composite spectradiscussed above. We also assume that each of these LAEsoccupies the lower-metallicity track ( Z neb < . Z (cid:12) )where the Z neb − O3 relation is double-valued (this as-sumption is discussed further below).Fig. 15 shows the oxygen abundances that are inferredfor our 9 continuum-undetected LAEs with measured O3ratios based on these assumptions. The measured O3ratios are shown as arrows on the left axis, while theinferred oxygen abundances (nebular metallicities) areshown on the bottom (top) axis. As in Fig. 2, blackpoints are LAEs undetected in our ground-based contin-uum images ( R > . HST images ( m AB, F160W > . Z neb − O3 curve with log U = − . . − . 0, with six LAEs below 12 + log(O/H) = 7.4( Z neb < . Z (cid:12) ). Increasing the assumed ionizationparameter would require even lower oxygen abundancesto produce the observed values of O3. While some in-dividual objects may have lower ionization parametersthan that assumed, we suggest that it is unlikely thatthe average ionization parameter is significantly loweramong these LAEs than the typical LAEs in our sam-ple for the reasons discussed above. We have assumedeach of our LAEs occupies the low-metallicity track ofthe Z neb − O3 curve; for all but two of the continuum-undetected LAEs, the high-metallicity track would pre-dict significantly super-solar average metallicities, whichwould be extremely suprising for galaxies that otherwiseappear to be young, low-mass galaxies. DISCUSSION The above results indicate that our population of faintLAEs exhibit distinct physical properties with respectto the population of brighter, more massive, and morerapidly star-forming LBGs. In this section we com-pare these properties to those of other extreme, low-mass galaxy samples, arguing that galaxies selected viaemission lines (including Ly α ) are representative of thelow-mass, low-luminosity population. We also discussthe mechanisms by which the nebular properties may belinked to galaxy mass and Ly α production and escape. Comparison to other extreme high- z galaxy samples As discussed in Sec. 1, some recent samples of galax-ies selected by their extreme nebular emission lines show similar stellar masses and other properties to the KBSS-Ly α LAEs described here. The three “extreme” LBGswith T e measurements presented by Steidel et al. (2014)have M ∗ = 10 . − . , SFR = 30 − 60 M (cid:12) yr − , andO3 = 0.79 − (cid:104) M dyn (cid:105) ≈ . M (cid:12) . This mass is ostensibly sim-ilar to that estimated for the KBSS-Ly α LAEs in T15( (cid:104) M dyn (cid:105) ≈ . M (cid:12) ), but Maseda et al. assume a geo-metric factor C ≡ r eff σ /GM dyn = 3, while T15 assumes C = 5. A consistent choice of estimator would suggestthat the Maseda et al. (2013, 2014) EELGs have dynam-ical masses ∼ (cid:12) yr − inferred from SED fitting) is roughly doubleour median LAE SFR (5 M (cid:12) yr − from dust-correctedH α ). Masters et al. (2014) present an even higher-SFRsample of EELGs, with average SFR = 29 M (cid:12) .Despite these differences, the EELG samples sharemany physical properties with the KBSS-Ly α LAEs, in-cluding low inferred metallicities. Maseda et al. (2014)calculate oxygen abundances for 7 EELGs from the di-rect T e method or strong-line indicators, finding 12 +log(O/H) = 7.45 − < T e metal-licity is consistent with these median values within 1 σ ,although neither EELG sample utilizes the +0.24 dexcorrection we assume for our T e measurement (Sec. 4.2).If we neglect this factor for consistency, then our esti-mated oxygen abundance 12 + log(O/H) = 7.80 ± σ ). Simi-larly, our lowest-metallicity objects appear to be at leastas low as the individual EELGs, with at least 5 LAEsin our sample having lower metallicities than the lowestEELGs according to our analysis in Sec. 6.3. Masterset al. (2014) observe a turnover in the R23-N2 plane at12 + log(O/H) (cid:46) M ∗ (cid:46) . M (cid:12) in a sample of z ∼ ∼ 50% of L ∼ L ∗ LBGs ex-hibit Ly α in emission (Shapley et al. 2003; Steidel et al.2010). A relatively unbiased selection of intrinsically-faint galaxies may be achieved through gravitationallensing, which has proven fruitful at selecting galaxieswith L (cid:28) L ∗ at z ≈ . − M ∗ ≈ . × − . × M (cid:12) . While not se-lected based on line emission, these galaxies exhibit emis-sion in many UV metal lines including N IV ], O III ],2 R. F. Trainor et al.C IV , Si III ], and C III ]. Stark et al. (2014) find thatLy α emission closely tracks the emission of other high-excitation lines such as C III ], as was previously seen byShapley et al. (2003). Furthermore, all 11 galaxies forwhich Ly α fell within the observed passband exhibitedLy α emission, with 10/11 galaxies having W Ly α (cid:38) α emit-ters increases as galaxy mass decreases, with ∼ 86% ofgalaxies with 10 . < M ∗ / M (cid:12) ≤ . at 3 < z < . α in emission with a typical equivalent width W Ly α ≈ α emission atlow galaxy masses therefore suggests that our sample offaint LAEs is likely to be fairly representative of the to-tal population of faint, low-mass, star-forming galaxiesat z ≈ − . ≤ M ∗ / M (cid:12) ≤ . and oxygen abundances 7.29 ≤ 12 + log(O/H) ≤ ≤ Z/Z (cid:12) ≤ − . ≤ log U ≤ − . 84 using (single-star) stellar modelsfrom Bruzual & Charlot (2003); these values are similarto those inferred for our LAE sample using the S99 mod-els. Based on our analysis in Sec. 6, we expect that Starket al. (2014) would have inferred lower ionization param-eters using stellar models including intrinsically-harderionizing spectra similar to the BPASS models we employhere (discussed further in Sec. 7.2 below).Finally, recent rest-optical galaxy photometry at z =3 − M UV ≈ − 20) at z ∼ III ]+H β ) > ≈ III ]+H β ) = 829˚A, comparable tothese high- z samples and significantly higher than theLM1 LBG composite from Steidel et al. (2016), whichhas EW([O III ]+H β ) = 238˚A. The 4 LAEs in our sam-ple that are undetected in HST/WFC3 (Fig. 2) requireEW([O III ]+H β ) (cid:38) − z ≈ − α LAEs presented in thispaper appear to have similar nebular properties to thefaintest galaxies and most extreme line-emitters selectedby other surveys at comparable redshifts (as well as thereionization epoch), although our sample is the first toinclude a large sample of rest-optical spectra of galaxiesin this luminosity and redshift regime. Origins of strong line emission in faint galaxies We now turn our discussion to the physical interpreta-tion of our observations: why is Ly α emission so stronglylinked to the nebular line properties and continuum lu-minosities of galaxies?The strong nebular line emission of faint galaxies ispartially a result of the relationship between mass and log([OIII] / H β ) W L y α () BPASS M max ∗ =300 M fl BPASS M max ∗ =100 M fl S99 α =1 . α =2 . α =2 . . Z ∗ /Z fl . Fig. 16.— Predicted W Ly α and O3 ratios from Cloudy photoion-ization models for BPASS (circles) and S99 (squares) model spectraof varying stellar metallicities (0 . Z (cid:12) ≤ Z ∗ ≤ Z (cid:12) with symbolsize increasing with Z ∗ ). The predictions are computed for a fidu-cial nebular metallicity Z neb = 0 . Z (cid:12) and ionization parameterlog U = − . 1. We plot multiple IMFs for each model, varying theupper mass cutoff for the BPASS models ( M max ∗ = 300M (cid:12) or100M (cid:12) ) and the IMF slope for the S99 models ( α = − . − . − . W Ly α and O3 ratios, providing a qualitative explanation for theBPT-Ly α relation and other nebular trends explored in this paper.Notably, however, the standard-IMF S99 models do not producevalues of W Ly α consistent with typical LAE measurements. metallicity; as discussed above, the low metallicities oflow-mass galaxies naturally produce strong emission inmany high-excitation nebular lines. However, the con-nection between Ly α emission and the excitation stateof nebular gas is less clear.One natural explanation of this link may be the shapeof the incident stellar spectra that drive the line emis-sion from the nebular gas. Both high excitation (param-eterized by the O3 ratio) and high W Ly α are indicatorsof an intrinsically hard incident spectrum. The intrin-sic Ly α luminosity of an ionization-bounded H II regionis approximately proportional to the total production ofionizing photons, so W Ly α is a measure of the ratio ofionizing to non-ionizing incident UV flux (modulo thesubsequent scattering and absorption of the Ly α pho-tons). Similarly, the O3 ratio is strongly dependent onthe shape of the ionizing spectrum, which may be concep-tualized as the ratio of ∼ − ∼ − W Ly α . The trend is espe-cially clear for the BPASS models, for which the stellarmetallicity strongly modulates the total ionizing photonproduction (Fig. 17) and thereby the secondary produc-tion of Ly α photons.The parameter ξ ion is defined as the number ofhydrogen-ionizing photons produced by a stellar popu-lation per unit UV luminosity (typically normalized at1500˚A). A value log( ξ ion / erg − Hz) = 25.2 has beenest-Frame Optical Spectroscopy of Ly α -Emitters 23 Z ∗ /Z fl l og ξ i o n ( e r g − H z ) BPASS M max ∗ =300 M fl BPASS M max ∗ =100 M fl S99 α =1 . α =2 . α =2 . Fig. 17.— Predicted ξ ion ratios for the same BPASS and S99model spectra presented in Fig. 16. The same low-metallicity stel-lar models that produce acceptable fits to the N2-BPT and W Ly α constraints (i.e., the BPASS models) likewise predict ξ ion ratiossignificantly higher than the “canonical” values assumed by typi-cal models of reionization (e.g., Robertson et al. 2015; dashed lineat log( ξ ion / [erg − Hz]) = 25 . assumed by recent work modeling reionization (e.g.,Robertson et al. 2013, 2015), which is appropriate for asingle-star population with a typical IMF in steady-state(e.g., the α = 2 . ξ ion at low metal-licity, even with the the same IMF ( M max ∗ = 100M (cid:12) ).Because reionization constraints impose a requirementon the total galactic emission of ionizing photons, whichis proportional to ξ ion × f esc,LyC , these models thereforereduce the global LyC escape fraction required to reion-ize the Universe (e.g., Ma et al. 2016).In addition, these high values of ξ ion also provide anatural explanation for the high ionization parametersinferred for our LAE sample. At fixed gas density, theionization parameter U is proportional to the numberdensity of ionizing photons . While the expected valueof U in high- z H II regions may not be obvious a pri-ori , a variation of ∼ ξ ion between the two populations. While avery young stellar population age could elevate ξ ion inindividual galaxies, our measurements of high U for alarge sample of LAEs–and their correspondence to typi-cal galaxies in their mass and luminosity range, as arguedabove–suggests that these faint galaxies efficiently pro-duce large numbers of ionizing photons in steady state .The strong dependence of ξ ion on Z ∗ among the BPASSmodels provides an alternative mechanism to modulatethe ionization parameter. Sanders et al. (2016) identifyan anti-correlation between gas-phase metallicity and U among continuum-selected galaxies from the MOSDEFsurvey. The similar trend seen here among the KBSSLAEs and LBGs which may indicate that the effect ofmetallicity on the hardness of the stellar spectra drivesthe large observed variation in U with galaxy luminosity. Technically, U in the Cloudy photoionization code is propor-tional to the number density of photons at the Lyman limit. Lastly, as discussed in Sec. 6.2, the hardness of theionizing field and the ionization parameter produce some-what degenerate effects on the nebular excitation (O3):the softer S99 models require significantly higher valuesof U to produce the same values of the O3 ratio. Bythis token, both the normalization and the shape of theBPASS ionizing spectra are favorable for high nebularexcitation. Firstly, their intrinsic hardness can producehigh O3 with values of U that are only moderately ele-vated with respect to more luminous populations. Sec-ondly, their high ξ ion values at low metallicities naturallyproduce the large total number of ionizing photons re-quired explain these U values at apparently fixed gasdensity.To summarize, invoking a stellar population model inwhich the spectra become significantly harder at lowmetallicities (whether via the specific BPASS modelsuite or a set of similar output model spectra) will self-consistently reproduce the strong Ly α and nebular lineratios observed for faint, high-redshift galaxies. Ly α emission and LyC leakage As discussed in Sec. 5.2.2, there are indications thatLy α -emitting galaxies have elevated O32 ratios withrespect to typical galaxies. Some studies have sug-gested that these ratios are indicative of density-boundedH II regions, in which the entire star-forming cloudbecomes ionized. Such regions would be expected tolack a partially-ionized boundary wherein low-ionizationspecies may dominate the local line emission and therebylower the luminosity-averaged measurement of the ion-ization ratio (see discussion by e.g., Jaskot & Oey 2013;Nakajima et al. 2013; Nakajima & Ouchi 2014). Someevidence for this behavior is seen in local observationsof H II regions using the ionization parameter mappingtechnique (IPM; Pellegrini et al. 2012; Zastrow et al.2013). In particular, the IPM measurements of the LargeMagellanic Cloud by Pellegrini et al. (2012) indicate thatoptically-thick H II regions are surrounded by ioniza-tion fronts that are dominated by low-ionization species(e.g., high [S II ]/[S III ] ratios), whereas optically-thin(i.e., density-bounded) regions are dominated by high-ionization species throughout. As an illustrative exampleof this phenomenon, Fig. 18 reproduces the results of aCloudy photoionization simulation in which a slab of gaswith a variable, uniform column density is illuminatedby a BPASS model spectrum. In the density-boundedcase (optically thin at the Lyman limit; τ (cid:28) ∼ τ (cid:29) Such density-bounded regions are highly interesting for While current galaxies samples (KBSS, MOSDEF) show alarge dispersion in inferred gas density, no trend is seen with metal-licity. In fact, 2 of the 3 extreme-excitation LBGs in Steidel et al.(2014) have above-average inferred densities ( n e ≈ − − ), which would require even higher values of ξ ion to producethe inferred ionization parameters. Specifically, we run a set of plane-parallel Cloudy simulationswith the Z ∗ = 0 . Z (cid:12) BPASS input spectrum, Z neb = 0 . Z (cid:12) ,log U = − . 1, and a variable stopping criterion based on the totaloptical depth at λ = 912˚A. Note that the normalization of the curve in Fig. 18 is depen-dent on the precise choice of incident radiation field and log U , butthe predicted difference in O32 between the density-bounded andionization-bounded cases is insensitive to these parameters. log τ O density bounded ionization bounded Fig. 18.— Predicted O32 ratios from Cloudy photoionizationmodels for a plane-parallel slab of gas with varying total opticaldepth at the Lyman limit ( τ ). Incident radiation field is thatof the BPASS Z ∗ = 0 . Z (cid:12) model, with log U = − . Z neb =0 . τ (cid:46) 1) ionized regions are characterized by elevatedO32 ratios. log τ W L y α () density bounded ionization bounded Fig. 19.— Predicted W Ly α ratio for the same photoionizationmodels presented in Fig. 18. Optically-thin ionized regions pro-duce little Ly α emission, which peaks at column densities of H I that are moderately optically thick to ionizing photons. Note thatthe Cloudy photonization code is not optimized to reproduce thebehavior of W Ly α at the highest values of τ , where Ly α trans-mission is dominated by resonant scattering in a dusty medium. studies of EoR galaxies because they produce large lo-cal escape fractions of ionizing photons (and potentiallyof Ly α photons, although Ly α production may be sup-pressed; Fig. 19). There are observational indicationsthat galaxies with high O32 ratios are more likely to leakionizing (LyC) photons: several recently-discovered LyCleakers at low-redshift (Izotov et al. 2016a,b) show highionization states (O32 > . z LyC leakers showsmaller values of O32 (Leitet et al. 2013; Borthakur et al.2014; Leitherer et al. 2016). At z ∼ 3, two confirmedLyC leakers are known: Ion2 (de Barros et al. 2016)and Q1549-C25 (Shapley et al. 2016). Ion2 was selectedbased on broadband continuum colors according to themethod of Vanzella et al. (2015) and is associated withextreme line ratios (O32 > rest ([O III ]) = 1500˚A;Vanzella et al. 2016). Conversely, Q1549-C25 appears to have more moderate line emission (EW rest ([O III ]+H β )= 256˚A) typical of KBSS LBGs.Given the diversity of known LyC-leakers, is unclearthat real high- z density-bounded H II regions must nec-essarily have high O32 ratios. Harder ionizing photonshave smaller ionization cross-sections and longer meanfree paths than lower-energy photons, which could causeH II regions to become hotter and more highly ionized atlarge radii. This effect may be stronger at high redshift,where we have argued that low-metallicity stellar popula-tions are likely to produce hard ionizing spectra. In addi-tion, any dominance of low-ionization species within ion-ization fronts of individual H II regions need not translateto a low O32 ratio in the luminosity-weighted, galaxy-averaged observations conducted for distant galaxies.Furthermore, Ly α production is extremely weak inH II regions with uniformly low gas column densities(Fig. 19). In more realistic simulations of Ly α produc-tion and escape in a clumpy, multi-phase ISM, Dijkstraet al. (2016) find that both ionizing and Ly α photonsescape through low-column-density sightlines, in agree-ment with observational indicators that a patchy distri-bution of gas is required for efficient photon escape. InT15, we found that the escape fraction of Ly α photonswas significantly related to a galaxy’s covering fractionof neutral (or low-ionization) gas. Similarly, the low- z LyC leaker discovered by Borthakur et al. (2014) hasa very low value of O32 = − . 5, but also exhibits alow covering fraction of low-ionization gas. Photons mayalso be scattered or extinguished far from their originalH II regions; Steidel et al. (2011) found that star-forminggalaxies emit Ly α radiation at large radii even when theyappear to be Ly α absorbers in slit spectroscopy. How-ever, the galaxies with high spatially-integrated values of W Ly α are those with centrally-concentrated Ly α emis-sion, suggesting that the bulk of Ly α (and potentiallyLyC) absorption occurs at small galactocentric radii.Together, these observations indicate that the distribu-tion of H I gas on many spatial scales plays a strong rolein scattering and extinguishing Lyman radiation, a factwhich likely produces much of the scatter in the relation-ships between W Ly α and nebular properties explored inSecs. 5 − 6. Nonetheless, both the nebular properties ofthe KBSS-Ly α LAEs and their neutral gas distributionspresented in T15 indicate that they are strong candidatesfor Lyman-continuum leakage and ideal analogs of EoRgalaxies. CONCLUSIONS In this paper, we have shown that the Ly α -emittingproperties of galaxies (including 60 faint LAEs and 368brighter LBGs) are closely linked to the properties oftheir embedded star-forming regions, as probed by rest-optical and rest-UV spectroscopy. This sample of galax-ies from the KBSS and KBSS-Ly α represents the largestset of combined Ly α and nebular-line spectroscopy ofgalaxies at any redshift and spans a large range of galaxyproperties, including luminosities, SFRs, masses, extinc-tions, ionization states, and net Ly α emission.By constructing composite spectra from our LAE sam-ple, we also set new constraints on the physical proper-ties of L ≈ . L ∗ galaxies at z ≈ − 3. The primaryconclusions of this work are summarized below:est-Frame Optical Spectroscopy of Ly α -Emitters 251. Faint LAEs have extremely high nebular excitation(parameterized by the [O III ] λ β ratio) con-sistent with most extreme LBGs in current surveys,which are likely the low-metallicity tail of the galaxydistribution. Fig. 5; Sec. 4 2. A 2.8 σ detection of the [O III ] λ II regions in these LAEshave high electron temperatures with respect to moremassive LBGs ( T e ,LAE = 1 . ± . × K). Calcu-lating a metallicity via the “direct” ( T e ) method givesa typical LAE oxygen abundance of 12 + log(O/H)= 8.04 ± Z neb = 0 . +0 . − . Z (cid:12) ) after correctingfor the − Fig. 6; Secs. 4.2 − 3. The continuum-faintest LAEs in our sample show ev-idence for the turnover in the [O III ] λ β ratiothat occurs at very low metallicities, and six LAEsappear to have oxygen abundances 12 + log(O/H) ≈ − Z neb ≈ . − . Figs. 2 & 15; Sec. 6.3 4. Across a broad range of LBG and LAE Ly α emissiv-ities, the locations of galaxies in the N2-BPT planevary systematically with Ly α equivalent width. Wefind that the variation of dust attenuation with metal-licity plays a minor role in this relation, but the ion-ization and excitation state of the star-forming regionsare much more strongly correlated with the net Ly α emission. In particular, the photoionization models ofthe LAEs require ionization parameters log U ≈ − . Figs. 7 − 14; Sec. 5 5. The rest-frame optical spectra of the KBSS-Ly α LAEsindicate stellar populations that produce harder spec-tra than typical stellar population models. Success-ful stellar models include those with very low stellarmetallicities (which are consistent with the low Fe/Oabundances reported elsewhere), and those that in-clude the effects of binary interaction on the evolutionof massive stars. In particular, we are unable to re-produce the properties of the highest- W Ly α LAEs ex- cept with stellar models that include binary evolution. Figs. 12 − 14; Sec. 6 6. In general, the nebular properties of faint LAEs at z ≈ − z (cid:38) Figs. 16 − 19; Sec. 7 Future work will include measuring additional globalproperties of these galaxies, including the variation ofnebular excitation and Ly α production with the phys-ical sizes, masses, and star-formation rates of individ-ual LAEs. Additional indicators of the nebular proper-ties (including ionization state and strong-line metallic-ity indicators) will provide valuable cross-checks of themeasurements inferred here. In a few years, JWST willbe able to obtain similar spectra of L ∼ . L ∗ galax-ies without being limited by ground-based atmosphericwindows, facilitating further analysis of the variation ofthese galaxy properties across populations and redshifts.We thank Eliot Quataert, Mariska Kriek, and Dawn Erbfor extremely useful discussions. In addition, we thankthe organizers of the Escape of Lyman radiation fromgalactic labyrinths conference at the Orthodox Academyof Crete in April 2016; this paper was much improvedby the talks and discussion that took place at that meet-ing. We are also grateful for the insightful commentsof our anonymous referee. This paper uses data col-lected through Keck program 2015B U42M, and we areindebted to the staff of the W.M. Keck Observatory whokeep the instruments and telescopes running effectively.We also wish to extend thanks to those of Hawaiian an-cestry on whose sacred mountain we are privileged to beguests. This work has been supported in part by theUS National Science Foundation through grants AST-0908805 and AST-1313472. RFT receives for supportfrom the Miller Institute for Basic Research in Scienceat the University of California, Berkeley. REFERENCESAbazajian, K. N., Adelman-McCarthy, J. K., Ag¨ueros, M. A.,et al. 2009, ApJS, 182, 543Alavi, A., Siana, B., Richard, J., et al. 2014, ApJ, 780, 143Aller, L. H., ed. 1984, Astrophysics and Space Science Library,Vol. 112, Physics of thermal gaseous nebulaeAmor´ın, R., P´erez-Montero, E., V´ılchez, J. M., & Papaderos, P.2012, ApJ, 749, 185Andrews, B. H., & Martini, P. 2013, ApJ, 765, 140Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009,ARA&A, 47, 481Baldwin, J. A., Phillips, M. M., & Terlevich, R. 1981, PASP, 93, 5Berg, D. A., Skillman, E. D., Croxall, K. V., et al. 2015, ApJ,806, 16Borthakur, S., Heckman, T. M., Leitherer, C., & Overzier, R. A.2014, Science, 346, 216Bresolin, F., Kudritzki, R.-P., Urbaneja, M. A., et al. 2016, ArXive-prints, arXiv:1607.06840Brinchmann, J., Pettini, M., & Charlot, S. 2008, MNRAS, 385,769Brocklehurst, M. 1971, MNRAS, 153, 471 Brott, I., de Mink, S. E., Cantiello, M., et al. 2011, A&A, 530,A115Brown, J. S., Croxall, K. V., & Pogge, R. W. 2014, ApJ, 792, 140Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000Campbell, A., Terlevich, R., & Melnick, J. 1986, MNRAS, 223,811Cardamone, C., Schawinski, K., Sarzi, M., et al. 2009, MNRAS,399, 1191Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345,245de Barros, S., Vanzella, E., Amor´ın, R., et al. 2016, A&A, 585,A51Dijkstra, M., Gronke, M., & Venkatesan, A. 2016, ArXiv e-prints,arXiv:1604.08208Dopita, M. A., Kewley, L. J., Heisler, C. A., & Sutherland, R. S.2000, ApJ, 542, 224Eldridge, J. J., & Stanway, E. R. 2009, MNRAS, 400, 1019—. 2016, ArXiv e-prints, arXiv:1602.03790Erb, D. K., Pettini, M., Steidel, C. C., et al. 2016, ArXiv e-prints,arXiv:1605.04919Erb, D. K., Shapley, A. E., Pettini, M., et al. 2006, ApJ, 644, 8136 R. F. Trainor et al.