THE SPECTROSCOPIC PROPERTIES OF Lyα-EMITTERS AT z ∼ 2.7: ESCAPING GAS AND PHOTONS FROM FAINT GALAXIES^*

The full parent sample of ∼800 photometrically identified LAEs will be described separately (R. Trainor et al. 2015, in preparation); this LAE sample was also used and discussed by Trainor & Steidel (2013). LAEs were identified on the basis of paired narrowband and broadband observations (from Keck I/LRIS-B) using a custom set of narrowband filters. A total of four narrowband filters were used, each with a bandpass constructed to select the wavelength of Lyα at one or more QSO redshifts (Figure 1). Objects were identified and photometry was performed using SExtractor in one- and two-image modes to extract narrowband and broadband magnitudes (${m}_{\mathrm{NB}}$ and ${m}_{\mathrm{BB}}$) sampling Lyα. Hereafter, ${m}_{\mathrm{BB}}$ refers to the measured LAE magnitude in the B and/or G filter used to estimate the continuum emission near Lyα, whichever is better matched at a given redshift (Table 1). Because the $B/G$ filter bandpasses include the Lyα emission line, we use ${\mathcal{R}}$-band measurements to sample the continuum without Lyα contamination. We conducted follow-up spectroscopy of the subset of objects identified to have a narrowband color excess ${m}_{\mathrm{BB}}-{m}_{\mathrm{NB}}\gt 0.6$, which corresponds to a limit in rest-frame Lyα equivalent width ${W}_{\mathrm{Ly}\alpha }\gtrsim 20$ Å. The success of our spectroscopic follow-up observations dropped significantly for ${m}_{\mathrm{NB}}\gt 26.5$, so this limit (approximately the 3σ depth of our narrowband observations) was adopted as the faint cut-off for the photometric and spectroscopic samples. This magnitude limit corresponds to an integrated narrowband flux ${F}_{\mathrm{Ly}\alpha }\approx$1 × 10⁻¹⁷ erg s⁻¹ cm⁻² for a continuum-free Lyα emission line, or ${F}_{\mathrm{Ly}\alpha }$ ≈ 6 × 10⁻¹⁸ erg s⁻¹ cm⁻² for an emission line with our median value of $\langle {W}_{\mathrm{Ly}\alpha }\rangle \approx 40$ Å. The apparent magnitude distribution of both the parent sample and the spectroscopic subsample of LAEs discussed in this paper are given in Figure 2. Both the spectroscopic and photometric samples have median $\langle {{\mathcal{R}}}_{\mathrm{AB}}(6930\;\mathring{\rm A} )\rangle$ ≈ 27. According to the galaxy luminosity functions measured by Reddy et al. (2008), this continuum magnitude corresponds to $L\sim 0.1{L}_{*}$ at z ∼ 2.7. Details of the QSO fields and the spectroscopic sample are given in Table 1.

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Table 1.  Lyα-emitter Field Descriptions

	${z}_{{\rm{Q}}}$	NB	BB
QSO Field	(±0.001)	Filter	Filter	${N}_{\mathrm{spec}}$
Q0100+13 (PHL957)	2.721	NB4535	B+G	20
HS0105+1619	2.652	NB4430	B	22
Q0142−10 (UM673a)	2.743	NB4535	B+G	22
Q1009+29 (CSO 38)	2.652	NB4430	B	35
HS1442+2931	2.660	NB4430	B	41
HS1549+1919	2.843	NB4670	G	95
HS1700+6416	2.751	NB4535	B+G	20
Q2343+12	2.573	NB4325	B	63

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Rest-UV spectra were obtained with Keck I/LRIS-B in the multislit mode using the 600/4000 grism and 560 nm dichroic. All objects were observed with 12 wide slits, but the spectral resolution is limited by the 06–08 seeing disk for these (typically spatially unresolved) LAEs. The effective resolution near the observed Lyα wavelength for these spectra is R ∼ 1300, corresponding to a velocity resolution σ_v ∼ 100 km s⁻¹. Spectroscopic observations were performed in sets of 3–4 1800 s exposures, for a total of 1.5–2 hr of total integration time per object. By the completion of the survey, we had obtained spectra for 415 of the 749 photometric LAE candidates, with some candidates observed on as many as three different masks. The observations were conducted and reduced in essentially the same manner as those of the KBSS and preceding surveys, a detailed description of which can be found in Steidel et al. (2003, 2004). Specifically, masks were constructed and targets assigned as described by Steidel et al. (2003), but with a minimum slit length of 11'' in order to provide better background subtraction for continuum-faint (${\mathcal{R}}\sim 27$) sources. The data were reduced (including flat-fielding, cosmic-ray rejection, background subtraction, flexure compensation, and wavelength/flux calibration) using a custom set of IRAF scripts as described in Steidel et al. (2003). The two-dimensional spectra were rectified using flat-field observations, and one-dimensional spectra were then extracted using the IRAF task apall with 10 pixel apertures (135, ∼2× the seeing FWHM). We detect little or no continuum emission in individual spectra, so all pixels in the aperture received equal weighting during the extraction and the object trace was not allowed to vary with wavelength along the rectified 2D spectrum. Note that the Keck I Cassegrain Atmospheric Dispersion Corrector removes the wavelength-dependent shifts in object position due to differential atmospheric refraction. The two-dimensional spectra were binned in two-pixel blocks along the wavelength axis during readout, and the one-dimensional extracted spectra were resampled to the median resulting wavelength scale of the observations, 1.26 Å pix⁻¹.

The resulting one-dimensional spectra were then subjected to an automated line-detection algorithm described here. First, each spectrum was smoothed with a kernel corresponding to the instrumental resolution (∼3.5 Å FWHM). A detection region of the spectrum was then isolated: in order to ensure that spectroscopically detected objects corresponded to their NB-selected counterparts, the algorithm only located emission lines that would fall between the 10% power points of the corresponding NB filter used to select them. The highest peak in this detection region was then used to define the first guess at the emission line wavelength. The significance of the detected peak was then estimated by

$$\begin{eqnarray}&&P(y)=1-{({\displaystyle \int }_{{y}_{\mathrm{max}}/{\sigma }_{y}}^{\infty }G(x)\;{dx})}^{{n}_{\mathrm{pix}}},\end{eqnarray} \tag{ 1 }$$

where ${y}_{\mathrm{max}}$ is the observed peak value (minus any measured continuum) in the smoothed spectrum, ${\sigma }_{y}$ is the sample standard deviation of the smoothed spectrum in the detection region, $G(x)={e}^{-{x}^{2}/2}/\sqrt{2\pi }$ is the normal distribution function, and ${n}_{\mathrm{pix}}$ is the number of pixels in the detection region of the spectrum. In this way, $P(y)$ represents the probability of measuring one or more pixels with value $y\geqslant {y}_{\mathrm{max}}$ within the detection region under the null hypothesis that the pixel values are normally distributed with variance ${\sigma }_{y}^{2}$. Spectra with $P(y)\geqslant 0.05$ were rejected as non-detections, while those with $P(y)\lt 0.05$ were designated candidate emission lines. This threshold was chosen because it closely reproduces the samples of significant and non-significant spectral Lyα detections identified by eye. The median signal-to-noise ratio (S/N) of the spectroscopic detections is 10.1. The total flux in each candidate emission line was then estimated both by Gaussian fitting and by direct integration of the unsmoothed spectrum. Finally, the line was re-fit using an asymmetric line profile:

$$\begin{eqnarray}{f}_{\lambda }(\lambda )=\{\begin{array}{lr}{{Ae}}^{-(\lambda -\mu )/2{\sigma }_{\mathrm{blue}}^{2}} & \lambda \lt \mu \\ {{Ae}}^{-(\lambda -\mu )/2{\sigma }_{\mathrm{red}}^{2}} & \lambda \geqslant \mu \end{array}\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{\alpha }_{\mathrm{asym}}\equiv {\sigma }_{\mathrm{red}}/{\sigma }_{\mathrm{blue}}.\end{eqnarray} \tag{ 3 }$$

Here, ${\sigma }_{\mathrm{blue}}$ represents the line-width measured from the "blue" side of the peak (λ < μ), while ${\sigma }_{\mathrm{red}}$ is the width on the "red" side of the peak ($\lambda \gt \mu$), where μ is the fitted peak of the Lyα profile. From these quantities, we define the asymmetry of the line shape, ${\alpha }_{\mathrm{asym}}$, a potential diagnostic of Lyα escape physics (Chonis et al. 2013; Zheng & Wallace 2014). Many lines were found to be multi-peaked, defined by the existence of a second peak in the smoothed spectrum at least 2.5σ above the continuum and within 1500 km s⁻¹ of the primary peak, separated from the primary peak by an inter-peak minimum. As these secondary peaks typically have lower S/N than the primary peak, they were fit using symmetric Gaussian profiles. No more than two Gaussian peaks were allowed in each fit. When fitting line profiles, the fits were constrained such that the fit width σ (both ${\sigma }_{\mathrm{blue}}$ and ${\sigma }_{\mathrm{red}}$ for asymmetric profiles) could not fall below the instrument resolution (σ > 1.5 Å). Measured line widths, asymmetries, and multi-peaked profiles are discussed in detail in Section 3.3. As demonstrated in that section, the resolution of these spectra is sufficient to resolve the peak width, separation, and asymmetry for the typical objects in our survey. However, we note that these spectra may not resolve spectral features on very small (δv ≲ 100 km s⁻¹) velocity scales, such as those predicted by radiative transfer models and observed in some high-resolution spectra of bright or nearby galaxies (Verhamme et al. 2008; Martin et al. 2015).

The observed wavelength of the Lyα emission line was measured via two methods: direct integration of the unsmoothed spectrum (i.e., the flux-weighted line centroid), and the fit value of μ (i.e., the peak of the fit asymmetric Gaussian profile). For multi-peaked lines, the primary peak is that which was detected by our first-pass line detection algorithm (i.e., the most significant spike in the smoothed spectrum). Henceforth in this paper, ${z}_{\mathrm{Ly}\alpha ,\mathrm{peak}}$ denotes the redshift of the Lyα line derived from the asymmetric Gaussian peak, while ${z}_{\mathrm{Ly}\alpha ,\mathrm{ave}}$ refers to the redshift derived from direct integration; these values are compared in Section 3.2.

We used spectroscopic and photometric cuts to eliminate non-Lyα contaminants from our sample. Because the narrowband filters used in this survey all have central wavelengths ${\lambda }_{c}\lt 4900$ Å, [O iii] emitters are excluded by design. [O ii] emitters (λλ3726,3729) may be selected at z ∼ 0.15–0.25 depending on the specific narrowband filter used for each field. However, the total comoving volume selected by these filters is ∼50× larger for Lyα at z ∼ 2.6 than for [O ii] at z ∼ 0.2. The [O ii] luminosity density is also very low at z ≈ 0.2 with respect to higher redshifts, and objects with [O ii] equivalent widths in emission greater than our observed-frame cut off (${W}_{\mathrm{obs}}\gt 72$ Å) are extremely rare (Hogg et al. 1998; Ciardullo et al. 2013). Furthermore, the [O ii] doublet should be marginally resolved in our σ_v ≈ 100 km s⁻¹ spectra, with a line separation ${\rm{\Delta }}{\lambda }_{\mathrm{OII}}\approx 220$ km s⁻¹. As shown in Section 3.3, there is no detected population of objects that have multi-peaked emission lines with ${\rm{\Delta }}{v}_{\mathrm{peaks}}\approx 200$ km s⁻¹, so we do not expect that low-redshift [O ii] emitters are a significant source of contamination to our photometric or spectroscopic samples.

The observed spectral range for each spectrum depends on the location of the corresponding slit on the mask, but most slits were placed to cover a rest-wavelength range 900 Å ≲ λ ≲ 1500 Å at z ∼ 2.7. As such, other contaminants to the LAE sample were considered by searching for anomalous emission lines outside of the Lyα detection window. A small number of such objects were found. All the spectroscopically identified contaminants were lower-redshift active galactic nuclei (AGNs) in which strong C iv λ1550 (z ∼ 1.9) or He ii λ1640 (z ∼ 1.7) emission was detected by our narrowband filter. In each case, Lyα, C iv, and He ii emission are all present with high equivalent width. Five objects were found where the narrowband excess was caused by C iv emission, and another 5 objects were selected due to He ii emission falling in the narrowband passband. All 10 objects were removed from both the spectroscopic and photometric samples. These constraints define a sample of 422 spectra for 318 unique LAEs. Using the contamination results, we estimate the contamination fraction for the photometric sample to be 10/(318 + 10) = 3.0%.

To facilitate comparison with samples of continuum-bright galaxies, we also analyze a sample of 65 LBGs from the KBSS-MOSFIRE (Steidel et al. 2014). These 65 galaxies are hereafter described as the KBSS LBG sample. Details of the object selection and data collection and reduction are described by Steidel et al. (2014) and references therein. The 65 KBSS LBG galaxies discussed here are a small subsample of the entire KBSS-MOSFIRE catalog that meet the following requirements:

• 1.  
  rest-UV spectra acquired using the same LRIS instrument setup (including the 600-line grism) as the KBSS-Lyα LAEs;
• 2.  
  Lyα emission spectroscopically detected by the same line-detection algorithm employed for the KBSS-Lyα LAEs (56% of the above objects);
• 3.  
  systemic redshift measurements acquired as part of the KBSS-MOSFIRE via rest-frame optical emission lines (similar to the KBSS-Lyα Multi-Object Spectrometer For InfraRed Exploration (MOSFIRE) subsample described in Section 2.3);
• 4.  
  a lack of broad, high-equivalent width C iv emission indicative of AGN activity (97% of objects meet this requirement).

The KBSS LBG sample provides a means of comparing the spectral properties of LAEs to objects ∼10× brighter in the UV continuum using the same spectral resolution and analysis methods. Note that ∼50% of all galaxies in the full KBSS-MOSFIRE sample have UV redshifts measurable only in continuum absorption lines. Such objects cannot be selected by narrowband searches, so they were omitted from the KBSS LBG sample to ensure appropriate comparison (criterion #2 above). However, note also that the KBSS LAEs have no photometric cut based on ${W}_{\mathrm{Ly}\alpha }$, as these galaxies occupy a large range of redshifts and do not generally have narrowband images probing their Lyα emission.

The line-fitting algorithm was changed slightly for the KBSS LBG spectra to accommodate the strong continuum, which often varies significantly on the redward and blueward sides of the Lyα line. When fitting the LBGs, a free parameter was added to provide a linear fit to the continuum over the line region, but the one-peak or two-peak asymmetric Gaussian fits were otherwise conducted in an identical manner for the LAE and LBG samples. In Section 4.3, we also consider a composite LBG spectrum from a survey of LBGs at z ∼ 3 (C. Steidel et al. 2015, in preparation). The data collection and reduction of the objects in this composite spectrum are similar to the other LAEs and LBGs described above and will be discussed in detail in future work.

QSO redshifts were determined as described in Trainor & Steidel (2012) and have estimated uncertainties ${\sigma }_{{\rm{z}},\mathrm{QSO}}\approx$ 270 km s⁻¹. The redshift distribution of LAEs with respect to their nearby QSO is shown for each field in Figure 3. On small scales, the redshift distribution of LAEs with respect to the hyperluminous QSOs (HLQSOs) is more meaningful to consider as a distribution of velocities. The relative LAE-QSO velocities are calculated as ${v}_{\mathrm{LAE}}=c({z}_{\mathrm{LAE}}-{z}_{\mathrm{QSO}})/(1+{z}_{\mathrm{QSO}})$. The distribution of QSO-centric velocities for our entire spectroscopic LAE sample is given in Figure 4. Here and elsewhere in this paper we assume that the LAEs have systemic redshifts given by ${z}_{\mathrm{LAE}}={z}_{\mathrm{Ly}\alpha }-200$ km s⁻¹ to account for the typical redshift of the Lyα emission peak with respect to systemic derived from our MOSFIRE data set (Section 2.3).

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For a small subset of these Lyα-selected objects, rest-frame optical spectra were also obtained via the new MOSFIRE (McLean et al. 2010, 2012) on the Keck I telescope. These data were taken over the course of the KBSS-MOSFIRE survey (Steidel et al. 2014). All the MOSFIRE data considered in this analysis are from the field around the HLQSO Q2343+12 (z = 2.573). H-band and/or K-band spectra were obtained for 43 LAEs in this field and reduced via the MOSFIRE-DRP; the observational strategies employed and reduction software are described in Steidel et al. (2014). Redshift fitting and one-dimensional spectral extraction were performed using the IDL program MOSPEC (A. Strom et al. 2015, in preparation). With 07 slits, these spectra have R ∼ 3600, σ_v ∼ 35 km s⁻¹. Of the 43 observed LAEs, 32 yielded robust redshifts via measurement of Hα (K-band, 29 objects), Hβ, and/or the [O iii] λλ4959,5007 doublet (H-band, 12 objects) in emission. Nine objects have measured redshifts in both bands. Four of the MOSFIRE objects do not meet the Lyα equivalent width threshold employed here to define LAEs in a strict sense (${W}_{\mathrm{Ly}\alpha }\gt 20$ Å), but these four are kept in the sample because they were otherwise selected via the same photometric techniques used to define the rest of the sample, and they all display strong Lyα emission in their spectra. Furthermore, the other photometric and spectroscopic properties of these four objects are typical with respect to the remainder of the MOSFIRE sample.

Additional information on these spectra is given in Table 2 and Figure 5. The redshift measured from the MOSFIRE spectra, whether from the H or K band, is hereafter denoted by ${z}_{\mathrm{neb}}$. In the nine cases where a measurement was obtained in both bands, the redshift measurement from the higher-S/N H was used, but both bands generally agree quite closely: the median redshift difference for the two bands is 17 km s⁻¹, roughly half the σ ∼ 35 km s⁻¹ resolution of these spectra. The fit redshifts have typical uncertainties σ_H ∼ 5 km s⁻¹ and σ_K ∼ 7–20 km s⁻¹ for the H- and K-band redshifts, respectively, based on their Gaussian fits.

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Table 2.  MOSFIRE Observations

Object Name	${W}_{\mathrm{Ly}\alpha }$	${z}_{\mathrm{Ly}\alpha }^{\mathrm{peak}}$ a	zHa	zKa	${v}_{\mathrm{Ly}\alpha }^{\mathrm{peak}}$	${v}_{\mathrm{Ly}\alpha }^{\mathrm{ave}}$	${\sigma }_{\mathrm{neb}}$ b	${\mathcal{R}}$	${F}_{\mathrm{Ly}\alpha }$ c	${F}_{{\rm{H}}\alpha }$ c	${F}_{\mathrm{Ly}\alpha }/$
	(Å)				(km s−1)	(km s−1)	(km s−1)	(mag)	(${10}^{-17}$)	(${10}^{-17}$)	${F}_{{\rm{H}}\alpha }$
Q2343-NB0280	52.6	2.5801	2.5777	⋯	201	364	34 ± 9	26.6	6.4 ± 0.2	⋯	⋯
Q2343-NB0308e	58.8	2.5690	2.5663	(2.5666)d	226	360	<35	26.4	4.0 ± 0.3	1.3 ± 0.3	3.1
Q2343-NB0345	36.9	2.5917	⋯	2.5876	343	414	21 ± 6	25.3	13.2 ± 0.4	3.8 ± 0.3	3.5
Q2343-NB0405	134.8	2.5892	2.5862	(2.5860)d	247	293	33 ± 8	27.1	2.9 ± 0.2	1.0 ± 0.2	2.9
Q2343-NB0565	313.9	2.5661	⋯	2.5635	215	54	34 ± 12	26.8	5.7 ± 0.3	1.3 ± 0.2	4.4
Q2343-NB0791	37.4	2.5710	⋯	2.5741	−259	−116	39 ± 9	⋯	3.6 ± 0.3	2.7 ± 0.3	1.3
Q2343-NB1154	54.1	2.5773	⋯	2.5765	65	219	<35	⋯	5.8 ± 0.2	1.0 ± 0.3	5.6
Q2343-NB1174	236.6	2.5509	⋯	2.5478	262	283	<35	⋯	12.5 ± 0.4	1.5 ± 0.3	8.6
Q2343-NB1361	90.6	2.5599	2.5587	(2.5586)d	105	50	36 ± 8	27.0	3.4 ± 0.2	0.3 ± 0.1	11.2
Q2343-NB1386	25.8	2.5691	⋯	2.5647	371	89	<35	>27.3	1.6 ± 0.2	1.1 ± 0.3	1.5
Q2343-NB1416	20.7	2.5602	2.5582	(2.5594)d	169	275	35 ± 14	26.8	1.8 ± 0.2	0.7 ± 0.3	2.4
Q2343-NB1501	35.2	2.5614	2.5593	(2.5592)d	180	158	71 ± 12	>27.3	1.7 ± 0.2	1.2 ± 0.4	1.4
Q2343-NB1518	22.3	2.5890	⋯	2.5860	251	238	<35	26.2	3.3 ± 0.2	0.8 ± 0.3	4.0
Q2343-NB1585	303.4	2.5669	2.5649	(2.5652)d	169	93	<35	>27.3	5.1 ± 0.2	0.6 ± 0.2	9.0
Q2343-NB1692	359.2	2.5625	⋯	2.5602	194	85	14 ± 9	26.8	5.6 ± 0.2	1.1 ± 0.3	5.0
Q2343-NB1783	35.0	2.5784	2.5767	(2.5766)d	143	167	51 ± 3	25.7	7.8 ± 0.2	2.0 ± 0.2	3.8
Q2343-NB1789	88.2	2.5471	⋯	2.5448	196	59	45 ± 16	>27.3	2.3 ± 0.2	1.4 ± 0.3	1.6
Q2343-NB1806	19.3	2.5982	⋯	2.5954	237	204	73 ± 19	26.7	1.2 ± 0.1	1.4 ± 0.3	0.8
Q2343-NB1828	26.7	2.5753	⋯	2.5724	247	216	38 ± 15	26.9	2.7 ± 0.3	1.0 ± 0.2	2.6
Q2343-NB1829	32.1	2.5782	⋯	2.5754	233	271	41 ± 8	25.9	5.7 ± 0.2	2.6 ± 0.3	2.2
Q2343-NB1860	23.6	2.5740	⋯	2.5741	−11	237	<35	25.7	1.2 ± 0.2	1.0 ± 0.3	1.2
Q2343-NB2211e	66.2	2.5776	2.5760	(2.5758)d	135	206	30 ± 13	26.9	4.3 ± 0.3	1.1 ± 0.2	4.0
Q2343-NB2571	29.4	2.5820	⋯	2.5850	−249	−503	38 ± 26	>27.3	1.4 ± 0.3	0.8 ± 0.2	1.8
Q2343-NB2785	14.2	2.5723	⋯	2.5785	−517	−367	<35	>27.3	1.3 ± 0.1	0.4 ± 0.1	3.2
Q2343-NB2807e	24.6	2.5479	2.5446	⋯	279	184	110 ± 8	23.8	23.4 ± 0.3	⋯	⋯
Q2343-NB2816	58.5	2.5782	⋯	2.5742	340	243	57 ± 23	>27.3	2.0 ± 0.1	1.5 ± 0.4	1.4
Q2343-NB2821	32.4	2.5800	⋯	2.5779	173	69	24 ± 23	⋯	1.3 ± 0.2	1.3 ± 0.4	1.0
Q2343-NB2834	7.2	2.5700	⋯	2.5683	142	−69	<35	>27.3	0.9 ± 0.1	0.5 ± 0.2	1.7
Q2343-NB3061	57.6	2.5788	⋯	2.5764	203	270	72 ± 24	26.5	2.2 ± 0.2	2.0 ± 0.5	1.1
Q2343-NB3170	90.0	2.5488	2.5475	⋯	113	152	15 ± 5	>27.3	2.6 ± 0.1	⋯	⋯
Q2343-NB3231f	110.4	2.5737	2.5711	(2.5695)d	218	151	43 ± 12	25.9	8.4 ± 0.2	1.0 ± 0.2	8.7
Q2343-NB3292	13.4	2.5700	⋯	2.5631	579	153	<35	>27.3	1.3 ± 0.2	0.6 ± 0.2	2.2

Notes.

^a ${z}_{\mathrm{Ly}\alpha }$, z_H, and z_K denote the redshifts measured from fitting the Lyα emission line, H-band emission lines (primarily [O iii] λ5007), and K-band emission lines (Hα exclusively). ^b ${\sigma }_{\mathrm{neb}}$ is the velocity width of the nebular emission line used to define ${z}_{\mathrm{neb}}$. Both the line widths and their associated uncertainties reflect the deconvolution of the ${\sigma }_{\mathrm{inst}}=35$ km s⁻¹ instrumental profile. ^cLine fluxes (in cgs units) are determined from a combination of spectroscopic and photometric measurements as described in Section 3.2. ^dIn the nine cases where both the $H\text{-}$and $K\text{-}$band spectra yielded redshifts, we adopted the higher-S/N $H\text{-}$band redshifts to define ${z}_{\mathrm{neb}}$. ^eThe nebular redshifts of Q2343-NB0308, Q2343-NB2211, and Q2343-NB2807 were measured from the [O iii] λ4959Å line because the λ5007Å line did not fall on the detector. ^fThe nebular redshift of Q2343-NB3231 was measured from the Hβ line (and cross-checked with Hα) because the [O iii] λ5007Å and λ4959Å lines did not fall on the detector.

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Our pre-existing ${\mathcal{R}}$-band image in the Q2343 field is rotated with respect to the narrowband and B-band images used to select LAEs, so ∼16% of the Lyα-imaged field does not currently have ${\mathcal{R}}$-band coverage. Objects falling in this region are omitted when discussing average ${\mathcal{R}}$-band properties of the LAEs. In particular, 4 of the 32 MOSFIRE LAEs have no measured ${\mathcal{R}}$ magnitudes (Table 2), but their continuum properties in other bands (B and NIR where available) are consistent with those falling within our existing ${\mathcal{R}}$ coverage. The 3σ ${\mathcal{R}}$-band limit is reported in Table 2 for objects with measured ${\mathcal{R}}$ magnitudes fainter than that value.

Velocity dispersions are measured (or constrained) for each MOSFIRE LAE from the Gaussian fit to the detected spectral line. As above, the highest-S/N line (generally [O iii] λ5007) width is used when multiple lines are detected. The measured line widths (deconvolved from the instrumental profile) range from ${\sigma }_{\mathrm{neb}}=14\pm 9$ to 114 ± 8 km s⁻¹ (Table 2), with a median $\langle {\sigma }_{\mathrm{neb}}\rangle =34$ km s⁻¹. The object with the largest fit dispersion (Q2343-NB2807) has a two-peaked nebular line profile that is not well-fit by a single Gaussian; with the exception of this object, no LAE has a fit dispersion larger than 73 km s⁻¹. Ten objects have line widths consistent with the MOSFIRE instrument profile and are given as limits (${\sigma }_{\mathrm{neb}}\lt 35$ km s⁻¹). The LAEs are generally unresolved in our ground-based images, and further analysis of the limited HST/WFC3 imaging in these fields is forthcoming. The similar LAE sample of Erb et al. (2014), however, have a median effective half-light radius a = 0.6 kpc in HST F814W photometry. Taking this value as a typical size for the KBSS-Lyα LAEs, we can estimate their dynamical masses via the formula ${M}_{\mathrm{dyn}}=5a{\sigma }^{2}/G$. As in Erb et al. (2014), we assume a spherical geometry for these systems, noting that the dynamical mass would be smaller for a disk-like geometry. Further discussion of the likely physical morphologies of these objects is given in Section 4.3. For the assumed geometries and sizes, the KBSS-Lyα LAEs would have dynamical masses 1.4 × 10⁸ ${\text{}}{M}_{\odot }\lt {M}_{\mathrm{dyn}}\lt 8.4\times {10}^{9}$ ${\text{}}{M}_{\odot }$.⁸ The median mass is $\langle {M}_{\mathrm{dyn}}\rangle =8.0\times {10}^{8}{\text{}}{M}_{\odot }$.

Postage stamps of each Lyα and nebular line spectrum in the MOSFIRE sample are displayed in Figure 5. The majority of the nebular redshifts are derived from Hα, for which the intrinsic flux ratio is ${F}_{\mathrm{Ly}\alpha }/{F}_{{\rm{H}}\alpha }\approx 8.7$ under the typical assumption of case-B (i.e., ionization-bounded) recombination and ${T}_{e}={10}^{4}$ K.⁹

The LAE Lyα line fluxes (${F}_{\mathrm{Ly}\alpha }$) are measured photometrically from their continuum-subtracted narrowband detections. Directly integrating the rest-UV spectrum yields a Lyα flux ∼2× smaller on average. This difference may be partially due to uncertainties in the absolute flux calibration of the rest-UV spectra, but the consistency between our stacked continuum spectra and broadband flux measurements (Section 4.1) suggests that this effect is minimal. Similarly, the photometric errors in the measured narrowband Lyα fluxes are estimated to be ≲15%. Rather, it appears that the differential slit losses between Lyα and continuum photons are significant within our 12 wide slits.

For the MOSFIRE subsample of LAEs with K-band spectra, Hα fluxes (${F}_{{\rm{H}}\alpha }$; Table 2) are estimated by a Gaussian fit to the emission line. Slit losses are difficult to estimate for individual faint objects, so the measured values have been multiplied by a factor 1.5–2.1 (depending on the mask) to account for the average slit loss measured for bright point sources on the same slitmasks (A. Strom et al. 2015, in preparation). Most LAEs in our sample do not have robust detections of both Hα and Hβ, so we have not corrected the Hα fluxes for dust attenuation, but the four objects with Hα and Hβ ${\rm{S}}/{\rm{N}}\gt 2$ have a mean ratio $\langle {F}_{{\rm{H}}\alpha }/{F}_{{\rm{H}}\beta }\rangle =3.3\pm 1.1$, consistent with the canonical (non-attenuated) case-B value ${F}_{{\rm{H}}\alpha }/{F}_{{\rm{H}}\beta }=2.86$ (Brocklehurst 1971).

The measured line ratios in Figure 5 vary considerably (${F}_{\mathrm{Ly}\alpha }/{F}_{{\rm{H}}\alpha }\sim$ 1–11, Table 2) with respect to that predicted by case-B recombination. If the intrinsic ${F}_{\mathrm{Ly}\alpha }/{F}_{{\rm{H}}\alpha }$ flux ratio is assumed to be 8.7 (and the Hα flux is not significantly affected by extinction), then the median ratio $\langle {F}_{\mathrm{Ly}\alpha }/{F}_{{\rm{H}}\alpha }\rangle =2.7$ suggests a typical Lyα escape fraction $\langle {f}_{\mathrm{esc},\mathrm{Ly}\alpha }\rangle =\langle {F}_{\mathrm{Ly}\alpha }^{\mathrm{observed}}/{F}_{\mathrm{Ly}\alpha }^{\mathrm{intrinsic}}\rangle \approx 30\%$. This ${F}_{\mathrm{Ly}\alpha }/{F}_{{\rm{H}}\alpha }$ ratio is consistent with that observed in the 4 objects with Hα line detections in the similar faint-LAE sample of Erb et al. (2014). If the Hα emission is attenuated by interstellar dust, then the intrinsic values of ${f}_{\mathrm{esc},\mathrm{Ly}\alpha }$ may be lower, but the measured values are considerably higher than previous estimates of ${f}_{\mathrm{esc},\mathrm{Ly}\alpha }\approx 5\%$ for typical high-redshift star-forming galaxies (Hayes et al. 2010; Steidel et al. 2011; Ciardullo et al. 2014). Such high Lyα escape fractions are suggestive of the high LyC escape fractions observed in samples of LAEs (Mostardi et al. 2013; Nestor et al. 2013) and may indicate low H i optical depths for photons escaping from star-forming regions in these galaxies. Given the proximity of these LAEs to HLQSOs, however, it may be that ${f}_{\mathrm{esc},\mathrm{Ly}\alpha }$ is elevated by the "fluorescent" boosting of the total Lyα flux from these objects.

For comparison, the KBSS LBGs have a median flux ratio $\langle {F}_{\mathrm{Ly}\alpha }/{F}_{{\rm{H}}\alpha }\rangle \approx 0.5$, or a corresponding escape fraction ${f}_{\mathrm{esc},\mathrm{Ly}\alpha }\approx 6\%$. The LBG Hα slit losses were corrected in a similar manner to the LAEs, and further analysis of the rest-frame optical spectra of the KBSS LBGs will be presented in A. Strom et al. (2015, in preparation). The LBGs lack narrowband Lyα photometry, so the Lyα fluxes were measured by direct integration of the rest-UV spectrum (after flux-calibrating the spectrum based on the broadband G-band flux). Steidel et al. (2011) measure Lyα aperture corrections for LBG spectra showing Lyα in net emission or absorption in comparison to LAEs, finding that LBGs with detected Lyα emission show similar differential slit losses to LAEs in our 12 slits. In this case the Lyα luminosities of the KBSS LBGs may be underestimated by a factor of ∼2×, and the escape fractions may be ${f}_{\mathrm{esc},\mathrm{Ly}\alpha }\approx 12\%$ in a larger aperture. This Lyα escape fraction is similar to that derived for Lyα-emitting LBGs (${f}_{\mathrm{esc},\mathrm{Ly}\alpha }=14.4\%$) by Steidel et al. (2011). It thus appears that our sample of Lyα-emitting, continuum-color selected KBSS LBGs have a broadly similar Lyα escape fraction with respect to previously studied samples of LBGs, and significantly smaller values than the KBSS-Lyα LAEs.

Given the small number of LAEs with Hα detections, it is difficult to investigate trends within the MOSFIRE LAE sample. In particular, we find no association between ${f}_{\mathrm{esc}}$ and the Lyα offset, peak multiplicity, or peak separation (${v}_{\mathrm{Ly}\alpha }$, ${f}_{\mathrm{mult}}$, and ${v}_{\mathrm{peaks}}$; see discussion in Sections 3.2–3.3). However, we find a significant trend between ${f}_{\mathrm{esc},\mathrm{Ly}\alpha }$ and ${W}_{\mathrm{Ly}\alpha }$, which are positively correlated with $p\lt 4\times {10}^{-3}$ for a Pearson correlation test. This result suggests that ${W}_{\mathrm{Ly}\alpha }$ is primarily an indicator of Lyα escape, not Lyα production among these faint galaxies. In fact, the relation between Hα luminosity (a standard indicator of SFR) and ${W}_{\mathrm{Ly}\alpha }$ is weakly negative in the sample. Given that a higher ${W}_{\mathrm{Ly}\alpha }$ at a given observed Lyα luminosity corresponds to a fainter UV continuum luminosity (another proxy for SFR), we suggest that ${W}_{\mathrm{Ly}\alpha }$ is likely anti-correlated with SFR among these faint LAEs. This effect is similar to the anti-correlation observed between ${W}_{\mathrm{Ly}\alpha }$ and UV SFR (or luminosity) seen in several previous studies (e.g., Ando et al. 2006; Ouchi et al. 2008; Kornei et al. 2010; Stark et al. 2010; Atek et al. 2014). We also find a tentative, negative association between ${W}_{\mathrm{Ly}\alpha }$ and ${\sigma }_{\mathrm{neb}}$ (the width of the nebular Hα and/or [O iii] emission). Because ${\sigma }_{\mathrm{neb}}$ traces the stellar velocity dispersion and thus the dynamical mass of the galaxy, this may suggest that higher ${W}_{\mathrm{Ly}\alpha }$ is associated with lower dynamical masses. However, further study of the stellar populations and SFRs of the LAEs (including our ongoing photometry and rest-frame optical spectroscopy of these objects) will be necessary to confirm the physical basis of these trends.

The offset of the Lyα line with respect to the systemic redshift was measured for each of the 32 LAEs in the MOSFIRE sample using the ${z}_{\mathrm{Ly}\alpha }$ and ${z}_{\mathrm{neb}}$ values estimated as described in Sections 2.2 and 2.3. The velocity offset was then inferred from the measured redshifts as

$$\begin{eqnarray}&&{v}_{\mathrm{Ly}\alpha }=\displaystyle \frac{{z}_{\mathrm{Ly}\alpha }-{z}_{\mathrm{neb}}}{1+{z}_{\mathrm{neb}}}c.\end{eqnarray} \tag{ 4 }$$

The velocity shift of the Lyα line with respect to the systemic redshift is clear from the panels in Figure 5. The majority (28/32; 88%) of spectra display the redshifted Lyα profile typical of star-forming galaxies, but there are several objects with minimal velocity shift, or even a dominant peak blueward of the systemic redshift. The distribution of measured velocity shifts (Equation (4)) is given in Figure 6. The typical Lyα shift of +200 km s⁻¹ is clearly visible. This shift is consistent with that found for the few samples of LAEs with systemic redshifts in the literature (e.g., McLinden et al. 2011; Chonis et al. 2013; Hashimoto et al. 2013; Shibuya et al. 2014), and significantly less than that previously measured in samples LBGs (300–400 km s⁻¹, Steidel et al. 2010). However, we demonstrate below that the detailed velocity distribution depends on the method by which the Lyα emission redshift is assigned.

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The two panels of Figure 6 show the effect of defining ${z}_{\mathrm{Ly}\alpha }$ by either the fitted peak (${z}_{\mathrm{Ly}\alpha ,\mathrm{peak}}$) or the flux-weighted centroid of the line profile (${z}_{\mathrm{Ly}\alpha ,\mathrm{ave}}$; see Section 2.2). Both methods yield qualitatively similar distributions, with median values $\langle {v}_{\mathrm{Ly}\alpha ,\mathrm{peak}}\rangle =198$ km s⁻¹ and $\langle {v}_{\mathrm{Ly}\alpha ,\mathrm{ave}}\rangle =176$ km s⁻¹. However, ${z}_{\mathrm{Ly}\alpha ,\mathrm{peak}}$ displays a tighter correlation with the redshift derived from nebular emission lines than ${z}_{\mathrm{Ly}\alpha ,\mathrm{ave}}$. The median absolute deviations (a scale estimator that is insensitive to outliers) of the two distributions of ${v}_{\mathrm{Ly}\alpha }$ are MAD(${v}_{\mathrm{Ly}\alpha ,\mathrm{peak}})=54$ km s⁻¹ and MAD(${v}_{\mathrm{Ly}\alpha ,\mathrm{ave}}$) = 93 km s⁻¹. The similarities between the two distributions suggest that either quantity is a reasonable proxy for the systemic redshift after correcting for the typical 200 km s⁻¹ offset, and even the individual velocities computed by both measurements are consistent within 100 km s⁻¹ for the majority of objects (Table 2). Because ${z}_{\mathrm{Ly}\alpha ,\mathrm{peak}}$ tracks ${z}_{\mathrm{neb}}$ more tightly, however, we adopt ${z}_{\mathrm{sys},\mathrm{Ly}\alpha }={z}_{\mathrm{Ly}\alpha ,\mathrm{peak}}-200$ as the best estimate of the systemic redshift in the absence of nebular emission line measurements.

The distribution of Lyα line offsets from the comparison KBSS LBG sample is also displayed in Figure 6, and there the differences between the two Lyα redshift estimators are more apparent. While the distribution of fit peak velocities ${v}_{\mathrm{Ly}\alpha ,\mathrm{peak}}$ is again sharply peaked around ${v}_{\mathrm{Ly}\alpha }$ ≈ 200 km s⁻¹, the centroid velocities ${v}_{\mathrm{Ly}\alpha ,\mathrm{ave}}$ are more extended, particularly toward higher (more strongly redshifted) velocities. The median velocity offsets for the LBG sample are $\langle {v}_{\mathrm{Ly}\alpha ,\mathrm{peak}}\rangle$ = 205 km s⁻¹ and $\langle {v}_{\mathrm{Ly}\alpha ,\mathrm{ave}}\rangle$ = 306 km s⁻¹. Note that our measurement of ${v}_{\mathrm{Ly}\alpha ,\mathrm{peak}}$ in particular suggests a significantly smaller Lyα offset than previous studies of LBGs. Qualitatively, the difference between the two distributions is due to the fact that the LBG Lyα emission lines have extended red tails (often combined with continuum flux levels that are higher on the red side of Lyα than the blue side) that draw the velocity centroid to higher/redder values. Fitting the Lyα emission line with a symmetric Gaussian model will likewise cause the fit emission-line center to be redder than the Lyα emission peak. While the LAE emission lines tend to be asymmetric as well, they typically have more symmetric profiles and/or stronger blue secondary peaks that compensate for the extended red wing. The LAEs also have less continuum emission that is more symmetric about the wavelength of Lyα than typical LBGs (e.g., the observed ratio of f₁₁₂₅ to f₁₃₂₅; see Section 4.3). The distributions of emission line widths, asymmetry, and peak multiplicity for each sample are discussed in Section 3.3 below.

Despite their differing line morphologies and photometric properties, it is significant that both the LAE and LBG samples have Lyα emission line peaks that are well-described by a uniform offset of ∼200 km s⁻¹ redward of the systemic redshifts. While the measured velocity of the Lyα peak may be strongly dependent on spectral resolution, its constancy across a broad range of galaxy luminosities suggests that it is less sensitive to galaxy properties than the Lyα emission centroid. For a sample of galaxies observed with the same spectral resolution, therefore, the Lyα emission peak appears to be a robust redshift indicator across a diverse range of galaxy types (with the caveat that ∼50% of z ∼ 2.4 LBGs have no net Lyα emission in their spectra; Steidel et al. 2011). We use this redshift calibration to create composite LAE spectra from our large sample of LAEs without nebular redshift measurements in Section 4.

In addition to the distribution of average or peak Lyα line velocities, it is interesting to compare the full velocity distributions of Lyα and nebular emission. Figure 7 displays the stacked Lyα and nebular line profiles of the 32 MOSFIRE LAEs. Of particular note is the breadth of the Lyα line with respect to the nebular line profile; assuming that the Lyα photons are generated by recombination processes in the same H ii regions that generate the nebular emission, the top panel of Figure 7 clearly displays the diffusion of the Lyα photons in velocity as they resonantly scatter through the surrounding H i gas. Fitting a Gaussian function to the stack of nebular lines yields a velocity width of ${\sigma }_{\mathrm{neb}}$ = 35 ± 3 km s⁻¹. The stacked Lyα profile has a width of ${\sigma }_{\mathrm{Ly}\alpha }$ = 115 ± 8 km s⁻¹ for the primary (red) peak. These figures reflect the deconvolution of the instrumental resolution of MOSFIRE (${\sigma }_{\mathrm{inst}}$ = 35 km s⁻¹) and LRIS (${\sigma }_{\mathrm{inst}}$ = 100 km s⁻¹) in their observed modes.¹⁰ The peak of the stacked Lyα spectrum is again quite close to +200 km s⁻¹, but there is a distinct component blueward of the systemic redshift as well. After subtracting the faint continuum, the fraction of Lyα line flux emitted with v < 0 is 16%. For comparison, we show the effective profile that would result from stacking all the Lyα lines at the redshifts derived from the Lyα line peak and then making a +200 km s⁻¹ shift in the bottom panel of Figure 7. The resulting profile is narrower (${\sigma }_{\mathrm{Ly}\alpha }$ = 85 ± 8 km s⁻¹), with only 11% of the line flux emitted at v < 0, roughly 2/3 the flux measured using the true systemic redshifts.

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The four MOSFIRE LAEs with ${v}_{\mathrm{Ly}\alpha }\lt 0$ compose an extremely interesting, though small, group of objects. Further analysis of this sample is ongoing, including spectroscopy and photometry to constrain the stellar contribution to the LAE luminosity, enrichment, and dynamics. While only three of these blueshifted LAEs currently have ${\mathcal{R}}$ photometry, their average flux in that band is ∼1/2× that of the LAEs with redshifted Lyα lines, tentatively suggesting that blueshifted LAEs have physical properties that are distinct from typical LAEs. Other properties associated with redshifted or blueshifted Lyα emission are discussed in the context of multi-peaked Lyα emission below.

As discussed above, star-forming galaxies are often associated with multi-peaked Lyα emission. In a systematic study of Lyα emission among ∼1500 star-forming galaxies at z ∼ 2–3, Kulas et al. (2012) found that ∼30% are multi-peaked, with some dependence on the spectral resolution and S/N of the observations. While most of these galaxies were observed at lower resolution, a subsample of their spectra were obtained with the same 600-line grism of Keck/LRIS used for our LAE sample and have similar integration times (∼1.5 hr). This subsample included 44 multi-peaked spectra, a multiplicity rate of 27%.

Yamada et al. (2012a) studied the Lyα peak morphologies of 91 LAEs at z ∼ 3 at similar resolution (R ∼ 1700), finding a ∼50% multiplicity rate. This heterogeneous sample contains 12 Lyα-blobs from Matsuda et al. (2004), as well as compact, faint LAEs similar to those of the KBSS-Lyα sample (although with a limiting Lyα flux ∼2× brighter, according to Yamada et al. 2012b).

For the KBSS-Lyα sample of this paper, multi-peaked systems were identified as described in Section 2.2. Of the 318 unique spectroscopically identified LAEs, 129 are found to be multi-peaked, for a multiplicity fraction of 40%. The criteria for identifying a secondary peak were not identical to that of Kulas et al. (2012); in particular, the significance threshold was not dependent on the magnitude or S/N of the primary peak, and no minimum peak separation was enforced. However, we found that adjusting the multiplicity criteria to match those of Kulas et al. as closely as possible did not significantly affect the overall rate of selection nor the spectral/physical properties of the selected sample.

Previous studies of Lyα kinematic multiplicity (among samples with or without systemic redshifts) typically group these lines into blue-peak dominant or red-peak dominant lines, motivated by the association of blue (red) peak dominance with inflowing (outflowing) gas in radiation transfer models (e.g., Zheng & Miralda-Escudé 2002; Dijkstra et al. 2006; Verhamme et al. 2006). Kulas et al. (2012) found that 67% of their 239 multi-peaked objects (the majority of which had lower spectral resolution than the KBSS-Lyα sample) have dominant red peaks. A selection of examples of the diverse Lyα spectral morphologies represented among the KBSS-Lyα LAEs is displayed in Figure 8, and the distribution of red/blue peak dominance in our sample is displayed in Figure 9. In the top panel of Figure 9, we show the distribution of inter-peak velocities, defined as ${\rm{\Delta }}{v}_{\mathrm{peaks}}=c({z}_{\mathrm{peak},\mathrm{pri}}-{z}_{\mathrm{peak},\mathrm{sec}})/(1+({z}_{\mathrm{peak},\mathrm{pri}})$. ${z}_{\mathrm{peak},\mathrm{pri}}$ is the redshift of the first peak identified by the line detection algorithm discussed in Section 2.2 (i.e., the peak of the asymmetric Gaussian profile fit to the highest peak in the smoothed spectrum), and ${z}_{\mathrm{peak},\mathrm{sec}}$ is the redshift corresponding to the mean of the second fit Gaussian component. For this definition, ${\rm{\Delta }}{v}_{\mathrm{peaks}}\gt 0$ corresponds to red-dominant systems, such that the primary peak is redward of the inter-peak trough.

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Of the 129 multi-peak LAEs, 96 (74%) have dominant red peaks (${\rm{\Delta }}{v}_{\mathrm{peaks}}\gt 0$), while 33 (26%) are blue dominant (${\rm{\Delta }}{v}_{\mathrm{peaks}}\lt 0$; Table 3). The red-dominant LAEs have a quite narrow distribution of peak separations, with a median value $\langle {\rm{\Delta }}{v}_{\mathrm{peaks}}\rangle$ = 560 km s⁻¹ and a standard deviation $\sigma ({\rm{\Delta }}{v}_{\mathrm{peaks}})$ = 220 km s⁻¹. Conversely, the blue-dominant LAEs have a larger velocity shift over a broader range: $\langle {\rm{\Delta }}{v}_{\mathrm{peaks}}\rangle$ = −660 km s⁻¹ and $\sigma ({\rm{\Delta }}{v}_{\mathrm{peaks}})$ = 300 km s⁻¹. A similar contrast can be seen in the flux distribution within these multi-peaked LAEs (Figure 9, bottom panel). The fraction of total Lyα flux in the red peak, ${F}_{\mathrm{red}}/{F}_{\mathrm{tot}}$, is defined as the integral of the redder of the two Gaussian components divided by the integral of the sum of the two components. There are 101 LAEs (78%) with ${F}_{\mathrm{red}}/{F}_{\mathrm{tot}}\gt 0.5$, an alternative definition of red-peak dominance. The sets of LAEs with ${\rm{\Delta }}{v}_{\mathrm{peaks}}\gt 0$ and ${F}_{\mathrm{red}}/{F}_{\mathrm{tot}}\gt 0.5$ overlap almost entirely,¹¹ but we use the prior definition (based on the significance of peaks in the smoothed spectrum) for consistency with Kulas et al. (2012) and other surveys that assume different model profiles.

Table 3.  LAE and LBG Emission-line Properties

	LAEs	MOSFIRE	KBSS
		LAEsa	LBGs
${N}_{\mathrm{obj}}$	318	32	65
$\langle {F}_{\mathrm{Ly}\alpha }\ \rangle$ b (${10}^{-17}$ cgs)	4.5 ± 0.8	4.6 ± 0.8	7.3 ± 1.6
$\langle {\sigma }_{\mathrm{Ly}\alpha }\rangle$ (km s−1)	144 ± 3	138 ± 8	195 ± 7
${N}_{\mathrm{blue}}$ c	⋯	4	4
${f}_{\mathrm{blue}}$ c	⋯	13%	6%
${N}_{\mathrm{mult}}$ d	129	13	29
${f}_{\mathrm{mult}}$ d	41%	41%	45%
${N}_{\mathrm{mult},\mathrm{blue}}$ e	33	3	6
${f}_{\mathrm{mult},\mathrm{blue}}$ e	10%	9%	9%
$\langle | {\rm{\Delta }}{v}_{\mathrm{peaks}}| \rangle$ (km s−1)	615 ± 14	608 ± 49	716 ± 35
$\langle {F}_{{\rm{H}}\alpha }\rangle$ (${10}^{-17}$ cgs)	⋯	1.3 ± 0.1	7.2 ± 0.7
$\langle {\sigma }_{\mathrm{neb}}\rangle$ (km s−1)	⋯	34 ± 4	84 ± 4

Notes.

^aParameters for the subset of LAEs with MOSFIRE nebular (systemic) redshifts. ^bAverages are given as mean values, with uncertainties denoting the standard error of the mean. ^cNumber (or fraction) of objects with a blueshifted Lyα line (${v}_{\mathrm{Ly}\alpha ,\mathrm{peak}}\lt 0$). ^dNumber (or fraction) of objects with multiple detected Lyα peaks. ^eNumber (or fraction) with multiple detected Lyα peaks that have a lower-velocity ("blue") dominant peak.

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Due to the presence of nearby HLQSOs in these LAE fields, it is important to discern what role the external illumination of the QSO (i.e., "fluorescence") may play in shaping the observed spectral morphology of the LAEs. Clearly, the fluorescing LAEs must inhabit the region of the environment illuminated by the QSO in order for the ionizing field to have an observable effect. As argued in Trainor & Steidel (2013), the combination of geometry and the finite QSO lifetime (measured to be ≲20 Myr) cause this fluorescence to be observable only when the LAE is in the foreground of the QSO, or less than ∼10⁷ lightyears (3.2 proper Mpc) distant in the background.

The redshift distribution relative to the QSOs of all the multi-peaked LAEs is shown in Figure 10. Care must be taken in comparing the redshift distributions of red- and blue-dominant LAEs based on the redshifts of their Lyα lines. Figure 10 shows the redshift distribution when the systemic redshift of each LAE is taken to be 200 km s⁻¹ blueward of the red Lyα peak, regardless of whether the redder peak is primary or secondary. The redshift distribution of red-dominant Lyα profiles is fairly symmetric, with a slight bias toward the QSO foreground. The blue-dominant LAEs, however, show a strong association with the region in the immediate background of the QSO. A two-sample KS test finds only a small (p ≈ 0.03) likelihood of both samples being drawn from the same distribution.

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Given the uncertainty in assigning redshifts to those sources without accurate systemic redshifts from optically thin nebular emission lines, it is unclear whether the blue-dominant LAEs are localized within the QSO field, or whether they differ from the red-dominant distribution at all. As noted above, blueshifted Lyα emission is a possible observational signature of infalling gas illuminated by a central source. Given the proximity of the HLQSOs, however, it is also possible that the detected emission has a significant fluorescent contribution. In this case, the blueshifted Lyα emission could conceivably correspond to outflowing gas illuminated externally by the nearby QSO, a situation that could explain the association of blue-dominant LAEs with the background of the QSO, where the geometry would naturally predict blueshifted emission from the QSO-facing side of a gaseous outflow. Only three of the blue-dominant LAEs currently have MOSFIRE spectra, but their systemic redshifts place them 0.4–1.2 pMpc in the background of the QSO (consistent with the Lyα-only measurements). Similarly, the 4 LAEs with MOSFIRE redshifts and ${v}_{\mathrm{Ly}\alpha ,\mathrm{peak}}\lt 0$ km s⁻¹ (that is, objects with blueshifted Lyα with respect to systemic) lie in the immediate background of the QSO (0.4–4 pMpc; hatched region in Figure 10), suggesting that external illumination may play a role in their spectral morphology as well.

Detailed predictions for fluorescent emission from gas with large bulk velocities and a realistic spatial distribution are unclear (although see work by Kollmeier et al. 2010), and it is difficult to draw robust conclusions without access to the systemic redshifts of these LAEs. Given the diversity of line morphologies and asymmetries even within the set of blue-dominant LAEs (Figure 8), it is unclear whether these atypical profiles are generated by a single mechanism. Further study of these "blue" LAEs, including additional rest-frame optical spectroscopy, is required to understand the physics of their Lyα emission and transmission.

Finally, in the absence of systemic redshift measurements and/or multiple emission peaks, the Lyα line asymmetry (${\alpha }_{\mathrm{asym}};$ Section 2.2) may also trace gas kinematics among these LAEs (see, e.g., Zheng & Wallace 2014). However, line asymmetry is often not evident in medium-resolution, low-S/N spectra. Not only will the measured line asymmetry be systematically diminished by the smoothing effect of the convolved line spread function, but noise peaks and unresolved emission line features may be fit by an extended tail by our automatic fitting algorithm.

Despite these issues, some trends can be seen in the relative distributions of Lyα line asymmetries. Figure 11 shows the distribution of ${\alpha }_{\mathrm{asym}}$ for blue-dominant and red-dominant multi-peaked LAEs. While both subsamples have broad distributions of ${\alpha }_{\mathrm{asym}}$ because of the effects described above, there is a clear tendency of the blue-dominant Lyα lines to have lower values of ${\alpha }_{\mathrm{asym}}$ (that is, an extended blue wing in the primary peak), while red-dominant LAEs typically have ${\alpha }_{\mathrm{asym}}\gt 1$ (extended red wings). The two distributions have a Kolmogorov–Smirnov probability of being drawn from the same underlying distribution p < 4 × 10⁻⁵. This result agrees with the findings of Yamada et al. (2012a), who found a similar relation (albeit with lower significance) in their smaller sample.

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We compare the distribution of Lyα morphologies between the KBSS-Lyα LAEs and the KBSS LBGs in Figures 12 and 13, as well as in Table 3. In the LBG sample, 29/65 (45%) have a detected secondary peak. Of these objects, 23/29 (79%) are red-peak dominant. Note that these rates are 40% and 74%, respectively, among the LAEs (Table 6). As described above, measured rates of Lyα peak multiplicity are dependent on both the resolution and S/N of the spectra. The KBSS LBGs considered in this paper were observed using the same instrument setup as the KBSS-Lyα LAEs and were analyzed using the same line-detection software (see Section 2.2); however, the typical LBG Lyα fluxes are significantly brighter (Table 6) and the spectral S/N is correspondingly higher. Secondary peaks of low relative significance are therefore more likely to be detected in the LBG sample than in our LAE sample. In particular, we find that the ratio of primary-peak flux to secondary-peak flux is larger among the LBGs than the LAEs, which may be caused by missing similarly faint secondary Lyα peaks in the LAE spectra. However, radiative transfer models of Lyα escape also predict that the primary/secondary flux ratio increases with outflow velocity (e.g., Verhamme et al. 2006). In either case, the frequency of Lyα peak multiplicity and blue-dominant Lyα peaks are broadly consistent between our LBG and LAE samples.

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However, the velocity distribution of Lyα flux varies significantly between the LAE and LBG samples. Figure 12 displays the distribution of fit Lyα emission line widths for both samples of objects. The measured line width is that of the primary Lyα peak, and is given by the average of the red and blue scale parameters of the asymmetric Gaussian fit (Equation (2)):

$$\begin{eqnarray}&&{\sigma }_{\mathrm{Ly}\alpha ,\mathrm{primary}}=\displaystyle \frac{{\sigma }_{\mathrm{red}}+{\sigma }_{\mathrm{blue}}}{2}.\end{eqnarray} \tag{ 5 }$$

The LAE sample has a median line width of 166 km s⁻¹, with 33% of spectra having a primary-peak line width less than 150 km s⁻¹. The LBG sample has a median line width of 210 km s⁻¹, with only 3% (two spectra) having a primary-peak line width less than 150 km s⁻¹. The LRIS spectral resolution ${\sigma }_{\mathrm{inst}}$ = 100 km s⁻¹ (which is the same for both the LAE and LBG samples) has been subtracted in quadrature. Note that nearly all the measured lines are well-resolved with respect to the resolution limit. A Kolmogorov–Smirnov test gives a probability p ≈ 10⁻¹⁰ of both samples being drawn from the same distribution.

A similar contrast is seen in the distribution of peak separations among the LAEs and LBGs with multiple detected emission peaks (Figure 13). Among the 129 LAEs with multiple detected peaks, the median peak separation is $\langle | {\rm{\Delta }}{v}_{\mathrm{peaks}}| \rangle =565$ km s⁻¹, while the 29 LBGs with multiple peaks have $\langle | {\rm{\Delta }}{v}_{\mathrm{peaks}}| \rangle =780$ km s⁻¹. Note that unlike Figure 9, only the absolute value of the separation is considered here. A Kolmogorov–Smirnov test gives a probability $p\approx {10}^{-3}$ of both samples being drawn from the same distribution. As above, the finite resolution of our spectra censors the distribution of peaks with small separations, but the typical separations observed exceed our resolution limit by a large factor, suggesting that we are able to resolve the intrinsic distribution of peak separations for each sample. Furthermore, our use of the same instrument setup and line-analysis algorithms for both the LAE and LBG samples allows us to demonstrate an instrinsic difference between the two populations.

In contrast to the results of Yamada et al. (2012a), we find no significant correlation between the Lyα peak width and peak separation among multi-peaked profiles for our LAE sample, and only a moderate association among the LBGs (Pearson correlation $r\approx 0.3$, $p\approx 0.05$). However, these parameters are highly correlated (although with significant scatter) in the combined LBG+LAE sample, for which a Pearson correlation test yields $p\approx {10}^{-4}$ ($r\approx 0.3$).

Here we have defined the peak separation by the velocity difference between the peaks of the two most dominant components of the Lyα emission line, rather than the flux-weighted centroids of those components. Because the typical Lyα emission lines have redshifted primary peaks with asymmetric extended red tails (particularly for the LBGs; Figure 6), using flux centroids or symmetric Gaussian fits to define the peak separation would lead to (1) a larger median peak separation for both samples, and (2) a larger difference between the LAE and LBG distributions.

For comparison, the distribution of nebular line widths for both the LAEs and LBGs is given in Figure 14. As discussed in Section 3.2, the nebular line widths trace the velocity dispersion of the stars and H ii regions within the galaxy. The larger nebular line widths of LBGs with respect to LAEs are therefore likely to reflect the larger masses of continuum-bright galaxies with respect to faint LAEs. Further discussion of the mass-dependence of the interstellar and circumgalactic properties of these galaxies is reserved for Section 5.

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In contrast, the velocity distribution of emergent Lyα flux depends most sensitively on the velocity distribution and the optical depth of the scattering H i gas. The observed spectral morphologies therefore suggest that LBGs are associated with higher velocity and/or more optically thick outflows than their LAE analogs. It is thus evident that the observational characteristics that govern a galaxy's selection by the narrowband-excess and/or continuum-color techniques (namely, the observed Lyα and continuum emission) must be linked to properties of the outflowing gas—whether directly (by the coupling of Lyα photons to interstellar and circumgalactic gas) or indirectly (through the star-forming regions that produce Lyα, far-UV, and ionizing photons and presumably provide the energy/momentum for large-scale galactic outflows). In the remainder of this paper, we separate these effects of gas velocity and optical depth on the emitted spectrum by considering the absorption and emission profiles in composite galaxy spectra.

While the resonance of the Lyα transition makes it a sensitive tracer of gas in and around high-redshift galaxies, this strong coupling can obscure the details of the physical processes driving Lyα absorption and emission. In particular, we noted in Section 3 that Lyα transmission is sensitive to a variety of factors, including the optical depth, covering fraction, dust content, and kinematics of the gas distribution. Because they produce degenerate effects on the Lyα profile, Lyα emission alone is insufficient to fully characterize the physical conditions among LAEs or high-redshift galaxies generally.

The measurement of absorption lines in the rest-UV continuum spectra of galaxies is thus a crucial tool for disentangling these effects. Kunth et al. (1998) analyzed the spectra of nearby Lyα-emitting galaxies, finding blueshifted metal absorption features from enriched, outflowing gas. This study noted the correspondence of the Lyα emission and metal absorption in tracing the velocity structure and porosity of the interstellar gas. At higher redshifts, the analysis of the continuum spectra of typical star-forming galaxies began with spectra of the gravitationally lensed $z\sim 2.7$ galaxy MS 1512-cB58 (Pettini et al. 2000, 2002) and was extended to non-lensed galaxies through stacking the spectra of many (∼1000) $z\sim 3$ LBGs by Shapley et al. (2003). These studies utilized the high S/N of the lensed or stacked spectra to extract metal abundances, ion-specific covering fractions, outflow velocities, and systemic redshifts for the galaxies while placing these properties in the context of their SFRs, masses, and Lyα emission properties. Steidel et al. (2010) presented both interstellar absorption line features and Lyα emission in the context of a unified kinematic model for gas outflows in LBGs (Section 5 of that paper). For faint LAEs such as those in our sample, constraints on the metal content and outflow velocities are especially interesting because they reveal the extent to which past and ongoing star formation are already having an effect on the chemistry and kinematics of these particularly young, low-mass galaxies.

LAEs are by selection generally faint in the continuum, so absorption measurements of comparable fidelity to those of Shapley et al. (2003) present a significant challege, particularly for objects as faint as those considered here. Hashimoto et al. (2013) studied the absorption profiles in a stack of four LAEs with systemic redshift measurements to measure outflow velocities, and Shibuya et al. (2014) conducted a similar analysis for four individual bright LAEs, finding typical outflow velocities ${v}_{\mathrm{abs}\;}\sim$ 100–200 km s⁻¹. As noted in Section 1, however, the objects in these studies have $B$-band magnitudes $\langle {m}_{{\rm{B}}}\rangle \sim 24$ ($L\sim {L}_{*}$), meaning that they easily fall within typical selection criteria for continuum-selected star-forming galaxies. While useful for studying the correlation between outflow velocity ${v}_{\mathrm{abs}}$ and ${W}_{\mathrm{Ly}\alpha }$, these samples are clearly far removed from the faint LAEs considered in this paper, with median continuum magnitude $\langle {m}_{{\rm{B}}}\rangle =26.8$ ($L\sim 0.1{L}_{*}$, ∼10× fainter than these previous samples).

For such faint objects, large samples are needed to obtain even a low-fidelity measurement of metal absorption. To make such a measurement, we stack the rest-UV spectra of all 318 spectroscopic KBSS-Lyα LAEs using a rest frame defined by ${z}_{\mathrm{sys},\mathrm{Ly}\alpha }={z}_{\mathrm{Ly}\alpha ,\mathrm{peak}}-200$ km s⁻¹ based on the redshift calibration of Section 3.2. As many of our objects have multiple LRIS spectra of their rest-UV continuum, we include all spectra for each object such that each spectrum receives equal weighting, effectively weighting each object by total exposure time.¹² Furthermore, two spectra with individually significant continua (possibly AGN) were removed from the sample in order to ensure that they did not dominate the stack; all the remaining spectra have S/N $\ll$ 1 per pixel in the continuum individually. Finally, the portion of each spectrum corresponding to $\lambda \approx 5577\pm 15\mathring{\rm A}$ in the observed frame was omitted from the stack in order to remove contamination from a bright sky line. In total, 422 LAE spectra were stacked, producing a final spectrum with an effective exposure time of ∼675 hr (all from the Keck I 10 m telescope).

An error spectrum was then generated for the stack via a bootstrapping procedure. 1000 iterations were performed in which 422 spectra were drawn (with replacement) from our sample and stacked to make a set of 1000 randomized spectral stacks. The standard deviation of values at each pixel was then used to define the error spectrum of the true stacked data.¹³ From this error spectrum, we estimate that the stack has a median S/N ∼ 10 per pixel in the range 1230 Å $\lesssim \ {\lambda }_{\mathrm{rest}}\ \lesssim$ 1420 Å, the range of interest for the absorption lines discussed below.¹⁴

Measurements were made of the absorption of six metal lines, corresponding to four spectral regions (Figure 15, Table 4). For each spectral region, the continuum level was independently estimated using the local median value, but the continuum estimates among all four regions are consistent to $\lesssim 2$% in $\lambda {f}_{\lambda }$ units. The measured continuum was also checked for consistency with the broadband photometry. At the median wavelength of the absorption lines (${\lambda }_{\mathrm{obs}}\sim 5000$ Å), the stacked continuum flux density is $7.5\times {10}^{-8}$ Jy (${m}_{5000}=26.72$), comparable to the mean Lyα-subtracted broadband $B/G$ flux ($7.9\times {10}^{-8}$ Jy; $\langle {m}_{\mathrm{BB}}\rangle =26.66$) measured photometrically among the 318 objects in the spectral stack. Absorption measurements were then made for the low-ionization lines Si ii λ1260, O i λ1302, Si ii λ1304, and C ii λ1334, as well as the higher-ionization doublet Si iv $\lambda \lambda$ 1393,1402. The equivalent width of absorption is estimated in each case by numerically integrating the set of contiguous pixels with ${f}_{\mathrm{norm}}\lt 1$ nearest the rest-frame metal-line wavelength in the normalized stack. The O i λ1302 and Si ii λ1304 absorption lines are partially blended, so the division between them was determined by visual inspection of the stacked spectrum. This division was cross-checked in bootstrapped composite spectra resampled at a range of wavelength scales. Uncertainties in the equivalent widths were computed by performing the same measurement for each line in each of the 1000 bootstrap spectra; the quoted error refers to the standard deviation of these bootstrap measurements. An absorption-weighted velocity was then measured for each line via numerical integration of the line profile: ${v}_{\mathrm{abs}}={\displaystyle \int }_{{\rm{\Delta }}v}[1-{f}_{\mathrm{norm}}(v)]{vdv}/{\rm{\Delta }}v$. While the equivalent widths in absorption of the two lines in the Si iv doublet were measured separately, they were constrained to have the same total absorption-weighted velocity.

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Table 4.  LAE Continuum Absorption Features

Ion	${\lambda }_{\mathrm{lab}}$ a	${f}_{\mathrm{osc}}$ b	${W}_{\mathrm{ion}}$ c	Akid
	(Å)		(Å)	(108s−1)
Absorption Features
Si ii e	1190.416	0.575	0.53 ± 0.15	⋯
Si ii e	1193.290	0.277	0.24 ± 0.11	⋯
Si ii	1260.422	1.22	0.53 ± 0.10	⋯
O i	1302.169	0.0520	0.43 ± 0.10f	⋯
Si ii	1304.370	0.0928	0.17 ± 0.08f	⋯
C ii	1334.532	0.129	0.32 ± 0.11	⋯
Si iv	1393.760	0.513	0.30 ± 0.12	⋯
Si iv	1402.773	0.255	0.21 ± 0.08	⋯
Emission Features
Si ii*	1264.738	⋯	⋯	30.4
Si ii*	1265.002	⋯	⋯	4.73
O i*	1304.858	⋯	⋯	2.03
O i*	1306.029	⋯	⋯	0.676
Si ii*	1309.276	⋯	⋯	6.23
C ii*	1335.663	⋯	⋯	0.476
C ii*	1335.708	⋯	⋯	2.88

Notes.

^aVacuum wavelength of transition. ^bOscillator strength from the NIST Atomic Spectra Database (www.nist.gov/pml/data/asd.cfm). ^cEquivalent width of absorption in stacked LAE spectrum (Figure 15). ^dEinstein A-coefficients from the NIST Atomic Spectra Database. ^eThe Si ii λλ1190,1193 doublet is in the continuum blueward of Lyα, which suffers from lower S/N and a high density of absorption and emission lines. As such, these features are only used here to constrain the saturation of Si ii λ1260. ^fThe O i λ1302 and Si ii λ1304 absorption lines are partially blended, so the division between them is somewhat uncertain.

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All the measured absorption lines have mean velocities $-100\lesssim \langle {v}_{\mathrm{abs}}\rangle \lesssim -200$ km s⁻¹ with absorption extending to ${v}_{\mathrm{abs}}\sim -500$ km s⁻¹ (where negative velocities indicate blueshifted absorption), in good agreement with the brighter LAE samples of Hashimoto et al. (2013) and Shibuya et al. (2014). We therefore find clear evidence for blueshifted metal absorption signatures in these $L\sim 0.1{L}^{*}$ LAEs, a strong indicator of the presence of metal-enriched outflowing gas.

Because the systemic redshifts are not precisely known for the LAEs in our stack, there may be some additional uncertainty in our measured velocities compared to those measured in samples with complete catalogs of systemic redshifts. However, our stacked spectra also show several fine-structure and nebular emission features (dashed vertical lines in Figure 15) that are more likely to trace the systemic galaxy redshifts; the correspondence of these peaks to the rest-frame wavelengths of these features further suggests that our corrected Lyα line measurements are a good proxy for the redshifts in these LAEs. Notably, we have not corrected the line strengths or velocities for emission from nearby fine-structure transitions; the effects of this contamination likely causes an underestimate of intrinsic absorption and overestimate of the velocity of Si ii λ1304 and C ii λ1334.

Galaxy outflows may also be characterized by the covering fraction of the UV continuum by absorbing materials and its optical depth. While these properties are typically degenerate for individual transitions (except at much higher S/N and resolution), they may be constrained independently when multiple transitions of the same species are present. In particular, the expected ratio of the equivalent widths of Si ii λ1304 and Si ii λ1260 is ${W}_{1260}/{W}_{1304}=12.3$ when both transitions are optically thin. The measured ratio of these lines in the LAE composite spectrum is ${W}_{1260}/{W}_{1304}=3.6$, consistent with a saturated Si ii λ1260 transition, with the caveat that the measured Si ii λ1304 absorption has small S/N and is partially blended with the O i λ1302 line. To clarify this measurement, we consider the absorption due to the Si ii $\lambda \lambda$ 1190,1193 doublet in the rest-EUV (${\lambda }_{\mathrm{rest}}\lesssim 1200$ Å) spectrum. The high density of absorption and emission lines and lower continuum level of the spectrum shortward of Lyα (including foreground Lyα absorption) result in larger uncertainties in these line strengths, but both lines of the doublet are detected with high significance.

The measured absorption equivalent widths (W) for each of the four Si ii transitions are given in Table 4, along with the corresponding vacuum wavelengths (λ) and oscillator strengths (${f}_{\mathrm{osc}}$). In the optically thin regime, these quantities are related to the column density of absorbing material by ${N}_{\mathrm{ion}}\propto {W}_{i}/{\lambda }_{i}^{2}{f}_{\mathrm{osc},i}$ for each transition of index i. Because the physical column density of a single ionic species must be single-valued, the quantity $W/{\lambda }^{2}{f}_{\mathrm{osc}}$ will likewise be constant for all ground-state transitions of the same ion unless one or more transitions have saturated. In this latter case, $W/{\lambda }^{2}{f}_{\mathrm{osc}}$ will decrease with increasing ${f}_{\mathrm{osc}}$.

The quantity $W/{\lambda }^{2}{f}_{\mathrm{osc}}$ is compared for the four Si ii transitions in Figure 16. The Si ii λ1190, λ1193, and λ1304 transitions are consistent with a single value of $W/{\lambda }^{2}{f}_{\mathrm{osc}}$, but the Si ii λ1260 absorption falls significantly below the weighted average of the other three lines, indicating saturation. While the other three transitions appear to be optically thin, both Si ii λ1193 and Si ii λ1304 have nearby excited fine-structure emission transitions that may bias our measurements toward lower equivalent widths, as discussed above. If the Si ii λ1304 line were saturated, however, the bottom of its absorption trough would reach a similar depth as the saturated Si ii λ1260 transition with respect to the local continuum (as is seen in some LBG samples; see Section 4.3), which is clearly not the case in the LAE composite spectrum (Figure 15). This suggests that any filling-in of the absorption by excited fine-structure emission has a small effect on the total measured absorption. The analysis of the composite spectrum thus strongly suggests that ${\tau }_{1260}\gt 1$, ${\tau }_{1304}\ll 1$, and ${\tau }_{1190}\sim {\tau }_{1193}\lesssim 1$ based on the consistency of the curve-of-growth analysis in Figure 16 (where ${\tau }_{\lambda }$ is the central optical depth of the Si ii transition at wavelength λ).

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Given the saturation of Si ii λ1260, the maximum depth of the line profile with respect to the continuum indicates a covering fraction of Si ii-enriched outflowing gas ${f}_{{\rm{c}}}\approx 0.3$ among the LAEs. While multiple unambiguous absorption features are not available for other low-ionization species in the composite, the consistency of the absorption profile depths and widths for the O i λ1302 and C ii λ1334 with the saturated Si ii λ1260 line suggests that those species are co-spatial with Si ii and have a similar covering fraction. We therefore take the covering fraction of low-ionization gas outflows to be ${f}_{{\rm{c}}}\approx 0.3$ for the LAE sample, noting the possible existence of narrow absorption components unresolved by our $R\sim 1300$ spectra.

The two lines of the Si iv doublet have a measured ratio ${W}_{1393}/{W}_{1402}=1.4$, suggesting that the doublet is also saturated (${W}_{1393}/{W}_{1402}=2$ on the linear part of the curve of growth). However, the weaker line has S/N ∼ 2, and ∼25% of the bootstrap spectra have ${W}_{1393}/{W}_{1402}\gtrsim 2$, so the transition may in fact be optically thin. The higher ionization potential of Si iv (33.5 eV) requires radiation from hot stars and/or collisional ionization in $T\gtrsim {10}^{4}\;{\rm{K}}$ gas, and therefore traces more strongly ionized gas in or around the galaxy. The depth of the two absorption lines thus suggests the presence of an ionized medium with an average covering fraction ${f}_{{\rm{c}}}\sim 20$% (or greater if the lines are optically thin). It is unclear whether this gas is co-spatial with the medium giving rise to the lower-ionization lines described previously; this relationship is probed further by comparing the velocity profiles of their absorption below.

It is important to note that all of the above constraints on the covering fraction of metal-enriched gas rely on the assumption that the metal-line photons scattered out of the galaxy spectrum are emitted away from our line of sight to the galaxy. In the limit that the scattering medium is entirely co-spatial with the observed light distribution from the galaxy (and that the scattering is isotropic and photon-conserving), we would expect that the net emission and absorption from scattering would be zero. In reality, many photons will be scattered at large radii with respect to the light profile of the galaxy, particularly for transitions where excited fine-structure states provide an alternative escape pathway with low optical depth. Given the spatial compactness of the LAEs, however, this "emission-filling" may reduce the observed absorption, particularly for those transitions without nearby excited fine-structure states such as Si iv λλ1393,1402. This effect may partially explain the lower measured value of f_c for the Si iv transitions, in addition to their unknown optical depth.

The velocity shift of Lyα emission shows a strong inverse trend with Lyα equivalent width in the collective populations of high-redshift LAEs and LBGs (Erb et al. 2014), but there are many mechanisms that could underly this relationship. If a change in outflow velocity is the driver, then we should expect the velocity profile of the metal absorption lines tracing the outflows to vary with ${W}_{\mathrm{Ly}\alpha }$ as well. Unfortunately, the S/N in stacked subsamples is too low to probe this effect in individual lines. However, we can boost the S/N by combining the line profiles for multiple lines that we expect to trace the same gas. In particular, we can stack the low-ionization lines (corresponding to more neutral H i gas) and the high-ionization lines (corresponding to more highly ionized H ii gas) and thereby extract enough signal to compare the variation of the gas velocity distribution with ${W}_{\mathrm{Ly}\alpha }$.

Spectra combined in this way are displayed in Figure 17 for three subsamples divided according to ${W}_{\mathrm{Ly}\alpha }$, with median ${W}_{\mathrm{Ly}\alpha }\approx 11$, 37, and 110 Å respectively. Because these stacks include features at multiple wavelengths, we subsampled them by a factor of two with respect to the original wavelength scale before stacking in order to maximize the velocity resolution of the stacks. Details of these subsamples are in Table 5.

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Table 5.  Lyα Spectroscopic Subsamples and Composite Lyα Emission Profiles

Subsample	$\langle {W}_{\mathrm{Ly}\alpha }\rangle$	$\langle {\mathcal{R}}\rangle$	${N}_{\mathrm{obj}}$	${N}_{\mathrm{spec}}$ a	${\sigma }_{\mathrm{red}}$ (km s−1)b	${\sigma }_{\mathrm{blue}}$ (km s−1)b	${\rm{\Delta }}v$ (km s−1)b
Lyα Redshiftsc
${W}_{\mathrm{Ly}\alpha }\geqslant 60$ Å	110Å	27.6	158	211	115 ± 5	191 ± 10	447 ± 7
$20\leqslant {W}_{\mathrm{Ly}\alpha }\lt 60$ Å	37Å	26.8	160	211	116 ± 5	276 ± 15	468 ± 7
${W}_{\mathrm{Ly}\alpha }\lt 20$ Åd	11Å	26.6	82	94	119 ± 7	353 ± 37	475 ± 10
KBSS LBGs	27Å	24.4	65	65	178 ± 10	226 ± 8	646 ± 20
Systemic Redshifts
MOSFIRE LAEs	44Å	26.9	32	57	131 ± 9	234 ± 14	490 ± 23
KBSS LBGs	27Å	24.4	65	65	215 ± 20	246 ± 11	568 ± 25

Notes.

^aBecause some objects were observed multiple times, and all available spectra were combined in each continuum stack, ${N}_{\mathrm{spec}}\gt {N}_{\mathrm{obj}}$. ^bThe parameters ${\sigma }_{\mathrm{red}}$, ${\sigma }_{\mathrm{blue}}$, and ${\rm{\Delta }}v$ are the velocity widths of the red peak, blue peak, and peak separation in the fit to the composite Lyα spectrum (Figures 17 and 18). The peak widths reflect the subtraction in quadrature of the LRIS instrumental resolution of ${\sigma }_{\mathrm{inst}}=100$ km s⁻¹. ^cComposite spectra constructed using Lyα redshifts, shifted by −200 km s^{−1. d}Objects observed on the basis of a narrowband excess and spectroscopically detected Lyα emission line, but which have ${W}_{\mathrm{Ly}\alpha }$ smaller than the adopted threshold of ${W}_{\mathrm{Ly}\alpha }\leqslant 20\;\mathring{\rm A}$.

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Several key features are apparent in the bottom panels of Figure 17. First, there is substantial absorption by low-ionization species in all three panels at the systemic redshift of the galaxy (v = 0), but there is little or no corresponding high-ionization absorption. At the negative edge of the absorption profiles (v ∼ −500 km s⁻¹), however, the high-ionization and low-ionization absorption are well aligned in each panel. This pattern may indicate that both ionized and neutral gas are present in the material most likely associated with an outflow, but that the interstellar medium is dominated by neutral H i and low-ionization metals at v = 0. As noted above, however, the Si iv transition is particularly sensitive to emission-filling, which will tend to systematically reduce the observed absorption at $v\approx 0$.

Second, if the absorption lines are assumed to be optically thick, there is a slight variation in covering fraction as a function of ${W}_{\mathrm{Ly}\alpha }$: ${f}_{{\rm{c}}}\sim 30$% for the ${W}_{\mathrm{Ly}\alpha }\sim 11$ Å sample, ${f}_{{\rm{c}}}\sim 20$% for the intermediate sample, and ${f}_{{\rm{c}}}\sim 25$% for the highest-${W}_{\mathrm{Ly}\alpha }$ sample. The decline in f_c from ${W}_{\mathrm{Ly}\alpha }\sim 11$ Å to ${W}_{\mathrm{Ly}\alpha }\sim 37$ Å is consistent with expectations for Lyα-emitting galaxies: Steidel et al. (2010) demonstrate that observed Lyα-emission is closely correlated with the covering fraction of the gas through which these photons escape. The increase in apparent f_c between the $\langle {W}_{\mathrm{Ly}\alpha }\rangle =37$ Å and $\langle {W}_{\mathrm{Ly}\alpha }\rangle =110$ Å samples may not be significant because the continuum emission is extremely faint in the latter stack; not only is the statistical error large, but small systematics in the spectroscopic background subtraction could be significant in the stack of these faint objects, possibly biasing the measured continuum level. However, the consistency between the photometric and spectroscopic continuum estimates suggests this effect should be quite small. In any case, it seems that the apparent depth of the interstellar absorption features correlates only weakly with ${W}_{\mathrm{Ly}\alpha }$ for the faintest, highest-${W}_{\mathrm{Ly}\alpha }$ bin of galaxies.

Third, there is some dependence in the maximum absorption velocity as a function of ${W}_{\mathrm{Ly}\alpha }$. While the absorption extends to ${v}_{\mathrm{abs}}$ ∼ −500 km s⁻¹ in all three panels, the ${W}_{\mathrm{Ly}\alpha }\sim 11$ Å stack shows absorption in Si iv extending to higher velocities at low optical depths. Conversely, the most-blueshifted edge of absorption in the ${W}_{\mathrm{Ly}\alpha }\sim 110$ Å stack extends no further than ${v}_{\mathrm{abs}}$ ∼ −400 km s⁻¹.¹⁵ It is important to note that the systematic velocities used here are derived from a constant correction to the Lyα redshift, and thus the evolution of the Lyα offset with ${W}_{\mathrm{Ly}\alpha }$ could theoretically mimic an evolution in absorption velocity with ${W}_{\mathrm{Ly}\alpha }$. However, despite previous measurements of the significantly smaller Lyα offsets among LAEs with respect to LBGs, we find that the peak of the Lyα profile has a consistent 200 km s⁻¹ redshift with respect to systemic at our observed resolution for both LBGs and LAEs (Section 3.2). Furthermore, no difference with ${W}_{\mathrm{Ly}\alpha }$ is observed in the most-redshifted edge of the low-ionization absorption (presumably corresponding to neutral interstellar gas at the systemic redshift) across the three panels of Figure 17; such a shift would be expected from a ${W}_{\mathrm{Ly}\alpha }$-dependent estimator of the systemic redshift. Lastly, the total velocity width of absorption decreases significantly with increasing ${W}_{\mathrm{Ly}\alpha }$ across the three panels, suggesting the presence of a real anti-correlation of Lyα equivalent width with outflow velocity among these faint LAEs.

Given that ${W}_{\mathrm{Ly}\alpha }$ is likely to be anti-correlated with SFR and stellar mass among these LAEs (as discussed in Section 3.1), we interpret the above trends as a positive correlation between SFR and outflow velocity. A similar analysis of the KBSS LBG sample (Figure 18, discussed further in Section 4.3) suggests a continuation of this trend to higher SFRs.

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The composite Lyα emission profiles for each subsample (top panels of Figure 17) show evidence for changes in outflow velocity with ${W}_{\mathrm{Ly}\alpha }$ as well. Each Lyα profile exhibits a narrow peak redward of the systemic redshift (by construction, as they are stacked on the basis of their peak Lyα redshifts) as well as an extended blue wing, which broadens with decreasing ${W}_{\mathrm{Ly}\alpha }$ (Figure 17). To quantify this effect, a two-component Gaussian fit was performed to each stacked Lyα profile with the following form:

$$\begin{eqnarray}{f}_{\lambda }(v) & = & {A}_{\mathrm{blue}}{e}^{-(v+{\rm{\Delta }}v/2)/2{\sigma }_{\mathrm{blue}}\;}\\ & & +{A}_{\mathrm{red}}{e}^{-(v-{\rm{\Delta }}v/2)/2{\sigma }_{\mathrm{red}}}+{f}_{0,\mathrm{cont}},\end{eqnarray} \tag{ 6 }$$

such that the fit profile consists of two Gaussian peaks of arbitrary height and width, but with equal and opposite shifts with respect to systemic ($\pm {\rm{\Delta }}v/2$). The model intentionally evokes an idealized outflow scenario in which the average LAE is surrounded by outflowing gas in both directions along the line of sight. In all three stacks, the red side of the Lyα profile diverges strongly from a Gaussian shape at large velocities, forming a broad red tail similar to that seen at v ≪ 0. In order to maintain the simplicity of the model, the spectrum at v > +500 km s⁻¹ was omitted from the fitting.

The resulting fits are displayed in Figure 17, with fit parameters given in Table 5. Both the width of the blue component and the separation of the blue and red peaks increases with decreasing ${W}_{\mathrm{Ly}\alpha }$. While the Lyα peak width and separation may be increased by raising the H i column density, such a scenario would not predict a corresponding increase in the velocity width of metal absorption transitions, which have significantly smaller optical depths than Lyα. The similarity of the extended, blueshifted Lyα emission to the metal absorption profile therefore indicates that emission from outflowing gas likely populates the wings of the Lyα emission profile. That is, we suggest that the extended Lyα emission observed at large redshifts and blueshifts with respect to systemic depends sensitively on the outflow velocity, rather than merely the optical depth of the scattering medium. Models for this behavior, including the dependence of Lyα transmissivity on both the amplitude and velocity gradient of outflowing gas, are discussed in detail by Steidel et al. (2010, 2011).

Radiative transfer simulations of Lyα transmission suggest that these processes can generate double-peaked emission profiles with asymmetric offsets with respect to the systemic redshift. In particular, Verhamme et al. (2006) and others find that a spherical shell of gas expanding with velocity ${V}_{\mathrm{exp}}$ can in many cases produce a blue peak at $v=-{V}_{\mathrm{exp}}$ and a red peak at $v=2{V}_{\mathrm{exp}}$. The stacked Lyα profiles in Figure 17 (or Figure 18, discussed below) are insensitive to the peak of the blue component and cannot discriminate between the two models (that is, whether the offset of the blue peak is equal to that of the red peak or half that of the red peak). However, the same qualitative relations hold for either model: the separation of the two peaks and the breadth of the extended blue and red components increases with increasing continuum luminosity.

While the trend of the inferred outflow properties with ${W}_{\mathrm{Ly}\alpha }$ is weak among the LAEs in this sample, we can probe a much larger range in galaxy properties by extending the sample to include continuum-bright galaxies. In particular, the composite Lyα profile of the KBSS LBGs (Figure 18) displays a continuation of several trends identified among the LAE subsamples in Figure 17. The KBSS LBGs all have systemic redshift measurements, so we can compare the results of stacking them by either their nebular redshifts (Figure 18, left panel) or their Lyα-derived redshifts (right panel, as in Figure 17). While the detailed profile depends on which redshift is employed, the LBG composites have broader and more widely separated peaks than any of the LAE subsamples, and the velocity extent of the broad tails of the Lyα emission again corresponds closely to the velocity extent of blueshifted absorption from the higher- and lower-ionization species. Note that the absorption profiles (bottom panels of Figure 18) are insensitive to which redshift indicator is used: the Si ii λ1260, C ii λ1334, and Si iv doublet absorption centroids each change by less than ∼25 km s⁻¹ when stacked according to the nebular or calibrated Lyα redshifts. This consistency suggests that our measurements of interstellar absorption velocities in the LAE composite are unaffected by the scarcity of systemic redshifts among the LAE sample.

In Figures 19–21, we compare the stacked spectrum of all 318 LAEs in this sample with two stacks of LBGs: the KBSS LBG (Steidel et al. 2014) sample, and another sample from a survey for LyC emission in $z\sim 3$ galaxies (C. Steidel et al. 2015, in preparation). A comparison of these two samples to the KBSS-Lyα LAE sample is given in Table 6.

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Table 6.  Comparison of LAE and LBG Continuum and Absorption Properties

Sample	$\langle z\rangle$	${m}_{1450}$ a	${M}_{1450}$ b	${W}_{\mathrm{Ly}\alpha }$ c	${N}_{\mathrm{obj}}$	${W}_{\mathrm{Si}\;{\rm{II}}}$ d	${v}_{\mathrm{Si}\;{\rm{II}}}$ e	${W}_{{\rm{C}}\;{\rm{II}}}$ d	${v}_{{\rm{C}}\;{\rm{II}}}$ e	${W}_{\mathrm{Si}\;{\rm{IV}}}$ d	${v}_{\mathrm{Si}\;{\rm{IV}}}$ e	fcf
		(mag)	(mag)	(Å)		(Å)	(km s−1)	(Å)	(km s−1)	(Å)	(km s−1)
KBSS-Lyα	2.70	27.0	−18.3	42.7	318	0.53	−98	0.45	−185	0.51	−190	0.3
KBSS LBGs	2.36	24.4	−20.7	27.2	65	1.67	−224	1.35	−201	1.98	−276	0.6
LyC LBGs	3.07	24.6	−21.0	21.5	74	1.50	−172	1.44	−176	2.41	−288	0.6

Notes.

^a ${m}_{1450}$ is the observed AB magnitude corresponding to the rest-frame $\lambda \sim 1450$ Å UV continuum. At $z\sim 2.7$ (KBSS-Lyα and KBSS LBGs), this correponds to the G band, whereas the ${\mathcal{R}}$ magnitude is used for the LyC LBGs at $z\sim 3$. For consistency with the other samples, the LAE ${m}_{1450}$ value is not Lyα-subtracted, though the Lyα emission dominates the broadband flux in many cases. ^b ${M}_{1450}$ is the absolute magnitude corresponding to ${m}_{1450}$ at the typical redshift of the sample $\langle z\rangle$. ^cBecause the LBG samples have no narrowband Lyα images, all three values of ${W}_{\mathrm{Ly}\alpha }$ here were measured spectroscopically for consistency. Note that the spectroscopic LAE sample has a mean photometric equivalent width ${W}_{\mathrm{Ly}\alpha }=85.6$ Å. ^d ${W}_{\mathrm{Si}\;{\rm{II}}}$, ${W}_{{\rm{C}}\;{\rm{II}}}$, and ${W}_{\mathrm{Si}\;{\rm{IV}}}$ are the equivalent widths in absorption of Si ii λ1260, C ii λ1334, and Si iv λ1393+λ1402 (combined), respectively. See Table 4 and Figure 15. ^e ${v}_{\mathrm{Si}\;{\rm{II}}}$, ${v}_{{\rm{C}}\;{\rm{II}}}$, and ${v}_{\mathrm{Si}\;{\rm{IV}}}$ are the absorption-weighted velocity of Si ii λ1260, C ii λ1334, and Si iv λ1393+λ1402. ^ff_c is the covering fraction of low-ionization gas implied by the depth of the saturated Si ii λ1260 absorption trough, which is consistent with the covering fraction implied by the depths of the O i λ1304 and C ii λ1334 transitions in each composite spectrum.

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As discussed in Sections 2.2 and 3.2, the KBSS LBG sample consists of 65 galaxies that each exhibit Lyα emission in their UV spectra and have accurate systemic redshifts measured from rest-frame optical emission lines. These rest-UV spectra were observed using Keck/LRIS-B with the 600-line grism (the same used for the KBSS-Lyα LAEs), providing a spectral resolution $R\sim 1300$, or ${\sigma }_{\mathrm{inst}}\approx 100$ km s⁻¹. There is significantly stronger metal absorption in each of the spectral lines shown in Figures 15 and 18, and the absorption profiles are both broader (extending to v ≈ −1000 km s⁻¹) and deeper (≲0.5× the continuum value) than the corresponding features in the LAE stack. The excited fine-structure and nebular emission lines (Figure 20), however, are well-matched to the corresponding LAE features, further validating the redshift offset employed for the KBSS-Lyα stack.

The LyC LBG sample consists of 74 galaxies, most of which do not have measured nebular redshifts; the redshifts for this sample were estimated via a combination of their Lyα emission and interstellar absorption redshifts with a calibration based on the results of Steidel et al. (2010) and Rakic et al. (2011). Furthermore, the composite spectrum was checked after stacking using stellar photospheric features. About 15% of these galaxies have redshifts derived solely from the Lyα line and assume a 300 km s⁻¹ offset (with respect to the Lyα centroid) based on stacks of the subset of objects with nebular emission redshifts. Like the LAE and KBSS LBG comparison samples, only objects with spectroscopically detected Lyα emission were included in the sample. The correspondence of the absorption and emission signatures of the stack to those of the KBSS LBG stack again demonstrates the efficacy of the calibration based on UV features. Being at higher redshifts than the other samples, these spectra were observed using a combination of the LRIS-R 600-line grating (covering the spectrum ${\lambda }_{\mathrm{rest}}\gtrsim 1200$ Å) and the LRIS-B 400-line grism (for ${\lambda }_{\mathrm{rest}}\lesssim 1200$ Å). This lower resolution was employed to maximize the S/N of the spectra shortward of Lyα (and the Lyman limit), where the observed spectrum becomes particularly faint. These spectra also have significantly larger integration times compared to the KBSS LBGs and KBSS-Lyα LAEs (8–10 versus 1.5–2 hr). Additionally, the higher redshifts of this sample ($z\sim 3$) with repect to the KBSS LBG sample ($z\sim 2.3$) cause the $1000\;\mathring{\rm A} \lt {\lambda }_{\mathrm{rest}}\lt 1200\;\mathring{\rm A}$ continuum to lie at observed wavelengths with significantly higher LRIS-B throughput, further boosting the S/N of the LyC LBG composite spectrum at these wavelengths with respect to that of the KBSS LBGs. This stack is thus particularly useful for comparing the absorption due to Lyβ and other EUV transitions among the LBG and LAE samples (Figure 21).

The absorption profiles of the two LBG composite spectra are quite similar (Figure 20). The velocity extent of the absorption is almost identical in both samples (${v}_{\mathrm{max}}\;\approx$−1000 km s⁻¹), though the LyC LBG stack shows slightly deeper absorption across all the lines. This difference may signify a difference in the galaxy properties: at $z\sim 3$, the LyC LBGs have a brighter average rest-UV luminosity than those at $z\sim 2.3$ (which have similar apparent magnitudes). The total equivalent width in interstellar absorption (Table 6), which is insensitive to the spectral resolution, is similar for the LyC and KBSS LBG stacks.

While the blending of Si ii λ1304 with O i λ1302 inhibits a direct measurement of the Si ii optical depth, Shapley et al. (2003) demonstrated that the Si ii λ1260 transition is typically saturated in similar samples of bright LBGs, and the absorption of the Si ii λ1190, λ1193, and λ1526 transitions in the LBG stacks are consistent with this interpretation. Furthermore, the consistency of the absorption profile depths among the low-ionization species in the LBG stacks suggests a gas covering fraction ${f}_{{\rm{c}}}\sim 0.6$ for enriched, neutral/low-ionization material for the two LBG samples. The observed line ratio of the Si iv doublet is ${W}_{1393}/{W}_{1402}\sim 2$ for both LBG stacks (as in Shapley et al. 2003), suggesting optically thin absorption and ${f}_{{\rm{c}}}\gtrsim 0.4$ for the ionized H ii gas.

The difference in absorption line strength between the LBG and LAE samples can likewise be seen in the Lyβ transition (Figure 21). While the LBG composite is almost completely absorbed at the Lyβ line, the LAE spectrum has significantly higher transmission ($\gtrsim 50$%). The continuum ratio ${f}_{1325}/{f}_{1125}$ (displayed as horizontal lines on the left side of Figure 21) also varies significantly between the LBG and LAE samples: the LBG composites have a flux ratio ${f}_{1325}/{f}_{1125}\approx 1.6$, while the LAE composite has ${f}_{1325}/{f}_{1125}\approx 1.3$. The flux ratio for the $z\sim 3$ LyC LBG composite is uncertain because the spectra at ${\lambda }_{\mathrm{rest}}\gtrsim 1200$ Å and ${\lambda }_{\mathrm{rest}}\lesssim 1200$ Å fall on different detectors (LRIS-R and LRIS-B) within the spectrograph, so it is not entirely clear how much of the observed variation in continuum absorption is due to physical differences in the LAE and LBG galaxy populations, rather than the changing transmissivity of the IGM with redshift (e.g., Madau 1995). Both effects are likely to be present, as the UV continuum level blueward of Lyα is particularly sensitive to the dust content and metallicity of the ISM (the latter due to metal-line blanketing) and the age of the stellar population, all of which are observed to be lower among LAEs than LBGs.

Through comparison of the LAE and LBG stacks, it seems clear that the qualitative links between Lyα emission and and interstellar absorption discussed in Shapley et al. (2003) persist down to far fainter continuum luminosities than those probed by samples of LBGs. The outflow velocity (represented by either the absorption-weighted mean or the highest-velocity edge of absorption) decreases with increasing ${W}_{\mathrm{Ly}\alpha }$ across the LBG and LAE subsamples, and the covering fraction of gas drops steadily with increasing ${W}_{\mathrm{Ly}\alpha }$ to at least the intermediate subsample of LAEs (${W}_{\mathrm{Ly}\alpha }\sim 37$ Å). The offset of the Lyα emission centroid likewise decreases from the LBG samples (+300 km s⁻¹) to the LAE stacks (+200 km s⁻¹). While further observations and modeling are required to determine the physics of star formation driven outflows, we suggest that our results provide an important link between the physical properties of these galaxies and those of the gas in and around them. We provide some initial interpretation of these results in the context of previous work below.