THE RELATIONSHIP BETWEEN STELLAR POPULATIONS AND Lyα EMISSION IN LYMAN BREAK GALAXIES^*

The data presented here are drawn from the LBG surveys of Steidel and collaborators, with approximately half of the observations described in Steidel et al. (2003, 2004) and half from subsequent programs by the same authors. These surveys employed photometric preselection in the $U_nG{\cal R}$ passbands in a variety of fields (Reddy et al. 2008) to target galaxies in the redshift interval z∼ 2–3. Follow-up optical spectroscopy of a subset of these galaxies, paired with supplemental near and mid-infrared photometry, has yielded an extensive data set upon which multiple studies have been based (e.g., Shapley et al. 2003, 2005; Adelberger et al. 2005a; Erb et al. 2006b; Reddy et al. 2008).

Here, we introduce a spectroscopic and photometric sample of z∼ 3 LBGs. These data were photometrically preselected with the following standard LBG $U_nG{\cal R}$ flux and color cuts:

$$\begin{equation} {\cal R}\le 25.5,\quad G-{\cal R}\le 1.2,\quad U_n-G\ge G-{\cal R}+1 \end{equation} \tag{ 1 }$$

where the U_n, G, and ${\cal R}$ passbands sample λ_rest∼ 900, 1200, and 1700 Å at z∼ 3, respectively. Object detection, color cuts, and photometry are discussed in Steidel et al. (2003). Multi-object optical spectroscopy was obtained using the Low Resolution Imaging Spectrometer (LRIS; Oke et al. 1995) on the Keck i 10 m telescope. The majority of the data (93%) were taken with the blue arm of LRIS (LRIS-B; McCarthy et al. 1998; Steidel et al. 2004), and the remainder of the data were obtained with LRIS prior to its blue arm upgrade in 2000 September. The LRIS-B data were collected using 300, 400, and 600 line mm⁻¹ grisms, which resulted in spectral resolutions of λ/Δλ = 1000, 1200, and 2000, respectively. The 400 (600) line mm⁻¹ grism was used for 55% (39%) of the observations, and the remaining ∼6% of the LRIS-B spectra were obtained with the 300 line mm⁻¹ grism. LRIS-B rest-frame wavelength coverage extended from ∼900 to 1500 Å and a typical integration time was 3 × 1800 s. The data were reduced (flat-fielded, cosmic ray rejected, background subtracted, extracted, wavelength and flux calibrated, and transformed to the vacuum wavelength frame) using IRAF scripts. Details of the data collection and reduction of both the preselection and spectroscopic samples are presented in Steidel et al. (2003).

Approximately 3% of the spectroscopically confirmed z∼ 3 LBGs were classified as either active galactic nuclei (AGNs) or quasi-stellar objects (QSOs) on the basis of broad lines and high-ionization emission features, respectively (Reddy et al. 2008). These objects were excluded from the spectroscopic sample, as were galaxies at redshifts z⩽ 2.7. The final sample, spanning 13 photometric preselection fields totaling 1700 arcmin², includes 321 objects with an average redshift of 〈z〉 = 2.99 ± 0.19 (Table 1, Figure 1). We note that this sample is distinct from previous studies of z∼ 3 LBGs (e.g., Shapley et al. 2001, 2003) in that the majority of these objects have corresponding near- and mid-infrared photometry.

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Near-infrared photometry in the J (λ_c = 1.25 μm) and K_s (λ_c = 2.15 μm) bands was obtained for a subset of the sample (8/13 fields) using the Wide Field Infrared Camera (Wilson et al. 2003) on the Palomar 5 m telescope. 102/321 objects (32%) were detected in K_s imaging and an additional 69 objects fell on the K_s images and were not detected. We assigned K_s upper limits corresponding to 3σ image depths (K_s∼ 22.2 (Vega); Erb et al. 2006b) to these 69 galaxies. J-band photometry was also obtained for 57/102 objects (56%) detected in the K_s sample. Details of the data collection and reduction of the near-infrared sample are presented in Shapley et al. (2005) and Erb et al. (2006b).

Mid-infrared imaging was obtained for 5/13 fields with IRAC on Spitzer. Observations at 3.6, 4.5, 5.8, and 8.0 μm were obtained for the GOODS-N (Dickinson et al. 2003; Giavalisco et al. 2004; Reddy et al. 2006a), Q1700 (Shapley et al. 2005), and Q1549, Q1623, and Q2343 (D. K. Erb et al. 2010, in preparation) fields, where 3σ IRAC detection limits ranged from 25.1 to 24.8 (AB). The mid-infrared data were reduced according to procedures described in Shapley et al. (2005). 112/321 objects (35%) have detections in at least one IRAC passband, and 34/321 objects (11%) have both K_s and IRAC detections.

In order to prepare the spectra for subsequent measurement and analysis, we transformed each spectrum into the stellar systemic frame where the galaxy's center of mass was at rest. To do so, we employed the procedure of Adelberger et al. (2003) to infer the galaxy's systemic redshift from measurements of its redshifts of both Lyα in emission and interstellar lines in absorption. For the spectra that clearly exhibited a double-peaked Lyα emission feature (12/321 objects), we adopted the convention of setting the Lyα emission redshift equal to the average redshift of the two emission peaks. This technique of inferring a zero-velocity center-of-mass redshift, as opposed to measuring it directly, was necessary due to the fact that stellar lines arising from OB stars (assumed to be at rest with respect to the galaxy) are too weak to measure in individual spectra at z∼ 3. Furthermore, a systemic redshift could not be measured from prominent LBG spectral signposts (e.g., Lyα or interstellar absorption lines) as these features trace outflowing gas which is offset from the galaxy's center-of-mass frame by several hundred km s⁻¹ (Shapley et al. 2003).

H i Lyα, typically the strongest feature in LBG spectra, is characterized by its equivalent width, W_Lyα, where we use a negative equivalent width to correspond to the feature in absorption. We present here a systematic method for estimating W_Lyα, taking into account the various Lyα spectroscopic morphologies that were observed in the sample. In particular, this method employs a more robust technique than used previously to determine the wavelength extent over which the Lyα feature should be integrated to extract a line flux.

We first binned the 321 systemic-frame spectra into one of four categories based on the morphology of Lyα: "emission," "absorption," "combination," and "noise." The spectra in the "emission" bin were clearly dominated by a Lyα emission feature, and a small subset of this sample exhibited two peaks in emission. The spectra in the "absorption" bin were dominated by a trough around Lyα, typically extending for tens of angstroms blueward of line center. The spectra deemed to be "combination" contained a Lyα emission feature superimposed on a larger Lyα absorption trough and the "noise" spectra were generally featureless around Lyα, save for a possible absorption signature whose secure identification was hindered by low signal-to-noise. Four example spectra, characterized as falling into each of these four bins, are shown in Figure 2.

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Each spectrum, regardless of its category classification, was fit with two average continuum levels, one blueward (1120–1180 Å; c_blue) and one redward (1225–1255 Å; c_red) of Lyα; these wavelength ranges were chosen to avoid the prominent Si iii and Si ii absorption features at 1206 and 1260 Å, respectively. We worked with both the spectra and the adopted continua in f_λ units (erg s⁻¹ cm⁻² Å⁻¹). Below, we briefly describe the procedure for calculating W_Lyα for each of the four morphological classification bins.

Emission: 189/321 objects (59%). The wavelength of the maximum flux value between 1213 and 1221 Å was calculated, as well as the wavelengths on either side of the maximum where the flux level intersected c_red and c_blue, respectively. These latter two wavelengths were adopted as the extremes of the emission feature. In a limited number of cases (12/188 objects), double-peaked spectra were individually examined to ensure that this methodology counted both peaks as contained within the Lyα feature. The IRAF routine SPLOT was next used to calculate the enclosed flux between the two wavelength bounds. The enclosed flux was then divided by the level of c_red to yield a measurement of W_Lyα in Å. The level of c_blue was not used in the calculation of W_Lyα due to its substantial diminution by the intergalactic medium (IGM).

Absorption: 50/321 objects (16%). The boundaries of the Lyα absorption feature were calculated in the same manner as those of the "emission" spectra described above, with the exception that the flux value between 1213 and 1221 Å was isolated as a minimum and the "absorption" spectra were initially smoothed with a boxcar function of width 6 pixels (∼2.5 Å) in order to minimize the possibility of noise spikes affecting the derived wavelength boundaries of the Lyα feature. These smoothed spectra were only used to define the extent of the Lyα line; the original unsmoothed spectra were used for the flux integration in IRAF and the enclosed flux was divided by c_red to yield W_Lyα.

Combination: 31/321 objects (10%). Objects in the "combination" bin were characterized by a Lyα emission feature superposed on a larger absorption trough. The boundaries of the Lyα feature were computed by beginning at the base of the Lyα emission peak and moving toward larger fluxes until the smoothed spectrum (see above) intersected c_red and c_blue, respectively (the same technique used for the "absorption" spectra). Flux integration and division by c_red were furthermore identical to those objects discussed above.

Noise: 51/321 objects (16%). For these spectra dominated by noise, we adopted set values for the endpoints of the Lyα feature based on the average boundary values of the absorption and combination spectra—1199.9 and 1228.8 Å. (The boundaries of the "emission" spectra were not included in this calculation, as the spectral morphologies of the "emission" galaxies differed greatly from those of the "noise" galaxies). As above, the integrated flux was divided by the level of c_red to yield W_Lyα.

Rest-frame equivalent widths ranged from −40 Å ≲ W_Lyα ≲ 160 Å, although one object (HDF–C41) had an equivalent width of ∼740 Å; we attributed this outlier to a continuum level in the spectrum comparable with zero and omitted this object from further analysis. The median equivalent width of the sample was ∼4 Å (Figure 3), consistent with values reported by Shapley et al. (2001, 2003) for z∼ 3 LBGs.

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A composite spectrum offers the distinct advantage of higher signal-to-noise over individual observations. We accordingly constructed several composite spectra from our sample, using, in each case, the same basic steps discussed below.

The one-dimensional, flux-calibrated, rest-frame input spectra of interest were stacked (mean-combined) using the IRAF scombine routine. Each input spectrum was scaled to a common mode over the wavelength range 1250–1380 Å and a small number of positive and negative outliers (< 10% of the data) were rejected at each pixel position to prevent poor sky-subtraction or cosmic ray residuals from affecting the composite spectrum. The final composite spectrum was then rebinned to a dispersion of 1 Å pixel⁻¹. A composite spectrum¹¹ of the entire sample is shown in Figure 4, where several photospheric and low- and high-ionization interstellar features are visible in addition to Lyα.

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We employed several statistical methods central to our investigation, including survival analysis techniques that were capable of analyzing data with limits ("censored data"). It was important to include limits in the statistical analysis as a non-negligible fraction of the sample (28%) was undetected in K_s imaging. We used ASURV ("Astronomy SURVival Analysis") Rev 1.2 (Isobe & Feigelson 1990; Lavalley et al. 1992), which implements the methods presented in Feigelson & Nelson (1985) and Isobe et al. (1986). The bivariate correlation tests Kendall τ and Spearman ρ were utilized, where, for each test, the degree of correlation is expressed in two variables: τ_K (r_SR) and P_K (P_SR). The first variable represents the test statistic and the second variable represents the probability of a null hypothesis (i.e., the probability that the data are uncorrelated). We also used routines from Numerical Recipes (Press et al. 1992), specifically the Kolmogorov–Smirnov (K–S) test between two data sets (kstwo), the Spearman's rank correlation (spear), and the Kendall's τ correlation (kendl1). The K–S test produces two outputs: D and P, where the former is the test statistic and the latter is the probability that the two samples are drawn from the same underlying population. spear and kendl1 are duplicates of the Spearman ρ and Kendall τ tests available in ASURV; we employed the ASURV routines when it was necessary to include data with limits.

First, we investigated the correlation between Lyα equivalent width and extinction, age, SFR, and stellar mass, respectively, using the Spearman ρ and Kendall τ bivariate correlation tests. For this analysis, we used the entire sample with population modeling, including galaxies with upper limits in the K_s passband (248 objects). We note that while the correlations shown in Figure 6 are not without scatter, we have employed a variety of quantitative statistical analyses that have yielded a consistent picture of how stellar populations are correlated with Lyα emission in z∼ 3 LBGs. Below, we introduce these results.

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E(B − V), age, and SFR all exhibited very strong correlations with W_Lyα (P_SR⩽ 0.0002 in each case),¹² whereas stellar mass was uncorrelated (P_SR = 0.8630). These results did not change when the 69 galaxies with K_s upper limits (and corresponding upper limits in mass and age) were excluded from the analysis (Table 2). In order to test the robustness of these results while taking into account the uncertainty on the best-fit parameters, we used the bootstrapping method. We created 100 bootstrap samples by randomly extracting one line from each object's 1000 entry confidence interval of stellar parameters (generated by perturbing the initial photometry according to its errors and then re-modeling the galaxy; Section 3) and then re-ran the Spearman ρ test on each of these 100 artificial samples. A null hypothesis was consistently ruled out at between the 3σ and 5σ levels for the SFR and E(B − V) bootstrap samples and at the 3σ level for the age sample. In the case of the stellar mass sample, where the null hypothesis was ruled out at only the 1σ level, the data do not support a correlation between W_Lyα and stellar mass. These bootstrap samples show that even when accounting for the uncertainty in best-fit parameters, a strong correlation exists between equivalent width and age, E(B − V), and SFR, respectively, such that objects with strong Lyα emission tend to be older, less dusty, and lower in SFR (more quiescent) than objects with weak or no Lyα emission.

As an independent test of the above results, we next used the rest-frame UV spectra to investigate how the morphology of the Lyα feature was, qualitatively, correlated with best-fit stellar population parameters. For this analysis, we limited our study to objects satisfying two criteria: (1) population synthesis modeling had been completed and (2) K_s photometry consisted of detections, not upper limits.¹³ Together, these criteria isolated 179 objects. For each stellar population parameter, we divided the objects into three groups ("tertiles") based on their best-fit value. A composite rest-frame UV spectrum was then constructed from each tertile according to the methodology presented in Section 2.4, for a total of 12 composite spectra (3 tertiles × 4 parameters; Figure 7). A strong correlation of equivalent width with age, E(B − V), and SFR was observed, such that stronger Lyα emission was more prevalent in older, less dusty, and more quiescent galaxies. At the same time, the strength of low-ionization interstellar absorption lines decreased with increasing Lyα emission strength (Shapley et al. 2003). We note that these trends were still present when the spectra were median-combined to make to the composites (as opposed to mean-combined).

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Next, we reversed the independent and dependent variables from the previous investigation and, this time, divided the sample into tertiles according to Lyα equivalent width. The mean equivalent widths of each tertile were −15.5, 2.8, and 33.1 Å, respectively. We then calculated the average stellar parameters of each tertile, in addition to the error on the mean (Figure 8). Consistent with the results of the bivariate correlation tests and the composite spectra divided by stellar population parameters discussed above, we found that as the average equivalent width varied from −15.5 Å to 33.1 Å, 〈t_⋆〉 increased from 440 Myr to 850 Myr, 〈E(B − V)〉 decreased from 0.24 to 0.14, and 〈SFR〉 decreased from 300 M_☉ yr⁻¹ to 70 M_☉ yr⁻¹. A weak positive correlation between best-fit stellar mass and equivalent width was observed, although, given the errors on the average masses, we chose to adopt the stance that stellar mass was generally insensitive to changes in equivalent width.

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From the three aforementioned investigations, a consistent picture has emerged: strong Lyα emission is associated with galaxies that are older, less dusty, and more quiescent than their counterparts with weaker Lyα emission or the line in absorption. We note that the trend of increasing Lyα strength with decreasing E(B − V) is a well-known result (e.g., Shapley et al. 2003; Reddy et al. 2006b; Pentericci et al. 2007). Deharveng et al. (2008), however, found no apparent correlation between Lyα equivalent width and UV color in a sample of 96 LAEs at z∼ 0.3, although we caution that the transformation from UV color to E(B − V) is sensitive to the geometry of the emitting stars and absorbing dust and may therefore not be constant for a heterogeneous population such as LAEs (e.g., Witt & Gordon 2000; Granato et al. 2000). The relationship between age and W_Lyα observed in our data—older objects exhibiting stronger Lyα emission than younger objects—is in agreement with the results of Shapley et al. (2003). The inverse correlation between dust-corrected SFR and W_Lyα that we observe has been noted by several authors as well (e.g., Ando et al. 2004; Reddy et al. 2006b; Tapken et al. 2007), although Nilsson et al. (2007) report a ∼2σ direct correlation between SFR and W_Lyα in a sample of 24 LAEs at z∼ 3.15. In contrast with the results presented here, however, Erb et al. (2006a) reported a correlation between stellar mass and Lyα strength in a sample of 87 star-forming galaxies at z∼ 2. These authors found that composite spectra constructed from the 30 least massive galaxies (〈M〉 = 5 × 10⁹ M_☉) and the 28 most massive galaxies (〈M〉 = 7 × 10¹⁰ M_☉) in their sample differed widely in nebular line strength, with the former sample exhibiting a pronounced Lyα emission feature and the latter sample showing a smaller Lyα feature superimposed on a larger absorption trough. Erb et al. (2006a) attributed these results to the lower velocity dispersion of the ISM in the less massive galaxies, where, following the arguments of Mas-Hesse et al. (2003), velocity dispersion and Lyα escape fraction are anti-correlated. We therefore conclude here that the observed correlations we find between W_Lyα and E(B − V), SFR, and age are supported by the work of others, whereas the lack of correlation between stellar mass and W_Lyα may either be a tenable result (and evidence of LBG evolution during the 1.1 Gyr intervening z = 2 and z = 3) or otherwise an indication that further studies of the relationship between W_Lyα and stellar mass at z∼ 3 are necessary.

The correlations discussed above were derived assuming the Calzetti et al. (2000) dust attenuation law. While this relation has routinely been applied to samples of high-redshift galaxies (e.g., Erb et al. 2006b; Gawiser et al. 2006; Gronwall et al. 2007), recent work by Reddy et al. (2006b), based on Spitzer MIPS observations, has suggested that dust extinction in young (t_⋆⩽ 100 Myr), UV-selected galaxies at z∼ 2 is often overestimated by modeling a given rest-frame UV color with the Calzetti et al. (2000) attenuation law. At z∼ 3, there have been no corresponding statistical studies, but Siana et al. (2008, 2009) have presented preliminary evidence for a similar trend based on two strongly lensed objects. On the other hand, for a single unlensed LBG at z∼ 2.8, Chapman & Casey (2009) find good agreement between the dust extinction inferred from the Calzetti et al. (2000) law and that estimated from the ratio of SCUBA 850 μm and rest-frame UV fluxes. Based on their findings, Reddy et al. (2006b) and Siana et al. (2008) accordingly proposed that a steeper, SMC-like extinction relation (e.g., Prévot et al. 1984) may be more appropriate for young objects.

With these results in mind, we assessed the uncertainties inherent in the choice of attenuation law. Limiting our analysis to the 179 objects without K_s upper limits, we re-modeled the 70 galaxies with t_⋆⩽ 100 Myr with a SMC-like extinction law (and retained the original fits assuming the Calzetti et al. (2000) law for the remaining 109 objects). In this mixed sample with some objects modeled with a SMC-like law and others modeled with the Calzetti et al. (2000) relation, we found no significant correlations between W_Lyα and stellar populations. We also investigated the effect of re-modeling all 179 galaxies, regardless of age, with a SMC-like attenuation law. In this case, we observed correlations between W_Lyα and E(B − V) and between W_Lyα and SFR. Given the uncertainties in adopting the SMC law for part or all of our sample, another approach consists of restricting our analysis to objects for which the validity of the Calzetti et al. (2000) law has not been questioned. When we omitted objects younger than t_⋆ = 100 Myr from our original analysis assuming the Calzetti et al. (2000) dust attenuation law, the trends between W_Lyα and E(B − V), age, and SFR, respectively, were still present (but only at a 2σ level of significance).

Given the lack of systematic studies of the dust attenuation law in z∼ 3 objects, and the uncertainty regarding the age at which a galaxy may transition from being fit with a SMC-like law to the Calzetti et al. (2000) law, we choose to present all analysis on results derived from assuming the Calzetti et al. (2000) attenuation law. We acknowledge that the choice of an extinction law is a systematic uncertainty in our analysis, yet the persistence of trends between Lyα and stellar populations in the sample limited to objects with t_⋆⩾ 100 Myr supports the analysis with the Calzetti law applied to the full sample.

We now turn to discussing our adoption of the Bruzual & Charlot (2003) population synthesis models. While other models more fully take into account the Thermally Pulsing Asymptotic Giant Branch (TP-AGB) stellar phase (e.g., Maraston 2005), a study of young star-forming "BzK" galaxies at z∼ 2 by Daddi et al. (2007) found that the Maraston (2005) and Bruzual & Charlot (2003) models yielded consistent M/L ratios; the LBGs in our sample are as least as dominated by the young stellar component as the Daddi et al. (2007) BzK objects. Furthermore, a significant fraction (∼40%) of our sample does not have IRAC coverage, and therefore our SED fitting only includes photometry out to the rest-frame V band (observed K_s band) where the effects of TP-AGB stars on the derived parameters are less pronounced. Additionally, and perhaps most importantly, we are concerned with trends in the data (rather than specific stellar population values). It is these trends that are preserved regardless of model choice; Lai et al. (2008) find that even though the Maraston (2005) models yield lower stellar masses and younger ages than Bruzual & Charlot (2003) models for two samples of objects, the distinction between the two samples is significant irrespective of which population synthesis model is adopted. Finally, we note that our population synthesis results are supported by empirical color differences (Section 4.4). In this sense, the choice of synthesis code is rendered less important—there are clearly intrinsic differences between objects.

In the next section, we divide the LBGs into two groups according to Lyα strength and compare the stellar populations of these subgroups in order to more generally comment on the differences between objects with and without strong Lyα emission.

From the perspective of examining Lyα emission, the simplest division of our data is according to Lyα equivalent width. We turn here to comparing the properties of objects with strong (W_Lyα⩾ 20 Å) Lyα emission and with weak Lyα emission, or the line in absorption (W_Lyα< 20 Å). Given our large sample size, these two groups each have sufficient membership to ensure robust statistics even when we restrict our analysis to only those objects with both stellar population modeling and no K_s upper limits (34 and 145 objects, respectively). We call these two groups LAEs and non-LAEs, respectively, where we differentiate these objects from LAEs isolated with narrowband filters by explicitly referring to the latter as narrowband-selected objects. The motivation for choosing 20 Å as the delineating equivalent width stems from the adoption of this value as a typical limit in narrowband LAE studies (e.g., Gawiser et al. 2007; Nilsson et al. 2009b; Pentericci et al. 2009). In order to investigate how stellar populations vary between LAEs and non-LAEs, we examined the age, E(B − V), stellar mass, and SFR distributions of both samples (Figure 9). We discuss below the striking differences between the properties of UV continuum-bright LAEs and non-LAEs.

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There is a remarkable dissimilarity between the age histograms of LAEs and non-LAEs: LAEs are generally fit with older best-fit ages than non-LAEs: LAEs have a median age more than four times that of the non-LAEs (763 Myr versus 181 Myr). LAEs furthermore lack the conspicuous overdensity of young objects (t_⋆< 100 Myr) that characterizes the non-LAE sample. The disparity in ages between LAEs and non-LAEs is reflected in the K–S test probability of ∼2% that the two age samples are drawn from the same underlying population.

The distributions of dust attenuations for the LAE and non-LAE samples differ significantly, with a median E(B − V) of 0.13 for the LAEs and 0.20 for the non-LAEs. While both populations have roughly the same distribution of E(B − V) values below 0.30, the non-LAE distribution is characterized by a tail of high extinction values. No LAEs have E(B − V) > 0.40, whereas 12/145 (8%) of non-LAEs do. The K–S test probability that the LAE and non-LAE extinction distributions derive from the same parent population is ∼2%.

The SFRs of LAEs and non-LAEs are markedly different, as the LAEs have a median rate of 25 M_☉ yr⁻¹ and the non-LAEs are characterized by a median rate of 59 M_☉ yr⁻¹. The relative quiescence of strong Lyα emitters is in contrast to the high SFR tail observed in non-LAEs, where SFRs in excess of 500 M_☉ yr⁻¹ are recorded for 22 objects.¹⁴ There is a ∼1% probability of these LAE and non-LAE SFR distributions are drawn from the same underlying population.

Unlike age, E(B − V), and SFR, the stellar mass distributions of LAEs and non-LAEs are not strongly dissimilar. The median value of the LAEs (1.1 × 10¹⁰ M_☉) is only 40% larger than that of the non-LAEs (7.9 × 10⁹ M_☉) and a K–S test predicts that the two distributions have a ∼27% chance of being drawn from the same parent distribution.

We have shown that three of the best-fit stellar population parameters—age, E(B − V), and SFR—have markedly different distributions in the LAE and non-LAE samples. LAEs are typically older, less dusty, and less vigorously forming stars than non-LAEs. We tested the robustness of these results by constructing bootstrap samples from the confidence intervals of best-fit stellar parameters (Section 4.2). The mean and the error on the mean (σ/$\sqrt{n}$, where n is the sample size) were calculated for each best-fit stellar population parameter in the LAE and non-LAE samples. This process was repeated for 100 bootstrap samples. For E(B − V), age, and SFR, we found that the means of the LAE and non-LAE samples were consistently offset by at least their errors. In terms of stellar mass, the LAEs samples had consistently larger values; we note, however, that the masses of the LAE and non-LAE samples were comparable within their errors. These results, in agreement with the histograms discussed above, support the observed correlation that galaxies with strong Lyα emission tend to be older, less dusty, and more quiescent than objects with weak Lyα emission, or the line in absorption.

In order to place the results of the previous section on a more empirical footing, we transition here from focusing on stellar parameters and instead examine more broadly the relative colors of objects with and without strong Lyα emission. We also contrast our data with SEDs of narrowband-selected LAEs from Gawiser et al. (2007) and Nilsson et al. (2007) with the aim of investigating the color differences, if any, between objects isolated with color cuts and narrowband filters. Our analysis is focused on the 179 objects in the LBG sample satisfying the criteria of population synthesis modeling and no K_s upper limits. This empirical approach is complementary to the stellar population modeling discussed previously, and is furthermore a non-parametric probe of the differences between objects with and without strong Lyα emission. Such a study is necessary given the well-known degeneracies among physical properties (e.g., dust extinction and age) derived from stellar population modeling (Shapley et al. 2003).

We find stark differences between the colors of LAEs and non-LAEs (Table 3), where all G magnitudes have been corrected for the contribution of Lyα (Section 3). Strong Lyα emitters have bluer $G - {\cal R}$ colors than non-LAEs ($\langle G-{\cal R} \rangle _{\rm LAE}$ = 0.54; $\langle G-{\cal R} \rangle _{\rm non-LAE}$ = 0.65) and this trend is consistent when a correction for IGM absorption (Madau 1995) is applied to the objects' G magnitudes ($\langle G_{\rm IGM corr.}-{\cal R} \rangle _{\rm LAE}$ = 0.36; $\langle G_{\rm IGM corr.}-{\cal R} \rangle _{\rm non-LAE}$ = 0.47). Given that non-LAEs have younger best-fit stellar ages than LAEs (Section 4.2), we expect that non-LAEs should have intrinsically bluer stellar continua than objects with strong Lyα emission. The fact that we instead observe redder $G - {\cal R}$ colors in these objects is evidence that non-LAEs are more strongly attenuated by dust than LAEs. This result is consistent with the larger E(B − V) values derived for the non-LAEs than the LAEs (Section 4.2).

Table 3. Average Photometry^a

Sample (〈z〉)	$\langle {{\cal R}}\rangle$ (σ)	〈G〉b (σ)	〈GIGMcorr.〉 (σ)	〈Ks〉c
LAEs (2.99)	24.31 (0.02)	24.85 (0.03)	24.67 (0.03)	21.24
Non-LAEs (2.97)	24.34 (0.01)	24.99 (0.01)	24.81 (0.01)	21.36

Notes. ^aGalaxies with K_s upper limits were omitted from this analysis, as were objects lacking stellar population modeling. ^bG magnitudes have been corrected to account for contributions from Lyα. ^cPhotometry calculated from best-fit SED, for objects lacking K_s imaging.

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LAEs and non-LAEs also differ in their ${\cal R}- K_s$ colors, where K_s magnitudes were inferred from best-fit SEDs for the 78 objects lacking near-infrared photometry. We find that LAEs are characterized by $\langle {\cal R}-{K_s} \rangle$ = 3.07, whereas non-LAEs are bluer by 0.1 mag with $\langle {\cal R}-{K_s} \rangle$ = 2.98. Given that the ${\cal R}$ and K_s passbands bracket the Balmer break for objects at z∼ 3, a redder ${\cal R} - K_s$ color is indicative of a larger Balmer break. A more pronounced Balmer break, in turn, is correlated with an older stellar population (e.g., Bruzual & Charlot 2003). Therefore, the result that LAEs have redder ${\cal R}- K_s$ colors than non-LAEs is empirical, non-parametric evidence that strong Lyα emitters are older on average. We have accordingly shown that the different colors of LAEs and non-LAEs are reflective of the trends discerned using stellar population modeling.

Composite best-fit SEDs of the LAE and non-LAE samples were assembled by directly summing the individual best-fit SEDs over the rest-frame range 912 Å–1.0 μm and normalizing by the number of constituent spectra (34 and 145, respectively). In Figure 10, we compare the composite LAE and non-LAE spectra with best-fit average SEDs from two studies of narrowband-selected LAEs. Data from Nilsson et al. (2007) and Gawiser et al. (2007), where the former include LAEs at z∼ 3.1 in the GOODS South Field and the latter encompass LAEs at z∼ 3.1 in the Extended Chandra Deep Field South, are shown both normalized and unnormalized with our LAE and non-LAE composite spectra. It is immediately apparent that the LBG-selected LAEs and non-LAEs are significantly brighter than the narrowband-selected LAEs (∼×2.3 mag in the ${\cal R}$ band). The LBG-selected objects also have redder $G- {\cal R}$ and redder ${\cal R} - K_s$ colors than both the Nilsson et al. (2007) and Gawiser et al. (2007) data. These differences in color are consistent with LBG-selected objects being both dustier and older than objects isolated with narrowband filters, as has been suggested by some authors (e.g., Gawiser et al. 2007; Nilsson et al. 2009b). The relationship between LBGs and narrowband-selected LAEs is far from clear, though; some authors hypothesize a continuity between at least portions of the two populations based on similarities in stellar mass, color, and clustering (e.g., Adelberger et al. 2005b; Gronwall et al. 2007; Gawiser et al. 2007; Lai et al. 2008; Verhamme et al. 2008) whereas others maintain that the large luminosity and W_Lyα discrepancies between LBGs and objects isolated with narrowband filters dictate separate evolutionary paths (e.g., Malhotra & Rhoads 2002).

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By virtue of broadband selection techniques, LBGs have characteristically brighter optical continua than narrowband-selected LAEs (${\cal R}\,\le$ 25.5 versus R∼ 27). As it is critical to disentangle how luminosity and stellar populations are related before attributing galaxy differences purely to the same mechanisms that modulate Lyα emission, it is of interest to investigate how, if at all, the derived properties of narrowband-selected LAEs are a natural result of preferentially isolating continuum-faint, line-bright objects. We compare our data with the work of several authors to explore the dependencies of Lyα emission, stellar populations, and spatial clustering on broadband luminosity and we discuss the applications of such investigations to both LBGs and narrowband-selected LAEs.

Luminosity and Equivalent Width. Recent work has suggested a correlation between luminosity and Lyα equivalent width, in the sense that few luminous LBGs have been observed with large equivalent widths (e.g., Shapley et al. 2003; Erb et al. 2006a; Ando et al. 2006; Ouchi et al. 2008; Vanzella et al. 2009; Pentericci et al. 2009). Several physical pictures have been suggested to explain this correlation, which has been noted in samples at redshifts z∼ 3–6. Verhamme et al. (2008) and Vanzella et al. (2009) hypothesized that different dust attenuations (from a luminosity-dependent chemical evolution history) could be responsible while Ando et al. (2006) suggested that an enhanced presence of H i gas around luminous LBGs could explain the lack of large Lyα equivalent widths in bright galaxies (consistent with the prediction of more massive galaxies residing in larger dark matter halos that are presumably richer in H i gas). Some authors, however, have conversely reported that the correlation between luminosity and Lyα equivalent width is tenuous, at best (e.g., Steidel et al. 2000; Verma et al. 2007; Stanway et al. 2007; Nilsson et al. 2009a). Given the ongoing debate about such a correlation, we examined our extensive data set to test for a deficiency of luminous objects with large Lyα equivalent widths.

We restricted our analysis to the 64 objects with W_Lyα ⩾ 20 Å in order to ensure completeness as a function of ${\cal R}$ magnitude, given that spectroscopic follow-up is biased toward objects with large, positive Lyα equivalent widths. These objects have W_Lyα < 160 Å and M_UV ranging from −20.0 to −22.4 (neglecting corrections for dust attenuation). This parameter space is comparable to that of Ando et al. (2006), where these authors suggest a threshold luminosity of M₁₄₀₀ = −21.5 to −21.0 above which objects are deficient in large W_Lyα values. We find that M_UV and W_Lyα are not correlated in our sample, where the Spearman ρ test statistic, r_SR, is −0.104 and the probability of a null hypothesis, P_SR, is 0.4076. Furthermore, we see no evidence for any such threshold luminosity in our data; when the sample is divided into bright (M_UV < −21.0) and faint (M_UV >−21.0) groups, the median W_Lyα of each group are identical (∼32 Å).

These results are contradictory to those presented by Shapley et al. (2003) who also examined a sample of z∼ 3 LBGs. The Shapley et al. (2003) sample, when limited to objects with W_Lyα ⩾ 20 Å, consisted of objects with absolute UV luminosities between −19.5 and −22.4 (neglecting corrections for dust attenuation). In those data, there is a significant correlation between M_UV and W_Lyα (r_SR = 0.274; P_SR = 0.0002). Dividing this sample into bright and faint subgroups, where the boundary luminosity is M_UV = −21.0, also yielded a pronounced difference in the median W_Lyα values of each group: M_UV(bright) = 35 Å and M_UV(faint) = 44 Å. Given that both our present sample and the Shapley et al. (2003) sample are composed of z∼ 3 LBGs, we hypothesize that one of the reasons our data may not exhibit a correlation between M_UV and W_Lyα is that our sample includes only a limited number of high equivalent width objects. Nine objects have W_Lyα ⩾ 70 Å and just one has W_Lyα ⩾ 100 Å in our data set whereas, in the Shapley et al. (2003) sample, 45 objects have W_Lyα ⩾ 70 Å and 20 have W_Lyα ⩾ 100 Å. After testing that our systematic approach to calculating Lyα equivalent width returned values consistent with those reported by Shapley et al. (2003), we combined our data with the 189 objects¹⁵ from Shapley et al. (2003) with W_Lyα ⩾ 20 Å. This combined sample of 243 objects, with equivalent widths measured in a uniform manner, was then tested for a correlation between M_UV and W_Lyα. We found only a moderate correlation (r_SR = 0.149; P_SR = 0.0202), where we hypothesize that the trend between M_UV and W_Lyα is simply not strong enough to be unequivocally detected in all samples. Furthermore, the correlation between M_UV and W_Lyα in these data may be masked by the relatively small range of M_UV probed by LBGs. Narrowband-selected LAEs exhibit a wider range of absolute luminosities (23.0 ≲ R≲ 27.0) than LBGs do (23.0 $\lesssim \,{\cal R}\,\lesssim$ 25.5); any trend between M_UV and W_Lyα will consequently be more pronounced in a sample of LAEs. In order to test this statement, we analyzed a sample of LAEs from Gronwall et al. (2007). We divided the data into two samples, where the first subsample included only objects brighter than the LBG spectroscopic limit and the second subsample was inclusive of all the data. The first subsample showed no correlation between M_UV and W_Lyα (r_SR = −0.015; P_SR = 0.9185) whereas the second subsample exhibited a strong correlation (r_SR = 0.585; P_SR = 0.0000). These results support our hypothesis that the trend between M_UV and W_Lyα at z∼ 3 is apparent only when considering data encompassing a large range in absolute luminosity. In Figure 11, we present a plot of M_UV versus W_Lyα for ${\cal R}\,\le$ 25.5, W_Lyα ⩾ 20 Å LBGs and the Gronwall et al. (2007) sample of narrowband-selected LAEs. Even if one assumes incompleteness in the Gronwall et al. (2007) sample at the faint end, the lack of large equivalent widths among bright objects is striking (but see Nilsson et al. 2009a). Ando et al. (2006) report a deficiency of bright objects with large equivalent widths in their sample of z = 5–6 objects; the fact that we observe several such objects here while those authors do not can be attributed to the small sample size of Ando et al. (2006).

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Luminosity and Stellar Populations. Understanding how luminosity and stellar populations are correlated is critical to commenting on the nature of LBGs and LAEs, given that the latter are commonly an order of magnitude fainter in optical broadband filters. Lai et al. (2008) examined a sample of 70 z∼ 3.1 LAEs, ∼30% of which were detected in the Spitzer IRAC 3.6 μm band. These authors found that the IRAC-detected LAEs were significantly older and more massive (〈t_⋆〉∼ 1.6 Gyr, 〈M〉∼ 9 × 10⁹ M_☉) than the IRAC-undetected sample (〈t_⋆〉∼ 200 Myr, 〈M〉∼ 3 × 10⁸ M_☉). In addition to having redder colors, the IRAC-detected sample was also approximately three times brighter in the R band. This correlation between luminosity and redness, age, and mass prompted Lai et al. (2008) to suggest that the IRAC-detected LAEs may be a low-mass extension of the LBG population. The relationship between luminosity and average dust attenuation was examined by Reddy et al. (2008), where these authors studied a sample of UV-selected objects at 1.9 ⩽ z< 3.4 and found no correlation between M_UV and E(B − V) over the absolute magnitude range 22.0 $\le \,{\cal R}\,\le$ 25.5. While bright objects do not appear to exhibit a correlation between dust attenuation and luminosity, Reddy et al. (2008) postulate that objects fainter than the LBG spectroscopic limit of ${\cal R}$ = 25.5 may have lower average dust attenuations than brighter objects. This has been confirmed by Bouwens et al. (2009), who examined a sample of objects at z∼ 2–6 over a larger dynamic range (0.1$L^*_{z \rm =3}$ to 2$L^*_{z \rm =3}$) than had been previously studied. These authors reported a correlation between UV luminosity and dust attenuation such that fainter objects are bluer. Given the correlation we find between E(B − V) and W_Lyα, the evolution of dust attenuation with UV luminosity may have implications for the fraction of LAEs as a function of UV luminosity (Reddy & Steidel 2009). These results have highlighted that examining objects over only a limited range of absolute magnitudes may mask an underlying correlation.

Luminosity and Clustering. Several authors have noted the different clustering properties of LBGs and LAEs, where the former exhibit a mean halo occupation of ∼100% (e.g., Conroy et al. 2008) in dark matter halos with minimum masses of ∼10^11.3 h⁻¹ M_☉ (e.g., Adelberger et al. 2005b; Conroy et al. 2008) and the latter cluster more weakly and appear to occupy only 1/100–1/10 of similarly clustered dark matter halos with lower limit masses of ∼10^10.6 h⁻¹ M_☉ (e.g., Gawiser et al. 2007). Given the direct dependence of clustering strength on UV luminosity (e.g., Ouchi et al. 2004; Adelberger et al. 2005b; Lee et al. 2006), the spatial differences between LBGs and LAEs may simply reflect the discrepancy in typical UV luminosity between the two samples. It is therefore of interest to investigate how the clustering strength of LAEs correlates with Lyα luminosity or Lyα equivalent width, given that these quantities govern the selection of LAEs. Discerning the relative clustering properties of objects with and without strong Lyα emission within the same UV luminosity range is critical to understanding the correlation between Lyα and galactic properties.

These results—that objects more luminous in the rest-frame UV may (1) be deficient in large Lyα equivalent widths and (2) be generally redder, older, and more massive relative to less luminous objects—may be the driving factors responsible for (faint, high equivalent width) narrowband-selected LAEs being typically younger, bluer, and less massive than (bright, lower equivalent width) LBGs.

As the LBG spectroscopic limit of ${\cal R}\,\le$ 25.5 necessarily limits our sample to a smaller absolute magnitude range than that probed by narrowband-selected LAEs (23.0 ≲ R≲ 27.0), the luminosity-dependent trends reported above for Lyα equivalent width, stellar populations, and clustering (e.g., Ando et al. 2006; Lai et al. 2008; Adelberger et al. 2005b) may only become apparent in narrowband-selected samples where the absolute luminosity range is significantly larger than it is in samples of LBGs. We remind the reader that while our conclusions are applicable to both LBGs and bright (${\cal R}\,\le$ 25.5) narrowband-selected LAEs, we are unable to make inferences about the population of faint LAEs. We refer the reader to Lai et al. (2008) for a discussion of these objects.

The equivalent width of the Lyα feature is a common benchmark that can be used to make comparisons between studies of LBGs and LAEs. Observing programs of flux-selected Lyα emitters typically employ a narrowband (∼50–100 Å) filter centered on the redshifted Lyα line, paired with a broadband filter used to characterize the local continuum. Samples are defined according to a minimum Lyα equivalent width—typically ∼20 Å in the rest frame—where W_Lyα is calculated photometrically by ratioing the flux in the narrowband filter to the flux density in the broadband filter. LBGs, on the other hand, are selected according to broadband flux and color cuts, with no implicit requirement on W_Lyα. Equivalent widths of LBGs are most commonly calculated spectroscopically, as these objects are characterized by relatively bright continua (${\cal R}\,\le$ 25.5). Given these different selection techniques and methods of calculating W_Lyα, it is of interest to compare the equivalent width distributions of LBG-selected LAEs and narrowband-selected LAEs. A difference in the W_Lyα distributions of these two populations would be indicative of an underlying dissimilarity between LBG-selected LAEs and narrowband-selected LAEs, even though both classes of objects can be broadly classified as strong Lyα emitters.¹⁶

For this analysis, we combined our present sample of 64 LBG-selected LAEs with the 179 objects from Shapley et al. (2003) satisfying the criterion of W_Lyα ⩾ 20 (measured using our methodology described in Section 2.3). Integrating these two data sets yields a large sample of z∼ 3 objects for which equivalent widths were measured in an identical manner. We find that these data are characterized by a median equivalent width of 42 Å and mean of 57 Å. In contrast, a sample of 160 LAEs at z = 3.1 in the Extended Chandra Deep Field South observed by Gronwall et al. (2007) had a median of ∼60 Å and a mean of ∼80 Å. We used the K–S test to quantify the likelihood that the LBG-selected LAEs and the narrowband-selected LAEs derived from the same parent equivalent width distribution. When the entire sample of objects from Gronwall et al. (2007) was considered, we found a probability of 3.5 × 10⁻⁴ that the objects shared a common equivalent width distribution. Alternatively, when we limited the Gronwall et al. (2007) data to include only objects satisfying the LBG spectroscopic limit of ${\cal R}\,\le$ 25.5, we obtained a probability of ∼0.95 that the equivalent widths of the LBG- and narrowband-selected LAE samples could be described as originating from the same population. This result, consistent with Verhamme et al. (2008), is indicative of the similarity in equivalent width of objects spanning comparable UV luminosities. Conversely, the probability that the equivalent widths of our sample of LBG-selected LAEs and the faint (R⩾ 25.5) Gronwall et al. (2007) LAEs derive from the same parent population is 8 × 10⁻⁸. Similarly, when the Gronwall et al. (2007) data are divided using the boundary R = 25.5, a K–S test yields a probability of 7.9 × 10⁻⁶ that the two equivalent width populations derive from the same parent distribution.

In other words, while the equivalent width distributions of LBG- and narrowband-selected LAEs are quite disparate when considered at face value, it appears that the bulk of this disparity can be attributed to the different luminosities probed by the respective samples. When narrowband-selected LAEs are restricted to objects more luminous than R = 25.5, a K–S test reveals a high probability that the equivalent width distributions of strong Lyα-emitting LBGs and bright LAEs derive from the same parent population. This similarity in equivalent width, when a standard continuum magnitude range is adopted, is consistent with the picture that bright LAEs represent the same population as Lyα-emitting LBGs (e.g., Verhamme et al. 2008).

As Lyα is susceptible to a variety of complex radiation transport effects including resonant scattering (e.g., Neufeld 1990) and the velocity field of the ISM (e.g., Verhamme et al. 2008), the escape of Lyα emission is a probe of the physical conditions of galaxies' ISMs. In the simplest case of a single-phase ISM in which gas and dust are well mixed, Lyα photons experience more attenuation than continuum photons due to the longer dust absorption path lengths expected for resonantly scattered radiation. To explain the large Lyα equivalent widths observed in some apparently dusty LAEs, the presence of a multi-phase ISM—in which dust is segregated in neutral clouds—has been proposed (Neufeld 1991; Hansen & Oh 2006; Finkelstein et al. 2009). In such a geometry, Lyα photons are scattered at the surface of dusty clumps while continuum photons penetrate the clumps and are preferentially scattered or absorbed. Galaxies in which the dust is segregated in neutral clouds are consequently predicted to exhibit larger Lyα equivalent widths than would be expected given their stellar populations.

We considered the likelihood of the above dust geometry in our sample of LBGs. Our methodology relied on comparing observed and predicted Lyα luminosities, where the former, L_Lyα(flux), was calculated simply from the Lyα line flux and the latter, L_Lyα(SFR), was derived from the conversion between SFR (from population synthesis modeling) and Lyα luminosity, assuming the conventions (Case B recombination; T_e = 10,000 K) of Kennicutt (1998) and Brocklehurst (1971):

$$\begin{equation} L_{\rm Ly \alpha (SFR)} = \frac{{\rm SFR}\,(M_{\odot }\,{\rm yr}^{-1})}{9.1 \times 10^{-43}} \end{equation} \tag{ 2 }$$

where SFR was calculated assuming a Salpeter (1955) IMF. Two similar parameters incorporating observed and predicted Lyα luminosities were of interest: the escape fraction, f_esc, and the relative escape fraction, f_esc,rel. The escape fraction is the ratio of observed to predicted Lyα luminosities, whereas the relative escape fraction is this same ratio with an extra term corresponding to a dust correction at the rest wavelength of Lyα. f_esc,rel is a probe of the degree to which Lyα and continuum photons experience the same level of dust attenuation. In the case that f_esc,rel = 1, Lyα and continuum photons are attenuated by the same E(B − V). On the other hand, a relative escape fraction less than unity is indicative of a dust geometry in which Lyα photons are attenuated more than continuum photons. Conversely, a galaxy in which dust is segregated in neutral clouds and where the Lyα flux is consequently enhanced relative to the continuum flux would have f_esc,rel > 1. We present the equations for f_esc and f_esc,rel below, where k'(1216) parameterizes the Calzetti et al. (2000) starburst attenuation law at 1216 Å:

$$\begin{equation} f_{\rm esc} = \frac{ L_{\rm Ly\alpha (flux)}}{ L_{\rm Ly\alpha (SFR)}}, \end{equation} \tag{ 3 }$$

$$\begin{equation} f_{\rm esc,rel} = f_{\rm esc} \times 10^{ 0.4E(B-V)\it k^{\prime }(\rm 1216)}. \end{equation} \tag{ 4 }$$

When calculating f_esc and f_esc,rel, we limited our analysis to only those objects with W_Lyα > 0 Å due to the unphysical nature of inferring a Lyα luminosity from a negative Lyα flux. We also required objects to have best-fit stellar ages older than 100 Myr in order to ensure the validity of Equation (2), which assumes continuous star formation for at least that duration (Kennicutt 1998). These criteria isolated a sample of 105 objects. We note that the questions raised about the nature of the dust extinction law for young objects (Section 4.2) are not of concern given this older sample. To correct for slit losses, we normalized the G magnitudes determined from photometry and spectroscopy; the latter were calculated by multiplying the G filter transmission curve (4780/1100 Å) over the optical spectra. The Lyα line fluxes were adjusted accordingly, where the median flux correction was an increase by a factor of ∼1.7 (0.6 mag). This procedure relies on the assumption that Lyα emission has the same spatial extent as broadband 940–1470 Å emission. While some recent work (e.g., Steidel et al. 2000; Matsuda et al. 2004; Hayashino et al. 2004) has suggested that Lyα and UV continuum emission may be spatially decoupled with Lyα more extended than continuum emission, in the absence of simultaneous high-resolution Lyα and UV continuum imaging for our entire sample we assume for simplicity that the line and continuum emission are coincident.

The calculated values of f_esc vary from 0.00 to 0.85. In Figure 12, we plot E(B − V) versus f_esc; we find a strong correlation in the sense that objects with large dust attenuations tend to have small Lyα escape fractions (r_SR= −0.712, P_SR = 0.0000). We note that this trend is consistent with the existence of LBGs in our sample exhibiting both Lyα in absorption and red UV continua, where these particular objects were not included in this analysis due to their negative Lyα fluxes. Other authors have derived similar results, although with significantly smaller sample sizes (e.g., Verhamme et al. 2008; Atek et al. 2009). The scatter present in our larger data set—some of which may be due to systematics in estimating f_esc—is a useful probe of the nature of Lyα radiative transfer in LBGs. We further discuss a physical picture of LBGs consistent with these f_esc results in Section 6.

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In order to investigate the nature of the gas and dust distributions for the objects in our sample, we derived the relative escape fraction of the 105 LBGs with W_Lyα > 0 Å and t_⋆ > 100 Myr. We found that 103 objects had f_esc,rel< 1 and the sample as a whole was characterized by $\langle f_{\rm esc}(\rm rel) \rangle$ = 0.27 (Figure 13). For comparison, Gronwall et al. (2007) and Nilsson et al. (2009b) report typical f_esc,rel values of ∼0.30 and ∼0.60 in LAE samples at z∼ 3.1 and z∼ 2.25, respectively. Even if we conservatively assume Lyα slit losses for our sample approaching a factor of 2 (Hayashino et al. 2004), these low relative escape fractions, well below unity, do not support the hypothesis in which dust is primarily segregated to neutral clouds in Lyα-emitting LBGs. We note that the absorption of Lyα photons by the IGM is not a plausible explanation for these low relative escape fractions; at z∼ 3, Lyα line fluxes are predicted to experience an IGM-induced decrement of only ∼20% (Madau 1995; Shapley et al. 2006). Furthermore, the observed symmetry of the Lyα lines in our sample (Figures 1 and 7) are indicative of minimal IGM absorption. Additionally, if one adopts a subsolar metallicity (in contrast to Z_☉ used in this paper), the calculated values of f_esc,rel will be lower than those presented here due to the fact that the ratio of the ionizing photon luminosity to the observed UV luminosity increases with decreasing metallicity (e.g., Leitherer et al. 1999). This result of relative escape fractions below unity indicates that Lyα appears to experience more attenuation than continuum photons, consistent with the physical picture of a homogeneous distribution of gas and dust in which resonantly scattered Lyα photons have longer dust absorption path lengths than continuum photons. Such a simple picture is likely not an accurate representation of the ISM of z∼ 3 LBGs; indeed, the ISM of our own Milky Way is known to be highly inhomogeneous (Dickey & Garwood 1989). However, our results suggest a scenario in which dust and gas are well mixed among the different phases of an inhomogeneous ISM.

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