Stellar Populations of Lyman Alpha Emitters

# Stellar Populations of Lyman Alpha Emitters at z=3 – 4Based on Deep Large Area Surveys in the Subaru-SXDS/UKIDSS-UDS Field

Yoshiaki Ono, Masami Ouchi, Kazuhiro Shimasaku, Masayuki Akiyama, James Dunlop, Duncan Farrah, Janice C. Lee, Ross McLure, Sadanori Okamura, and Makiko Yoshida
Department of Astronomy, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
Observatories of the Carnegie Institution of Washington, 813 Santa Barbara Street, Pasadena, CA 91101, USA
Carnegie Fellow
Research Center for the Early Universe, Graduate School of Science, The University of Tokyo, Tokyo 113-0033, Japan
Astronomical Institute, Graduate School of Science, Tohoku University, Aramaki, Aoba, Sendai 980-8578, Japan
Department of Physics and Astronomy, University of British Columbia, 6224 Agricultural Road, Vancouver V6T 1Z1, Canada
SUPA Institute for Astronomy, University of Edinburgh, Royal Observatory, Edinburgh EH9 3HJ, UK
Department of Astronomy, Cornell University, Ithaca, NY 14853
Astronomy Centre, University of Sussex, Falmer, Brighton, UK
Hubble Fellow
Accepted 2009 November 11. Received 2009 October 28; in original form 2009 May 20
###### Abstract

We investigate the stellar populations of Lyman emitters (LAEs) at and in deg of the Subaru/XMM-Newton Deep Field, based on rest-frame UV-to-optical photometry obtained from the Subaru/XMM-Newton Deep Survey, the UKIDSS/Ultra Deep Survey, and the Spitzer legacy survey of the UKIDSS/UDS. Among a total of LAEs ( for and for ), only are detected in the band, i.e., brighter than mag. Eight of the -detected LAEs are spectroscopically confirmed. In our stellar population analysis, we treat -detected objects individually, while -undetected objects are stacked at each redshift. We find that the -undetected objects, which should closely represent the LAE population as a whole, have low stellar masses of , modest SFRs of yr, and modest dust extinction of . The -detected objects are massive, , and have significant dust extinction with a median of . Four -detected objects with the reddest spectral energy distributions, two of which are spectroscopically confirmed, are heavily obscured with , and their continua resemble those of some local ULIRGs. Interestingly, they have large Lyman equivalent widths Å. If these four are excluded, our sample has a weak anti-correlation between Ly equivalent width and . We compare the stellar masses and the specific star formation rates (sSFR) of LAEs with those of Lyman-break galaxies (LBGs), distant red galaxies, submillimetre galaxies, and - or -selected galaxies with photometric redshifts of . We find that the LAE population is the least massive among all the galaxy populations in question, but with relatively high sSFRs, while NIR-detected LAEs have and sSFR similar to LBGs. Our reddest four LAEs have very high sSFRs in spite of large , thus occupying a unique region in the versus sSFR space.

###### keywords:
cosmology: observations — galaxies: formation — galaxies: evolution — galaxies: high-redshift — galaxies: stellar content —
pagerange: Stellar Populations of Lyman Alpha Emitters at Based on Deep Large Area Surveys in the Subaru-SXDS/UKIDSS-UDS FieldStellar Populations of Lyman Alpha Emitters at Based on Deep Large Area Surveys in the Subaru-SXDS/UKIDSS-UDS Fieldpubyear: 2009

## 1 Introduction

Lyman emitters (LAEs) are a galaxy population which are common in the high redshift Universe. In the last decade, many observations have succeeded in detecting LAEs from up to , primarily based on narrow-band imaging to isolate Lyman emission (e.g. Hu et al., 1998; Rhoads et al., 2000; Iye et al., 2006). Over a thousand LAEs are now photometrically or spectroscopically identified (e.g. Hu et al., 2002; Ouchi et al., 2003; Malhotra & Rhoads, 2004; Taniguchi et al., 2005; Shimasaku et al., 2006; Kashikawa et al., 2006; Dawson et al., 2007; Murayama et al., 2007; Gronwall et al., 2007; Ouchi et al., 2008).

Most LAEs have relatively faint, blue UV continua and large Ly equivalent widths (EWs). These properties collectively suggest that they are young star-forming galaxies with low metallicities (e.g. Malhotra & Rhoads, 2002). In this sense, they may serve as building blocks of larger galaxies in hierarchical galaxy formation.

Stellar population analysis is helpful to further constrain the nature of LAEs. Recent multiwavelength observations covering near-infrared wavelengths have enabled analysis of the stellar populations of LAEs, and there is growing evidence that not all LAEs are primordial as described above. Table 1 summarises studies of the stellar populations of LAEs, including the work presented here. Gawiser et al. (2007) have performed a stacking analysis of LAEs at , and concluded that LAEs have low stellar masses (), young-age components ( Myr), and small dust extinctions () (see also Gawiser et al., 2006; Nilsson et al., 2007). Pirzkal et al. (2007) have studied nine LAEs at found by HST/ACS slitless spectroscopy in the Hubble Ultra Deep Field, to show that these faint LAEs are all very young ( Myr) with low masses () and small dust extinctions (). On the other hand, Lai et al. (2007) have concentrated on three spectroscopically confirmed LAEs at with IRAC detection, and derived relatively large stellar masses, , mild dust extinctions (), and a wide range of age, Myr. Lai et al. (2008) have studied both IRAC-detected and undetected LAEs at by the stacking method, to find that LAEs posses wide ranges of age ( Myr – Gyr) and mass () without dust extinction. Finkelstein et al. (2009) have analysed LAEs individually, which are either IRAC-detected or undetected. Their results also show wide ranges of stellar population age ( Myr), stellar mass (), and dust extinction ().

However, most of the samples constructed to date are not necessarily large and deep enough to constrain the average stellar populations of LAEs and to study rare, massive LAEs which may be a bridge to more massive and/or evolved objects like LBGs. In addition, correlations between stellar population parameters have not been addressed well.

Recently, Ouchi et al. (2008) have constructed the largest available sample of and LAEs in an about deg of the Subaru/XMM-Newton Deep Field (SXDF) from deep optical broadband and narrowband data. These large survey data enable us not only to find many massive LAEs, but also to place better constraints on less massive (i.e., average) LAEs using stacking analysis. Our sample used in this study consists of () LAEs at () covered by deep images taken with the UKIRT/WFCAM from UKIDSS Ultra Deep Survey (UDS; Warren et al., 2007) and m images taken with the Spitzer/IRAC from the Spitzer legacy survey of the UDS field (SpUDS; PI: J. Dunlop), among which () are detected in the band (i.e., brighter than the detection limit of the -band image). The band corresponds to the rest-frame and bands at and , respectively. For -undetected LAEs we make median stacked images for individual bandpasses. Since the vast majority (%) are undetected in , the spectral energy distributions (SEDs) constructed from stacking should closely represent the whole LAE population at each redshift. Since the time interval between the two redshifts is not so large (the age of the universe is Gyr at and Gyr for ), we treat the LAEs at and collectively as objects at , without discussing possible evolution between the two redshifts. In this paper, we show the results of our stellar population analysis of these LAEs. We also compare the stellar populations of LAEs with those of other high redshift galaxy populations. The contribution of LAEs to the cosmic star formation density and the stellar mass density is also evaluated.

The outline of this paper is as follows. In Section 2, we present our data and LAE sample. The SED fitting method is described in Section 3. In Section 4, we present and discuss our SED fitting results. A summary is given in Section 5. Throughout this paper, we use magnitudes in the AB system and assume a flat universe with (, , ) (, , ).

## 2 Data

### 2.1 Optical and NIR Images

Deep images of the SXDF were taken with Suprime-Cam on the Subaru Telescope by the Subaru/XMM-Newton Deep Survey project (SXDS; Furusawa et al., 2008). Ouchi et al. (2008) combined this public data set with their own imaging data taken with Suprime-Cam through two narrowband filters, (Å, Å) and (Å, Å), and constructed samples of and LAEs over a sky area of deg. These numbers are the logical sum of the spectroscopically-confirmed and photometrically-selected LAEs in Ouchi et al. (2008). They are selected as objects with narrow-band excesses and IGM absorption features shortward of Lyman seen in color-color diagrams. The line-of-sight depth corresponding to the FWHM of the narrow-band filter is comoving Mpc for NB503 and comoving Mpc for NB570. For all LAEs, -diametre aperture magnitudes were measured in each bandpass (Ouchi et al., 2008).

About % of the SXDF Suprime-Cam field was imaged in the , , and bands with the wide-field near infrared camera WFCAM on the UKIRT in the UKIDSS/UDS project (Lawrence et al., 2007). The UKIDSS/UDS is underway, and we use Data Release 3 for this study. We align the images with the SXDS optical images using common, bright stars, and then smooth them with Gaussian filters so that the PSF sizes of the images match those of the optical images (FWHM ). The limiting magnitudes over a -diametre aperture are calculated to be , , and . Because the zero-point magnitudes for the images are given in the Vega system, we convert them into AB magnitudes using the offset values given in Table 7 of Hewett et al. (2006).

The SpUDS covers deg of the overlapping area of the SXDS and UDS fields (Figure 1). This deg area corresponds to an effective survey volume of Mpc for LAEs and Mpc for LAEs, respectively. All of the SpUDS IRAC images are geometrically matched to the optical images. We calculate the limiting magnitude over a -diametre aperture to be , , , and in the , , , and m IRAC bands, respectively.

### 2.2 Photometry

In this paper, we only analyse LAEs in the overlapping area of deg where the Suprime-Cam, WFCAM, and IRAC data (either channel 1+3 or 2+4) are all available. We perform , , and photometry with a -diametre aperture at the position of LAEs in the narrowband images, using the IRAF task apphot.

We then convert -diametre aperture magnitudes in the optical and bands into total magnitudes in the following manner. First, we select bright and isolated point sources in the -band image, the deepest among all the images, and measure fluxes in a aperture and in a series of larger apertures up to with an interval of of . Since we find the fluxes to level off for apertures, we define -aperture magnitudes as total magnitudes. Then, we select point sources in the -band image, measure fluxes over and apertures, and calculate an accurate offset between these two aperture magnitudes to be mag. For each of the optical and bandpasses, we subtract mag from -aperture magnitudes to obtain total magnitudes for our LAEs.

For the Spitzer/IRAC four bands, we measure -diametre aperture magnitudes for each LAE and converted them to total magnitudes by applying the aperture correction given by MUSYC survey222
. The correction values are , , , and mag for m, m, m, and m, respectively.

### 2.3 The LAE samples used for the stellar population analysis

Table 2 summarises our LAE samples used for the stellar population analysis. Our original sample consists of LAEs at and LAEs at , among which and have been spectroscopically confirmed, including two newly confirmed objects using Magellan/IMACS (Section 2.5).

We regard an object as LAE with AGN and exclude it from our analysis if it has a counterpart either in the XMM-Newton X-ray catalogue (Ueda et al., 2008) or in the VLA radio catalogue (Simpson et al., 2006), or its spectrum has emission lines typical of AGN, such as like SiIV, CIV, and HeII (for details, see Section 4.6 in Ouchi et al., 2008). It should be noted, however, that we cannot completely exclude contamination from X-ray-faint, radio-quiet, and/or heavily obscured AGNs.

In the stellar population analysis, we treat objects detected in the band individually, while we stack -undetected objects at each redshift to make an average SED and fit it with stellar population synthesis models. The band corresponds to the rest-frame and bands for and , respectively, both of which are redward of the Å break. We find that the stacked objects of the two redshifts are both detected in . Since as high as of our sample are undetected in (see below), the stacked SEDs of -undetected objects is considered to represent closely the whole LAE population at the two redshifts.

### 2.4 K-detected LAEs

Among a total of () LAEs at (), () are found to be brighter than the -band magnitude (i.e., mag). Among these , () objects at () are found to host AGN (judged from the X-ray and radio data and spectroscopic data as described above), and objects at are found to be significantly confused by their neighbouring objects. we do not use them for the stellar population analysis. We then visually inspect the images of the remaining -bright objects, and find that one object is likely to be a false detection, because it is not detected in any of the other IR bands (, , and IRAC bands) and it falls on a low quality part of the -band image. Next, we examine the SEDs of the remaining objects over the range from the band to the IRAC m band, to find that one has an SED consistent with a late-type star, with a peak near the band. After removal of these two objects, the number of LAEs brighter than is five for and six for . Hereafter, we call them -detected LAEs. Table 3 summarises their photometry, , EW, and redshift.

We have found that the source center of NB503-N-21105 in the narrow band (Ly) offsets from those in the broad bands (continuum) by about one arcsec. We thus cannot rule out the possibility that NB503-N-21105 is an LAE with a chance projection of a galaxy along the line-of-sight. However, the two components are more likely to be physically connected, because the narrow-band image is elongated to the direction of the offset.

NB570-N-32295 has a power-law like spectrum over the whole wavelength range up to m. Although we find that this spectrum is reproduced reasonably well by a stellar system (see Section 3.2), we cannot completely rule out a possible contamination from an AGN.

### 2.5 New Spectroscopy of Two Red Objects

Six out of the -detected LAEs have been spectroscopically identified by Ouchi et al. (2008) and Ouchi et al. in preparation. Among the remaining five, we selected two red objects, NB503-N-21105 and NB570-N-32295, and carried out spectroscopy with the Inamori Magellan Areal Camera and Spectrograph (IMACS) on the Magellan I Baade m telescope at the Las Campanas Observatory. The observation was made on 2008 December 19 with the WB filter and the lines mm grism whose blaze angle is degrees. We chose a slit width of . The on-source exposure time was seconds under the seeing condition. The spectral coverage was Å. The spectral resolution and the corresponding velocity resolution are and km s at Å, and and km s at Å. The data were reduced with the COSMOS pipeline version 2.12.

We present the reduced 2D and 1D spectra in Figure 2. Both objects have a single, strong emission line ( detection for NB503-N-21105 and detection for NB570-N-32295) and have no other emission line or detectable continuum emission444There is an emission-like feature around [C IV] in the spectrum of NB570-N-32295. We find, however, that there is a strong sky emission line at this wavelength and that this feature is statistically insignificant, being consistent with a residual of sky subtraction.. The central wavelength of the single line is Å for NB503-N-21105, and Å for NB570-N-32295. We conclude that both objects are a real LAE from the following discussion. If NB503-N-21105 is an [O III] ([O II]) emitter, H ([O III]) emission should be detected at Å ( Å). Similarly, if NB570-N-32295 is an [O III] ([O II]) emitter, H ([O III]) emission should be seen at Å ( Å). We summarise the spectroscopic results in Table 4.

### 2.6 Stacking of K-undetected LAEs

Among the LAEs fainter than the magnitude, () at () have all broadband data from to m and do not show AGN features, to be used for the stellar population analysis. We call these LAEs -undetected LAEs. We make median-stacked multi-waveband images separately for the two redshifts. Table 5 summarises their photometry, average , EW derived from narrow-band and -band magnitudes, and redshift. In Figure 3, we show the histograms of the rest-frame Ly EWs for all and -undetected LAEs, to confirm that the -undetected LAEs are representative of the whole sample.

### 2.7 Applications of Broadband Color Selections

#### 2.7.1 LBG Selection

We examine whether the six -detected LAEs at are selected as LBGs, by applying the colour selection criteria for LBGs (e.g. Ouchi et al., 2004; Yoshida et al., 2006). None of them are found to meet the criteria. This is probably because our objects tend to have redder UV slopes than typical LBGs, or the -band image is not deep enough to detect Lyman break, or the redshift of is close to the edge of the redshift range covered by the selection criteria.

In addition, we apply the colour criteria to the -undetected LAEs at and find that only seven satisfy the criteria. We also find that the stacked LAE at does not meet the criteria.

#### 2.7.2 DRG Selection

We then apply the colour criterion for distant-red galaxies (DRGs), , to our sample, and find that none of the -detected LAEs and the two stacked LAEs satisfies the DRG criterion. We also apply the colour criterion to the best-fit model SEDs for these LAEs derived from our SED fitting (Section 3). Among the 11 -detected LAEs, model SEDs for three (NB503-N-21105, NB570-N-32295, and NB570-C-24119) meet the criterion. The former two have very red SEDs and have very large dust extinction (). We will focus on this kind of LAEs in Section 4.2.

## 3 Sed Fitting

### 3.1 Method

After obtaining rest-frame UV-to-optical photometry for the -detected and stacked LAEs, we analyse their stellar populations by the standard SED fitting method (e.g., Furusawa et al., 2000; Papovich et al., 2001). We use the stellar population synthesis model of GALAXEV (Bruzual & Charlot, 2003, hereafter BC03) to produce model SEDs. Most of the previous studies have used BC03 (Table 6). We make a large set of mass-normalised model SEDs, varying star-formation timescale, age, and dust extinction (or ). These SEDs are then redshifted to and and convolved with ten bandpasses, , and IRAC four bands, to calculate flux densities. For each LAE, we search for the best-fit SED that minimizes

 χ2=∑i[f(i)obj−Mstarf(i)model(age,E(B−V)⋆,τ)]2σ2(f(i)obj), (1)

where is the observed flux density in the -th bandpass, is the mass-normalised model flux density in the -th bandpass, is the star-formation timescale, and is the photometric error in the -th bandpass. Because is the amplitude of a model SED, we obtain the best-fit for each set of (age, , ) by solving , and calculate . Then we search for the set of the best-fit parameters that gives the minimum . The errors in the best-fit SED parameters correspond to confidence interval () for each parameter.

We do not use either - or -band photometry in the fitting, since -band photometry suffers from the IGM absorption shortward of the Lyman wavelength and -band photometry is contaminated from Ly emission. The amount of the IGM absorption considerably differs by the line of sight. Ly fluxes can be estimated from narrow and broad band photometry, but they have an uncertainty of a factor of (see Figure 15 of Ouchi et al., 2008). The shortest broadband we use for SED fitting is the band, which corresponds to Å and Å for and LAEs. These wavelengths are very close to Ly and short enough to cover the wide range of SEDs.

We adopt Salpeter’s initial mass function (Salpeter, 1955) with lower and upper mass cutoffs of and . We fix the metallicity to , considering the fact that LBGs at tend to have subsolar metallicies at (a strongly lensed LBG, cB58: Pettini et al., 2000; Teplitz et al., 2000) and (four bright LBGs: Pettini et al., 2001). Although Shapley et al. (2004) reported that very massive LBGs with have approximately the solar metallicity, Erb et al. (2006) found that less massive () LBGs at similar redshifts have subsolar metallicities (see also, Maiolino et al., 2008). It appears to be reasonable that the metallicites of typical LAEs are lower than (and at most comparable to) those of typical LBGs.

We also examine models with and , and find that while the best-fit stellar mass is insensitive to metallicity over this range, the best-fit age and dust extinction become higher with decreasing metallicity. However, the dependencies of age and dust extinction on metallicity are not so strong: for both parameters, the change from the best-fit value for the model is within its errors.

The star formation timescales examined are (i) constant star formation and (ii) exponentially decaying star formation with four -folding times of Gyr, and we search for the best-fit SED separately for the cases (i) and (ii). As explained in the next section, we adopt the results for constant star formation for our discussion of stellar populations. For dust extinction, we use Calzetti’s extinction law (Calzetti et al., 2000) and vary over and with an interval of .

Models of constant star formation have three free parameters, stellar mass, age, and dust extinction, while models of exponentially decaying star formation have one more parameter, -folding time.

### 3.2 Results

Figures 4 and 5 show the results of the SED fitting for objects at and . For each object, the blue and red curves correspond respectively to the best-fit SEDs for constant star formation and for exponentially decaying star formation. Both SEDs give similarly good fits for most of the objects, implying a difficulty in constraining the star formation history.

The best-fit parameters are summarised in Table 7 for constant star formation and Table 8 for exponentially decaying star formation. The reduced tends to be slightly larger for the model of exponentially decaying star formation. This may be because the -folding time interval adopted is too large ( dex) to fine-tune model SEDs. In any case, adding the -folding time as a free parameter does not significantly improve the fit.

It is found from these tables that the two models give very similar stellar masses, and thus that the stellar mass is a robust parameter against the assumed star formation history. Dust extinction is also relatively insensitive to the star formation history. The only exception is NB570-W-59558, for which for constant star formation and for exponentially decaying star formation. On the other hand, age and SFR largely differ between the two models for some objects. The ages of two objects (NB570-C-24119 and NB570-W-59558) differ by more than one order of magnitude, and the SFRs of seven objects (NB503-S-65716, NB503-S-94275,NB503-N-21105, NB503--undetected, NB570-C-24119, NB570-N-32295, NB570-W-59558) differ by more than one order of magnitude. All but one of these seven objects have Gyr, i.e., burst-like star formation histories. In other words, these objects are equally well fitted by two extremes, constant star formation and burst-like star formation, and our data cannot discriminate between them. It will be resolved by deeper NIR imaging (e.g., Pozzetti & Mannucci, 2000) and/or other independent observations such as submillimetre imaging.

In the following discussion, we will adopt the results for constant star formation, because (i) the values of reduced are lower for constant star formation for all but one object and (ii) it is easy to compare our results with previous SED studies on LAEs since most of them have also adopted constant star formation.

Most of the LAEs have a brighter -band magnitude than the best-fit SED. The reason for this discrepancy is not clear, but a possible reason is that the -band flux density is affected by [O III] and H emission. On the basis of the relations between SFR and [O III] and H emission strengths (Kennicutt, 1998; Moustakas et al., 2006), we find that these lines may significantly increase -band flux densities if SFR is higher than [ yr]. However, since most of the objects have SFR yr, this effect cannot explain the observed excesses. Another possible reason is that a relatively faint magnitude, , is adopted for the boundary of -detection. Our -detected sample may include objects whose magnitude happens to be brighter than the true value due to positive sky noise at the position of the objects. However, most of the -detected objects are also detected in at least one of the , , and the four IRAC bands, suggesting that they are truly bright in the near-infrared wavelengths and thus that the systematic brightening of is not very strong. We infer that the systematic brightening of , if any, does not significantly affect the best-fit SEDs which are determined from the overall shapes of observed SEDs from to IRAC m bands. Indeed, we perform the SED fitting excluding photometry, and find that for any object the best-fit parameters which are different from the original values only within the errors, although the best-fit stellar masses tend to be slightly ( dex) smaller.

Most of the errors in the best-fit parameters of NB503--undetected are larger than those of NB570--undetected in spite of a larger number of objects being stacked in NB503. This is because NB503--undetected is fainter in most bandpasses as shown in Table 5. The LAE sample includes fainter objects than the sample since the limiting magnitude in NB503 is fainter by mag (see Section 2.2 in Ouchi et al., 2008). Thus, the -undetected objects in the sample are on average fainter than those in the sample. We also note that the reduced is smaller for NB503--undetected. We infer that this is not only because the observed -band flux density for NB570--undetected is much brighter than the best-fit SED (see Figure 5), but also because the magnitude errors of NB503--undetected are larger.

Some new population synthesis models include thermally pulsating asymptotic giant branch (TP-AGB) stars (e.g., Maraston, 2005; Bruzual, 2007). Inclusion of TP-AGB stars should have little effect on the SED fitting for most LAEs, because LAEs are in general very young and have subsolar metallicities (e.g., Pentericci et al., 2009; Gawiser, 2009). In our sample, however, four objects (NB503-N-42377, NB503-S-45244, NB570-W-55371, and NB570-C-24119) have relatively old ages of Myr and thus their NIR fluxes could be dominated by TP-AGB stars. We fit a new version of GALAXEV which includes TP-AGB stars (Charlot & Bruzual, in preparation) to these four, and obtain almost the same results as for BC03, except decreases in stellar mass of dex.

## 4 Results and Discussion

Figure 6 shows the distributions of the best-fit parameters derived from the SED fitting. The stellar masses of the -detected LAEs are distributed over , while those of the -undetected LAEs are much less massive (). The -detected LAEs have a large variety of dust extinction with , while the -undetected LAEs have mild dust extinction. The ages of our LAEs are distributed over around yr. The age distribution of the -detected objects could be bimodal, although its statistical significance is low. The ages of the -undetected LAEs are around the median of the -detected LAEs. The SFRs of the -detected LAEs span a wide range of yr, while those of the -undetected LAEs are between yr.

The of NB570--undetected is significantly larger than that of NB503--undetected. This may merely reflect the fact that NB570--undetected is more massive and thus has produced more metal. On the other hand, this could reflect some evolution of the LAE population between the two redshifts. Indeed, it is found in Table 9 that LAEs at can have comparable to or larger than that of NB570--undetected.

We find that four objects have extremely large extinction : NB503-N-21105, NB570-N-32295, NB570-S-88963, and NB570-W-59558555This object is equally well fitted by two extremes: a young and dusty starburst galaxy with constant SFH, and an old and dead galaxy with exponentially decaying SFH. This is caused by the age-dust degeneracy. Although our data cannot discriminate between them, we treat this object as a young and dusty starburst galaxy in this section (see details in Section 3.2). Their properties (other than age) are clearly different from the other LAEs, as we can see in the following subsections. We label the four objects as R1 – R4 in most of the forthcoming figures. These four red LAEs may be a distinct population, and we will discuss this in Section 4.2.

### 4.1 Correlations among Stellar Population Parameters

Table 9 summarises the results of the stellar population analysis of LAEs reported so far. In this subsection, we examine correlations among stellar population parameters, referring to the previous studies.

#### 4.1.1 M1500−MV versus M1500

Figure 7 plots in large symbols rest-frame UV-to-optical colour () against UV(Å) absolute magnitude () for our LAEs. For conservative discussion, rest-frame Å and -band absolute magnitudes of our sample are derived from the best-fit SEDs, not from observed - and -band photometry (see details in Section 3.2).

For the -detected LAEs, nine are distributed in a similar region in the versus plane to the LBGs. The remaining two are faint in and extremely red (). Indeed, these are two of the four dusty LAEs, R1 and R2. On the contrary, the -undetected LAEs, which occupy % of our sample, have bluer colours and much fainter magnitudes than the LBGs. The existence of -bright LAEs suggests that not all LAEs at are low-mass galaxies with blue colours and that LAEs are a heterogeneous population with wide ranges of stellar mass, age, and/or dust extinction (e.g., Lai et al., 2008; Finkelstein et al., 2008, 2009; Pentericci et al., 2009).

We also compare our LAEs with those in the literature at similar redshifts. The IRAC-detected LAEs by Lai et al. (2008) have similar and to the LBGs. On the other hand, the NIR-undetected LAEs by Gawiser et al. (2007) and Lai et al. (2008) have as blue colours and faint magnitudes as our -undetected LAEs. The NIR-undetected LAE by Nilsson et al. (2007) has redder than the other NIR-undetected LAEs, probably because their -band image is relatively shallow (Table 1).

#### 4.1.2 Stellar Mass versus MV and M1500

The left panel of Figure 8 shows stellar mass as a function of rest-frame -band absolute magnitude for our LAEs calculated from best-fit SEDs. As expected, the -detected LAEs have comparable stellar masses to the -detected LBGs, spanning over , while the -undetected LAEs are much less massive, with . Our results broadly agree with previous studies. This figure shows that LAEs have a wide range of stellar mass.

The dashed lines indicate four mass-to-luminosity ratios. It is found that our -undetected LAEs have slightly lower ratios than the average -detected LAEs and LBGs, suggestive of younger ages.

The right panel of Figure 8 plots stellar mass against rest-frame UV absolute magnitude. All but two of the -detected LAEs are distributed in a region similar to the LBGs. The two exceptions are R1 and R2. The very faint magnitudes with respect to high of R1 and R2 are mainly due to the extremely large dust extinction (see Table 7). The -undetected LAEs are much fainter in UV wavelengths and much less massive than the LBGs.

#### 4.1.3 Star Formation Rate versus M1500 and L(Lyα)

The left panel of Figure 9 plots the star formation rate against the rest-frame UV absolute magnitude. For all objects SFRs are calculated from the best-fit SEDs. For the case of , SFR approximately correlates with , and we plot this correlation with the dotted line using (Madau et al., 1998):

 SFR[M⊙yr−1]=L1500[ergs−1Hz−1]8×1027. (2)

Reflecting the wide range of , the -detected objects are widely scattered above the dotted line. Some objects with very low extinction are located on the dotted line, while the four objects with extremely large extinction (R1 – R4) have SFRs more than two orders of magnitude higher than those expected from the observed . Except for R1 – R4, the -detected LAEs have similar ranges of SFR and to the LBGs.

The -undetected LAEs have SFRs of yr and their offsets from the dotted line are within an order of magnitude because of the modest dust extinction. NB570--undetected is offset nearly an order of magnitude because of its relatively heavy dust extinction (Table 7).

The right panel of Figure 9 shows star formation rate versus observed Lyman luminosity. Based on the relation between H luminosity and star formation rate (Kennicutt, 1998) under case B approximation (Brocklehurst, 1971), star formation rate is related with Lyman luminosity as:

 SFR[M⊙yr−1]=9.1×10−43L(Lyα)[ergs−1]. (3)

The dotted line shows this relation. Star formation rates derived from SED fitting are found to be higher than those from equation (3). This can be explained by several reasons. Ly photons can be attenuated by dust, and scattered in the interstellar and intergalactic medium. Ly photons are resonantly scattered and heavily attenuated especially under a homogeneous ISM. Intrinsically, the Ly emissivity is also affected by the age, metallicity, and IMF. In addition, the of objects without spectroscopic redshifts tends to be underestimated due to the triangle shapes of the narrow-band filters. NB570--undetected lies well above equation (3), probably due to its relatively large .

#### 4.1.4 Stellar Mass, Age, and E(B−V)⋆ versus EW(Lyα)

The top panel of Figure 10 shows stellar mass versus EW(Ly). The -detected objects are massive and have a wide range of EW(Ly) over Å, but mostly in the range Å. On the other hand, the -undetected objects are less massive and have consistently high values of Å. Considering that the -undetected objects closely represent the whole LAE population, we can conclude from this figure that massive LAEs with high EW(Ly) are rare.

There is a weak anti-correlation between stellar mass and EW(Ly), if the four red objects (R1 – R4) are excluded. This anti-correlation is qualitatively consistent with the finding by Pentericci et al. (2009) in their LAE sample from to that more massive objects have in general smaller EW(Ly).

This anti-correlation is not due to the Lyman emission of more massive objects being more heavily absorbed by dust. For example, NB570-W-55371 has a small extinction () and a small EW(Ly) ( Å), while NB503-S-94275 with a moderate extinction () has a large EW(Ly) of Å and the -undetected objects with have a large EW(Ly) of Å. Indeed, the bottom panel of Figure 10 shows no significant correlation between and EW(Ly). A cause of the anti-correlation may be that the geometry of dust in LAEs changes with stellar mass in the sense that more massive galaxies have a less clumpy distribution for some reason. As Neufeld (1991) points out, the fraction of Ly photons escaping from a galaxy is higher for a clumpy cloud distribution than for a uniform distribution. This effect can explain the observed SEDs of LAEs at (Finkelstein et al., 2009).

The middle panel of Figure 10 shows stellar age versus EW(Ly). There seems to be a weak anti-correlation between stellar age versus EW(Ly).

In the bottom panel of Figure 10, the small squares indicate the four averaged values of LAEs at by Pentericci et al. (2009). A probable reason for their very small is that they have been selected using the LBG technique and thus have blue colours. The crosses represent the data for local star forming galaxies given in Giavalisco et al. (1996). In comparison to our LAEs, these local galaxies have on average smaller EWs. This might suggest a more uniform cloud distribution for local galaxies, if Neufeld (1991) picture is correct.

#### 4.1.5 Lyα escape fraction versus E(B−V)gas

We define the Ly escape fraction by:

 fesc(Lyα)=Lobs(Lyα)[ergs−1]Lint(Lyα)[ergs−1], (4)

where [erg s]