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The Subaru/XMM-Newton Deep Survey (SXDS). IV. Evolution of Lya Emitters from z=3.1 to 5.7 in the 1 deg^2 Field: Luminosity Functions and AGN

We present luminosity functions (LFs) and various properties of Lya emitters (LAEs) at z=3.1, 3.7, and 5.7, in a 1 deg^2 sky of the Subaru/XMM-Newton Deep Survey (SXDS) Field. We obtain a photometric sample of 858 LAE candidates based on deep Subaru/Suprime-Cam imaging data, and a spectroscopic sample of 84 confirmed LAEs from Subaru/FOCAS and VLT/VIMOS spectroscopy in a survey volume of ~10^6 Mpc^3 with a limiting Lya luminosity of ~3x10^42 erg/s. We derive the LFs of Lya and UV-continuum (~1500 \AA) for each redshift, taking into account the statistical error and the field-to-field variation. We find that the apparent Lya LF shows no significant evolution between z=3.1 and 5.7 within factors of 1.8 and 2.7 in L* and phi*, respectively. On the other hand, the UV LF of LAEs increases from z=3.1 to 5.7, indicating that galaxies with Lya emission are more common at earlier epochs. We identify six LAEs with AGN activities from our spectra combined with VLA, Spitzer, and XMM-Newton data. Among the photometrically selected LAEs at z=3.1 and 3.7, only ~1 % show AGN activities, while the brightest LAEs with logL(Lya)>~ 43.4-43.6 erg/s appear to always host AGNs. Our LAEs are bluer in UV-continuum color than dropout galaxies, suggesting lower extinction and/or younger stellar populations. Our stacking analyses provide upper limits to the radio luminosity and the f(HeII)/f(Lya) line fraction, and constrain the hidden star formation (+low-luminosity AGN) and the primordial population in LAEs.


Introduction
Lyα emitters (LAEs) provide clues to evolution and formation of galaxies. Most of LAEs are known as star-forming galaxies at z ≃ 2 − 7 with a faint-UV continuum, but a prominent Lyα emission line, which are produced by star-forming activities with a typical star-formation rate of ∼ 1 − 10M ⊙ yr −1 (e.g., Cowie & Hu 1998;Ouchi et al. 2003;Gawiser et al. 2006;Pirzkal et al. 2006). LAEs are believed to have a negligible fraction of AGN activities, since an X-ray detection has been reported for only one LAE at z ∼ 3 (Gawiser et al. 2006, see also Wang et al. 2004). The strong Lyα emission and a blue UV continuum color imply a young metal-poor star-forming galaxies (Malhotra & Rhoads 2002;Finkelstein et al. 2007). Recent infrared observations and population synthesis models indicate that typical stellar mass of LAEs is as small as ∼ 10 8 − 10 9 M ⊙ and that the stellar age is as young as 10 Myr (Pirzkal et al. 2006; see also Chary et al. 2005;Gawiser et al. 2006;Lai et al. 2006;Nilsson et al. 2007). LAEs show a compact UV morphology with a size smaller than 1 kpc (Pascarelle, Windhorst, Keel, & Odewahn 1996;Pirzkal et al. 2006). The fraction of LAEs (or galaxies with a Lyα emission line) increases at faint UV magnitudes (Ouchi et al. 2003;Ando et al. 2006;Shimasaku et al. 2006). These pieces of evidence suggest that LAE samples include a young low-mass population at high-z.
More interestingly, some of LAEs have a Lyα emission line with a large rest-frame equivalent width (EW) of EW 0 > 240Å that cannot be explained by a star-formation with a Salpeter IMF (Malhotra & Rhoads 2002;Dawson et al. 2004;Shimasaku et al. 2006). It is reported that about 10-40% of spectroscopically-identified LAEs have an EW 0 of > 240Å at z = 4.5 (Dawson et al. 2004) and z = 5.7 ). The population synthesis models indicate that such large EW objects would have a top heavy IMF, a very poor metallicity and/or a very young age< 10 7 yr (Charlot & Fall 1993;Malhotra & Rhoads 2002;Schaerer 2003, see also Kudritzki et al. 2000). Large-EW objects often show a spatiallyextended Lyα envelope whose projected size can be as large as 100 kpc (Steidel et al. 2000). These objects are referred to as Lyα blobs. Lyα blobs are originally discovered in an overdensity region of Lyman break galaxies (LBGs) at z ∼ 3 (Steidel et al. 2000;Matsuda et al. 2004, see also Dey et al. 2005). However, recent deep surveys also find Lyα blobs in blank fields (Nilsson et al. 2006;Saito et al. 2006). Some of these Lyα blobs show evidence of AGN activities (Dey et al. 2005), while others are not (Matsuda et al. 2004;Saito et al. 2006). Theoretical studies predict that these large-EW objects with an extended Lyα profile are candidates of cooling clouds (e.g. Yang et al. 2006) and population III galaxies (e.g. Schaerer 2003), which are at the very beginning stage of galaxy formation. Thus, LAEs are keys to understanding the early stage of galaxy formation with less-massive (or dwarf) population some of which include young galaxies even at the very beginning stage of radiating clouds and population III. The studies of LAEs complement the recent work of high-z massive and/or old galaxies (e.g. van Dokkum et al. 2006;Kriek et al. 2006;Daddi et al. 2007).
In spite of increasing observational data of LAEs, evolution of LAEs is not clearly understood. Most of observational results agree that the LF of Lyα luminosity shows no evolution at z = 3 − 6 within the errors of measurements. (e.g. Rhoads & Malhotra 2001;Ouchi et al. 2003;Hu et al. 2004;Yamada et al. 2005;van Breukelen et al. 2005;Shimasaku et al. 2006;Tapken et al. 2006;Murayama et al. 2007; c.f. Maier et al. 2003). Although these measurements qualitatively agree, the constraints on the LF evolution are weak, due to the small statistics and field variations. Indeed, the presence of large-scale structures of LAEs has been reported (Shimasaku et al. 2003;Ouchi et al. 2005a) at these redshifts, which produce a significant source gradient even within a 0.2 deg 2 field (Ouchi et al. 2003;Hu et al. 2004). Note that the narrow-band LAE studies observe a thin slice (∆z = 0.1) of the Universe whose survey volume is about 1/10 of that of dropout or LBG surveys (∆z = 1) at a given search area (see e.g. Ouchi et al. 2004b). We need to obtain statistical properties of LAEs including clustering with a good accuracy. Moreover, we should investigate rare populations of LAEs with a large EW or AGN, which are essential for understanding galaxy formation and its relation to the formation of massive black holes.
Here we carry out a systematic wide-field narrow-band survey for LAEs at z = 3.1 − 6.6 in the wide-field (1 deg 2 ) Subaru/XMM-Newton Deep Field (SXDS) that is covered by deep Subaru optical images (i ′ [5σ] = 27.0; Furusawa in preparation) and the near-infrared images of UKIDSS/Ultra Deep Survey (UKIDSS/UDS; Lawrence et al. 2006) as well as VLA (Simpson et al. 2006a), XMM-Newton (Ueda et al. in preparation), and Spitzer (Lonsdale et al. 2003). Except for the data of z = 6.6 LAEs, we have completed narrowband imaging for z = 3.1, 3.7 and 5.7 LAEs. In this paper, we show properties of LAEs at z = 3.1 − 5.7. Note that the first results from the z = 5.7 data have been presented in Ouchi et al. (2005a). Our systematic survey will not only put strong constraints on properties of LAEs at z = 3.1 − 5.7, but also give the useful baselines to be compared with higher redshift LAEs for studying reionization of the Universe (Malhotra & Rhoads 2004;Kashikawa et al. 2006).
We show photometric and spectroscopic data, and make the spectroscopic samples in Section 2. We define the photometric samples of LAEs in Section 3. The AGNs in our LAE samples are presented in Section 4. We derive LFs of LAEs and investigate evolution of the LF in Section 5. In Section 6, we address the properties of LAEs, such as EW, UV-continuum slope, star-formation rate, and AGN activity. We discuss our results and summarize them in Sections 7 and 8, respectively. We will present clustering and stellar population of these LAEs in two companion papers of Ouchi et al. (in preparation) and Ono et al. (in preparation).
We do not use, either contaminated areas with halos of bright stars and CCD blooming or low signal-to-noise (S/N) regions located around the edge of the FoV, which are caused by dithering. After we reject these bad areas, the effective total areas are 0.983, 0.965, and 1.034 deg 2 for NB503, NB570, and NB816 images, respectively. These effective areas correspond to the survey volumes of 7.0 × 10 5 Mpc 3 (z = 3.1), 6.1 × 10 5 Mpc 3 (z = 3.7), and 9.2 × 10 5 Mpc 3 (z = 5.7), if we assume a simple top-hat selection function of LAEs whose redshift distribution is defined by the FWHM of narrow-band filters.
During the observations, we took images of spectrophotometric standard stars of GD50 and GD71 in NB503 and NB816 bands and GD248, G93-48, and GD50 in NB570 band (Oke 1990;Bohlin et al. 1995). These standard stars were observed 1 − 4 time(s), when the sky was thought to be photometric. We calculate photometric zero-points from photometry of standard stars. We check these photometric zero points with the narrow-and broadband images by comparing with colors of stellar objects in our field and 175 Galactic stars calculated from spectra given in Gunn & Stryker (1983). We find that the colors of stellar objects in our data are consistent with those of Gunn & Stryker's stars within 0.01 − 0.05 magnitude. The photometric-zero points thus obtained are regarded as more accurate than 0.05 mag in the entire 1 deg 2 field.
Our narrow-band images are registered to match the coordinates of SXDS broad-band images based on hundreds of stellar objects commonly detected in both narrow-and broadband images. The astrometry of our objects is the same as those of SXDS version 1.0 catalog (Furusawa et al. in preparation). The errors in the relative positions of objects are ∼ 0 ′′ .04 in r.m.s. The r.m.s accuracy of the absolute positions is estimated in Furusawa et al. (in preparation) to be ∼ 0 ′′ .2. After the registration, we homogenize the PSF sizes of broad and narrow-band images, referring to these stellar objects. The PSF sizes of narrow-band images match to those of broad-band images with an accuracy of δFWHM ≃ 0 ′′ .01.

Photometric Catalogs
Source detection and photometry are performed using SExtractor (Bertin & Arnouts 1996). We measure both MAG AUTO of SExtractor and 2 ′′ .0-diameter aperture magnitudes. We adopt MAG AUTO as total magnitudes, while we use a 2 ′′ .0-diameter aperture magnitude to measure colors of objects in order to obtain colors of faint objects with a good signal-to-noise ratio. We make NB503-, NB570-, and NB816-detection catalogs, and limit to NB503 < 25.3, NB570 < 24.7, and NB816 < 26.0, respectively, that correspond to about 5σ detection limits on a 2 ′′ .0-diameter aperture. Our NB503-, and NB816detection catalogs contain 98,907,64,362,and 278,458,respectively. We correct the magni-tudes of objects for Galactic extinction of E(B − V ) = 0.020 (Schlegel, Finkbeiner, & Davis 1998).

Spectroscopic Data
We carried out spectroscopic follow-up observations for our LAE candidates with Faint Object Camera and Spectrograph (FOCAS; Kashikawa et al. 2002) Yamada et al., and Sekiguchi et al., the slits of our objects shared the eight MOS masks with those of the other targets. The on-source exposure time ranges typically from 7200 to 10800 seconds. These spectroscopic observations were made with SY47 order-cut filter and 300 lines mm −1 grating having the blaze wavelengths of 5500Å (300B) with a slit width of 0 ′′ .8. The spectral range and resolution are λ = 4900 − 9400Å and λ/∆λ ≃ 500 − 1000, respectively.
The VIMOS spectroscopy was conducted in the programs of Simpson et al. (in preparation) and Saito et al. (2007). The Simpson et al.'s observations were made between UT 2004 Dec 17 and UT 2006 Jan 2. The medium resolution grating was used with the GG475 order sorting filter, which provides a spectral resolution λ/∆λ ≈ 580 over the wavelength range 4800Å-1 µm. Each mask was observed with 1 × 2700 + 2 × 1350 second exposures, often on separate nights. Data reduction is described in detail in Simpson et al. (in preparation) but broadly followed the standard pipeline method. The Saito et al.'s observations were carried out in 2004 November 6 to 9. The HR-Orange grism and the GG435 order-cut filter were used for MOS masks with a slit width of 1 ′′ .0. The spectral resolution of these observations is R ≈ 2160Å, which is > 2 − 4 times higher than the other observations of our spectroscopy. The effective on-source integration time was 4-7 hours. Data reduction and details of observations are described in Saito et al. (2007).

Spectroscopic Catalogs and Samples
We took spectra for objects with colors similar to LAEs which show a narrow-band excess and a continuum break in blue band. We observed 128 and 29 objects at z = 3.1/3.7 and 5.7, respectively. Since we share the MOS masks with targets from the other projects, we had tight constraints on our target selection for spectroscopy. Thus, we include unreliable LAE candidates with colors similar to foreground objects and very faint narrow-band magnitudes, some of which potentially have a bright Lyα emission line redshifted to the edge of passband of our narrow band. As a result, we have identified line emitters from 60% of our targets. Although the success rate of identification is not high by the constraints of our spectroscopy, this target selection allows us to obtain spectra for objects in wide color and magnitude ranges.
In addition to these spectra for our LAEs, we use the SXDS version 1.0 spectroscopic data taken with Subaru/FOCAS and AAO/2dF. The combination of these and our data provide 3,233 spectroscopic redshifts in our field (Akiyama et al. in preparation). We refer this catalog to estimate the contamination rates of our LAE sample in Section 3.2. Figure 2 presents the redshift distribution of our sources from the combined catalogs.
We have investigated our spectra with an emission line at the passbands of our narrow bands. We carefully check the possibilities of low-z [Oii], [Oiii], and Hα emitters. For z = 3.1 LAE candidates with an emission at ∼ 5000Å, we look at the spectrum at the wavelengths of an Hα line of a z = 0.004 [Oiii]  and [Oii] lines, respectively. However, no nebular emission lines enter in the wavelengths of our optical spectra for a z = 1.2 [Oii] emitter. Because our spectral resolution is not high enough to clearly identify an [Oii] doublet, we examine the possibility of an [Oii] emitter by the detection of blue continuum in B or V bands whose 2σ upper limits reach very deep magnitudes of B = 28.7 and V = 27.7. In this way, we discriminate low-z emitters from high-z LAEs. We also visually inspect images and spectra, and remove spurious objects. By these analyses, we have identified 41, 26, and 17 LAEs at z = 3.1, 3.7, 5.7. We refer to these 84 LAEs as the spectroscopic samples of LAEs. In Figures 3-5 we show spectra of z = 3.1 − 5.7 LAEs, together with snapshots of broad-and narrow-band images. Table 2 summarizes the properties of LAEs with a spectrum. Figure 6 plots the redshift distribution of these spectroscopically-identified LAEs at z = 3.1, 3.7, and 5.7.
3. Photometric Samples of Lyα Emitters at z = 3.1 − 5.7 3.1. Definitions of z = 3.1, 3.7, and 5.7 Lyα Emitters We plot color-magnitude diagrams in Figure 7 for objects in our photometric and spectroscopic catalogs. Each panel of Figure 7 shows narrow-band excess color and narrow-band magnitude for NB503, NB570, and NB816. Figure 8 presents two-color diagrams based on the NB503-, NB570-, and NB816-detection catalogs, together with colors of model galaxies and Galactic stars. Colors of model objects indicate that LAEs can be isolated from low-z galaxies and Galactic stars by their narrow-band excess of Lyα emission and red continuum colors.
We compare colors of galaxies in our LAE samples with those of the 3,233 spectroscopicallyidentified objects which include LAEs and foreground/background interlopers. As expected, spectroscopically-identified LAEs are located in the upper-right part of the two-color diagrams.
Based on these color diagrams, we define the selection criteria of three LAE samples: where B 2σ , V 2σ , and R 2σ are 2σ limiting magnitudes of B, V , and R images, i.e. B = 28.7, V = 27.7, and R = 28.0, respectively. With these criteria, we include the objects with no detectable continuum in V (for z = 3.1 and 3.7) and i ′ (for z = 5.7). Thus, these photometric samples are complete to the narrow-band magnitude limits, which include all the Lyα emitting objects at these redshifts either with or without a detectable-UV continuum. The narrow-band excess colors, V − NB503 > 1.2, V − NB570 > 1.3, and i ′ − NB816 > 1.2, isolate an emission line object at each redshift with a flat continuum (f ν =const) whose restframe EW is greater than ≃ 45Å. Note that the actual EW limits for our LAE samples are different from ≃ 45Å, since LAEs do not have a flat continuum, but a continuum break, i.e. Gunn-Peterson trough, between blue and red sides of Lyα emission. Thus, the narrow-and broad-band colors do not provide a clear limit of EWs. We estimate the limits of rest-frame EWs to be approximately ∼ 64Å, ∼ 44Å, ∼ 27Å for our z = 3.1, 3.7, and 5.7 LAE samples with models of our Monte-Carlo simulations described in Section 5.1.
We apply these selection criteria to our photometric catalogs. We use NB503-, NB570-, and NB816-detection catalogs and find 356, 101, and 401 LAEs at z = 3.1, 3.7, and 5.7, respectively. In this way, we obtain LAE samples composed of 858 photometrically-identified LAEs in total. We refer to these 858 LAEs as the photometric samples of LAEs, which are summarized in Table 3. Note that these photometric samples are purely composed of objects satisfying the selection criteria of eq. (1), (2), or (3). Our photometric samples do not include spectroscopically-identified LAEs escaping from the photometric criteria.
Figures 9-11 show surface densities of LAEs. The red circles are the average surface densities. The black points with 5 different symbols indicate the surface densities in 5 subfields (≃ 0.2 deg 2 ) of Suprime-Cam, i.e., SXDS-C, -N, -S, -E, -W. The detection completeness is corrected with the simulations described in Section 3.2. For these completeness-corrected points, the difference of surface densities among the five ≃ 0.2 deg 2 fields are negligible for all narrow-band detected objects, but are as large as a factor of, say, ≃ 2 − 5, for LAEs. These large differences probably come from field-to-field variation as well as Poisson errors. We evaluate the field-to-field variation in our survey area, σ g , with where σ DM and σ DM :1F oV are the rms fluctuation of dark matter in all the survey volume of 1 deg 2 and Suprime-Cam's 1-FoV volume (≃ 0.2 deg 2 ), respectively. We calculate the fluctuations of dark matter with the power spectrum, adopting the transfer function given by Bardeen, Bond, Kaiser, & Szalay (1986). σ g:1F oV is the fluctuation of number density of LAEs for the 1 FoV. Σ g:1F oV andΣ g are LAE's surface densities of the 1 FoV and the average of survey area.
Since these estimates of field-to-field variation are based on a large but single contiguous field, it is important to check whether our field is located at the sky of an overdense or underdense region. In fact, a large-scale overdensity or underdensity of Lyα sources could also be produced by an inhomogeneous distribution of Lyα absorbers (i.e. neutral hydrogen) along the line of sight.
In Figure 11 we compare the surface densities of our LAEs with those on completely different sky areas but selected with the same NB816 filter by Shimasaku et al. (2006) and Hu et al. (2004). We find that the surface densities of our z = 5.7 LAEs are consistent with those of Shimasaku et al. (2006) and Hu et al. (2004) within the scatters and Poisson errors of our 5 sub-fields. Moreover, Figure 11 shows that Shimasaku et al.'s and Hu et al.'s measurements scatter around our average surface-density curve. Thus, we conclude that our single contiguous 1 deg 2 field has no signature of overdensity or underdensity, and that our 5 sub-fields represent the average field-to-field variation.
In the same manner as the calculations of surface densities, Figure 12 plots color distributions with the uncertainties of field variance for our LAE samples. In Section 5.1, we compare these color distributions (as well as the surface densities) with those reproduced by our Monte-Carlo simulations, and determine the best-estimates of luminosity function by χ 2 fitting.

Completeness and Contamination of the Samples
First, we estimate the detection completeness of each narrow-band images, f det , as a function of narrow-band magnitude. We distribute 7875 artificial objects that mimic LAEs on our original 1 deg 2 images after adding photon noise, and detect them in the same manner as for the detection of our LAE catalogs with SExtractor. We repeat this process 10 times, and compute the detection fraction. We find that the detection completeness is typically 80 − 90% for relatively luminous sources which are 0.75 magnitude brighter than the magnitude cuts of our samples (i.e. NB503 ≤ 24.55, NB570 ≤ 23.95, and NB816 ≤ 25.25). The detection completeness is 50 − 60% even for the faintest magnitude bin of our samples (i.e. NB503 = 24.8 − 25.3, NB570 = 24.2 − 24.7, and NB816 = 25.5 − 26.0). Second, we estimate the contamination of our photometric LAE samples, which we need to consider in calculating the LF. We use our spectroscopic catalog of 3,233 objects (Section 2.4). We define the contamination fraction, f cont , with where N in LAE and N in all are the numbers of spectroscopically-identified LAEs and all spectroscopic objects, respectively, lying in our color criteria (i.e. eqs 1-3).
Since we have spectroscopic objects with no identification (see Section 2.4), we calculate f cont for the following two extreme cases. If we omit the unclear objects, we find N in LAE /N in all = (29/29, 14/14, 11/11) for z = (3.1, 3.7, 5.7). Note that we see no obvious interlopers in our photometric samples. In case that all the no-identification objects are interlopers, N in LAE /N in all = (7/8, 6/7, 3/4), where we take magnitude cuts of (NB503, NB570, NB816) = (24.0, 24.0, 24.5) that are bright enough to be completely identified by our spectroscopy. Thus, the contamination rates are taken within the ranges of f cont = (0 − 13%, 0 − 14%, 0 − 25%) for z = (3.1, 3.7, 5.7) photometric LAE samples, respectively. Since these contamination rates are negligibly small, we do not correct them for contamination. It is notable that statistical errors from contamination cannot be as large as ∼ 30%.

AGN and Multi-Wavelength Detection in our Samples
We identify AGNs in LAEs with our spectra and SXDS multi-wavelength images of radio, sub-mm, mid-infrared, and X-ray, and investigate AGN activities in out LAEs. We summarize the properties of these AGNs in Table 4. In this section, we formally define the positional uncertainty of optically-identified LAEs, σ opt = F W HM/2.35, with a FWHM of narrow-band morphology.

Spectra with AGN signatures
We find 3 and 1 objects at z = 3.1 and 3.7 whose spectrum shows high-ionization lines, such as Nv, Civ, Heii, and Ciii], originated from AGN activities. Figure 13 plots spectra of these four objects. All of these AGNs show broad lines in these high-ionization lines with a line width of v FWHM 1000km −1 , although the line width for one of these object, NB503-N-35820, has a large uncertainty. Radio bright objects, i.e. radio galaxies, are also included in our sample. The properties of these AGNs are presented in Table 4.
We also find that NB503-N-42377 shows a marginal (∼ 2σ) Civ emission. Although a typical high-z AGN has a line ratio of Lyα/Civ= 5 − 10 (e.g. McCarthy 1993), NB503-N-42377 has Lyα/Civ 25. With the facts of the marginal Civ detection and the large flux ratio of Lyα/Civ, we rule out an AGN being the dominant power source of Lyα for NB503-N-42377, and do not classify this object as an AGN.

X-ray Detection
We use a deep XMM-Newton EPIC image of SXDS, and identify an X-ray counterpart of LAEs with the combined X-ray catalog of SXDS ver 5.0 (Ueda et al. in prep.). This X-ray catalog is made of sources with a detection likelihood greater than 7 in either of 6 bands, 0.3-0.5, 0.5-2, 2-4.5, 4.5-10, 0.5-4.5, and 2-10 keV (see Ueda et al. in prep). We calculate a combined positional error by taking a sum of square errors of optical and X-ray positions. Although there are 3 X-ray counterpart candidates with a < 2σ level of the combined error, we find by our visual inspection that one of the candidate, NB503-N-87126, clearly appears to be confused by the neighboring foreground objects. This X-ray counterpart is regarded as a foreground object. We thus identify 2 X-ray counterparts; 1 and 1 counterparts at z = 3.1 and 3.7, respectively (Table 4). No counterparts are found for z = 5.7 LAEs.

Infrared Detection
The Spitzer MIPS 24µm-band image is investigated for infrared counterparts of LAEs. We use relatively shallow data of the Spitzer Wide-area InfraRed Extragalactic (SWIRE; Lonsdale et al. 2003) survey. The SWIRE MIPS data cover almost entire SXDS field of a 0.9 deg 2 , and miss only 13, 6, and 15 LAEs 1 at z = 3.1, 3.7, and 5.7, respectively, which are located at the edge of our SXDS-W field (see Figure 1 of Morokuma et al. 2007 submitted). The depth of MIPS data is σ = 48µJy (Shupe et al. in preparation; see Ivison et al. 2007). We run SExtractor to detect and measure source fluxes with a 12 ′′diameter aperture. We apply the aperture correction of a factor of 1.698 to the aperture fluxes (see http://ssc.spitzer.caltech.edu/mips/apercorr/). We have cross matched our LAEs with MIPS sources detected at a > 5σ level, i.e. > 240µJy. We find 3 (and 0) MIPS counterparts at z = 3.1 (at z = 3.7 and 5.7) within the 3σ positional allowance of our LAEs (Table 4).

Sub-mm Detection
We compare the positions of LAEs with SCUBA 850µm sources of Submm HAlf-Degree Extragalactic Survey (SHADES; Coppin et al. 2006). The rms noise level is ≃ 2.2mJy. The SHADES image covers an ∼ 360 arcmin 2 area at the center of SXDS-C, which corresponds to about 10% of our 1 deg 2 SXDS field. In this SHADES region, we have about 16, 6, and 3 LAEs at z = 3.1, 3.7, and 5.7, respectively. These LAEs include one X-ray emitting LAE of NB503-C-49497 at z = 3.128 (see Table 4). The beam size of the sub-mm image is as large as F W HM = 14.7 arcsec. Following Ivison et al. (2007), we search counterparts with a positional error circle of radius 8 arcsec. We find no submm counterparts in our LAEs (including the X-ray emitting LAE) located at the SHADES area. We extend our search radius up to 12.5 arcsec for completeness. We find that a z = 5.7 LAE of NB816-C-90169 falls on the large search radius of a submm source of Sxdf850.5 (Coppin et al. 2006). However, on our optical images this submm source is very likely centered at a foreground galaxy of SXDS-iC-086385 with i ′ = 21.11. Thus, we conclude that none of our LAEs has a sub-mm emission down to ≃ 3 − 5mJy in the SHADS area.

Radio Detection
We investigate radio properties of LAEs with deep VLA 1.4-GHz radio image of the SXDS (Simpson et al. 2006a). This radio image reaches an rms noise level of 12µJy beam −1 . We search a radio counterpart of LAEs in a 3x3 pixel box of the VLA image (1 pixel=1.25 arcsec). A radio source with a signal-to-noise ratio of > 5 are identified as a radio counterpart in the same manner as Simpson et al. (2006b). We then visually inspect LAEs with radio contours, and find that two LAEs are detected in the radio image 2 (Table 4).

LAEs Hosting AGN
As summarized in Table 4, we find that 4 z = 3.1 and 1 z = 3.7 LAEs have a detection in the multi-wavelength data. Figure 14 presents the spectral energy distribution (SED) of these AGN-LAEs, together with those of the average radio quiet/loud quasars (Elvis et al. 1994). We also plot a UV-optical spectrum of Telfer et al. (2002); Richards et al. (2003) that is normalized to the average SED of (Elvis et al. 1994). We refer to these average SEDs+spectrum as QSO templates.
Since the detection limits of infrared and X-ray (and radio) bands are as large as νL ν 10 44 (10 41 ) erg s −1 , LAEs with any multi-wavelength counterparts likely host AGN. In fact, we have 3 spectroscopically-identified LAEs with multi-wavelength counterparts ( Table  4). The spectroscopic classifications of these LAEs indicate that all of these LAEs have AGN. Thus, we classify all of 5(= 4 + 1) LAEs with multi-wavelength detection as AGN. In addition to these 5 AGNs identified by multi-wavelength data, we have 4 spectroscopicallyidentified AGNs. Since 3 AGNs have both a multi-wavelength detection and spectroscopic identification, the number of our LAEs with an AGN (hereafter AGN-LAEs) is 6 in total:

Lyα Luminosity Functions
We derive luminosity functions (LFs) of LAEs at z = 3.1, 3.7, and 5.7 from our photometric samples. First, we calculate LFs with a simple classical method that was taken by most of previous studies (e.g. Ouchi et al. 2003;Ajiki et al. 2003;Hu et al. 2004;Malhotra & Rhoads 2004. We obtain the number densities of LAEs in each magnitude bin by simply dividing the observed number counts of LAEs in a given narrow band by the effective survey volume defined as the FWHM of the bandpass times the area of the survey. Here, we calculate the Lyα luminosity of each object with the response curves of narrow and broad bands by subtracting the continuum emission measured from the continuum magnitude from the total luminosity in the narrow band, assuming that Lyα enters in the central wavelength of the narrow band. In this calculation, we use total magnitude of narrow-band images. The continuum emission is estimated by the narrow-band excess color (i.e. color of narrow-band and broad-band) defined with a 2 ′′ aperture, so as to keep high signal-to-noise ratios and to avoid the effects of source confusion on broad-band images with high source density. To check the accuracy of this calculation, Figure 15 compares Lyα fluxes measured from our images and spectra for our spectroscopic samples. Figure 15 shows that both measurements agree well within error bars for most of LAEs. These values mostly scatter within the range of difference of a factor of 2.
Figures 16-18 present the LFs from this classical method. Note that we corrected the detection-completeness by weighting with f det measured in Section 3.2. To check the field-tofield variation and the accuracy of our results, we plot the estimates of LFs from the entire 1 deg 2 field (filled circles), together with those from the five ≃ 0.2 deg 2 fields (open symbols). In Figures 16-17, we calculate the errors of field-to-field variations with eq. (4), and include these errors in the error bars of LFs for the entire 1 deg 2 field. We find that the field-to-field variations are as large as a factor of ≃ 2 − 5 among the five 0.2 deg 2 fields, although the typical scatters of the 0.2 deg 2 results are not far beyond the errors of Poisson statistics. Then we obtain the best-fit Schechter function (Schechter 1976 The classical method is accurate when the narrow-band filter has an ideal boxcar shape. However, since the shapes of actual filters used in LAE surveys are rather close to a triangle, the classical method potentially suffers from the following two uncertainties. (a) The narrow-band magnitude of LAEs of a fixed Lyα luminosity varies largely as a function of redshift. Thus Lyα luminosity may be over-or under-estimated for some LAEs. (b) The selection function of LAEs in terms of EW also changes with redshift; the minimum EW value corresponding to a given (fixed) narrow-band excess, such as i ′ − NB816 for z = 5.7 LAEs, becomes larger when the redshift of the object goes away from the redshift corresponding to the center of bandpass.
In order to avoid such uncertainties, we perform Monte Carlo simulations to find the best-fit Schechter parameters for the Lyα LF. These Monte Carlo simulations are developed by Shimasaku et al. (2006), and the details of simulations are described in their paper. We briefly summarize the procedure of these simulations. We generate a mock catalog of LAEs with a set of the Schechter parameters (α, φ ⋆ , L ⋆ ) and a Gaussian sigma of probably distribution of EW, σ EW . We uniformly distribute them in comoving space over the redshift range of all LAEs that can be selected with our narrow-band filter. We 'observe' these LAEs with the narrow-and broad-bands same to the real band responses (Figure 1), and add to their flux densities photon noise corresponding to the actual observation. We select LAEs by the same criteria as for selecting the actual LAEs, and derive the number densities and color distributions from the mock catalog. We compare these results with the observational measurements of number densities and color distributions. By performing this set of simulations over a wide range of the parameters, we find the best-fit Schechter parameters by χ 2 fitting. We compare the results of these simulations with the observational measurements corrected for the detection completeness, since the simulations are not affected by the detection completeness, f det . In Figures 9-12, we plot the predicted surface densities and color distributions of LAEs for some parameter sets.
The difference in χ 2 for α values is found to be insignificant. We fix the α value to -1.0, -1.5, and -2.0, and carry out χ 2 fitting, varying φ ⋆ , L ⋆ , and σ EW . Figures 9-11 present that all three models of α = −1.0, −1.5, and −2.0 reproduce the observed counts well, although shallower α gives a slightly better fit. This suggests that the Lyα LF of LAEs is approximated well by the Schechter function. The best-fit parameters, thus obtained, are summarized in Table 5. We adopt the α = −1.5 results as the fiducial set of the best-fit Schechter parameters (see Gronwall et al. 2007). Our best-fit Schechter parameters with α = −1.5 are The best-fit Schechter functions for α = −1.5 obtained above are shown in Figures 16-18 with the solid lines. Note that the LFs from the classical method (filled circles) are consistent with the best-fit Schechter functions from our simulations. This means that the simple method gives a good approximation. This is probably because the uncertainties (a) and (b) in the classical method are negligible and/or cancel with each other. The number densities of the best-fit Schechter functions are slightly larger than those of the classical method. This slight difference can be explained by the underestimates of the number density and Lyα luminosity with the classical method due to the large survey volume of the top-hat redshift distributions and the small Lyα flux measured with a bandpass of the triangle-shaped narrow bands.
Note that these best-fit LFs are based on our LAE samples selected with a limit of EW (Table 3). If we extrapolate the EW distribution down to EW = 0Å with our simulations, we can obtain estimates of the LFs for all LAEs with EW > 0Å. We refer a φ ⋆ value of LFs for all (EW > 0Å) LAEs as for φ ⋆ 0 , and present the best-fit φ ⋆ 0 in Table 5. These φ ⋆ 0 values only differ from φ ⋆ by ∼ 10%. There are two reasons for this small difference: (i) The typical distribution of EW, σ EW , is much wider than that of EW limit of our selection, EW lim (see Tables 3 and 5). (ii) the EW range missed by our selection (0 < EW < EW lim ) is significantly shorter than that of our selection (EW > EW lim ). The combination of these facts provide this small (∼ 10%-level) difference between φ ⋆ and φ ⋆ 0 .

Comparison with Previous Measurements
We overplot previous measurements of Lyα LFs for z ≃ 3, 4 and 6 in Figure 19. Our LFs of z ∼ 3 and 4 agree very well with all of the previous measurements typically within the error bars. It is noticeable that the best-fit Schechter function of Gronwall et al. (2007) (from the 0.3 deg 2 survey) shows an extremely good agreement with ours within a factor of ∼ 0.1, although the luminosity range of their measurements is limited to the relatively faint luminosity (i.e. log L ≃ 42 − 43 erg s −1 ).
In the bottom panel of Figure 19, the previous measurements of z ∼ 6 LAEs show large scatters over Poisson errors. However, our measurements are consistent with those of Shimasaku et al. (2006) (red open circles) as well as the recalculated LF of Hu et al. (2004) (squares), both of which are based on deep and moderately-wide (≃ 0.2 deg 2 ) field imaging and spectroscopy. Moreover, z = 5.7 LF of the recent 2-deg 2 imaging survey of Murayama et al. (2007) (red open diamonds) agrees with ours within 1σ error bars at log L > 43.0 erg s −1 where the measurements of Murayama et al. (2007) are complete. (Note that the imaging data of Murayama et al. (2007) are shallower than ours by ∼ 1 magnitude, and that the data points of Murayama et al. (2007) are not corrected for incompleteness.) The best-fit Schechter function of Malhotra & Rhoads (2004) (dotted line) is significantly lower than our LFs. Shimasaku et al. (2006) and Tapken et al. (2006) have also pointed out that the measurements of Malhotra & Rhoads (2004) are lower than their LFs. Our z = 5.7 LF is consistent with the measurements of Ajiki et al. (2006) (stars) and Tapken et al. (2006) (hexagon) within the error bars, but our measurements would be systematically higher than theirs. This difference is probably originated from i) the method of Lyα luminosity estimates from photometric data, ii) the detection-completeness correction and iiii) field-tofield variation raised by smaller field surveys of Ajiki et al. (2006) and Tapken et al. (2006). The differences in selection criteria for LAEs between our sample and the others are probably not a main reason for this discrepancy, since, for our data, changing the i ′ −NB816 threshold over 1.2 -1.5 only makes a difference in number density by 11%.

Evolution of Lyα Luminosity Function
Our LFs are appropriate to identify an evolutionary trend of LF, since our LFs from z = 3.1 to 5.7 are derived by the same procedure with similar data sets from the same instrument. In Figure 19, we compare our Lyα LFs of LAEs at z ∼ 3, 4, and 6. The LFs do not change within error bars at these redshifts. The left panel of Figure 20 shows the error ellipses of Schechter parameters of our LFs at z = 3.1 − 5.7. All the 2σ-error contours well overlap each other. At the fixed slope of α = −1.5, the best-fit parameters of LFs change from z = 3.1 − 5.7 only by factors of 1.8 and 2.7 in L * and φ * , respectively. Since these error ellipses are obtained by our observational data whose limiting Lyα EW is different at each redshift, we also plot in the right panel of Figure 20 the ellipses for all LAEs with a positive emission (EW > 0) which are obtained from the extrapolation with our simulations. In this case, the overlaps of z = 3.1 and z = 3.7 error ellipses become smaller. However, the error ellipses of z = 5.7 LAEs are much larger than those of z = 3.1 and 3.7. These large z = 5.7 error ellipses still appear to be consistent with z = 3.1 and 3.7 error ellipses. The results for LAEs with EW > 0 are similar to those for the observed LAEs. This is because the number density of observed LAEs (φ * ) differs from that of all LAEs (φ * 0 ) only by ∼ 10%, as discussed in Section 5.1. Thus, we conclude that Lyα LFs of LAEs do not evolve by more than a factor of 2-3 either in luminosity or number density, and that drastic evolution in the Lyα LF of LAEs from z ∼ 3.1 to z = 5.7 is ruled out. It should be noted that the central positions of z = 3.7 contours appear to be shifted to brighter L * and lower φ * than those of z = 3.1 and 5.7, although this shift is not significant within 1 − 2σ levels This small shift may indicate a moderate evolution of LFs between these redshifts. However, it is possible that AGNs at the bright-end LF more strongly affect the Schechter fit of z = 3.7 LF than that of z = 3.1 and 5.7 LFs, due to the shallow detection limit of our z = 3.7 LAEs (see Section 4.6).
Note that Lyα fluxes from high-z objects are generally attenuated by neutral hydrogen of intervening inter-galactic medium (IGM). It is known that high-z galaxies have an asymmetric Lyα emission whose blue side of line is more strongly absorbed by neutral hydrogen of IGM than low-z galaxies. (e.g. Hu et al. 2004;Shimasaku et al. 2006). Thus, the Lyα LFs in Figure 19 (solid lines) should be called apparent-Lyα LFs. Due to the absorption of IGM, we cannot directly measure intrinsic-Lyα fluxes that are emitted from LAEs. However, we can constrain the evolution of intrinsic-Lyα LFs with apparent-Lyα LFs. First, the lower limits of intrinsic-Lyα LFs are obviously given by the apparent-Lyα LFs (solid lines of Figure 19). Second, we can estimate the intrinsic-Lyα luminosity with the average Gunn-Peterson (GP) optical depths. The GP optical depths are estimated in various studies. Here, based on the results of Fan et al. (2006) (Fan), Madau (1995) (Madau), and Meiksin (2006 Figure 21 correspond to the intrinsic-Lyα LFs that we estimate. This figure indicates that intrinsic-Lyα LFs may evolve significantly, and that luminosities and/or number densities of LAEs are intrinsically brighter/higher at z = 5.7 than z = 3.1. Note that we estimate these intrinsic-Lyα LFs with two assumptions. The first assumption is that the density of neutral hydrogen atoms in the intervening IGM is the cosmic average value at each epoch. However, hydrogen clouds around LAEs are likely more ionized by the UV radiation from LAEs. On the other hand, the chance of intervening galaxies with molecular hydrogen probably increases around LAEs, due to clustering of galaxies. The second assumption is that the intrinsic-Lyα emission of LAEs has a symmetric profile whose central wavelength is not red-or blue-shifted. Shapley et al. (2003) find in a composite spectrum of z = 3 LBGs that Lyα emission is redshifted by 360 km s −1 from the average of continuum absorption lines. Because the typical Lyα FWHM of LAEs is as small as < 300 km s −1 (e.g. Rhoads et al. 2003;Hu et al. 2004;Shimasaku et al. 2006), the IGM will absorb only a small fraction of Lyα photons if they are redshifted by about 360 km s −1 . However, this is true only if Lyα properties of LAEs are similar to those of z = 3 LBGs. In fact, the typical Lyα FWHM of LAEs is smaller than that of z = 3 LBGs (450 ± 150 km s −1 Shapley et al. 2003). It is possible that the velocity offset of Lyα emission may also be smaller in LAEs than in LBGs (360 km s −1 ). In this way, the inferred intrinsic-Lyα features (such as those found in Figure 21) are real only if these two assumptions are correct. We need high-resolution spectroscopy for LAEs and sophisticated numerical simulations to assess the intrinsic-Lyα LF, and to derive a reliable conclusion on its evolution.
In summary, it is interesting that apparent LF of LAEs does not show a significant evolution over the long redshift range of z = 3.1 to 5.7. We point out the possibility that evolution of IGM and LAEs may be tuned to realize this no evolution at z = 3.1 − 5.7, if the amount of external absorption changes with redshift.

UV Luminosity Functions
We derive the UV LFs of our LAEs at z = 3.1, 3.7, and 5.7. We use our LAE catalogs, and obtain UV-continuum luminosities from magnitudes of a broad band whose bandpass does not include Lyα but only continuum emission. We choose R magnitudes for z = 3.1 and 3.7 LAEs, and z ′ magnitudes for z = 5.7 LAEs, where the corresponding wavelengths are ∼ 1300 − 1600Å in rest frame. We apply no k-corrections to the UV magnitudes, since the difference of UV magnitudes in this narrow-wavelength range is negligibly small for LAEs with a flat continuum (Section 6.3). We calculate number densities from the survey volume and the number counts as a function of UV magnitudes by weighting with the detection completeness (Section 3.2). Note that we need a careful estimation of total magnitudes of broad band. Since the aperture sizes and shapes of MAG AUTO magnitudes are defined by the sources on the narrow-band images, the MAG AUTO magnitudes of broad-band images could be contaminated by the neighboring continuum sources. Thus, we identify and deblend sources on our broad-band images with SExtractor, and cross-match the broad-band sources with our LAEs. If a LAE do not have a corresponding broad-band source detected over a 3σ level, we just use photometry of a 2 ′′ -diameter aperture. We refer to these magnitudes as a total magnitudes of broad band, and derive UV LFs with these magnitudes. For comparison, we also calculate the LFs from the simple 2 ′′ -diameter aperture photometry with no completeness correction. These simple estimates provide lower limits of UV LFs. Figure 22 shows the UV-LFs of our LAEs, together with the previous measurements of LAEs and dropout galaxies (or LBGs) at each redshift. Our UV-LFs are consistent with those of Hu et al. (2004) and Shimasaku et al. (2006) at z = 5.7, although their measurements show slightly higher number densities than ours. To check the consistency, we calculate z = 5.7 LF in the same manner as Shimasaku et al. (2006) who simply used 2 ′′ -diameter aperture magnitudes with aperture corrections estimated with their NB816 image. Our LF by the method of Shimasaku et al. (2006) presents a very good agreement with that of Shimasaku et al. (2006). However, we find that the aperture corrections defined with NB816 band overestimate the broad-band magnitudes. This is because the Lyα morphology in the narrow band is generally more extended than UV morphology on the broad band. Thus, we take our best estimates based on the MAG AUTO magnitudes with the source deblending on the broad-band images.
In Figure 22, we find that UV-LFs of LAEs do not change at z ≃ 3 − 4, but evolve from z ∼ 4 to 5.7. There exist an emergence of UV-bright LAEs at z = 5.7. We compare these UV LFs with those of dropout galaxies. At z = 3−4, number densities of our LAEs are as much as 10% of dropout galaxies down to M UV ≃ −20, which corresponds to ≃ M * UV or ≃ M * UV + 1 Sawicki & Thompson 2006;Beckwith et al. 2006;Yoshida et al. 2006;Vanzella et al. 2006b). Note that the EW limit of our z = 3 − 4 LAE samples is ≃ 40 − 60Å. This ratio of Lyα emitting galaxies to dropout galaxies is consistent with that reported by Shapley et al. (2003) who find that 25% and ∼ 2% of their z = 3 dropout galaxies have Lyα emission line with EW 0 ≥ 20Å and EW 0 ≥ 100Å, respectively. On the other hand, at z = 5.7, the number densities of our LAEs seems comparable to, or at least more than 50% of, dropout galaxies at z ∼ 6, where the EW limit of our z = 5.7 LAE is about ≃ 30Å. Spectroscopic studies of Dow-Hygelund et al. (2006) report that 6 Lyα emitting galaxies with EW 0 ≥ 20Å are found in their i ′ -dropout sample of CL1252 and HUDF parallel fields, and conclude that about ∼ 30% of i ′ -dropout galaxies have a Lyα emission line. This result is consistent with the measurements of previous studies (Stanway et al. 2004a,b;Vanzella et al. 2006a). More recently, Stanway et al. (2007) show that 16 out of 24 i ′ -dropout galaxies do not have a Lyα emission line with EW 0 ≥ 25Å in the GLARE/HUDF field. Most of the previous spectroscopic studies of i ′ -dropout galaxies suggest that ∼ 30% of i ′ -dropout galaxies down to ∼ L * have a Lyα emission line with EW 0 ≥ 20Å. It is not clear why our ratio of dropout galaxies and LAEs is higher than those of spectroscopic results. There are three possible explanations. The first is the difference of the definition in the ratio. We compare the ratio of LAEs to dropout galaxies at the same redshift, but Dow-Hygelund et al. (2006) and Stanway et al. (2007) obtain the ratio of Lyα emitting dropouts to all the dropouts. If all the LAEs are identified by dropout technique, these two ratios should be comparable. However, LAEs with no significant continuum are likely missed by the dropout selection. Moreover, the i dropout selection systematically misses the strong Lyα emission lines at z 6. The selection differences may cause the discrepancy between these two ratios estimated by the different methods. In fact, the theoretical model of Dijkstra & Wyithe (2007) suggests that LAE selections identify more population III galaxies with a large EW than dropout selections, and that the EW distribution of LAEs should not be the same as that of dropouts. The second explanation is that LFs of dropout galaxies have systematic errors. Indeed, we compare the LFs of dropout galaxies of Bouwens et al. (2006) to estimate the ratio. However, the measurements of dropouts' LFs scatter by a factor of 2 or more in the different estimates by various authors. We show the uncertainties of estimates with the gray shade in Figure 22. The third explanation is the evolution of UV LFs from z = 5.5 to 6.5 as claimed by Dow-Hygelund et al. (2006). The UV-LFs of dropout galaxies decrease in number density and/or luminosity from z ∼ 4 to 6 (e.g. Lehnert & Bremer 2003;Shimasaku et al. 2005;Bunker et al. 2004), and even more significantly evolve from z ∼ 6 to higher redshifts of z ∼ 7 − 8 ). Since i-dropout galaxy samples distribute over z = 5.5 − 6.5, the LFs of i-dropout galaxies are measured at higher redshifts in average than that of our LAEs (i.e. z = 5.7). This would not allow us to obtain the accurate ratio of Lyα emitting population to dropout galaxies. For these reasons, it is likely that the simple comparison between LFs of dropout galaxies and LAEs would not give a ratio between all z ∼ 6 objects and Lyα emitting population.
It is interesting to compare the shapes of UV LF of LAEs and dropout galaxies. At z = 3 − 4, we find a significant deficit of UV-bright LAEs with respect to dropout galaxies. This deficit of UV-bright LAEs are reported by Ouchi et al. (2003) at z = 4.9 based on the comparison of dropout and LAE LFs. This tendency is also consistent with the results of Section 6.2 and the claims of Ando et al. (2006); Shimasaku et al. (2006); Vanzella et al. (2006b) who find that UV-bright galaxies do not have a large Lyα EW from spectroscopic samples at z = 5 − 6. On the other hand, this tendency cannot be clearly seen for z ∼ 6 in Figure 22, probably due to the large uncertainties of LF of dropout galaxies.
We fit the Schechter function, to the UV LFs, where C ≡ 0.4 ln (10): α is the power-law slope, φ * is the normalization factor, and M * is the characteristic absolute magnitude. We fit the Schechter function with the measurements over a 5σ level (filled circles in Figure 22). Since the faintest points of our z = 3.7 LAEs appear to be suffered from the incompleteness of source detection, we do not use the point for the fitting. Since our LAE samples are not enough to derive α, we fix the slope to α = −1.5. For our z = 3.7 sample, we fix the M * to the best-fit M * value of our z = 3.1 LAEs. We summarize the results of the fitting in Table 6.
We find no evolution at z ∼ 3 − 4, even considering the error bars. The difference between z = 3.1 and 3.7 LFs is within 50% in number density or luminosity. On the other hand, UV LFs of LAEs evolve significantly from z ∼ 3 − 4 to 6. If it comes from the pure luminosity evolution, the UV LFs brighten by a ∼ 1 magnitude from z ∼ 3 − 4 to z = 5.7. Note that the EW limits of our selections are different between these redshifts. However, the difference of sample selection only changes by ∼ 10% in number density, according the results of our simulations (Section 5.1). Thus, this evolutionary trend of UV LFs is not affected by the selection effects.

Lyα-and UV-Luminosity Densities Contributed from Lyα Emitters
We calculate Lyα and UV-luminosity densities of our LAEs from the luminosity functions (LFs) derived in sections 5.1 and 5.2. We show Lyα and UV-luminosity densities in Tables 5 and 6, respectively. These tables present Lyα (UV) luminosity densities down to our observational detection limits, ρ obs Lyα (ρ obs UV ), and total luminosity densities down to zero luminosity by extrapolation, ρ tot Lyα (ρ tot UV ). These observational and total luminosity densities provide approximated lower and upper limits. For a reference, we estimate total Lyα luminosity densities of LAEs with EW > 0, from our simulations, which are shown under ρ tot 0Lyα in Table 5.
In Table 5, the total Lyα luminosity density is ∼ 10 40 erg −1 s −1 Mpc −3 at z = 3.1 − 5.7, and does not change within a 1σ level from z = 3.1 to 5.7. Table 6 shows that the total UV luminosity density would increase from ∼ 4 × 10 25 erg −1 s −1 Hz −1 Mpc −3 to ∼ 8 × 10 25 erg −1 s −1 Hz −1 Mpc −3 at z = 3 − 4 to 5.7, although the difference is only a 1 σ level because of large errors. This possible increase of UV luminosity density could be due to the fact that UV bright LAEs increase at z = 5.7 as shown in Figure 22.
Note that the entire Lyα (and UV) emission is not only originated from star-formation activities, but also from cooling radiation, shock winds, and AGN, and that Lyα (and UV) emission is attenuated by dust and IGM. However, we roughly estimate the contribution of star-formation from LAEs with those luminosity densities to check the consistency with the previous studies. We use the simple prescription of Lyα luminosity, L Lyα , and star-formation rate, SF R, combining the relation of Hα luminosity and star-formation rate (Kennicutt 1998) and the case B approximation (Brocklehurst 1971). With the assumptions of Salpeter IMF and solar metallicity (Madau, Pozzetti, & Dickinson 1998), the relation between UV luminosity and star-formation rate, is: where L UV is the UV luminosity measured in 1500Å. In Figures 19 and 22, we plot ticks of star-formation rates corresponding to Lyα and UV luminosities based on these formulae of eqs (9) and (10). Assuming these equations, SFRs of a typical (L * ) LAE are SF R(M ⊙ yr −1 ) = (5.3 +0.8 −0.6 , 9.3 +1.6 −1.4 , 6.2 +2.7 −1.9 ) and (4.5 ± 2.0, ∼ 4.5, 9.4 ± 7.0) at z = (3.1, 3.7, 5.7), which are estimated from Lyα and UV-continuum L * , respectively. Thus, a typical LAE has a SFR of ≃ 5 − 10 M ⊙ yr −1 at z = 3.1 − 5.7, although these SFRs are correct under the assumptions given by eqs. (9) and (10).
The SFRD from UV luminosity density may increase from z = 3.1 to 5.7 by a factor of 2, but again the large errors do not distinguish between evolutionary effects and uncertainties. If we take into account the large error bars, SF RD ≃ 5 − 9 × 10 −3 M ⊙ yr −1 Mpc −3 at z = 3.1 − 5.7. We compare these SFRDs with those estimated from dropout galaxies. The results of SFRD measurements with no dust correction show that the SFRDs of dropouts are ≃ 2 − 3 × 10 −2 M ⊙ yr −1 Mpc −3 at z ∼ 3 − 6 Bouwens et al. 2006;Hopkins 2006). Thus, LAEs contribute roughly about ≃ 20−40% of the entire cosmic SFRD at z = 3 − 6.
6. Properties of Lyα Emitters 6.1. Statistics of Lyα Equivalent Width Figure 23 presents the histogram of rest-frame equivalent width (EW 0 ) for our LAEs. We calculate EW 0 of our LAEs from our photometric measurements by the modeling described in Section 5.1. We then obtain two estimates of the EW 0 distribution by (i) taking the best measurements of EW 0 for each LAE and (ii) summing the probability distribution of EW 0 that is defined by errors of EW 0 . We show in Figure 23 these two estimates with (i) histograms (+Poisson errors) and (ii) solid curves. We find that the results of (i) and (ii) agree fairly well for z ∼ 3 and 4 LAEs. However, for our z ∼ 6 LAEs, we see a significant difference at EW 0 = 100 − 150Å. This discrepancy between (i) and (ii) for z ∼ 6 LAEs is probably due to the large errors of the relatively shallow off-band (i.e. z ′ -band) photometry. Thus, we regard the difference of (i) and (ii) as the uncertainties of our measurements. The gray histograms and curves indicate the EW 0 distribution for all of our photometricallyselected LAEs. Since our three LAE samples at z = 3.1, 3.7, 5.7 do not have the same limits of Lyα luminosity and EW 0 , we make subsamples of LAEs that share the same detection limits for comparison. We set log L(Lyα) 42.6 erg s −1 and EW int 0 70 − 80Å for the limits of our subsamples, because our three LAE samples are complete in these limits. The histograms of these subsamples are plotted with black lines at each panel. We compare these histograms with those for spectroscopically identified LAEs. Although the statistical accuracy is limited for the spectroscopic LAE samples, the EW 0 distributions of spectroscopic and photometric samples are consistent.
In Figure 24 we plot gray areas showing the EW 0 distributions for the subsamples with the uncertainties of (i) and (ii). We find no clear evolution of EW 0 distribution from z = 3.1 to 5.7 with the uncertainties of our measurements. Since these EW 0 distributions are based on the apparent EW, we correct for the absorption of IGM with the average attenuation at z = 3.1, 3.7, 5.7 (see Section 5.1.2). We present in Figure 24 the distribution of intrinsic EW 0 (i.e. EW 0 corrected for IGM absorption) with cyan, blue, and red regions for z = 3.1, 3.7, and 5.7, respectively. The IGM corrected histograms of z = 3.1 and 3.7 appear to be comparable within the large uncertainties of our measurements. The histogram of z = 5.7 (red histogram) would be systematically different from those of z = 3.1 and 3.7, and could imply that z = 5.7 LAEs may tend to have a large intrinsic EW 0 . However, the uncertainty of EW 0 measurements is as large as the difference of histograms between at z = 3.7 and z = 5.7. We cannot reject the possibility of no evolution of intrinsic EW 0 from z = 3.7 to 5.7.
We investigate the fraction of large-EW LAEs with the subsamples. We define a threshold of EW int 0 ≥ 240Å with an intrinsic EW, following previous studies (e.g. Malhotra & Rhoads 2002;Dawson et al. 2004;Shimasaku et al. 2006;Saito et al. 2006). This threshold of EW int 0 corresponds to the apparent EW of EW app 0 = 192Å, 175Å, and 130Å, assuming the average attenuation of IGM (Section 5.1.2). We find that the fractions and errors of the large-EW LAEs in our subsamples are (z, fraction, fraction within 95th percentile)= (3.1, 0.21, 0.11-0.29), (3.7, 0.26, 0.16-0.40), and (5.7, 0.25, 0.15-0.33) by calculations of (i). 4 From the calculations of (ii), we obtain the similar fractions of 0.20, 0.20, and 0.27 for z = 3.1, 3.7, and 5.7 LAEs. There is a possible but slight implication of the evolution of the fraction of large-EW LAEs from z = 3.7 to 5.7 in the results of (ii). However, again, this possible evolution is very uncertain due to the large errors of EW measurements. The best estimates of the fraction are 20 − 30% for z=3.1-5.7. Thus, we conclude with these uncertainties that the fraction of large-EW LAEs is 10-40% at z = 3.1−5.7, which does not significantly change from z = 3.1 − 5.7 within this percent range.
We compare our fraction of large-EW LAEs with those of Shimasaku et al. (2006) for z = 5.7 LAEs. Since Shimasaku et al. (2006) calculate this fraction with the threshold of apparent EW 0 of ≥ 120Å (c.f. 130Å in above calculations), we use this threshold of apparent EW 0 ≥ 120Å here. With this threshold, we find the fraction and 95th-percentile range of 0.34 and 0.24-0.42 for our z = 5.7 LAEs. These numbers are vary consistent with those claimed by Shimasaku et al. (2006) who obtain 30-40%. Figure 25 presents rest-frame Lyα EW (EW 0 ) as a function of UV-continuum magnitude for our spectroscopic samples. The effective wavelength of UV magnitude is ∼ 1300 −1600Å. The details of UV-magnitude measurements are presented in Section 5.2. Figure 25 also plots EW 0 from previous studies of dropout galaxies and LAEs. On the right panel of Figure 25, EW 0 of z ∼ 6 objects show a clear deficit of large EW 0 objects in the bright magnitude (M UV −21.5). This trend is found by Ando et al. (2006) for z = 5 − 6 galaxies, and discussed in Shimasaku et al. (2006); Stanway et al. (2007) for z ∼ 6 objects. We confirm their findings on our plot of z ∼ 6 objects. For z ∼ 3 and 4 objects shown in Figure 25, we find the trend very similar to that of z ∼ 6. We see no large EW 0 objects with EW 0 80Å for UV-bright (M UV −21.5) objects. At z = 3, this trend is also reported by Shapley et al. (2003) who find that the Lyα emission strength increases toward fainter magnitudes in their spectra of LBGs.

UV-Continuum Color and Extinction
We present UV-continuum colors as a function of UV magnitude for our spectroscopically identified LAEs at z = 3.1 and 3.7 in Figure 26. This figure compares those of dropout galaxies at the similar redshift. Except for AGN, typical z = 3 − 4 LAEs have i ′ − z ′ (or R − i ′ ) colors of 0.05. The UV-continuum colors of our LAEs are consistent with those of z = 4.5 LAEs (Finkelstein et al. 2007). On the other hand, dropout galaxies (or LBGs) generally have colors of ≃ 0.1. Thus, LAEs appear to be bluer than dropout galaxies in a UV-continuum color. This color difference indicates that LAEs are younger or less-dusty than dropout-galaxy population. We discuss more details in Section 7.5.

Composite Spectra
We make a composite spectrum each for our z = 3.1, 3.7, and 5.7 LAEs. From our spectroscopic samples, we exclude AGNs (Table 4) and LAEs with uncertain identification (Table 2). We also do not include the spectrum of NB503-N-42377 that has a marginal Civ line, so as to obtain the average of typical LAE spectra (see Section 4.1). Thus, we use 36, 25, and 15 spectra of z = 3.1, 3.7, and 5.7, respectively. Since some of spectra have systematic differences originated from a faint AGN and/or errors of cosmic rays and subtraction of sky etc., we calculate a mean flux with rejections of two largest and smallest values at each wavelength. Figure 27 shows the composite spectra of our LAEs whose average redshifts are z = 3.13, 3.68, and 5.68. We have also performed the median stacking, and find no qualitative differences between the rejected-mean and median results. The Lyα luminosity of the composite spectrum is L(Lyα) = (6.3 ± 0.1, 8.5 ± 0.2, 9.5 ± 0.3) × 10 42 erg s −1 at z = (3.13, 3.68, 5.68). We have a signal-to-noise ratio high enough to detect UV continua in z = 3.13 and 3.68 spectra, but not in z = 5.68 spectrum.
The composite spectrum of z = 5.68 LAEs has Lyα emission line with a clear asymmetry, which is a typical emission feature of high-z objects. The spectra of z = 3.13 and 3.68 do not show a significant asymmetry in Lyα. This is because a typical spectral resolution of our z = 3.1 and 3.7 LAEs is not high enough to resolve the asymmetry of Lyα (R ∼ 500; c.f. R ∼ 1000 for z = 5.7 LAEs). Moreover, the IGM absorption at z = 3 − 4 is not as strong as z = 5.7, which provides a weak asymmetric feature in Lyα emission at z = 3 − 4.
We find no significant absorption lines in these composite spectra, probably due to the combination of the weak metal absorption of LAEs and the relatively poor signal-to-noise ratios of our composite spectra. 5 The composite spectra of z = 3.13 and 3.68 cover the wavelength of Heiiλ1640 emission. The inset panels of Figure 27 magnify the spectra around this wavelength. No significant feature is found for Heii at z = 3.13 and 3.68. We calculate upper limits of Heii flux, f HeII , and estimate the 3σ upper limits of the ratio, f HeII /f Lyα , where f Lyα is Lyα flux. We obtain meaningful 3σ upper limits of the ratio, f HeII /f Lyα = 0.02 and 0.06 for z = 3.13 and 3.68 LAEs, respectively Since Heii emission is an indicator of primordial populations, i.e. population III stars and cooling radiation, our upper limits place constraints on primordial populations at z = 3 − 4. Although theoretical models predict the existence of primordial populations at these redshifts (Scannapieco et al. 2003;Jimenez & Haiman 2006), we have found no signature at the level of the upper limits of the present observations. Since the ratio of f HeII /f Lyα is predicted as small as ∼ 0.1−0.001 for population III star formation and cooling radiation (e.g. Schaerer 2003;Yang et al. 2006), we need future surveys whose upper limits reach at the level of f HeII /f Lyα ≃ 0.001.

Evolution of Luminosity Functions
We have found four pieces of evidence that provide a general picture in the evolution of LAEs: (1) apparent-Lyα LFs of LAEs show no evolution from z = 3.1 to 5.7. (2) These apparent-Lyα LFs and the average Gunn-Peterson optical depth indicate that intrinsic-Lyα LFs of LAEs must have brighten in the luminosity and/or increased in the number density from z = 3.1 to 5.7. (3) The UV LFs of LAEs show the increase of luminosity and/or number densities from z = 3.1 to 5.7. (4) The rest-frame intrinsic-Lyα EW, EW int 0 , distribution of LAEs does not change or positively evolves from z = 3.1 to 5.7.
The evolution of intrinsic-Lyα LFs is caused by the emergence of Lyα emitting objects with a bright UV continuum or the increasing trend of Lyα EW 0 for LAEs at z ∼ 5.7. There are three possible explanations for the evolution of LAEs. First, the amount of dust mixed in HII regions may decrease in average from z = 3.1 to 5.7, and the extinction of Lyα luminosity through the resonance scattering decreases selectively. This implies that at z = 5.7 even UV bright galaxies have a detectable Lyα emission line. The second explanation is that the young Universe at z = 5.7 has numerous exotic Lyα populations such as metal-poor population III and/or cooling clouds. The third explanation is that the fraction of Lyα-absorbed galaxies is lower at higher redshifts, due to an decrease in the amount of HI gas in and around galaxies with redshift. In fact, some z ∼ 3 LAEs show such an HI absorption originating from an inflow and/or outflow in their spectra (e.g. Tapken et al. 2007), although the evolution of such HI clouds has not been observationally understood. The CDM-based hierarchical model predicts that galaxies at higher redshifts are generally more compact (e.g. Mo et al. 1998;Somerville et al. 2006). It is possible that the star formation in such compact high-z galaxies is so efficient that cold gas is immediately converted into stars. If high-z LAEs are such compact galaxies, they will have little HI gas and thus their Lyα emission from HII regions can escape without absorption. If this hypothesis is true, we may be able to explain the evolutionary connection between LAEs and dropouts: the internal mass density of LAEs decreases with cosmic time by mergers and thus they evolve into dropout galaxies that are more massive and have more HI gas.
It should be noted that the evolutionary trend of UV-LF of LAEs is opposite to that of dropout galaxies. The UV-LFs of dropout galaxies show a significant decrease in luminosity and/or number density from z ∼ 4 to z ∼ 6 (e.g. Lehnert & Bremer 2003;Shimasaku et al. 2005;Bunker et al. 2004). In case of luminosity evolution, UV-LFs of dropouts get faint from z ∼ 3 to 6 by a factor of 1.7 +0.4 −0.3 ). On the other hand, UV-LFs of LAEs brighten by ∼ 1 magnitude, if it comes from the pure luminosity evolution. This difference of LFs implies that Lyα emitting population is more dominant at z = 6 than z = 3 at the given UV luminosity range.

AGN fraction and Evolution of Faint AGN
We identify 6 AGN-LAEs in total. In our photometric samples of LAEs (satisfying our color-selection criteria), we find that 3 out of 356 z = 3.1 LAEs and 1 out of 101 z = 3.7 LAEs host AGNs (Section 4.6). Thus, the fraction of AGNs is about 1% at z = 3.1 and 3.7, which is consistent with the result of Gawiser et al. (2006). Note that the detection limits of our LAEs reach (1 − 4) × 10 42 ergs s −1 (∼ 0.2 − 0.4L * Lyα ). This AGN fraction is the lower limit, since our multi-wavelength data are probably not deep enough to identify faint AGNs. We estimate the relation between Lyα luminosity and the detection limits of our multi-wavelength data. By the comparison of our detection limits and the QSO templates in Figure 14 (see Section 4.6 for the definition of QSO templates), our X-ray data likely reach the deepest detection limit for AGNs among our multi-wavelength data. We normalize the QSO templates to the detection limit of our X-ray data, and measure Lyα luminosities of the QSO templates. We find Lyα-luminosity limits of L(Lyα) = 9.5 × 10 42 and 1.5 × 10 43 erg s −1 for z = 3.1 and 3.7 objects, respectively, assuming that the SED of AGN-LAEs is the same as the QSO templates. Down to these Lyα-luminosity limits, we find 3 out of 25 (1 out of 8) photometrically selected LAEs have an AGN at z = 3.1 (z = 3.7). Thus, the AGN fraction is estimated to be ∼ 10% down to L(Lyα) ≃ 1 × 10 43 erg s −1 for z = 3.1 and 3.7 LAEs. This Lyα-luminosity limit corresponds to ≃ 2L * Lyα . Note that the AGN fraction of LAEs is as small as 10% even with this bright detection limit of Lyα luminosity. If we take a Lyα limit for the very bright luminosity of log L(Lyα) > 43.6 and > 43.4 erg s −1 in our z = 3.1 and 3.7 samples, respectively, all of LAEs (2 out of 2 LAEs and 1 out of 1 LAE at z = 3.1 and 3.7) have AGN activities. These very bright limits correspond to the brightest bins of our LF in Figure 19 (see Section 5.1). There appear possible humps of LF at z = 3.1 and 3.7 which are produced by the AGN-LAEs. The number density in these brightest bins is about ∼ 10 −5 Mpc −3 . Thus, a shallow wide-field LAE survey generally finds this AGN-LAE population. Steidel et al. (2002) have obtained the fraction of AGNs in their z = 3 LBG samples down to ≃ M * + 1 with optical spectra. They have found the AGN fraction of 3% for their LBG sample with a relatively faint continuum limit of ≃ M * + 1. Since the detection limits of this study is different from ours, we cannot directly compare the AGN fraction of their LBGs and our LAEs. Since we find the AGN fraction (and its lower limit) of our LAEs is 10% (and 1%) for our ≃ 2L * Lyα (and the entire [∼ 0.2 − 0.4L * Lyα ]) samples, the AGN fraction of LAEs and LBGs would be comparable.
For z = 5.7 LAEs, we identify no AGN with our spectra or multi-wavelength data. In the same manner as the calculations above, we estimate a Lyα detection limit of z = 5.7 LAEs that corresponds to the X-ray luminosity limit with the QSO templates. We find that the Lyα detection limit is L(Lyα) ∼ 4 × 10 43 erg s −1 , but we have no LAEs with L(Lyα) > 4 × 10 43 erg s −1 . On the other hand, there are two AGN-LAEs that are brighter than L(Lyα) ∼ 4 × 10 43 erg s −1 (i.e. log L(Lyα) > 43.6 erg s −1 ) at z = 3.1. Therefore, it may imply that LAEs with a bright AGN such found at z = 3 would disappear at z = 5.7. In fact, no AGN signatures such as Nv emission have been confirmed in spectra of the brightest z = 5.7 LAEs that are found in other wide-field studies (Westra et al. 2006). No detection of AGN in z = 5.7 LAEs implies that the number density of LAEs with AGN activities would drop from z = 3 to 5.7. Recent QSO surveys have measured QSO luminosity functions accurately, and found that the space density of bright QSOs with M UV < −26.7 decreases from z = 3 to 6 by more than an order of magnitude (e.g. Croom et al. 2004;Fan et al. 2001Fan et al. , 2004. This trend is the same as that of our finding in our LAE samples. Because our AGN-LAEs are as faint as M UV ≃ −23 − −21, our AGN-LAEs probe for evolution of relatively faint AGN. Thus, evolution of faint AGNs appears to follow the evolution of QSOs. This faint-AGN evolution implies that not only bright QSOs but also faint AGNs can provide less significant contribution than star-forming galaxies for reionizing the Universe at z 6. In other words, UV radiation from star formation likely becomes more dominant than that from faint AGNs at z ∼ 6.

Star-Formation Rates Indicated from Multi-Wavelength Data
In Section 4, we have identified AGNs with our multi-wavelength data. The multiwavelength data are too shallow to identify star-forming activities at high redshifts. The limiting SFRs of our multi-wavelength are as large as ∼ 10 4 M ⊙ yr −1 for our X-ray and 24µm data and ∼ 1000M ⊙ yr −1 for our radio data, respectively. However, we find that our radio data provide a meaningful limit on SFR of our LAEs by stacking analysis. We exclude LAEs with an individual radio detection, and stack radio images of our photometrically selected LAEs in the same manner as Simpson et al. (2006b). The stacked images show no detection in the radio band. The 3σ-upper limits of the stacked images are f 1.4GHz = (1.8, 7.0, 2.7) µJy for our z = (3.1, 3.7, 5.7) LAEs.
The relationship between SFR and radio luminosity (L 1.4GHz ) is given by for high-mass stars (M > 5M ⊙ ; Condon 1992; see also Serjeant et al. 2002), where ν is the frequency and α is the non-thermal ratio spectral index (α ≃ 0.8). Assuming this SFR v.s. radio-luminosity relation, we obtain 3σ upper limits of SF R = (29, 162, 160) M ⊙ yr −1 for our z = (3.1, 3.7, 5.7) LAEs. Thus, the average SFRs of LAEs are smaller than ≃ 30 and 160 M ⊙ yr −1 at z = 3.1 and 3.7/5.7, respectively. The result of our z = 5.7 LAEs is similar to that of Carilli et al. (2006) who report the 2σ upper limit of f 1.4GHz = 2.5 µJy (i.e. ∼ 100 M ⊙ yr −1 ) for their stacked radio image of z = 5.7 LAEs in COSMOS field. The upper limits of radio SFR are consistent with the SFRs of typical (L * ) LAEs, ≃ 5 − 10 M ⊙ yr −1 (Section 5.3), estimated from UV and Lyα luminosities. This agreement between radio and optical SFRs implies that majority of LAEs are not associated with dusty starbursts with significant (×10 − 100) hidden star-formation. It is consistent with the fact that no LAEs are detected in submm bands (Section 4.4). These results support the small-dust extinction of LAEs from the blue UV-continuum color (Section 7.5). On the other hand, no significant excess of radio SFR may reject the possibility of an extremely-top heavy initial mass function for star-formation of LAEs, since radio fluxes are originated from non-thermal radiation of supernovae at the final stage of massive stars.
No radio detections in the stacked images also suggest that typical LAEs do not harbor low-luminosity radio AGNs at z = 3.1 − 5.7 (see also Carilli et al. 2006 for z = 5.7 LAEs). The radio fluxes of our AGN-LAEs are f 1.4GHz ≃ 100 − 200µJy (Table 4) at z = 3.1 and 3.7, while our 3σ upper limits of stacked images are 1.8 − 7.0µJy. Thus, typical LAEs do not have a low-luminosity radio AGN whose flux is brighter than 1/10 − 1/100 of typical radio AGN-LAEs at z = 3 − 4. Figure 25 shows that UV-bright (M UV −21.5) galaxies do not have a large EW 0 (EW 0 80Å) at z = 3 − 6. Ando et al. (2006) suggest that UV-bright galaxies are a dusty and chemically-evolved population, and that such UV-bright galaxies do not have a large EW. There are two other possibilities to explain this trend. First, the average stellar population of UV-bright galaxies would be older than that of UV-faint galaxies. Since Lyα emission can be efficiently produced by hard-UV continuum from early-type stars, galaxies can emit a strong Lyα emission of EW 0 100Å within ∼ 10 Myr after a starburst (Schaerer 2003). Second, HI clouds of inter-stellar medium or inflows may be rich in UV bright population, and absorb a Lyα emission line. It is likely that the combination of age, neutral hydrogen, dust, and metallicity makes the deficit of large EW galaxies at bright UV magnitude.

Implications from the Blue UV continuum
We find that UV-continuum colors of LAEs are bluer than those of dropout galaxies in Section 6.3. This implies that LAEs are less-dusty and/or younger population than dropout galaxies. Although more detailed analysis with near-infrared data and population synthesis models will be presented in Ono et al. (in preparation), we compare the UV-continuum colors of LAEs with a simple model.  have obtained the relation between i ′ − z ′ color and dust extinction, E(B − V ), with the stellar population synthesis model (Bruzual & Charlot 2003) and the extinction law (Calzetti et al. 2000) which reproduce a typical UV-optical SED of dropout galaxies at z ∼ 3. The relation of color and dust extinction is,  also confirm that this relation agrees with the one of local starbursts. This relation assumes that the difference of UV color (or UV slope) is caused by dust extinction, since the model fixes the age, metallicity, initial mass function, and star-formation history. We apply this simple model to our LAEs in Figure 26. Figure 26 implies that LAEs have an extinction of E(B − V ) 0.05, while that dropout galaxies typically have E(B − V ) ∼ 0.1 − 0.2. There are some very blue LAEs whose UV colors scatter around −0.2 − 0.0. The colors of these objects are still comparable to the color of E(B − V ) = 0.0 within a ≃ 2σ level. However, if this very blue UV color is true, the colors of LAEs can be explained not only by extinction, but also by stellar population that is bluer than that of typical dropout galaxies. Gronwall et al. (2007) estimate E(B −V ) of z = 3.1 LAEs with the independent approach, i.e. the comparison of UV and Lyα luminosity. They have obtained E(B − V ) < 0.05, which is consistent with ours.

Conclusions
We have made a photometric sample of 858 LAE candidates and a spectroscopic sample of 84 confirmed LAEs at z = 3.1, 3.7, and 5.7 down to L(Lyα) 3 × 10 42 erg s −1 in a 1 deg 2 sky of the Subaru XMM-Newton Deep Survey Field. Based on these samples, we have studied photometric and spectroscopic properties with the aid of multi-wavelength data from X-ray to radio. The major findings of our study are summarized below.
1. We derive the LF of Lyα emission for each redshift and provide the best-fit Schechter parameters as summarized in Table 5, by carefully taking into account the statistical error and the field-to-field variation. We find that the apparent Lyα LF shows no significant evolution between z = 3.1 and 5.7. Evolution, if any, is limited within factors of 1.8 and 2.7 in L * and φ * , respectively. Although no evolution of the Lyα LF over 3 z 5.7 has already been suggested by previous studies, we now have much stronger and more reliable constraints with smaller systematic and statistical errors. Since the average Lyα opacity of the IGM is larger at earlier epochs, the absence of evolution in the apparent Lyα LF implies an intrinsic brightening of Lyα luminosity with increasing redshift being canceled out by increasing absorption of the IGM. We note, however, that this claim is true only if the two assumptions made in Section 5.1.2 are correct.
2. The LF of UV continuum for LAEs shows an increase in number density and/or UV luminosity from z ∼ 3 − 4 to 5.7. This evolution of the UV LF is consistent with the plausible evolution in the intrinsic Lyα LF, since we find that the distribution of the rest-frame intrinsic EW of LAEs does not change or positively evolves with redshift. On the other hand, the UV LF of dropout galaxies is known to show an opposite evolutionary trend to that of LAEs, namely, a decrease in number density and/or UV luminosity with increasing redshift. This implies that the ratio in number density of LAEs to dropout galaxies increases from z ∼ 3 − 4 to 5.7, and that galaxies with Lyα emission are more common at earlier epochs.
3. We identify six LAEs (in total) with AGN activities. In our photometric sample, three out of 356 z = 3.1 LAEs and one out of 101 z = 3.7 LAEs host AGNs. Thus, the lower limit of the AGN fraction down to (1 − 4) × 10 42 erg s −1 (∼ 0.2 − 0.4L * Lyα ) is ≃ 1% at z = 3.1 and 3.7. We use QSO templates given in the literature to find that ∼ 10% of LAEs are AGNs above the Lyα luminosity where our sample is complete, L(Lyα) ≃ 1 × 10 43 erg s −1 (≃ 2L * Lyα ). It is notable that 100% of LAEs (2 out of 2 LAEs and 1 out of 1 LAE at z = 3.1 and 3.7) host AGNs at the bright end of the LF with log L(Lyα) > 43.6 and > 43.4 erg s −1 at z = 3.1 and 3.7, respectively. Shallow and wide-field narrow-band imaging would be an efficient way to search for LAEs hosting AGNs. 4. We obtain the 3σ upper limits of stacked radio images, f 1.4GHz = (1.8, 7.0, 2.7) µJy for our z = (3.1, 3.7, 5.7) LAEs. These upper limits indicate SF R = (29, 162, 160) M ⊙ yr −1 at z = (3.1, 3.7, 5.7) based on the SFR-radio luminosity relation of Condon (1992). These upper limits are consistent with the SFRs estimated from Lyα and UV luminosities. Thus, the majority of LAEs are not associated with dusty starbursts with significant (×10 − 100) hidden star-forming activities. No radio detections in the stacked images also indicate that typical LAEs do not harbor a low-luminosity radio AGN at z = 3.1−5.7. At z = 3−4, typical LAEs do not have a low-luminosity radio AGN whose flux is brighter than 1/10 − 1/100 of typical radio AGN-LAEs of our SXDS field. 5. The fraction of LAEs that have very large Lyα EWs does not change significantly over 3.1 ≤ z ≤ 5.7; the fraction of objects with EW int 0 ≥ 240Å is 10-40 %. 6. If we naively assume that all of the Lyα or UV emission in our LAEs originate from star-forming activities, LAEs contribute about ≃ 20 − 40% of the entire cosmic SFRDs at z = 3 − 6. 7. We find a deficit of large-EW galaxies with bright UV continuum emission at all three redshifts. This finding not only confirms the previous results of Shapley et al. (2003); Ando et al. (2006); Shimasaku et al. (2006) for z = 3 and 5 − 6, but also claims that this trend is common in the early universe. This deficit is probably caused by a combination of old ages and large amount of neutral hydrogen, dust, and metallicity in UV-bright galaxies.
8. The UV-continuum colors of LAEs are generally bluer than those of dropout galaxies at the same UV luminosity. If we assume that LAEs have the same stellar population as dropout galaxies, then the UV spectral slope of LAEs indicates E(B − V ) 0.05. The very blue LAEs probably have extremely low dust extinction and/or very young stellar populations. 9. We stack the spectra of the confirmed LAEs to estimate the 3σ upper limit of f HeII /f Lyα to be 0.02 for z = 3.1 and 0.06 for z = 3.7. These low f HeII /f Lyα values are consistent with no or little primordial population being included in our sample.
We are grateful to Mark Dijkstra, Eric Gawiser, Kim Nilsson, and Edward Westra for their helpful comments. We thank the anonymous referee for his/her constructive suggestions and comments that improved this article. M.O. has been supported by the Hubble Fellowship program through grant HF-01176.01-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. M.O. acknowledge support via Carnegie Fellowship. Archival broad-band data † † . 1 · · · ‡ The FWHM of PSFs in the reduced image. The value in parenthesis indicates the FWHM of PSF that is matched with broad-band images in each field. † The limiting magnitude defined by a 5σ sky noise in a 2 ′′ -diameter circular aperture. † † The archival broad-band data of SXDS presented in Furusawa et al. (in preparation). We summarize the properties of the 5-field images on a single line. Note that the exposure time is not a total of the 5 fields, but 1 field. More details are presented in Table 2 of Furusawa et al. in preparation.     -20.4 7.6 · · · NB816-S-70769 02:17:43 -05:28:07 5.685: 23.9 26.1 3 · · · 17.8 ± 1.2 122.9 +41.6 −27.6 -20.5 8.5 · · · NB816-S-77389 02:17:50 -05:27:08 5.693 24.3 > 27.0 6.1 · · · 11.9 ± 1.9 106.4 +107.0 a See the published version for the exact coordinates with decimals. ‡ In column (4), ":" marks objects with an uncertain spectroscopic identification. † "conf" in the columns (7) and (8)   (3) ‡ 2 ′′ -diameter aperture magnitudes. † The approximate limit of Lyα luminosity. † † The approximate limit of rest-frame apparent equivalent width of Lyα emission. The corresponding intrinsic equivalent widths corrected for the IGM absorption are estimated to be EW int 0 = 80, 60, and 50Å, for z = 3.1, 3.7, and 5.7 samples, respectively.  4.4 ± 1.4 · · · < 240 · · · · · · · · · < 60 3.0 -21.65 8.5 · · · NB570-N-34841 02:18:31.379 -04:43:54.77 3.724 Sooooo · · · · · · < 1.3 · · · < 240 · · · · · · · · · < 60 14.5 -23.79  5) The identification of AGN-LAEs in our spectroscopy and multi-wavelength data. "X", "I", "M", or "R" means that the LAE has either an X-ray, infrared, submm, or radio detection. The flags of "S" and "P" indicate a spectroscopically identified AGN and an object satisfying our color-selection criteria of LAEs, respectively. ("o" means no detection or identification in the corresponding condition.) (6) and (12): ID names in the X-ray and radio data presented in Ueda et al. (in preparation) and Simpson et al. (2006a), respectively. (7),(9), and (13): Separation between positions of the optical center and a counterpart of X-ray, infrared, and radio. (8), (10), (11), and (14): Fluxes of X-ray 2-10 keV (in 10 −15 erg s −1 cm −2 ), infrared 24µm (in µJy), submm 850µm (in mJy), and radio 1.4GHz (in µJy), respectively. For the upper limits of X-ray fluxes, we assume an absorption of neutral hydrogen with a column density of 10 22 cm −2 and a spectral power of γ = 1.8. We omit the effects of X-ray reflection, which provides the most conservative upper limit in column (8). (15) Lyα luminosity in 10 43 erg s −1 derived from our photometric data. (16) Total UV magnitude in AB mag. (17) FWHM in the narrow band in physical kpc. (18) Type of object. "BL" indicates an AGN with a broad-line emission (v FWHM 1000 km s −1 ) in high ionized lines (i.e. Nv, Siiv, Civ, Heii, and/or Ciii]). NB503-N-35820 shows a possible broad line with 1321 ± 362 km s −1 in Civ, although the signal-to-noise ratio is as small as 4.   and UV luminosity densities (in 10 25 erg s −1 Hz −1 Mpc −3 ) calculated with the best-fit Schechter parameters down to the observed limit of UV luminosity, i.e. M 1500 = −18.9, −19.7, and −20.6, for z = 3.1, 3.7, 5.7, respectively. (9): Inferred total UV luminosity densities integrated down to M 1500 = ∞ with the best-fit Schechter parameters. † For the z = 3.7 LF, we fix M * 1500 to -19.8 that is the best estimate of our z = 3.1 LF.  Ouchi et al. 2003;Shimasaku et al. 2003) and NB921 (gray solid lines). NB921 filter is used for our on-going observations in the SXDS field. These response curves include atmospheric absorption, quantum efficiency, and transmittance of optical elements of the telescope and instrument. Bottom panel : The spectrum of night-sky emission. Note that the passbands of the narrow-bands do not include a strong sky emission.      The black dots plot colors of all the detected objects. The photometrically-selected LAEs are presented with filled circles and triangles. The LAEs of triangles have a broad-band (V or i ′ ) magnitude fainter than that of the 2σ level, and show the lower limits of the narrowband excess color. The red and blue open circles denote spectroscopically-identified objects in the redshift range of LAEs and interlopers, respectively. We define the redshift ranges of LAEs as z = 3.09 − 3.18, 3.63 − 3.75, and 5.60 − 5.78 in the diagrams of NB503, NB570, and NB816, respectively (see Figure 6 for these redshift ranges). The red and black squares mark AGNs from our multi-wavelength data (Table 4) with and without a spectroscopic redshift, respectively. For a display purpose, we place symbols at the narrow-v.s. broadband color of 2.8 for objects with a color redder than 2.8. The green lines indicate 3σ errors of the colors of narrow v.s. broad bands for a source with a color of V − NB503 = −0.10, V − NB570 = 0.04, and i ′ − NB816 = 0.16, which correspond to the average color of all objects. The solid and dashed lines represent the 2σ limit of a broad band, and the color cut of narrow-band excess. Note that the narrow-band magnitudes, i.e. NB503, NB570, and NB816, are total magnitudes, while the colors of V − NB503, V − NB570, and i ′ − NB816 are defined with a 2 ′′ -diameter aperture. The red and blue circles/triangles indicate spectroscopically identified objects in and out of the LAE redshift range, respectively. We take the LAE redshift range same as that of Figure 7. The red squares mark spectroscopically identified AGNs found in our multi-wavelength data (Table 4). For a display purpose, we place symbols at V − NB503 = 3.3 for the objects with a color of V − NB503 > 3.3. The objects with no continuum (V -band) detection below a 2σ level are plotted at a color of B − V = 0.6. The error bars at the upper-right corner indicate 1σ errors for a typical LAE whose brightness is the median magnitudes of our photometrically selected LAEs. The solid line shows the color criteria of eq. (1) for sources with a detection in the broad band (V ). The colors are defined with a 2 ′′ -diameter aperture. The curves present tracks of model galaxies at different redshifts. Pink lines indicate model-LAE SEDs which are composite spectra of a 0.03 Gyr single burst model galaxy Bruzual & Charlot 2003 and a Lyman α emission (EW rest (Lyα)=22Å); from the left to right, three different amplitudes of IGM absorption are applied: 0.5τ eff , τ eff , and 1.5τ eff , where τ eff is the Madau's (1995) original median opacity. The narrow-band excess in each of the peaks in the red lines indicates the Lyman α emission of LAEs at z = 3.1. Green lines show 6 templates of nearby starburst galaxies (Kinney et al. 1996) up to z = 2, which are 6 classes of starburst galaxies with different dust extinction (E(B − V ) = 0.0 − 0.7). The narrow-band excess peaks in the green line correspond to the emission lines of [Oiii](z = 0.004), Hβ(z = 0.03), or [Oii](z = 0.3). Black lines show colors of typical elliptical, spiral, and irregular galaxies (Coleman, Wu, & Weedman 1980) which are redshifted from z = 0 to z = 2. Yellow star marks show 175 Galactic stars given by Gunn & Stryker (1983). Middle panel: Same as the left panel but for z = 3.7 LAEs. Right panel: Same as the left panel but for z = 5.7 LAEs. We do not show the error bar of a R − i ′ color at the upper-right corner, because a typical LAE has no R-band flux above a 1σ noise level. Fig. 9.-Surface densities of objects detected in the NB503 data. The lower and upper points indicate surface densities of our z = 3.1 LAEs and all the objects detected in the narrow band, respectively. Black circles, hexagons, triangles, squares, and pentagons plot the surface densities of a ∼ 0.2 deg field, SXDS-C, SXDS-N, SXDS-S, SXDS-E, and SXDS-W, respectively. We distinguish between the raw and completeness-corrected surface densities with the open and filled symbols, respectively. The red filled circles represent the surface density averaged over our ≃ 1 deg 2 survey field. The errors are given by Poisson statistics for black symbols, while the errors of red symbols are made by the geometric mean of Poisson errors and field-to-field variation of eq. (4). For the presentation purpose, we slightly shift all the black points along the abscissa. The exact magnitude of a black point is the same as a magnitude of neighboring red point. The vertical axis on the right side indicates the numbers of objects, i.e. N/(0.5mag), identified in our ≃ 1 deg 2 survey area. The solid, dotted, and dashed lines present the surface densities of LAEs reproduced by our simulations for the cases of α = −1.5, −1.0, and −2.0, respectively (see Section 5.1 for more details).  Figure 9, but for NB570 data. Fig. 11.-Same as Figure 9, but for NB816 data. The blue and cyan squares are the surface densities of z = 5.7 LAEs detected with the same NB816 filter but in different sky areas by Shimasaku et al. (2006) and Hu et al. (2004), respectively. The red histogram is the same as the black-solid histogram, but with a completeness correction. The error bars of the red histogram are given by the geometric mean of Poisson errors and field-to-field variation of eq. (4). The right-hand vertical axis on each panel indicates the numbers of LAEs for the ≃ 1 deg 2 histogram. We plot color distribution reproduced by our simulations of fixed α = −1.5 with dotted, dashed, solid, and dot-dashed lines, whose σ EW values are presented in the legends.  Table 4). Dotted lines with the legend indicate wavelengths of a typical emission from AGN. "⊕" marks the wavelengths where significant residuals of sky subtraction remain due to strong OH sky lines on a faint continuum. Filled and open symbols represent an object with and without a spectroscopic identification, respectively. Solid and dotted curves are the templates of radio-quiet and radio-loud AGNs taken from Elvis et al. (1994); Telfer et al. (2002); Richards et al. (2003) (see text). The thick and thin curves indicate the template SEDs normalized with the detection limits of Lyα and X-ray, respectively. The horizontal solid bars present our detection limits in X-ray, infrared, and radio bands. , and spectra, f Lyα (spec), for our LAEs at z = 3.1 (left), 3.7 (middle), and 5.7 (right). The circles and diamonds indicate LAEs with FOCAS and VIMOS spectra, respectively. Since our FOCAS observations used a relatively narrow slit, we apply slit-loss corrections for the Lyα fluxes of FOCAS. The error bars of circles and diamonds show the ranges of a 95% confidence level.

Table 2. Lyα Emitters with spectroscopic redshifts
The solid line at each panel presents the equality of f Lyα (phot) and f Lyα (spec). We plot dotted lines for the differences from the equality by a factor of 2.  The left panel shows the ellipses for our observational data, while the right panel presents those for all LAEs with a positive emission (EW > 0) estimated by our simulations. Blue, green, and red contours represent z = 3.1, 3.7, and 5.7 LAE-LFs with the fixed slope of α = −1.5. Thick and thin lines indicate 1 and 2σ confidence levels, respectively.  -Histogram of the rest-frame Lyα equivalent widths (EW) for our LAEs at z = 3.1 (top), 3.7 (middle), and 5.7 (bottom). The black histograms and curves represent the bestestimate EW 0 and the EW 0 probability distribution estimated from errors of measurements, respectively, for photometrically selected LAEs with log L(Lyα) 42.6 and EW int 0 70−80. The gray histograms and curves are the same, but for all the photometrically selected LAEs. The ticks of vertical axes indicate a fraction (left-hand side) and the number (right-hand side) in a bin size of ∆EW = 50Å. The right-hand ticks correspond to the number of all the photometrically selected LAEs. The red histograms present the EW 0 distribution of our spectroscopically identified LAEs. On the bottom panel, the magenta histogram and black dashed line show the best-estimate EW 0 and the EW 0 probability distribution for z = 5.7 LAE sample obtained by DEIMOS spectroscopy in the Subaru Deep Field ).  Figure 23, but for the comparison of histograms for apparent ("No IGMcorr") and intrinsic ("IGMcorr") EW 0 from z = 3.1 to 5.7. At each panel, the gray region indicates the apparent EW 0 histogram with uncertainties whose area corresponds to the allowed parameters of the black curves and lines (+error bars) of Figure 23. The cyan, blue, and red areas are the same as the gray regions, but for intrinsic EW 0 corrected for the IGM absorption, assuming the average Lyα opacity (see text). For comparison, we repeatedly plot the z ∼ 4 gray and blue areas with the black and blue meshes, respectively, on the top and bottom panels.  Shapley et al. (2003), which are the average of the four subsamples of Steidel et al. (2003). On the right panel, the filled squares represent z = 5.7 LAEs of Shimasaku et al. (2006). The stars and diamonds present EW 0 of z ∼ 6 dropout galaxies from Stanway et al. (2007) and the compilation of Ando et al. (2006). The crosses plot EW 0 of z ∼ 5 dropout galaxies presented in Ando et al. (2006). The dotted lines are loci of the constant Lyα luminosity for 10 44 , 5 × 10 43 , 2 × 10 43 , 10 43 , 5×10 42 , and 1×10 42 erg s −1 from top left to the bottom. The shaded regions present the magnitude range with EW-large emitters (M UV −21.5), which is claimed by Ando et al. (2006). Fig. 27.-Composite spectra of our LAEs at z = 3.13 (left), 3.68 (middle), and 5.68 (right). The dotted lines indicate the wavelengths of interstellar absorption from star formation, or high ionized emission lines from AGN activities. The plots of spectrum are magnified in the inset boxes for wavelength ranges of Lyα (left) and Heii (right). For the z = 5.68 LAE, we only show the inset box of Lyα, since our spectrum does not cover the wavelength of Heii emission for z = 5.7 objects.