PHYSICAL PROPERTIES OF SPECTROSCOPICALLY CONFIRMED GALAXIES AT z ⩾ 6. I. BASIC CHARACTERISTICS OF THE REST-FRAME UV CONTINUUM AND Lyα EMISSION^*

Table 1 shows the list of the galaxies presented in this paper. There are a total of 67 spectroscopically confirmed galaxies at 5.6 ⩽ z ⩽ 7: 62 of them are from the SDF and the remaining 5 are from the Subaru XMM-Newton Deep Survey (SXDS; Furusawa et al. 2008) field. They represent the most luminous galaxies in terms of Lyα luminosity for LAEs or UV-continuum luminosity for LBGs in this redshift range.

The SDF covers an area of ∼876 arcmin², and its optical imaging data were taken with Subaru Suprime-Cam in a series of broad and narrow bands (Kashikawa et al. 2004). Especially noteworthy are the deep observations with three narrowband (NB) filters, NB816, NB921, and NB973, corresponding to the detection of LAEs at z ≃ 5.7, 6.5, and 7. The full widths at half-maxima (FWHMs) of the three filters are 120, 132, and 200 Å, respectively. So far the SDF project has spectroscopically confirmed more than 100 LAEs at z ≃ 5.7, 6.5, and 7, and more than 40 LBGs at 6 ⩽ z ⩽ 7. Our SDF galaxy sample contains 22 LAEs at z ≃ 5.7 (Shimasaku et al. 2006; Kashikawa et al. 2011), 25 LAEs at z ≃ 6.5 (Taniguchi et al. 2005; Kashikawa et al. 2006, 2011), and the z = 6.96 LAE (Iye et al. 2006). The LAEs at z ≃ 5.7 and 6.5 were selected in a similar way, and have a relatively uniform magnitude limit of 26 mag in the narrow bands NB816 and NB921, so they are from a well-defined flux-limited sample. Our SDF sample also contains 14 LBGs at 5.9 ⩽ z ⩽ 6.5 (Nagao et al. 2004, 2005, 2007; Ota et al. 2008; Jiang et al. 2011); two of them have not been previously published. These LBGs were selected with different criteria and thus have inhomogeneous depth. The z'-band magnitude limit is 26.1 mag in Nagao et al. papers, 26.5 mag in Ota et al. (2008), and 27 mag in Jiang et al. (2011). For the details of candidate selection and follow-up spectroscopy, see the original galaxy discovery papers above.

Five galaxies in our sample, including two LBGs at z ≃ 6 (Curtis-Lake et al. 2012) and three LAEs at z ≃ 6.5 (Ouchi et al. 2010), are from the SXDS. The two LBGs are very bright (z' < 25 mag) and have been analyzed by Curtis-Lake et al. (2013). The SXDS optical imaging data were also taken with Subaru Suprime-Cam in the same broad and narrow bands, but cover five times larger area than the SDF does (Furusawa et al. 2008).

In Table 1, the first 62 galaxies are from the SDF and the last 5 galaxies are from the SXDS. Columns 2 and 3 list the object coordinates. They are re-calculated from our own stacked optical images (see Section 2.2), and are fully consistent with those given in the galaxy discovery papers (typical difference <01). Column 4 lists the redshifts, measured from the Lyα emission lines of the galaxies. The galaxy discovery papers used different values for the rest-frame Lyα wavelengths (i.e., 1215, 1215.67, or 1216 Å) for redshift measurements. We convert all these redshifts to the redshifts listed in Table 1 by assuming a rest-frame Lyα line center of 1215.67 Å. The last column shows the reference papers of the objects. We will explain the rest of the table in the following subsections.

The galaxies in this paper were discovered in the SDF and the SXDS. The SDF public imaging data include stacked images in five broad bands BVRi'z' and two narrow bands NB816 and NB921. The flux limits for these data are given in Kashikawa et al. (2004). However, the public data do not include the data taken recently (also by Subaru Suprime-Cam), and the data taken in the y and NB973 bands. Therefore, we produced our own stacked images by including all available images in the Subaru archive, as explained below.

Our data processing began with the raw images obtained from the archival server SMOKA (Baba et al. 2002). Raw images with point-spread function (PSF) sizes greater than 12 were rejected. The data were reduced, re-sampled, and co-added using a combination of the Suprime-Cam Deep Field REDuction package (SDFRED; Yagi et al. 2002; Ouchi et al. 2004) and our own IDL routines. Each image was bias (overscan) corrected and flat-fielded using SDFRED. Then bad pixel masks were created from flat-field images. Cosmic rays were identified and interpolated using L.A. Cosmic (van Dokkum 2001). Saturated pixels and bleeding trails were also identified and interpolated. For each image, a weight mask was generated to include all above-mentioned defective pixels. We then used SDFRED to correct the image distortion, subtract the sky background, and mask out the pixels affected by the Auto-Guider probe. After individual images were processed, we extracted sources using SExtractor (Bertin & Arnouts 1996) and calculated astrometric and photometric solutions using SCAMP (Bertin 2006) for the final image co-addition. In order to match the public SDF images, we used the public R-band image as the astrometric reference catalog in SCAMP. Both science and weight-map images were scaled and updated using the astrometric and photometric solutions measured from SCAMP. Instead of homogenizing PSFs to a certain value as was done for the public data, we incorporated PSF information into the weight image so that the weight was proportional to the inverse of the square of the PSF FWHM. We re-sampled and co-added images using SWARP (Bertin et al. 2002). The re-sampling interpolations for science and weight images were LANCZOS3 and BILINEAR, respectively. We modified SWARP so that it performs sigma-clipping (5σ rejection) of outliers when co-adding images.

We produced images in the six broad bands BVRi'z'y and three narrow bands NB816, NB921, and NB973. The final products are a stacked science image, and its corresponding weight image, for each band. The pixel and image sizes of our products are the same as those of the public SDF images. The typical PSF FWHM is 06–07. We determined photometric zero points from the public SDF images whose zero points were known. The SXDS optical imaging data were reduced in the same way as we did for the SDF.

Our SDF broadband images are deeper than the public images in the Ri'z' bands, because the SDF team obtained more imaging data from Subaru recently, and we included all the available data above. For example, the public z'-band image has a depth of z' = 26.1 mag (5σ detection in a 2'' diameter aperture) with a total integration time of ∼7 hr. To date, the total z'-band data amount to ∼29 hr. Our new z'-band image has a depth of ∼27.0 mag, 0.9 mag deeper than the public image. In addition, the public data do not have images in the y and NB973 bands. The SDF y-band imaging data were taken with two different sets of CCDs (MIT and Hamamatsu), and have been used to search for z ≃ 7 LBGs (Ouchi et al. 2009). Although the fully depleted Hamamatsu CCDs are twice as sensitive as the MIT CCDs in the y band, their sensitivity (quantum efficiency) curves have similar shapes. Therefore, we stacked all the images taken with both sets of CCDs, as Ouchi et al. (2009) did in their work. The total integration time was 24 hr, and the depth was about 26.0 mag.

In Table 1, Columns 5–7 show the total magnitudes of the galaxies in one of the three narrow bands (NB816, NB921, or NB973, depending on redshift) and two broad bands z'y. For a given object in a given filter, its total magnitude is measured as follows. We first use SExtractor to measure the aperture photometry of the object in a circular 20 diameter, after the local sky background is subtracted. In cases where galaxies are close to their neighbors, we use a circular 16 diameter. Then an aperture correction is applied to correct for light loss. The aperture correction is determined from more than 100 bright, but unsaturated point sources in the same image. Almost all our galaxies are point-like objects and are not resolved in the SDF images. In cases where galaxies clearly show extended features, we use MAG_AUTO magnitudes as the best estimates of the total magnitudes. In Table 1, we did not list broadband photometry for the galaxies with weak detections (<5σ) in the J band. These galaxies are excluded in most of our analysis in this paper. Detections below 3σ in any of these bands are not listed as well. We carefully check each object, and find that object No. 12, a z ≃ 5.7 LAE, is overlapped by a bright foreground star (this was also pointed out in the galaxy discovery paper). The separation between the two objects is only ∼025, so we are not able to do photometry for this galaxy. We will not use this galaxy in the following analysis.

Figure 1 shows the transmission curves of six Subaru Suprime-Cam filters, including three broadband filters i'z'y and three narrowband filters NB816, NB921, and NB973. We do not show the other three bluer filters, BVR, because our galaxies were not detected in these bands. In the Appendix, we show the thumbnail images of the galaxies in one of the three Subaru Suprime-Cam narrow bands and the three broad bands i, z', and y.

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We obtained HST near-IR imaging data for a large sample of spectroscopically confirmed SDF galaxies at 5.6 ⩽ z ⩽ 7 from three HST GO programs 11149 (PI: E. Egami), and 12329 and 12616 (PI: L. Jiang). The three programs together with our Spitzer programs (see the next subsection) were designed to characterize the physical properties of these high-redshift galaxies. The HST observations were made with a mix of strategies. As the proposal for GO program 11149 was written, HST/WFC3 had not yet been installed. Our plan was to observe 20 bright galaxies with NICMOS in the F110W (hereafter J₁₁₀) and F160W (hereafter H₁₆₀) bands. The observations were made with camera NIC3. The exposure time was two orbits per band per pointing (or per object), split into four exposures. The total on-source integration per band was about 5400 s. We performed sub-pixel dithering during the four NICMOS exposures to improve the PSF sampling and to remove bad pixels and cosmic rays.

After we finished several targets, NICMOS failed, and then WFC3 was installed in 2009 May. Since WFC3 has much higher sensitivity, the rest of the galaxies in GO 11149 and all the galaxies in GO 12329 and 12616 were observed with WFC3. Because of the larger FOV of WFC3 and the increasing number of known z ⩾ 6 galaxies in the SDF, we changed our observing strategy for GO 12329 and 12616. We chose the regions that cover at least three galaxies (up to five) per HST/WFC3 pointing. By doing this we were able to observe many galaxies in a small number of telescope pointings. We used F125W (hereafter J₁₂₅) and H₁₆₀ in these two programs. In GO 12329, the exposure time was one orbit per filter per pointing. We found that some galaxies in our sample were barely detected with this depth. Therefore in GO 12616, all new WFC3 pointings had a depth of two orbits (on-source integration ∼4800 s; see Windhorst et al. 2011 for the anticipated sensitivity in two-orbit WFC3 exposures). We also re-observed most galaxies that were observed in GO 12329, so that they have a total of two-orbit depth per band. As in the NICMOS observations above, the WFC3 observation of each pointing (per band) was split into four exposures. Sub-pixel dithering during the exposures was also performed to improve the PSF sampling and to remove bad pixels and cosmic rays. The transmission curves of the three WFC3 filters are plotted in Figure 1.

As we mentioned above, several galaxies in our sample were found in the SXDS. They were covered by the UKIDSS Ultra-Deep Survey (UDS). Their HST/WFC3 near-IR data were obtained from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS; Grogin et al. 2011; Koekemoer et al. 2011). The exposure depth of the CANDELS UDS data is 1900 s in the J₁₂₅ band and 3300 s in the H₁₆₀ band. They are shallower than our WFC3 data for the SDF.

In the Appendix, we show the thumbnail images of the galaxies in the two HST near-IR bands J₁₁₀ (or J₁₂₅) and H₁₆₀. Note that the J₁₂₅-band image of the z = 6.96 LAE (No. 62) was obtained from GO program 11587 (Cai et al. 2011). This image also covers another two objects (No. 2 and No. 59) in our sample. Due to the high sensitivity of WFC3, the majority of the galaxies in our sample are detected with high significance in the near-IR images. Only 15 of them—among the faintest in the optical bands—have weak detections (<5σ) in the J band.

Our WFC3 data processing began with individual flat-fielded, flux-calibrated WFC3 infrared exposures delivered by the HST archive. Each pointing used a standard four-point dither pattern to obtain uniform half-pixel sampling. All exposures for each pointing were combined using the software Multidrizzle (Koekemoer et al. 2002), with an output plate scale of 006 pixel⁻¹ and a pixfrac parameter of 0.8. For our observations, this provides Nyquist sampling of the PSF and relatively uniform weighting of individual pixels. The rms maps were also derived from the Multidrizzle weight-map images, following the procedure used in Dickinson et al. (2004) that accounts for correlated noise in the final images.

Our NICMOS NIC3 data were reduced using a fully automated pipeline NICRED (Magee et al. 2007). NICRED starts its processing with raw science data and calibration files, and sequentially runs a set of steps from basic calibration to final mosaic generation. The most important part of the reduction is the basic calibration, because the NICMOS data suffer from variable bias, electronic ghosts, and cosmic-ray persistence. The basic procedure is as follows. NICRED first removes electronic ghosts, handles variable bias, rejects cosmic rays, and subtracts sky background. It then removes possible cosmic-ray persistence and residual instrument signatures. The rest of the procedure are common steps, including flat fielding, a nonlinearity correction, image alignment, and registration, etc. It finally creates drizzled images and the corresponding weight maps. The pixel size in the final products is 01, half of the native size.

We list the near-IR photometry of the galaxies in Columns 8–10 in Table 1. All galaxies were observed in the H₁₆₀ band and one or two of the J bands (J₁₁₀ and/or J₁₂₅). We perform photometry using SExtractor in dual-image mode with rms map weighting. The J band is used as the detection image. A single set of parameters is used for detection in all images. We compute the total magnitudes of the objects in both filters by using MAG_AUTO elliptical apertures, with a Kron factor of 1.8 and a minimum aperture of 2.5 semimajor radius, then applying aperture corrections. The aperture corrections are calculated by running SExtractor again with five Kron factors between 2.0 and 4.0, analyzing thousands of sources in the range J < 26 mag. We calculate a sequence of median correction versus Kron factor, which we extend to infinite radius with an exponential fit. All final photometry apertures are visually inspected, to screen against contamination from nearby objects or spurious detections. Detections below 5σ in the J band, or detections below 3σ in the H band, are not listed in Table 1.

We obtained Spitzer/IRAC imaging data for the SDF from two GO programs 40026 (PI: E. Egami) and 70094 (PI: L. Jiang). In GO 40026, we observed 20 luminous galaxies at z ⩾ 6, which were also the targets of our HST program 11149. The observations were made in IRAC channel 1 (3.6 μm) and channel 2 (4.5 μm). The other two channels (5.8 and 8.0 μm) were observed simultaneously. We used the cycling dither pattern with medium steps and a frame exposure time of 100 s. The on-source integration time per channel per pointing is 3 hr. In GO 70094 (during the Spitzer warm mission), we modified our observing strategy and observed high galaxy surface density regions, so that we can observe a large number of galaxies with slightly more than 10 telescope pointings. The cycling dither pattern with small steps was used with a frame exposure time of 100 s. We focused on IRAC channel 1 and increased on-source integration time to ∼6 hr per pointing. The two programs imaged roughly 70% of the SDF to a depth of 3–6 hr. They covered all the 62 SDF galaxies in channel 1 and 51 (out of 62) galaxies in channel 2.

The IRAC data processing began with the cBCD (corrected Basic Calibrated Data) products and associated mask and uncertainty images delivered by the Spitzer Science Center (SSC) archive. The image fits headers were updated to match the astrometry in the SDF optical images. Then the images were processed, drizzled, and co-added using the SSC pipeline MOPEX. This is a fully automated procedure. The final images have a pixel size of 06, roughly a half of the IRAC native pixel scale. The IRAC images for the SXDS galaxies were obtained from the SSC archive (programs 60022 and 80057). The data were reduced in the same way above. In the Appendix (the last two columns), we show the thumbnail images of the galaxies in the two IRAC channels.

Mid-IR photometry is complicated by source confusion. Galaxies in deep IRAC images are often blended with nearby neighbors, so accurate photometry requires proper deblending and removing neighbors. We will present IRAC photometry of our galaxies in the third paper of this series.

The rest-frame UV-continuum slope provides key information to constrain young stellar populations in galaxies. For z ⩾ 6 LBGs in the literature, especially those selected from HST photometric samples, their UV slopes are usually measured from two broad bands J₁₂₅ and H₁₆₀ that do not cover Lyα emission. Recent studies show that high-redshift LBGs generally have steep UV slopes and low dust content (e.g., Bouwens et al. 2009, 2012b; Dunlop et al. 2012a; Finkelstein et al. 2012; González et al. 2012; Walter et al. 2012). For example, Bouwens et al. (2009) found that β decreases from β ≃ −1.5 at z ≃ 2 to β ≃ −2 at z ≃ 6. Finkelstein et al. (2012) showed that β changed from β ≃ −1.8 at z ≃ 4 to β ≃ −2.4 at z ≃ 7. Extremely steep slopes of β ≃ −3 have been reported in very faint z ≃ 7 galaxies (e.g., Bouwens et al. 2010). It was also found that lower-luminosity galaxies tend to have steeper slopes (e.g., Bouwens et al. 2012b; González et al. 2012). Recently, the results on the blue colors in high-redshift LBGs have been questioned by Dunlop et al. (2012a) and McLure et al. (2011), who claimed that previous measurements were significantly affected by contaminants in the photo-selected LBG samples and the low signal-to-noise (S/N) ratios of faint objects, and that the extremely steep slopes were caused by the so-called β bias. This bias is partly produced by the removal of galaxies with larger (redder) β values from the sample as lower-redshift interlopers, which would preferentially remove flux-boosted sources in the H₁₆₀ band and skew the β distribution to smaller (i.e., bluer) values as a result. As pointed out by Bouwens et al. (2012b), this β bias can be large if the same bands (J₁₂₅ and H₁₆₀) are also used to select LBGs. With a more restricted selection of LBGs candidates from the same HST data set, Dunlop et al. (2012a) and McLure et al. (2011) found that the average slope of z ≃ 7 LBGs is β ≃ −2, which is not steeper than the bluest galaxies at z ⩽ 4. They further found no relation between β and the UV-continuum luminosity. As the debate is still going on (e.g., Bouwens et al. 2012b; Finkelstein et al. 2012; Dunlop et al. 2012b), the key is to construct a high-redshift galaxy sample that is free from such a bias.

Our galaxy sample presented here is unlikely to be strongly affected by this β bias, not only because these galaxies have spectroscopic redshifts but also because our original source selection did not utilize any information on the rest-frame UV-continuum slope. Furthermore, we did not include weak detections in our analysis. For many galaxies, especially the z ≃ 5.7 LAEs and z ≃ 6 LBGs, β was measured from more than two bands. It should be pointed out, however, our LBGs were spectroscopically confirmed to have strong Lyα emission, which could bias the LBG sample to galaxies with lower extinction and thus to those with bluer UV-continuum slopes.

Figure 3(a) shows the rest-frame UV-continuum slopes β as a function of M₁₅₀₀, the absolute AB magnitude of the continuum at rest frame 1500 Å. M₁₅₀₀ is calculated from B × λ^β in Equation (1). Figure 3 only includes the galaxies that have measured β in Table 2. These galaxies cover the brightest UV luminosity range M₁₅₀₀ < −19.5 mag. For the galaxies that do not have measured β, they do not have reliable detections (<5σ) in the near-IR bands, so they are usually fainter than M₁₅₀₀ = −19.5 mag (see Section 4.2 and Figure 6). The green circles in Figure 3(a) represent the LBGs at z ≃ 6, and the blue and red circles represent the LAEs at z ≃ 5.7 and 6.5 (including z ≃ 7), respectively. The values of M₁₅₀₀ and β are also listed in Columns 2 and 3 of Table 2. Our measurements of β are reliable because of the secure redshifts and multi-band photometry. As we addressed above, the slopes are calculated from all available broadband data that do not cover the Lyα emission line. For any β that was derived from more than two bands, its error is usually smaller than 0.4. So most of the z ≃ 5.7 LAEs and z ≃ 6 LBGs have relatively small errors on β. For the z ≃ 6.5 LAEs, their slope errors are generally larger, as many of them were only detected in the two near-IR bands in addition to NB921.

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The galaxies in Figure 3 apparently have steep UV-continuum slopes that are roughly between β ≃ −1.5 and β ≃ −3.5. The weighted mean is β = −2.29, and the median value is β = −2.35. This slope is slightly steeper than those from previous observations (e.g., Bouwens et al. 2012b; Dunlop et al. 2012a, 2012b; Finkelstein et al. 2012) and simulations (e.g., Finlator et al. 2011; Dayal & Ferrara 2012) in the literature. The slope β also appears to show weak dependence on M₁₅₀₀ that lower-luminosity galaxies have steeper slopes. The dashed line is the best linear fit to all the data points. This trend is caused by the several most luminous galaxies at M₁₅₀₀ ≃ −22 mag. These luminous galaxies have red colors β ≃ −1.8. If we exclude these galaxies in our fit, the trend almost disappears. The dash-dotted line in the figure illustrate the result by displaying the best fit to the galaxies at M₁₅₀₀ > −21.7 mag, and its slope is consistent with zero.

In the above analysis, galaxies with near-IR detections below 5σ in the J band were discarded. This has negligible impact on our results. Our HST near-IR data have relatively uniform depth (two orbits per band per pointing), so the 5σ detection cut indeed puts a flux limit on M₁₅₀₀ in Figure 3(a), which does not affect our results in the bright region M₁₅₀₀ < −19.5 mag. We also perform two simple tests to investigate whether large errors on photometry or β have strong impact on our results. In the first test, we stack the images of nine galaxies whose errors of β (σ_β) are greater than 0.8 in Figure 3, and then measure photometry and calculate β on the stacked images in the J₁₂₅ and H₁₆₀ bands. The input images are scaled so that the galaxies have the same magnitude in the J₁₂₅ band before stacking, otherwise the final image would be dominated by the brightest objects. The stacked images have much higher S/N ratios. The nine galaxies have a median slope of β ≃ −2.1. The slope for the stacked object is β = −2.2 ± 0.2, which agrees with the median value of the individual galaxies. The result is shown as the magenta star in Figure 4, where the gray circles represent the same galaxies shown in Figure 3(a). In the second test, there are 10 galaxies with β < −2.8 that have both J₁₂₅ and H₁₆₀ images. The median value of their slopes is β ≃ −3.0. We stack their images in the same way as we did above. The slope for the combined object is β = −2.9 ± 0.2, which is also consistent with the median value of the individual galaxies. The magenta square in Figure 4 represents the combined object. From these tests, our measurements of β are not biased even for faint objects with relatively large photometric errors.

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It is generally believed that high-redshift galaxies have steep UV slopes β, and β changes with redshift: higher-redshift galaxies tend to be bluer due to less dust extinction. The relation between β and UV luminosity (M_UV, or M₁₅₀₀ in this paper) is still controversial. In Figure 4, we compare our results with recent studies (Bouwens et al. 2012b; Dunlop et al. 2012a; Finkelstein et al. 2012). Bouwens et al. (2012b) found a correlation between β and M_UV at all redshifts in a range of 4 < z < 7. They claim that galaxies have bluer UV colors at lower luminosities. The green triangles in Figure 4 represent the average slopes at z ∼ 6 from their study. Dunlop et al. (2012a) used a more restricted selection of LBGs by excluding low S/N detections from a similar HST data set. They found that high-redshift galaxies have an average slope of β ≃ −2, and it does not change with M_UV. The blue crosses in Figure 4 represent the average slopes at 5 < z < 7 from their study. Finkelstein et al. (2012) also found that β shows minor relation with M₁₅₀₀ in the redshift range from z = 4 to 8. The red diamonds in Figure 4 represent the average slopes at z ≃ 6 from their study.

Figures 3 and 4 suggest that in our sample there is little dependence of β on M₁₅₀₀ in the range of M₁₅₀₀ < −19.5 mag. The three studies mentioned above were all based on HST data that are ∼1–2 mag deeper than ours. In the luminosity range of M₁₅₀₀ < −19.5 mag, these studies do not show evidence of a significant correlation either, though there is likely a weak trend at the fainter range M₁₅₀₀ > −19.5 mag. Therefore, it is possible that the reported correlation between β and M_UV, if exists, is mainly driven by very faint galaxies.

The mean value of our measured β is −2.3. It is slightly steeper than β = 2.1–2.2 by Bouwens et al. (2012b) in the same luminosity range, and is also steeper than β ≃ −2 by Dunlop et al. (2012a) and Finkelstein et al. (2012). This is due to the nature of our sample. The galaxies in the previous studies are photo-selected LBGs. Our galaxies are spectroscopically confirmed and have strong Lyα emission lines, suggesting that they likely have lower dust extinction, and thus steeper UV slopes.

It is not clear whether high-redshift LAEs and LBGs represent physically different galaxy populations. Early observations found that LAEs at z = 5–6 are smaller and less massive compared to LBGs, and thus constitute younger stellar populations (e.g., Dow-Hygelund et al. 2007; Pirzkal et al. 2007). However, this apparent difference could be a direct result of selection effects, and LAEs may represent a subset of LBGs with strong Lyα emission lines (e.g., Dayal & Ferrara 2012). Whether or not LAEs and LBGs have similar populations will be reflected in their physical properties. For example, if LAEs are substantially younger, they are expected to have steeper UV slopes.

In Figures 3 and 4, the distribution of our slopes β for the z ≃ 5.7 and z ≃ 6.5 LAEs are β = −2.3 ± 0.5 and β = −2.0 ± 0.8, respectively. The β distribution for the LBGs is β = −2.5 ± 0.4. Although the scatters are large, the LAE slopes are apparently not steeper than the LBG slopes in our sample. They are also not steeper than the slopes of the LBGs in previous studies mentioned above, which is contrary to the assumption that LAEs contain younger stellar populations than LBGs do. This indicates that most LAEs are probably not as young as what was previously suggested.

The majority of our galaxies have slopes β > −2.7 in Figure 3(a). There are a fraction of galaxies whose slopes are steeper than −2.7. Some of them have relatively small errors around σ_β ∼ 0.4. The existence of these β ≃ −3 galaxies are statistically robust (not a distribution tail). In Figure 3(b), our statistical test shows that the distribution of the observed β is broader and flatter than the distribution of β expected if all the galaxies have an intrinsic β = −2.3 with the observed uncertainties. It clearly indicates a statistically significant excess of galaxies with β ≃ −3. These galaxies do not show distinct properties in many aspects, such as Lyα EW and UV morphology. The existence of these β ≃ −3 galaxies in our sample is intriguing. The UV colors cannot be arbitrarily blue for a given initial mass function (IMF). For the commonly used Salpeter IMF, a β ≃ −3 usually means a very young stellar population with extremely low metallicity and no dust content, regardless of star formation histories (e.g., Finlator et al. 2011; Wilkins et al. 2011). In particular, the β < −3 galaxies, if confirmed by future deeper observations, will be challenging for current simulations (Finlator et al. 2011). In addition, the broad distribution of the observed β also suggests significant intrinsic scatter in dust and/or age. Detailed discussion is deferred to the next paper when we perform SED modeling with the IRAC data.

From Figure 3, the five most luminous galaxies at M₁₅₀₀ ≃ −22 mag have UV slopes β ≃ −1.8, which is significantly redder than the mean value β = −2.3 of the sample. The measurements of β are robust since these galaxies are very bright and detected in almost all the broad bands redward of Lyα. In particular, they are all detected at high significance in the IRAC bands. Their Lyα emission is relatively small compared to their UV-continuum emission. From the HST images, they have very extended morphologies, even with double or multiple cores, suggesting that they are interacting systems with enough amounts of dust to redden their UV colors. These galaxies are similar to the luminous galaxies at z ∼ 6 found by Willott et al. (2013) in the Canada–France–Hawaii Telescope Legacy Survey. Willott et al. (2013) selected a sample of luminous galaxies with M_UV ≃ −22 in a 4 deg² area and found that their galaxies have very red colors with a typical slope β = −1.4, which is caused by large dust reddening of A_V > 0.5.

Spectroscopic data generally provide reliable line luminosities, but this becomes complicated for z ⩾ 6 galaxies. During the spectroscopic observations of these galaxies, the total integration time is at least a few hours per object or per slit mask. Sometimes the images of one object are taken in different nights. Light loss varies with many parameters, such as varying seeing, different observing conditions, possible offsets between targets and slits, and even the sizes of targets. So it is difficult to accurately correct for light loss. In addition, even with a few hour integration on the largest telescopes, the spectral quality of many galaxies are still poor, simply because they are faint. All of the above effects can easily result in large uncertainties in the measurements of their Lyα luminosities.

Photometric data provide an alternative way to measure the observed Lyα flux, especially for LAEs. We have high-quality narrowband and broadband photometry and secure redshifts. Our procedure used all available data and was straightforward. The Lyα luminosities of the LAEs were derived from narrowband photometry after their underlying continua were subtracted. For the majority of the LAEs in our sample (EW ⩾ 20Å), their narrowband photometry is dominated by Lyα emission, meaning that the real Lyα emission is smaller—but not much smaller—than the total narrowband photometry. Therefore, we neither significantly overestimate the Lyα luminosity (the maximum is the total narrowband emission), nor significantly underestimate it (the minimum is at least a half of the maximum for most LAEs).

The measurements of our Lyα luminosities for LBGs are less accurate. For most of the LAEs, their narrowband photometry is dominated by the Lyα emission, so their Lyα luminosities can be well determined. For the LBGs, Lyα luminosities were calculated from the z'-band photometry. The z' band is very broad, and its photometry is almost completely dominated by the UV-continuum flux. Therefore, even small uncertainties on the z'-band photometry or on measurements of UV continuum will cause very large uncertainties on the Lyα emission. Therefore, for the Lyα luminosities of our LBGs, we directly adopt the values from the galaxy discovery papers, which were derived from optical spectra. All the measured Lyα luminosities are given in Column 4 of Table 2.

Figure 5 compares our Lyα luminosities of the LAEs to those given in Kashikawa et al. (2011). The upper panel shows the comparison between our luminosities and the luminosities from the photometric data in the galaxy discovery papers. The photometric data used in these papers are usually the narrowband and z'-band photometry. Our results are well consistent with these previous measurements with a small scatter. The lower panel shows the comparison between our measurements and the measurements from the spectroscopic data in Kashikawa et al. (2011). The two results also agree with each other, although our measurements are slightly larger and the overall scatter is larger than that in the upper panel.

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Column 5 of Table 2 lists the Lyα EWs of the galaxies that have measured UV-continuum properties in Section 3.1. These galaxies are also shown as filled circles in Figure 6. The bluest galaxy with an unusual β = −4.37 is excluded. We also estimate EWs for the LAEs that have weak or none detections (<5σ) in the J band. These galaxies could potentially have very large EWs. In order to estimate their EWs (or the lower limits of EWs), we assume a UV slope β = −2.3 and compute UV flux from their J-band photometry. Almost all these galaxies are detected at >2σ in the J band. If a detection is below 2σ, we use 2σ as an approximation. The measurements are shown as the open circles in Figure 6. The upper panel shows the relation between the Lyα luminosity and UV-continuum luminosity M₁₅₀₀. The Lyα luminosity has a weak dependence on M₁₅₀₀. The lower panel displays the measured Lyα EWs as a function of M₁₅₀₀. Our galaxies have moderately strong EWs in the range from ∼10 to ∼200 Å. The median EW value of LAEs is 81 Å, consistent with those given in Kashikawa et al. (2011). As expected, the LAEs with weak near-IR detections have much higher EWs roughly between 100 and 300 Å.

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Figure 6 (lower panel) shows that lower-luminosity galaxies tend to have higher EWs. It has been a longstanding debate whether this is a real relation, or just the result of a selection effect, i.e., in a flux-limited survey, lower-luminosity galaxies naturally have larger EWs in order to be detected in imaging data or identified in spectroscopic data. Many papers have reported this inverse relation between Lyα EW and UV luminosity to be real at z ⩾ 3 (e.g., Shapley et al. 2003; Ando et al. 2006; Reddy et al. 2008; Stark et al. 2010), while others claimed that the relation is not obvious, when the selection effects are properly taken into account (e.g., Nilsson et al. 2009; Ciardullo et al. 2012). In Figure 6, there is an apparent lack of large-EW LAEs at the high-luminosity end that does not suffer from this selection effect (Ando et al. 2006), suggesting that the relation in our sample is likely real. However, the relation should be weaker than it appears, because we have missed faint galaxies with small Lyα EWs by selection. We will further assess the effects of the source selection on the shape of the EW(Lyα)–M_UV relation in Section 5.1. As we will mention in the next subsection, one explanation for the relation between Lyα EW and UV luminosity (if exists) is that the escape fractions of Lyα photons in higher-SFR (i.e., higher UV luminosity) galaxies are smaller (e.g., Forero-Romero et al. 2012; Garel et al. 2012).

We estimate SFRs from the UV-continuum luminosity and Lyα luminosity, respectively. The UV SFR is derived by

$$\begin{equation} {\rm SFR (UV)} = 1.4 \times 10^{-28}\ L_{\nu }({\rm UV})\ M_{\odot }\ {\rm yr}^{-1}, \end{equation} \tag{ 2 }$$

where L_ν(UV) is the UV-continuum luminosity (Kennicutt 1998; Madau et al. 1998). We use the average of the luminosities at rest frame 1500 and 3000 Å to compute L_ν(UV). For the Lyα SFR, we use the expression

$$\begin{equation} {\rm SFR} ({\rm Ly}\alpha) = 9.1 \times 10^{-43}\ L({\rm Ly}\alpha)\ M_{\odot }\ {\rm yr}^{-1}, \end{equation} \tag{ 3 }$$

which is based on the line emission ratio of Lyα to Hα in Case B recombination (Osterbrock et al. 1989) and the relation between SFR and the Hα luminosity (Kennicutt 1998). The derived SFRs are listed in Columns 6 and 7 of Table 2.

Figure 7 compares the two estimated SFRs without correction for dust extinction. As in Figure 6, the filled circles are the galaxies with reliable measurements. These galaxies have moderate SFRs from a few to a few tens of M_☉ yr⁻¹. The open circles are the galaxies with weak near-IR detections, and their measurements of SFRs are crude. Because they have large Lyα EWs and weak UV-continuum flux (Figure 6), they show small UV SFRs (∼1–2 M_☉ yr⁻¹) and high SFR(Lyα)-to-SFR(UV) ratios. For the purpose of comparison, we correct SFR(Lyα) for the IGM absorption. Lyα emission at high redshift is complicated by factors, such as the resonant scattering of Lyα photons and the IGM absorption, and it is difficult to model Lyα radiative transfer and predict intrinsic Lyα emission (e.g., Zheng et al. 2010; Dijkstra et al. 2011; Yajima et al. 2012; Silva et al. 2013). We thus do not correct individual galaxies. Instead, we derive an average Lyα flux reduction for all the galaxies. The average correction is calculated from the composite Lyα line of Kashikawa et al. (2011) by assuming that the intrinsic Lyα profile is symmetric around the peak of the composite line. The dotted line in Figure 7 illustrates the average correction of 24%. When the effect of the IGM absorption is taken into account in this way, the UV and Lyα SFRs for most luminous galaxies (filled circles) are reasonably consistent within a factor of two.

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Figure 7 shows a trend that the SFR(Lyα)-to-SFR(UV) ratio becomes increasingly smaller toward higher SFRs. The dashed line illustrates this trend by displaying the best loglinear fit to the data points. This trend is already suggested by the relation between EW(Lyα) and M₁₅₀₀ in Figure 6, since SFR(UV) reflects M₁₅₀₀ and EW(Lyα) mimics SFR(Lyα)/SFR(UV). Accordingly, this trend has also been shaped by the selection effect due to the nature of the flux-limited sample, i.e., we have missed low SFR(UV) galaxies with low SFR(Lyα)-to-SFR(UV) ratios. Therefore, the real trend of the SFR(Lyα)-to-SFR(UV) ratio, if exists, should be much weaker than it appears. This trend could also be due partly to the relation between SFRs and the escape fractions of Lyα photons. The model of Garel et al. (2012) predicts that at high redshift, the escape fractions of Lyα photons in low-SFR galaxies are close to 1, but become smaller in galaxies with higher SFRs (see also, e.g., Forero-Romero et al. 2012). This is also consistent with Curtis-Lake et al. (2012), who found that in a sample of luminous (high SFRs) z ⩾ 6 LBGs, the Lyα SFRs are only ∼40% of the UV SFRs.

Figure 6 shows an apparent correlation between EW(Lyα) and M₁₅₀₀ in our sample. As we already mentioned, the relation is affected by the nature of the flux-limited sample, i.e., the limiting Lyα line flux (and therefore the limiting line luminosity) associated with both narrowband and spectroscopic observations. In Figure 8(a), we plot the current LAE samples at z ≃ 5.7 and 6.5, as well as those from another large LAE survey at z ≃ 3.1, 3.7, and 5.7 by Ouchi et al. (2008). The diagonal dotted line is defined by an Lyα luminosity of 2.5 × 10⁴² erg s⁻¹, which roughly corresponds to the limits of these surveys. The figure illustrates that the slope of the EW(Lyα)–M_UV relation is largely shaped by the limiting luminosity, which censors sources that would fall below the diagonal dotted line. In addition, as pointed out by Ciardullo et al. (2012), EW is a derived quantity from the emission line and underlying continuum, so any relation between EW and the line (or continuum) flux may suffer from correlated errors. Such correlated errors could result in an apparent relation by scattering objects toward one direction (Ciardullo et al. 2012).

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Although nothing definite can be said about the properties of high-redshift LAEs below our detection limit, it is natural to expect that the distribution of LAEs extends toward smaller EW(Lyα). Therefore, it would be interesting to see how the population of low-redshift low-luminosity LAEs compares with the high-redshift population shown in Figure 8(a). In Figure 8(b), we include the sample of Galaxy Evolution Explorer (GALEX) selected z ≃ 0.2–0.4 LAEs presented by Cowie et al. (2010, 2011a). The figure shows that this low-redshift LAE sample contains the kind of LAEs that would be missed at high redshift (i.e., below the dotted line). Once these low-luminosity LAEs are included, the EW(Lyα)–M_UV correlation could diminish. This is consistent with the fact that no evolution has been established with the EW distribution of LAEs from z ≃ 0.2–0.4 to z ≃ 3 (Cowie et al. 2010) and from z ≃ 3.1 to 5.7 (Ouchi et al. 2008). This may suggest the possibility that although bright LAEs are more abundant at high redshift, the underlying Lyα EW distribution may be fairly invariant. However, we also caution that the lack of a correlation in Figure 8(b) is partly caused by another selection effect in these LAE samples, namely, EW(Lyα) ⩾20 Å, which produces a sharp horizontal boundary at the bottom. In addition, the mix of different samples in Figure 8 could dilute intrinsic relations (if exist).

Given these selection effects, it is difficult to determine with the current LAE samples how strong the correlation between EW(Lyα) and M_UV is. To perform such an analysis in a statistically meaningful manner, we will need a much larger LAE sample, as pointed out by Nilsson et al. (2009). For the discussion in the subsequent sections, we will assume two extreme cases: (1) the slope of the EW(Lyα)–M_UV correlation is as steep as seen in Figure 6 (the dashed line in the lower panel), and (2) the slope of the EW(Lyα)–M_UV correlation is completely flat. As we shall see, these two limiting cases will minimize/maximize the size of the LAE population and therefore their contribution to the rest-frame UV luminosity density.

In this paper, we call galaxies found by the narrowband technique LAEs and those found by the dropout technique LBGs. This is a widely used definition. Strictly speaking, this LAE/LBG classification only reflects the methodology that we employ to select galaxies. It does not necessarily mean that the two types of galaxies are intrinsically different. A galaxy with strong Lyα emission could be detected by the both techniques. Another popular definition of LAEs is based on the rest-frame EW of the Lyα emission line. One galaxy is an LAE if its Lyα EW is greater than, for example, 20 Å. With this definition, almost all the galaxies in our sample are LAEs, as seen from Figure 6. This definition with Lyα EW is physically more meaningful. However, the measurements of Lyα EWs are usually accompanied with large errors. Furthermore, one can easily obtain a flux-limited sample, but not an EW-limited sample.

It is not yet totally clear whether high-redshift LAEs and LBGs represent physically different populations. Direct comparison between LAEs and LBGs is difficult. The procedure of obtaining a spectroscopic sample of LAEs is relatively straightforward. LAE candidates are selected based on their Lyα luminosities (and one or more broadband photometry), and follow-up spectroscopic identification is also based on their Lyα luminosities. This results in a complete flux-limited sample in terms of Lyα luminosity. For LBGs at z ⩾ 6, candidate selection is based on broadband colors, but spectroscopic identification is based on Lyα luminosity. Therefore, the resultant LBG sample is inhomogeneous in depth of either Lyα luminosity or UV-continuum luminosity, and represents only a subset of LBGs with strong Lyα emission.

So far, we did not find significant differences between our LAEs and LBGs in the UV luminosity range of M₁₅₀₀ < −19.5 mag. Figures 3 and 4 have shown that they have similar UV-continuum slopes. The LAEs do not exhibit steeper slopes than the LBGs, indicating that their underlying stellar populations are not very different. To examine the relation between LAEs and LBGs further, one useful tool is the EW(Lyα)–M_UV plot in the form of Figures 6 and 8. We expect the two populations to have a large overlap, but the focus here is on the non-overlapping population(s) that can be picked up by one selection method but not by the other. For example, the LAE selection may pick up galaxies with extremely large EW(Lyα) whose continuum emission is so faint that they will drop out of LBG samples. Alternatively, the LBG selection can pick up galaxies with small EW(Lyα) which do not show up in LAE samples. Therefore, we would like to know how significant/insignificant such non-overlapping populations between LAEs and LBGs are.

Figure 9 plots EW(Lyα) and M_UV of high-redshift LAEs (from Figure 8) and LBGs together. The latter sample comes from this work (z ≃ 6) and from Stark et al. (2010) (z ≃ 3–6). The figure suggests that there is no significant difference between the LAE and LBG populations in terms of the EW(Lyα) and M_UV distributions. The two populations occupy roughly the same region on the plot. For example, we do not see any sign of enhanced Lyα strengths among the LAE population. This implies that the LBG selection would almost fully recover the LAE population. In other words, there are very few LAEs with exceptionally large Lyα EWs that would drop out of the LBG selection due to their faintness in continuum. The reverse (i.e., LBGs that would escape the LAE selection due to weak Lyα emission) is difficult to assess with our current sample because our spectroscopic program was not designed as an extensive follow-up of LBGs. In the next section, we will construct the UV-continuum LF of LAEs and examine how it compares with the UV-continuum LF of LBGs.

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Because of the deep HST images, we were able to detect almost all the LAEs at a significance of >2σ. This allows us to derive the UV-continuum LF of LAEs directly from the data. The UV LF of LAEs together with the UV LF of LBGs will help us estimate the fraction of galaxies that have strong Lyα emission, and constrain the contribution of LAEs to the total UV ionizing photons. Our LAEs are from an Lyα flux-limited (not EW-limited) sample, so they have different detection limits of Lyα EWs at different UV luminosities (see Figures 8 and 9). In this subsection, we will derive the UV LF of LAEs with Lyα EWs greater than 20 Å, by extrapolating the observed LAE population down to this EW threshold.

We first compute the number densities of the LAEs without extrapolating the LAE population to the EW threshold of 20 Å. The area covered by our LAEs is calculated from the area of the whole LAE sample given in Kashikawa et al. (2011), by matching the number of our LAEs to the number of the whole LAE sample. We do not use the actual area that our HST observations covered, because we selected high surface density regions of galaxies for the HST programs (see Section 2.3). We then incorporate the completeness corrections from Kashikawa et al. (2011). Completeness is calculated for individual galaxies, as it is a function of narrowband magnitude. The resultant number densities are shown as the thick blue and red lines in Figure 10. They set the absolute lower limits on the UV LF of LAEs at z = 5.7 and 6.5.

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We then extrapolate the densities to EW = 20 Å using the Lyα EW distribution function. Figure 11 shows the Lyα EW distribution of the LAEs in our sample. We assume that the EW distribution is an exponential function $n\propto e^{-w/w_0}$, where w is EW and w₀ is the e-folding width. It is often assumed that w₀ is correlated with UV luminosity (e.g., Kashikawa et al. 2011; Stark et al. 2011). We assume that w₀ is a loglinear function of M₁₅₀₀: log(w₀) = a + b × (M₁₅₀₀ + 20), where a and b are scaling factors. Given the small numbers of the galaxies, it is not realistic to obtain reliable measurements for both a and b. Therefore, we consider the two extreme cases mentioned in Section 5.1: (1) b = 0.225, where we assume that the slope of the EW(Lyα)–M₁₅₀₀ correlation is as steep as seen in Figure 6 (the dashed line in the lower panel); and (2) b = 0, where the slope of the correlation is completely flat. These two limiting cases will minimize (b = 0.225)/maximize (b = 0) the size of the LAE population. The real b value is between 0 and 0.225. We then determine a by fitting the exponential function to the EW distribution of the LAEs with M₁₅₀₀ < −19.5 mag in our sample. The best fit is shown in the top panel of Figure 11. With the derived a and assumed b, we can calculate the Lyα EW distribution at any luminosity. The other panels in Figure 11 show the predicted EW distributions for the two extreme cases with the dashed (b = 0.225) and dash-dotted (b = 0) lines.

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The shaded regions in Figure 10 show the UV LFs of LAEs corrected to EW(Lyα) = 20 Å for the two extreme cases. Their lower and upper boundaries represent the lower and upper limits of the LFs. The 1σ statistical uncertainties have been included. At M₁₅₀₀ < −20.5 mag, no correction is actually applied, because our sample is complete at EW = 20 Å down to this magnitude. Toward fainter magnitudes, the correction becomes increasingly larger, and the difference of correction between the two cases also becomes larger. In the faintest end, the difference of the number densities between the lower and upper limits is larger than a factor of three.

The cyan and green curves in Figure 10 show the UV LFs of photo-selected LBGs from the literature (Bouwens et al. 2007, 2011; McLure et al. 2009; Ouchi et al. 2009), compared to our results. At the bright end, the LAE UV LFs are roughly comparable to the LBG LFs,¹¹ consistent with similar results reported by Ouchi et al. (2008) and Kashikawa et al. (2011). This suggests a large fraction of LAEs among the brightest LBGs. Such high fraction has been observed by Curtis-Lake et al. (2012), who found that the LAE fraction in a sample of very bright (M_UV ⩽ −21 mag) UDS LBGs is about 50%. Stark et al. (2011) reported a lower fraction (20% ± 8%) of LAEs with EW(Lyα) >25 Å in a sample of bright z ∼ 6 LBGs (−21.75 < M_UV < −20.25). We note, however, their sample contains a small fraction (10%) of LAEs with M_UV < −21 mag, so their LAE fraction is dominated by the galaxies at M_UV > −21 mag. Our LAE fraction (∼35%) in a similar range of −21 < M_UV < −20 is not much different from theirs, given their slightly higher EW limit. Note that the measurements of the LAE fraction among the brightest galaxies are subject to large uncertainties owing to the small numbers of galaxies available.

In Figure 10, the UV LF of LAEs at the faint end is even more uncertain, as it depends critically on how we extend the EW(Lyα) distribution toward EW = 20 Å, which is far below our detection limits. Current ground-based spectroscopy is not yet able to reach this regime. Depending on the value of b we assume, the faint-end slope of the LAE UV LF could be almost as steep as that of the LBG UV LF (b ∼ 0) or significantly flatter (b > 0). If we maximize the LAE UV LF by assuming b ∼ 0, we have to apply a large incompleteness correction (> × 10 at the faintest end) to account for LAEs down to EW(Lyα) = 20 Å. It means that the Lyα EW distribution must be highly concentrated on small EWs, so that the observed LAEs represent a small sub-group of high-EW galaxies that constitutes a tiny fraction of the overall LAE population. Despite this uncertainty, it is reasonable to conclude with Figure 10 that the number density of LAEs falls significantly short of that of LBGs at the faint end. This result could have an important implication for the population of galaxies that were responsible for cosmic reionization. It implies the existence of a large population of LBGs with weak Lyα emission (EW < 20 Å). Because the UV LF slope of LBGs is steep, the vast majority of the UV photons would come from very faint galaxies (far below L*). This suggests that the LBG population with weak Lyα emission dominate the UV photon budget for cosmic reionization.

In Figure 10, the comparison between the UV LFs of LAEs at z ≃ 5.7 and 6.5 is straightforward, and it shows little evolution. This supports the previous claim that the Lyα LF evolution from z ∼ 5.7 to 6.5 is due to an increasing neutral fraction of the IGM between the two redshifts and not due to the evolution of the LAE galaxy population (Kashikawa et al. 2006, 2011). These studies showed that the Lyα LF evolves rapidly from z ∼ 5.7 to 6.5, and pointed out in particular that there is a lack of luminous LAEs at z ∼ 6.5. In contrast, the evolution of the UV LF of LAEs between the two redshifts is much more modest. This was explained by the increasing neutral fraction of IGM from z ∼ 5.7 to 6.5 that attenuates Lyα emission. In these studies, the UV-continuum luminosities were measured from the SDF z'-band imaging data, which can only detect bright LAEs, and are also contaminated by Lyα emission (and Lyman break) for z ≃ 6.5 LAEs. Our HST data were deep enough to detect almost all the LAEs in our sample, so our measurements of UV-continuum luminosities are more robust. We confirm the consistency of the UV LFs of LAEs at z ≃ 5.7 and 6.5, which rules out the possibility of a strong intrinsic galaxy evolution between the two redshifts, and strengthens the interpretation that the increasing neutral fraction of IGM causes the strong evolution of the Lyα LF toward z ≃ 6.5.