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Ly-alpha emitting galaxies at redshift z~4.5 in the LALA Cetus field

We present a large sample of Ly-alpha emitting galaxies spectroscopically confirmed at z~4.5, based on IMACS spectroscopic observations of candidate LAEs in the LALA Cetus field. We identify 110 z~4.5 LAEs based on single line detections with no continuum emission blueward of the line. The Ly-alpha confirmation rate varies from<50% to 76% for candidates selected in different narrowband filters at slightly different redshifts. We find a drop in the LAE density at redshift 4.50+-0.03 from redshift 4.39-4.47 by a factor of 66%, which could be a large scale void in the distribution of star-forming galaxies (~18Mpc along the line of sight and ~80Mpc across). The sample includes many objects with equivalent widths>200A. These large EW candidates are spectroscopically confirmed at the same rate as candidates with more modest EWs. A composite spectrum of all 110 confirmed LAEs shows the characteristic asymmetry of the Ly-alpha line. It also places new and stringent upper limits on the CIV 1549/Ly-alpha and HeII 1640/Ly-alpha line ratios, providing a new upper limit on the fraction of active galactic nuclei in Ly-alpha selected galaxy samples, and on the contribution of Pop III populations. Finally, we calculate the Ly-alpha luminosity function for our z~4.5 sample, which is consistent with those at other redshifts, showing that there is no evolution in Ly-alpha luminosity function from z~3.1-6.6.


Introduction
The number of known high redshift galaxies has grown rapidly in the past decade, thanks to efficient wide field cameras and effective selection techniques (i.e., the dropout technique and Lyα line search technique). Narrowband imaging surveys have become the most efficient approach for finding high redshift Ly-α emission lines galaxies. Great successes have been achieved recently in detecting high redshift Lyα emitters using this technique (e.g. from z = 3 to z = 6.96, see Iye et al. 2006;Rhoads et al. 2000Rhoads et al. , 2003Rhoads et al. , 2004Wang, Malhotra & Rhoads 2005;Tapken et al. 2006;Westra et al. 2006;Shimasaku et al. 2004Shimasaku et al. , 2006Kashikawa et al. 2006;Ajiki et al. 2006;Ouchi et al. 2005;Hu et al. 2002Hu et al. , 2004Dawson et al. 2004Dawson et al. , 2007 and references therein). Large well defined samples of high redshift Lyα emitting galaxies are essential to study the nature of these galaxies (stellar population, mass etc, e.g. Lai et al. 2008;Pirzkal et al. 2007;Finkelstein et al. 2007;2009a), the mechanism of Lyα production (Malhotra & Rhoads 2002) and escape (Finkelstein et al. 2008), the luminosity function and its evolution (Dawson et al. 2007;Malhotra & Rhoads 2004Ouchi et al. 2008), and spatial clustering of star forming galaxies in the early universe (Wang et al 2005;Ouchi et al 2005;Malhotra et al. 2005;Kovač et al. 2007).
The Large Area Lyman Alpha (LALA) survey (e.g., Rhoads et al. 2000) has obtained deep narrowband images in several fields, yielding a large sample of Lyα emitters at z ≈ 4.5 (Dawson et al. 2004;, and z ≈ 5.7 (Rhoads & Malhotra 2001;Rhoads et al. 2003;Wang et al. 2005), plus a smaller sample at z ≈ 6.5 . In this paper, we present the spectra of 110 confirmed Lyα emitters at z ≈ 4.5 in LALA Cetus field with the Inamori-Magellan Areal Camera and Spectrograph (IMACS, Dressler et al. 2006) on the 6.5 meter Magellan I Baade Telescope. Together with our previously confirmed sources from Keck observations (Dawson et al. 2004(Dawson et al. , 2007, we now have an overall sample of 171 spectroscopically confirmed Lyα emitters at z ≈ 4.5.
To study the continuum emission properties of our candidates, we used deep broadband images in B W , R, I band from the NOAO Deep Wide Field Survey (NDWFS; Jannuzi & Dey 1999). We followed reasonably standard practices in our narrowband imaging data reduction and our Ly-α galaxy candidate selection, which are described in detail elsewhere (Rhoads et al 2000, Rhoads & Malhotra 2001, Wang, Rhoads & Malhotra 2005. Briefly, our selection criteria are: A) > 5σ detection in a narrowband filter; B) a narrowband excess of > 0.75 magnitude, so that > 50% of the narrowband flux comes from an emission line; C) significance of the narrowband excess > 4σ; and D) < 2σ detection in B W band.
We identified a total of 226 candidate Lyα-emitters at z ≈ 4.5 in our primary sample. The numbers of candidates selected in each narrow band filter are presented in Table  1. Additionally, we performed an extended catalog selection using the spectral overlap of adjacent filters to go to fainter flux levels. In this case, we extended the first criterion to > 3σ detection in one narrowband filter but > 5σ when stacking two spectrally overlapping filters. Other criteria are the same. This leads to another 38 candidates, which comprise our extended catalog.

Spectroscopic Observations
In 2005 September 3-5 we obtained spectroscopy of 194 candidate z ≈ 4.5 Ly-α emitters in the LALA Cetus field (167 from our primary sample, plus 27 from the extended catalog) using the Inamori-Magellan Areal Camera and Spectrograph (IMACS, Dressler et al. 2006) on the 6.5 meter Magellan I Baade Telescope. We used the short camera (f/2, with a 27.2 ′ diameter field of view), and used the 300 line grism (λ blaze = 6700Å, 1.34Å/pixel) in combination with a 5650-9200Å blocking filter to prevent overlap of higher order spectra. All observations employed 10.0 ′′ × 1.0 ′′ slitlets. The IMACS f/2 pixel scale is 0.2 ′′ /pixel. The corresponding spectral resolution is ≈ 7Å(though it could be somewhat better for compacat objects observed in subarcsecond seeing). Five multislit masks (see Table 2) were observed for 2.5 to 3.3 hours in 0.5 hr increments. Thanks to the large field of view of IMACS, we were able to target around 50 candidate Lyα-emitters in each mask, along with roughly 120 other targets. Of these, 45 candidates were covered by more than one masks.
The data were reduced using the IMACS version of the Carnegie Observatories System for MultiObject Spectroscopy (COSMOS) data reduction package 1 . We first determined 2d wavelength solutions for each science exposure using arc lamp exposures taken immediately before or after. We found relatively large wavelength residuals (∼ 6 pixels) in the course of this calibration, perhaps pointing to inaccuracies in the geometric coefficients describing the layout of the detector chips in the focal plane. Regardless of their origin, these residuals are repeatable from exposure to exposure. They therefore do not significantly affect our search for Lyα emission lines, though they do lead to extra uncertainties in the line wavelengths we determine (see below for details) and sky substraction.
After wavelength calibration, each frame was first bias-subtracted and flat fielded. We then performed sky subtraction following the algorithm described by Kelson (2003), and extracted 1D spectra from the 2D spectra using the task "extract-2dspec" for each slit. Frequently, this procedure produced an apparently "negative" blue continuum in the 1D spectra of our confirmed Lyα emitters, indicating small systematic errors in the software's measured sky level. In these cases, we checked that the continuum level appears to be zero in the 2D spectra, and then applied an additive correction to the 1D spectrum. We note that none of our subsequent scientific results rely on the continuum level measured in the spectroscopic data.
To control for possible spatial shifts along the slits between individual exposures of a mask, we measured the trace locations of the 30 brightest continuum sources in the mask. We corrected for any measured shifts while stacking the exposures for each mask, to increase the quality of the stacked 2D spectra. We also identified and removed cosmic ray hits while stacking the multiple exposures of each mask. Finally, we extracted the 1D spectra (2Å per bin) using the gaussian extraction algorithm.

Line Identification
We identified 110 single emission lines as Lyα at z ≈ 4.5, among our 194 observed candidates. Of these, 97 are new spectroscopic confirmations. We present a catalog of the 110 confirmed LAEs at z ≈ 4.5 in LALA Cetus field in Table 3. In Fig. 1 we presented the narrowband flux distributions of the targeted and confirmed LAEs in different narrowbands, and in Fig. 2 we present a set of sample IMACS spectra of confirmed LAEs.
We also identify 6 foreground sources which either show multiple lines or blue continuum. The remaining 78 targets were classified as nondetections. Of the nondetections, there are 10 whose expected emission line wavelength range (based on the narrowband data) is covered or partially covered by the IMACS ccd chip gap (which has a width of ≈ 80Å). These ten include one source previously confirmed as a Lyα emitter with Keck LRIS spectrum by Dawson et al. (2004). The non-detections could Following Rhoads et al. (2003Rhoads et al. ( , 2004 we perform two measurements of the line asymmetry. For both measurements, we first determine the wavelength of the emission line peak (λ p ), and the data points where the line flux exceeds 10% of the peak on the blue side (λ 10,b ) and the red side (λ 10,r ). The "wavelength ratio" is defined as a λ = (λ 10,r -λ p )/(λ p -λ 10,b ), and the "flux ratio" a f as the ratio of the accumulated line flux between λ 10,r and λ p to that of between λ p and λ 10,b . In Fig. 3 we plot a λ versus a f for the 110 single lines emitters. The errorbars are obtained through one thousand Monte Carlo simulations in which we added random noise to each data bin. Both measurements are expected to be > 1 for asymmetric profile of high redshift Lyα emission line due to the absorption by neutral hydrogen in outflows from star-forming galaxies and IGM.
Due to the low resolution and limited spectral quality of our IMACS spectra, for most of the lines, we are unable to secure identification of asymmetric profile, i.e., with a λ or a f >1 at statistically significant level. This can be clearly seen from the large errorbars of a λ and a f in Fig. 3. Considering the large errorbars, we find all but 1 sources statistically satisfy (within 1σ) a λ > 1 or a f > 1, and all but 3 sources satisfy both. This indicates that the spectral quality is insufficient for us to secure or exclude Lyα identification based on line asymmetry measurements. For the rest the search for Hβ and [O III] λ5007 is not possible because of the limited spectral coverage (or due to strong sky emission lines). For these sources, secure identification of [O II] λ3727 required higher spectral resolution to resolve the doublet, which is not possible by our IMACS spectra. Luckily, most of the foreground [O II] λ3727 emission line galaxies have been excluded from our candidate list by excluding sources detected in blueward broadband, and the contamination of [O II] λ3727 in spectroscopically securely confirmed sample was verified to be very low (e.g. Dawson et al. 2004;. For instance, with Keck DEIMOS spectra, Dawson et al. (2007) have identified two [O II] λ3727 versus 59 Lyα lines based on line profile, among candidate LAEs mostly selected similarly in LALA Boötes field. In this paper, we identify all the 110 single lines as Lyα lines.

Comparison with Dawson et al.
With previous Keck observations, Dawson et al. (2004; have confirmed a total of 17 LAEs at z ≈ 4.5 in LALA Cetus field. While designing our IMACS masks, we gave lower priorities to these previous confirmed LAEs, in order to maximize the total number of LAE candidates with spectroscopic coverage. Thanks to the large field of view of IMACS, we still have 13 of previous confirmed LAEs covered by IMACS observations. 12 of the 13 sources are confirmed at z ≈ 4.5 independently with the IMACS observations. The only one without IMACS confirmation has the expected line wavelength covered by IMACS chip gap. In Fig.  4 we plot the observed Keck redshifts versus IMACS redshifts for these 12 sources, which demonstrates the uncertainties in the IMACS wavelength calibration (δz 1σ = 0.005 at z ≈ 4.5). Our IMACS exposures also covered 7 candidates in Cetus field which were previously reported as non-detections with Keck spectra (Dawson et al. 2004;. None of these candidates showed any emission line in the IMACS spectra either. These results suggest that our IMACS spectra achieve sensitivities comparable to our previous Keck observations. The 17 confirmations reported by Dawson et al (2004; were drawn from a total of 26 LAE candidates observed with Keck in the LALA Cetus field, for a success rate of 65%. We note that 24 out of these 26 candidates were selected from Ha0, Ha4 or Ha8 band (since final, full-depth reductions of the Ha12 and Ha16 filter images were not available at the time of the Keck observations). For the Ha0, Ha4 and Ha8 bands alone, the success rate of Dawson et al. is 71%. Our IMACS success rate for these same three filters is 66%, consistent with Dawson et al.

Equivalent width distribution
In our previous studies among others(e.g. Malhotra & Rhoads 2002;Dawson et al. 2004;Kudritzki et al. 2000), large fractions of candidate LAEs were reported to show rest-frame Lyα line EW above 240Å, which is too large for normal stellar populations, unless they have a top-heavy initial mass function (IMF), zero (or very low) metallicity, and/or extreme youth (age < 10 6 yr). Significant contributions of type 2 active galactic nuclei (AGNs) to the large line EW has been ruled out (see §4.2 below). The large line EW could also likely be due to the clumpy and dusty inter-stellar medium in the galaxy which could attenuate the continuum photons but resonantly scatter the line photons at the surface of the dusty clouds, thus increase the observed EW (Neufeld 1991;Hansen & Oh 2006;Finkelstein et al. 2007;2009).
Could the candidate LAEs with higher EW based on photometry (i.e. these with no continuum detection) be contaminations due to noise spikes, or spurious features? Our large spectroscopic sample enable us to perform a statistical test on this issue. In Fig. 5 we plot the distributions of the broad to narrow band flux density ratio for our confirmed z ≈ 4.5 LAEs, foreground sources and spectroscopically undetected sources. The Lyα line EW is a monotonic decreasing function of the broad to narrow band flux density ratio. In the figure we can see that these spectroscopically confirmed LAEs and undetected sources have a consistent distributions of broad to narrow band flux density ratio. A Kolmogorov-Smirnov test shows that two distributions are indistinguishable (p = 85%). This demonstrates that high EW candidates are confirmed at the same rate.
In table 3 we also present the line equivalent width for all the spectroscopically confirmed z ≈ 4.5 galaxies. Due to the large uncertainty in estimating the continuum level from optical spectra, we utilize narrow and broad band photometry to derive the line equivalent width. Following Maholtra & Rhoads (2002), we calculate the rest frame line EW as where F Lyα is the Lyα line flux, f λ the continuum flux density, W N and W R the widths of the R band (1568Å) and the narrow band (80Å), and R and N the integrated fluxes in the R band and narrow band respectively. (2002), we find only 50% of the confirmed LAEs show measured line EW < 240Å in the rest frame. The rest either show larger EW or no detection of continuum at all. It's clear that the uncertainty in line EW mainly comes from that of the continuum, especially for high EW sources, we thus calculate the uncertainty of the line EW by applying 1σ errorbar to the measured R band flux. In many cases that the upper limits of the line EW can not be constrained, lower limits are given.

Consistent with Malhotra & Rhoads
We point out that the line EW distributions of different selected samples are sensitive to the selection criteria adopted. Particularly, the requirement of broad band detection (i.e. Hu et al. 2004) would exclude very high EW sources. For instance, only 1 out of 7 LAEs at redshift 3.7 selected by Fujita et al. (2003) in Subaru/XMM-Newton Deep Field show rest frame line EW above 200Å (based on narrow and broad band photometry), however, this is after they excluded the candidates without broadband detection, most of which (6 out 7), if located at redshift 3.7, show line EW above 200Å, consistent with LALA surveys. The EW distribution is also likely sensitive to the relative depths of the broad and narrow band images, e.g., deeper broad band images could enable detection of more sources with smaller EWs because more sources with stronger continuum could pass the selection due to smaller broadband flux uncertainty.
We have presented above that most of the sources with high EWs have no broadband detection at all. It's interesting to note that if we sum the broad and narrow band fluxes for all the confirmed LAEs, we obtained an average EW of 182 +26 −20Å . If we sum the broad and narrow band fluxes for the confirmed LAEs with < 3σ continuum detection (100 out of 110), we derived an average EW of 316 +102 −62Å . This also demonstrates that a large population of these individual LAEs have high EW.
One final concern on the weak continuum level is whether they are physically weak or due to selection bias. That is, did the selection favor the sources whose broad band fluxes were underestimated due to random fluctuations? If this were an important effect, there should be one immediate consequence: these high EW sources would be systematically brighter in an independent broadband image. We adopted the independent broadband images obtained with MMT (Finkelstein et al. 2007; to test this possibility. In Fig. 6 we plot CTIO R band flux versus MMT r' "flux" for 44 confirmed LAEs with r' band coverage. Here the MMT r' "flux" was scaled by a factor which was derived by requiring that the clipped average R − r ′ color be zero for the full list of sources well detected in both images. We note that the band pass of MMT r' band is not identical to that of CTIO band, however, considering MMT r' band has much better efficiency between 6500Å to 7200Å than CTIO R band, while CTIO R band extends to 8000Å with transmission below 40%, the fluxes from two bands are comparable for our purpose. From the figure we can see that these LAEs have consistent r' band fluxes, suggesting the possible selection bias we mentioned above, if there is any, is weak. The clearest exception is that fluxes that appear negative in the R band image (and whose R fluxes are therefore surely underestimated due to photon noise) mostly have r' fluxes that are zero or slightly positive. EW calculations show that 24 out of 44 confirmed LAEs with r' band flux measurements have EW above 240Å based on old R band measurements, while 21 of the 44 show EW above 240Å based on r' band fluxes. The EW calculations based on r' band fluxes have been adjusted to the r' band transmission curve. We conclude that the high EWs we have obtained are physically real, and cannot be fully ascribed to selection bias.

The stacked spetrum
Stacking a large number of spectra could further help us understand the nature of the line emitters, especially for those with low signal to noise ratio. In Fig. 7 we present the stacked spectrum of all 110 confirmed Lyα emitters at z ≈ 4.5. We perform a varianceweighted co-addition of the 110 spectra. In each wavelength bin, data points from each spectrum (normalized by the peak flux of the Lyα 1216Å emission line) were averaged using two sigma clipping algorithm (one iteration) to remove artifical features due to sky line residuals, ccd edges, etc.
In the composite spectrum, the only visible line feature is the asymmetric Lyα line (highlighted in the cutout of Fig. 7). In the co-added spectrum, we obtained a λ = 1.46±0.16, and a f = 1.42±0.09, consistent with those expected from the asymmetric profile of high redshift Lyα emission line. The errorbars on a λ and a f are also estimated based on large number of Monte Carlo simulations in which we added random noise to each data bin.
In the co-added spectrum, we searched for possible CIV λ1549 and He II λ1640 line in the vicinity of expected wavelengths, however, neither of them could be detected at above 2σ level. Based on the flux uncertainties in the spectra, we obtained 2σ detection limit (by fixing the line width to that of Lyα) to the flux ratio of f (CIV λ1549)/f (Lyα) and f (He II λ1640)/f (Lyα), which are 3.7% and 7.4% respectively. These constraints are significantly stronger than we previously obtained based on 11 LAEs spectra with Keck (8% and 13% respectively, Dawson et al. 2004).

Large scale structures
We find significantly different success rates and total numbers of candidates obtained in images from different narrowband filters (see Table 1). The small number of candidates in the Ha16 filter can be ascribed to the shallower depth in the Ha16 narrow band image, and the lower success rate could thus be due to a higher percentage of contamination from noise spikes (assuming the total number of spurious detections due to noise spikes per image remains constant) and asteroids (with a small number of frames, asteroids could leave more spurious features in the stacked image).
The Ha12 narrowband image has the same depth as Ha0, Ha4 and Ha8 bands, yet has many fewer candidates detected. This indicates that the source density at the redshift 4.50±0.03 is much smaller than that in the redshift range of 4.39 -4.47 (covered by Ha0, Ha4 and Ha8 filter). The success rates and number of candidates in Ha0, Ha4 and Ha8 filters are similar, with Ha8 having marginally more candidates, and a marginally lower confirmation rate.
In Fig. 8 we plot the spatial distributions of the candidates selected in each narrowband image. Similar large scale structure has been reported at various redshifts elsewhere (e.g. see Ouchi et al. 2005, Wang et al. 2005, Palunas et al. 2004, Kovac et al. 2007. Quantitative analysis on the large scale structures presented in Fig. 8 requires careful examination on the candidate selection effect, the coverage of mask design, and the success rate of each mask in each narrow band, etc, which is beyond the scope of this paper. However we note that the amplitude of the drop in LAE source density at redshift 4.50±0.03 (66%) 2 is consistent with the cosmic variance calculation (Trenti & Stiavelli 2008), which gives a 40% cosmic variance (1σ) for the volume of our survey.

Active Galactic Nucleus(AGN) Fraction
Significant contributions of AGNs to the large line EW has been ruled out with deep X-ray exposure and optical spectra (e.g. see Malhotra et al. 2003;Wang et al. 2004;Dawson et al. 2004;Gawiser et al. 2006). Deep X-ray images can be used to test whether these LAEs are AGNs, since they are expected to be strong X-ray emitters based on their Lyα emission line. However, with two deep Chandra ACIS exposures (∼ 180 ks each), we were unable to detect any of the 101 LAE candidates in LALA Boötes and Cetus field. The stacking technique helps to establish a strong constraint (3σ) to the average X-ray luminosity of L 2−8keV < 2.8 × 10 42 ergs s −1 , and we estimated that < 4.8% of the LAEs in LALA Boötes and Cetus field could be possible AGNs (Wang et al. 2004). No AGN lines have been identified in the obtained individual and composite spectra either (Dawson et al. 2004; and this paper). Dawson et al. (2004) have presented an upper limit of CIV to Lyα line flux ratio of 8% (2σ) based on the composite spectrum of 11 LAEs at z ≈ 4.5.
In §3.4 we have presented the composite spectra of 110 Lyα emitters at z ≈ 4.5. Even in the composite spectrum, CIV line is invisible. A much stronger upper limit to the CIV line flux is derived, which is < 3.7% (2σ) of the Lyα flux, while typical ratio of CIV to Lyα line in type II AGNs 3 is 22% (Ferland & Osterbrock 1986). This confirms previous results that the AGN contribution to LAEs is rather small. The formal upper limit from the CIV line is 3.7/22 = 17%. This is somewhat weaker than our earlier X-ray based limits , Wang et al 2004, but is an entirely independent constraint. Interestingly, this limit is below the AGN detection fraction for nearby (redshift z ∼ 0.3) LAEs, reinforcing the observation of AGN fraction evolution by Finkelstein et al (2009b).

Population III stars
The search for the first generation (or Pop III stars) is one of the major targets in observational studies. However, until now there is no strong evidence of the detection of Pop III stars, and the search for such objects remains a major observational challenge (Schaerer 2008). Recent numerical calculations have shown that since Lyman continuum flux increases with decreasing metallicity in stellar populations, very low metallicity stellar population can produce strong Lyα line with maximum EW > 400 -850Å for Z < 10 −5 Z⊙ (e.g . Schaerer 2003;Tumlinson, Shull & Venkatesan 2003). Besides strong Lyα emission line, Pop III or very low metallicity stellar population is also expected to produce strong He II λ1640 due to its much stronger He II ionizing continuum. Thus many studies have been performed to search for strong He II λ1640 emission line in the spectra of high redshift LAEs, but no positive detection has been obtained yet. Malhotra & Rhoads (2002) and Ouchi et al. (2008), we have found a large population of spectroscopically confirmed LAEs with rest frame Lyα line EW above 240Å. We have stated above that these high EWs are real. This is in contrast to low EWs found at z = 3.1 & 2.2 (Gronwall et al. 2007;Nilsson et al. 2009), whether this is due to cosmic evolution or different selection criteria is not clear. We have also ruled out significant contribution of AGN to the large EW ( §4.2). Another possibility to the observed large Lyα EW is due to very metal-poor or Pop III stars. However, in both the individual and the coadded IMACS spectra, we detect no evidence of He II λ1640 emission line. In the co-added spectrum, the He II λ1640 emission line flux is constrained to be 7.4% (2σ) of that of Lyα. Such an upper limit can be converted to log (Q He+ /Q H ) < -1.4, where Q He+ and Q H are ionizing fluxes for He+ and H respectively (Schaerer 2003). This upper limit is close to the maximum predicted values for metal-free populations with IMFs including very massive stars (up to 500 M⊙, see Fig. 5 of Schaerer 2003). This indicates that although He II λ1640 is not detected in our composite spectrum, the derived upper limit is insufficient yet to rule out the existence of Pop III (or very metal-poor) stars in our LAEs at z ≈ 4.5. Considering the fraction of Pop III galaxies among LAE sample at z ∼ 4.5 could be rather small (such as a few percent, e.g. Scannapieco, Schneider & Ferrara 2003), the derived upper limit can not even rule out some model which predict comparable He II λ1640 and Lyα line fluxes for Pop III populations (e.g. Tumlinson et al. 2003).

Lyα Luminosity Function
We have presented a large spectroscopically confirmed LAE sample at z ≈ 4.5. In this section we present the Lyα luminosity function based on this sample. Due to the large uncertainty in flux calibration in spectroscopic observations, we adopt photometric measurements to calculate the Lyα fluxes. The Lyα fluxes were derived from narrowband and broadband photometry, where f Lyα = f nbf continuum *w nb and f continuum = (f R -f nb )/(w Rw nb ). The line luminosities of the confirmed LAEs were calculated assuming a cosmology model of H0 = 71 km/s/Mpc, Ω m = 0.27 and Ω λ = 0.73.
For each confirmed LAE, we first calculated the comoving volume V max over which the source could be selected by our survey from z min to z max , which are 4.36 and 4.65 respectively through band Ha0 to band Ha16. The survey area is 35 ′ × 35 ′ . Effects of different flux limits in narrow bands were also taken into account. We show the incompleteness of our spectroscopical observations in Fig. 9. In the figure we plot the fraction of spectroscopically targeted LAEs as a function of Lyα line flux. Such incompleteness was taken into account while calculating the luminosity function. To be conservative, we assume that all the spectroscopically non-detected sources are not LAEs.
The derived Lyα luminosity function of LAEs at z ≈ 4.5 is plotted in Fig. 10. Following Malhotra & Rhoads (2004), we fit the luminosity function with a Schechter function During the fit, we fixed the slope α at -1.5 since our data is insufficient to have it constrained. The best-fit parameters are L * = 6.3 ± 1.5 × 10 42 erg s −1 and Φ * = 3.5 ± 1.3 × 10 −4 Mpc −3 .
Considering the large uncertainties in the measurements and differences in Lyα emitting galaxies selection criteria among different research groups, the best-fitted L * and Φ * are consistent with the range of values found in various surveys at 3 z 6.5 (see the lower panel in Fig. 10).

Summary
We have presented the largest spectroscopic sample of z ≈ 4.5 Ly-α emitting galaxies yet studied. Examining the properties of this sample, we reach several conclusions: (1) Large equivalent width Ly-α emitters, which we have earlier reported as a common feature of narrowband-selected samples (Malhotra & Rhoads 2002), are spectroscopically confirmed at the same rate as less spectacular line emitters. Thus, the high equivalent width sample is not dominated by noise spikes. Nor can the large equivalent widths be solely a byproduct of calculating the EW using the same broad band data employed in candidate selection, because our large EW subsample changes little when we calculate EW using an independent broad band image completely independent of object selection.
(2) The CIV 1549Å line is (on average) 3.7% of the Ly-α line strength, placing an upper limit of 17% on the AGN fraction in the Ly-α selected sample. This limit is independent of the X-ray to Ly-α ratio in AGN and therefore complements earlier limits on the AGN fraction based on X-ray photometry.
(3) The HeII 1640Å line is 7.4% of the Ly-α line strength. This is the most stringent limit to date on the HeII emission from these objects. Though it does not strongly rule out many Population III models yet, it is nearly deep enough to do so and could be combined with a few similarly sized samples in future.       In the co-added spectrum, neither CIV λ1549 nor He II λ1640 line could be detected in the vicinity of expected wavelengths, and 2σ detection limits were given in the text.