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The Astrophysical Journal, 595: 589­602, 2003 October 1
# 2003. The American Astronomical Society. All rights reserved. Printed in U.S.A.

STAR FORMATION AT z $ 6: i-DROPOUTS IN THE ADVANCED CAMERA FOR SURVEYS GUARANTEED TIME OBSERVATION FIELDS1,2 R. J. Bouwens,3 G. D. Illingworth,3 P. Rosati,4 C. Lidman,4 T. Broadhurst,5 M. Franx,6 H. C. Ford,7 D. Magee, ´ N. Benitez,7 J. P. Blakeslee,7 G. R. Meurer,7 M. Clampin,8 G. F. Hartig,7 D. R. Ardila,7 F. Bartko,9 R. A. Brown,8 C. J. Burrows,8 E. S. Cheng,10 N. J. G. Cross,7 P. D. Feldman,7 D. A. Golimowski,7 C. Gronwall,11 L. Infante,12 R. A. Kimble,10 J. E. Krist,7 M. P. Lesser,13 A. R. Martel,7 F. Menanteau,7 G. K. Miley,6 M. Postman,7 M. Sirianni,7 W. B. Sparks,2 H. D. Tran,9 Z. I. Tsvetanov,7 R. L. White, 7,8 and W. Zheng7
Received 2003 April 18; accepted 2003 June 10
3

ABSTRACT Using an i þ z dropout criterion, we determine the space density of z $ 6 galaxies from two deep ACS GTO fields with deep optical-IR imaging. A total of 23 objects are found over 46 arcmin2, or $0:5 ô 0:1 objects arcminþ2 down to zAB $ 27:3(6 ), or a completeness-corrected $0:5 ô 0:2 objects arcminþ2 down to zAB $ 26:5 (including one probable z $ 6 active galactic nucleus). Combining deep ISAAC data for our RDCS 1252-2927 field (JAB $ 25:7 and Ks;AB $ 25:0; 5 ) and NICMOS data for the Hubble Deep Field­ North (J110;AB and H160;AB $ 27:3, 5 ), we verify that these dropouts have relatively flat spectral slopes, as one would expect for star-forming objects at z $ 6. Compared with the average-color ( ¼ þ1:3) U-dropout in the Steidel et al. z $ 3 sample, i-dropouts in our sample range in luminosity from $1.5Lö (zAB $ 25:6) to $0.3Lö (zAB $ 27:3) with the exception of one very bright candidate at z850;AB $ 24:2. The half-light radii vary from 0 > 09 to 0 > 21, or 0.5 kpc to 1.3 kpc. We derive the z $ 6 rest-frame UV luminosity density (or star formation rate density) by using three different procedures. All three procedures use simulations based on a slightly lower redshift (z $ 5) V606 -dropout sample from Chandra Deep Field­South ACS images. First, we make a direct comparison of our findings with a no-evolution projection of this V-dropout sample, allowing us to automatically correct for the light lost at faint magnitudes or lower surface brightnesses. We find 23% ô 25% more i-dropouts than we predict, consistent with no strong evolution over this redshift range. Adopting previous results to z $ 5, this works out to a mere 20% ô 29% drop in the luminosity density from z $ 3to z $ 6. Second, we use the same V-dropout simulations to derive a detailed selection function for our i-dropout sample and compute the UV-luminosity density [Ï7:2 ô 2:5÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3 down to zAB $ 27]. We find a 39% ô 21% drop over the same redshift range (z $ 3­6), consistent with the first estimate. This is our preferred value and suggests a star formation rate of 0:0090 ô 0:0031 M yrþ1 Mpcþ3 to zAB $ 27, or $0:036 ô 0:012 M yrþ1 Mpcþ3 by extrapolating the luminosity function to the faint limit, assuming ¼ þ1:6. Third, we follow a very similar procedure, except that we assume no incompleteness, and find a rest-frame continuum luminosity that is $2­3 times lower than our other two determinations. This final estimate is to be taken as a lower limit and is important if there are modest changes in the colors or surface brightnesses from z $ 5 to z $ 6 (the other estimates assume no large changes in the intrinsic selectability of objects). We note that all three estimates are well within the canonical range of luminosity densities necessary for reionization of the universe at this epoch by star-forming galaxies. Subject headings: galaxies: evolution -- galaxies: formation -- galaxies: high-redshift

1. INTRODUCTION

The Hubble Deep Field (HDF) campaign has been highly influential in shaping our understanding of star formation

in the high-redshift universe (Williams et al. 1996; Casertano et al. 2000; Ferguson, Dickinson, & Williams 2000). Early results demonstrated that the star formation rate density as measured from the rest-frame continuum

1 Based on observations made with the NASA/ESA Hubble Space Telescope, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with programs 7817, 9290, 9301, and 9583. 2 Based on observations collected at the European Southern Observatory, Paranal, Chile (LP166.A-0701). 3 Astronomy Department, University of California, Santa Cruz, CA 95064; bouwens@ucolick.org; gdi@ucolick.org 4 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany. 5 Racah Institute of Physics, Hebrew University, Jerusalem, Israel 91904. 6 Leiden Observatory, Postbus 9513, NL-2300 RA Leiden, Netherlands. 7 Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218. 8 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. 9 Bartko Science & Technology, P.O. Box 670, Mead, CO 80542-0670. 10 NASA Goddard Space Flight Center, Laboratory for Astronomy and Solar Physics, Code 680, Greenbelt, MD 20771. 11 Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802. 12 Departmento de Astronom´a y Astrofisica, Pontificia Universidad Catolica de Chile, Casilla 306, Santiago 22, Chile. ´ ´ i 13 Steward Observatory, 933 North Cherry Avenue, University of Arizona, Tucson, AZ 85721.

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UV increased from z $ 4 to an apparent peak around z $ 1­3 (Lilly et al. 1996; Madau et al. 1996; Connolly et al. 1997; Cowie, Songaila, & Barger 1999). While these results were largely solidified by Steidel et al. (1999) with his widearea U-dropout survey, the addition of NICMOS data to the HDF-N data demonstrated that this trend continued to z $ 6 (Thompson, Weymann, & Storrie-Lombardi 2001; Dickinson 2000, in preparation; Bouwens, Broadhurst, & Illingworth 2003, hereafter BBI). Unfortunately, these studies were limited enough in area to raise doubts about how representative they really were of the high-redshift universe. They also suffered from a lack of deep high-resolution imaging at wavelengths intermediate between the optical regime and the near-infrared, necessary for obtaining a more detailed look at the z $ 6­7 universe. Deep NICMOS observations have been useful in addressing this latter shortcoming, but only partially because of its small field of view. Fortunately, the installation of the ACS (Ford et al. 1998) on the Hubble Space Telescope (HST ) has helped to redress several of these issues, crucially including for the first time imaging in the z band, permitting a more secure detection of objects at high redshift (z $ 5­6). Moreover, its 10-fold improvement over WFPC2 in surveying capability allows large areas to be surveyed to nearly HDF depths (Ford et al. 2003), the Great Observatories Origins Deep Survey (GOODS) being a notable example (Dickinson & Giavalisco 2002). Here we describe some early work done using deep ACS data to extend these searches to z $ 6 to establish the prevalence of galaxies in this era. Interest in star formation at z $ 6 has been particularly intense lately because of recent absorption-line studies of three QSOs at z > 5:8, suggesting that reionization may have happened at about this epoch (Fan et al. 2001, 2002; Becker et al. 2001). In this work, we consider two fields from the ACS GTO program, RDCS 1252-2927 and the HDF-N, in our search for z $ 6 objects. Both fields have deep ACS i and z data and infrared observations, important for securely identifying z $ 6 objects. Relative to other work (Yan, Windhorst, & Cohen 2003; Stanway, Bunker, & McMahon 2003), the present search is slightly deeper, with better IR data to confirm the redshift identifications. In fact, our use of the HDF-N field is especially propitious, given the exceptionally deep WFPC2 and NICMOS images available to examine faint z $ 6 candidates. We put this new population in context by comparing them with lower redshift expectations, projecting z $ 5 galaxy samples from the CDF­S GOODS to z $ 6 with our cloning formalism previously used in work on the HDFs (Bouwens, Broadhurst, & Silk 1998a, 1998b; BBI). We begin by presenting our data sets, describing our procedure for doing object detection and photometry, and finally discussing our z $ 6 i-dropout selection criterion (x 2). In x 3, we present our results. In x 4, we describe a comparison against the wide-area GOODS sample and then use these simulations to make three different estimates of the z $ 6 rest-frame continuum UV luminosity density (x 5). Finally, in x 6 and x 7, we discuss and summarize our findings. Note that we denote the F775W, F850LP, F110W, and F160W bands as i775 , z850 , J110 , and H160 , respectively, and we assume ÏM ; ö ; h÷ ¼ Ï0:3; 0:7; 0:7÷ in accordance with the recent Wilkinson Microwave Anisotropy Probe (WMAP) results (Bennett et al. 2003).

2.1. Data Two different fields from our ACS GTO program are particularly useful for i-dropout searches. The first involves deep ACS WFC i775 and z850 images of RDCS 1252-2927, a z ¼ 1:235 cluster. RDCS 1252-2927 was selected from the ROSAT Deep Cluster Survey (Rosati et al. 1998; P. Rosati et al. 2003, in preparation). Three orbits in i775 and five orbits in z850 were obtained at four overlapping pointings, arranged in a 2 á 2 grid with an overlap of $10 so that the overlapping regions ($10 arcmin2) were covered to a depth of six orbits in i775 and 10 orbits in z850 with a small central region ($1 arcmin2) being covered to a depth of 12 orbits in i775 and 20 orbits in z850 . The ACS images were aligned, cosmic-ray rejected, and drizzled together using the ACS GTO pipeline (Blakeslee et al. 2003). Very deep integrations were obtained on ISAAC over four overlapping regions on RDCS 1252-2927 (covering 40 á 40 ,or $44% of our 36 arcmin2 ACS mosaic). A total of 24.1 and 22.7 hr were invested in the Js and Ks integrations, respectively ($6 and $5.8 hr at each of the four offset positions)14. These observations reached JAB ¼ 25:7 (5 ) and Ks;AB ¼ 25:0 (5 ) in the shallower, nonoverlapping regions and JAB ¼ 26:5 (5 ) and Ks;AB ¼ 25:8 (5 ) in the small (10 á 10 ) central region, with an FWHM for the pointspread function (PSF), which was almost uniformly $0 > 45 across the entire IR mosaic. These data were then aligned with our optical data and resampled onto the same 0 > 05 pixel grid. The second field utilizes deep ACS observations of the HDF-N, taken as part of our GTO program, 2.5 orbits in i775 and 4.5 orbits in z850 . These data were supplemented with 1.5 orbits in i775 and three orbits in z850 from the GOODS program in this field (representing three epochs of the GOODS program) to yield a total depth of four orbits in i775 and 7.5 orbits in z850 over an effective area of 10 arcmin2. To complement the ACS i and z data, both the HDF-N optical data (Williams et al. 1996) and JH infrared data from the Dickinson (1999) campaign were aligned and registered onto the same 0 > 05 pixel scale as our ACS fields, leaving the WFPC2 data with an FWHM of $0 > 18 for the PSF and the NICMOS data with an FWHM of $0 > 25. The NICMOS images reached J110;AB $ 27:3 (5 ) and H160;AB $ 27:3(5 ). The i775;AB ¼ 25:64 and z850;AB ¼ 24:84 CALACS (02/ 20/03) zero points (M. Siranni et al. 2003, in preparation) are assumed throughout, along with a galactic absorption of E ÏB þ V ÷ ¼ 0:075 and 0.012 for the two fields (from the Schlegel, Finkbeiner, & Davis 1998 extinction maps), resulting in a correction of þ0.11 and þ0.02 mag to the z850 zero point for RDCS 1252-2927 and the HDF-N, respectively (and a correction of þ0.15 and þ0.024 mag for the i775 filter). 2.2. Detection and Photometry Briefly, object detection is performed on the basis of our deep WFC z850 images after smoothing the images with a 0 > 09 FWHM Gaussian kernel and looking for 4.5 peaks. Photometry is obtained on all detected objects with
14

We assume Js ¼ J .


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SExtractor (Bertin & Arnouts 1996) using two scalable apertures, the inner one to measure colors and the outer one to estimate the total flux. For both sets of IR data, similarly scaled apertures are used to measure colors, but a correction is applied on the basis of the z850 image to estimate how much flux is lost in the IR because of PSF smoothing. Because of correlation in the noise, a concerted attempt was made to model the noise so that a relatively realistic treatment of uncertainties could be applied throughout the analysis (Appendix A). A more comprehensive description of our techniques for object selection and photometry is given in BBI.15 In total, 4632 and 1261 objects were recovered in the RDCS 1252-2927 and HDF-N fields, respectively. Most spurious detections were eliminated by demanding that each object be a 6 detection within one Kron radius (Kron 1980; typically $0 > 15). Areas contaminated by optical ghosts or satellite trails were not included in the analysis (the excluded area was <0.5%). A number of spurious detections were found around bright stars or elliptical galaxies, a problem exacerbated by the rather extended wings on the z850 PSF. After some preliminary cleaning, all point sources were removed from our catalogs ($503 and $37), the rationale being to eliminate very red stars, which might otherwise masquerade as high-redshift objects. We found that the SExtractor stellarity parameter adequately identified stellar objects. While such a cut might eliminate genuine z $ 6 star-forming objects, all the very red [Ïi775 þ z850 ÷AB > 1:5] pointlike objects ($4) were found to have much redder z þ J colors ($1.2) than most of the probable z $ 6 objects, and therefore a stellar identification seemed reasonable [see the systematic color differences between pointlike and extended Ïi775 þ z850 ÷AB > 1:5 objects in Fig. 1]. We note that an examination of red i þ z > 1:3 pointlike objects in our fields revealed one probable z $ 6 active galactic nucleus (AGN; Appendix B). 2.3. Dropout Selection The Lyman break technique takes advantage of the increasingly strong deficit of flux at high redshift caused by the intervening Ly forest eating into the spectrum short° ward of 1216 A (Madau 1995). Combining this with flux information redward of the break permits one to determine the spectral slope redward of the break and therefore relatively robustly distinguish the objects of interest from intrinsically red galaxies at lower redshift, as demonstrated by extensive spectroscopic work done on a variety of different dropout samples (Steidel et al. 1996a, 1996b; Steidel et al. 1999; Weymann et al. 1998; Fan et al. 2001). For our filter set, the i775 þ z850 color measures the spectral break, and the z850 þ J color defines the spectral slope redward of this break. In Figures 1 and 2, we illustrate how a starburst spectrum (100 Myr continuous star formation) attenuated with various opacities of dust [E ÏB þ V ÷ ¼ 0:0, 0.2, and 0.4] would move through this color-color space as a function of redshift. In both plots, it is clear that beyond z $ 5:5, the template i þ z colors become very red (>1.2) while the z þ J colors remain very blue (<0.5­1). For reference, we also include the colors of
15 Note that our procedure for object detection and photometry is ´ different from that used by the GTO team (Blakeslee et al. 2003; Benitez et al. 2003).

Fig. 1.--Color-color diagram of Ïi775 þ z850 ÷AB vs. Ïz850 þ J ÷AB illustrating the position of our RDCS 1252-2927 i-dropout sample (shaded region) relative to the photometric sample as a whole.¸Tracks for a 108 yr starburst with various amounts of extinctions have been included to illustrate both the typical redshifts (labeled for z ¼ 5:5 and z ¼ 6) and SED types included in the selection window. The low-redshift (0 < z < 2) tracks for typical E, Sbc, and Irr spectra have been included as well to illustrate the region in color-color space where possible contaminants might lie. There is a clear separation between the i þ z > 1:3 pointlike objects (crosses) and i þ z > 1:3 extended objects ( filled squares) along the z þ J axis. The distribution of objects in color-color space led us to adopt Ïi þ z÷ > 1:5 as our generalized i-dropout selection criteria. In all cases, error bars represent 2 limits. The clump at Ïi775 þ z850 ÷AB $ 0:9 and Ïz850 þ J ÷AB $ 1 is an earlytype galaxy from the cluster.

Fig. 2.--Same as Fig. 1, but for i-dropouts from the HDF-N. Note that the NICMOS J110;AB filter shown here is distinct from the ground-based JAB filter used in Fig. 1.


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possible lower redshift interlopers by using the Coleman, Wu, & Weedman (1980) spectral templates. After considerable experimentation, we adopted a simple Ïi775 þ z850 ÷AB > 1:5 cut throughout in our selection of idropouts. This color cut is motivated by evaluating object selection in regions where we have both ACS and infrared data. We present such data in Figures 1 and 2 from our RDCS 1252-2927 and HDF-N fields, providing 2 upper limits for objects without significant infrared flux. We have also lightly shaded those regions in i þ z, z þ J color space where z > 5:5 i-dropouts are expected to lie: Ïi Ïi
775 775

þz þz

850 ÷AB 850 ÷AB AB

> 1:5 ; > Ïz775 þ J ÷AB × 0:7 ; < 0:9 ; z
850;AB

Ïz

775

þ J÷

< 27:3

objects in our fields with i þ z > 1:3 (46 objects), we find the following contamination fraction as a function of i þ z color: 0% for i þ z > 1:7, 13% for i þ z > 1:5, and 21% for i þ z > 1:3. (Note that this estimate is for samples from which the point sources [stars or AGNs] have already been removed.) While our data set contains two i þ z $ 1:3­1.4 objects that are apparently elliptical galaxies or extremely red objects (EROs) at $25.3, z þ K $ 2 and z þ K $ 3 (Fig. 4), all the objects with i þ z > 1:5 have infrared colors consistent with their being at high redshift. This small contamination fraction (13%) allows us to substantially increase the size of our z $ 6 sample by including Ïi775 þ z850 ÷AB > 1:5 objects without IR coverage. A total of 11 such objects satisfy these criteria: 10 from RDCS 1252-2927 and one from the HDF-N.
3. RESULTS

for RDCS 1252-2927 and Ïi
775

þz

850 ÷AB 850 ÷AB 110 AB

> 1:5 ; > Ïz775 þ J110 ÷AB × 1:0 ; < 0:6 ; z850;AB < 27:3

Ïi775 þ z Ïz775 þ J

÷

for the HDF-N. A quick glance shows that objects with very red (>1.5) i þ z colors also have blue z þ J colors and lie exclusively in this region, thereby validating our basic selection criteria. Over the 21 arcmin2 for which we have infrared coverage, we find 11 objects in RDCS 1252-2927 and one object in the HDF-N that satisfy our i þ z > 1:5 cut. The i775 z850 JKs and i775 z850 J110 H160 images for these objects are shown in Figure 3, along with plots showing their position in color-color space, fits of plausible spectral energy distributions (SEDs) to the broadband fluxes, and an estimated redshift. The photometric redshifts are estimated using a ´ Bayesian formalism similar to that outlined in Benitez (2000), using a prior that matches the observed distribution of z $ 3 spectral slopes (Steidel et al. 1999). Our typical idropout has a signal-to-noise ratio (S/N) of $2­5 in the infrared, more than adequate to put good constraints on the spectral slope redward of the break. To illustrate this and to indicate how different the i-dropouts really are from possible low-redshift contaminants, we show three i þ z > 1:3 objects with red z þ J > 0:8 colors in Figure 4. For reference, we also include a figure with the z ¼ 5:60 Weymann et al. (1998) object from the HDF-N to show the position of a spectroscopically confirmed z > 5:5 object on these diagrams (Fig. 5). Having presented our entire sample of i-dropouts with infrared coverage, we now move on to quantifying the contamination rate due to low-redshift interlopers. The most obvious way of doing this is simply to count the fraction of objects with i þ z > 1:5 that satisfy the two-color criteria we specified above versus those that do not. Unfortunately, for many objects we have only limits and not precise measures of the IR colors, leaving us with cases for which we are not sure whether an object lies in our sample or not. Therefore, following Pozzetti et al. (1998) in their analysis of dropouts in the HDF-N, we resort to the use of Kaplan-Meier estimators with censoring (Lavalley, Isobe, & Feigelson 1992), in which the implicit assumption is that censoring is random, e.g., that objects with and without limits are drawn from the same parent distribution. Given the narrow range of magnitudes and sizes in our sample we believe this assumption to be approximately satisfied. Performing this analysis on all

In summary, we find 21 objects over 36 arcmin2 in our RDCS 1252-2927 field and two objects over 10 arcmin2 in our HDF-N field that satisfy the i-dropout criterion (i þ z > 1:5) we defined in the previous section. There is deep IR coverage for 12 of these objects over both fields. Except for one bright z850;AB ¼ 24:2 object that met our i-dropout selection cut, i-dropouts in our sample range in magnitude from 25.6 down to our completeness limit, z850;AB $ 27:3. For reference, an average-color (UV powerlaw index  ¼ þ1:3) Lö object from the Steidel et al. (1999) z $ 3 sample would have z850;AB $ 26:1, suggesting a population of objects with typical luminosities ranging from $0.3Lö to $1.5Lö .16 Binning these objects into 0.5 mag intervals, we illustrate in Figure 6 how the surface density of i-dropouts varies as a function of magnitude. Our typical idropout has a half-light radius of 0 > 15 or 0.9 kpc, although we find them at all sizes ranging from the limit of the PSF (0 > 09) to 0 > 29, above which our sample starts to become incomplete. We list all objects that lie in our i-dropout sample in Table 1, providing positions, magnitudes, colors, half-light radii, and the SExtractor stellarity parameter. Only 13% ($1 or 2 objects) of the Ïi775 þ z850 ÷AB > 1:5 objects without IR magnitudes are likely to be low-redshift contaminants (x 2.3).
4. PREDICTIONS

Before getting into a detailed discussion of the luminosity density at high redshift, perhaps the simplest way to begin interpreting what we see at z $ 6 is to compare it with the z $ 5 V-dropout sample we previously selected from the HDF-N and HDF-S (BBI). In that work, we used our cloning machinery (Bouwens et al. 1998a, 1998b; BBI) to project the z $ 3 U-dropout population to z $ 4­5 for comparison with our z $ 4 B and z $ 5 V-dropout samples. We found an overall drop in the rest-frame continuum UV luminosity density (46% decrease to z $ 5), as well as a modest decrease in the physical size of objects at higher redshifts relative to the z $ 3 population.
16 Our z 850;AB ¼ 24:2 object (1252-5224-4599) would therefore be a rather bright and suspiciously rare $6Lö object. Even if this object is a lowredshift contaminant (and we have no reason to believe that it is), it does not appear to represent a very large source of contamination, given the lack of similarly bright objects to zAB $ 25:6 and relative homogeneity of objects faintward of that.


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Fig. 3.--Postage stamps in i775 z850 JKs of the 12 i-dropouts (z $ 6) identified in our ACS fields over the 21 arcmin2 for which we had infrared coverage (11 i-dropouts did not have measurements in the IR). The i775 z850 J110 H160 postage stamps are shown for the object from the HDF-N. The optical and IR images are smoothed with 3 á 3 and 6 á 6 boxcars, respectively. The position in i þ z, z þ J space is also indicated, along with the broadband SEDs and estimated redshift. As in Figs. 1 and 2, we have included lines denoting the way starburst objects (108 yr bursts) with various dust attentuations would move through color-color space as a function of redshift. We have also included the tracks of possible interlopers. As in Table 1, the prefix 1252- denotes an object from RDCS 1252-2927. The postage stamps are 3 > 0 á 3 > 0.

We would now like to move this comparison out to higher redshift, using our HDF V-dropout sample to make an estimate for the surface density of i-dropouts on the sky. Unfortunately, the HDF-N V-dropout sample we derived in that work ½ÏV606 þ I
814 ÷AB

therefore resort to using a much larger area V-dropout sample from the CDF-S GOODS fields (R. J. Bouwens et al. 2003, in preparation). The virtue of this sample is both its size (130 objects) and its ACS (PSF FWHM $0 > 09) resolution. Our selection criteria for this sample were ÏV
606

> 1: 5 ;
AB

þi

775 ÷AB 775 ÷AB 850 ÷AB

> 1: 7 ; > 1:1875Ïi775 þ z850 ÷AB × 1:225 ; < 1:2 ; and z850;AB < 27:2 ;

ÏV606 þ I814 ÷AB > 3:8; ÏI814 þ H160 ÷ I814;AB > 24 ; and I814;AB < 27:6

þ 1:54 ;

ÏV606 þ i Ïi775 þ z

contains only one object brighter than IAB ¼ 26:5 and hence is not extremely useful in this regard. (The fainter V-dropouts would not be detectable at z $ 6 to the current depths.) We

where the SExtractor stellarity was less than 0.85 in the z850 image (nonstellar with high confidence). We selected this sample from essentially the entire area of the CDF-S, i.e., 150


Fig. 3.--Continued


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26.36±0.12

25.03±0.07

23.32±0.07

22.15±0.06

z~1.5

i

z 1252-4390-2952

J

Ks

26.67±0.24

25.29±0.13

24.37±0.15

23.28±0.12

z~1.2

i

z 1252-5798-5407

J

Ks

>27.58

26.11±0.24

25.25±0.28

24.85±0.30

z~5.4

i

z 1252-2815-2609

J

Ks

Fig. 4.--Postage stamps in i775 z850 JKs of several i þ z > 1:3 objects with moderately red z þ J colors. In all three cases, objects are clearly visible in the infrared, illustrating the basic value of our infrared data for distinguishing high-redshift objects from low-redshift interlopers. The top two objects are likely to be low-redshift (z $ 1:2­1.5) elliptical galaxies. The third object, though likely at high redshift, did not make our i-dropout selection cut. The postage stamps are 3 > 0 á 3 > 0.

arcmin2 ($30 times the area of the HDF), so it should be moderately representative of the universe at z $ 5. Compared with our HDF sample, this V-dropout sample has a similar distribution of redshifts and luminosities. The methodology for the generation of this sample remains that of BBI. With our cloning machinery, we project objects from our V606 -dropout sample to higher redshift by using the product of the volume density, 1=Vmax , and the cosmological volume. We explicitly include pixel-by-pixel k-corrections, cosmic surface brightness dimming, and PSF variations in calculating the appearance of these objects to z $ 5:5 and beyond. Assuming no evolution in the properties of these samples, we ran Monte Carlo simulations to predict the number of i-dropouts that would be observed in our RDCS 1252-2927 field and HDF-N fields. We explored searches at two different depths: three orbits in i775 and five orbits in z850 versus six orbits in i775 and 10 orbits in z850 . We then

weighted these predictions by the fractional area observed to these two different depths (65% at the shallower depth and 35% at the deeper). The result is that we predict finding 12:1 ô 1:0 and 4:7 ô 0:4 i-dropouts in our RDCS 1252-2927 and HDF-N fields, respectively. The quoted uncertainties reflect the finite size of the input V606 -dropout sample (see Bouwens et al. 1998a, 1998b). By adding sample variance (simple Poissonian statistics), this works out to 12:1 ô 3:6 idropouts in our RDCS 1252-2927 field versus the 20 observed (18.7 after the 13% correction for the low-redshift contamination) and 4:7 ô 2:2 i-dropouts in our HDF-N field versus the two observed (1.9 after correction for contamination), indicating a slight reduction in the numbers from z $ 6to z $ 5 but more realistically consistent with no evolution (see Table 2). We combine the two fields to derive i-dropout number counts and again compare with the noevolution predictions (Fig. 6), finding 23% ô 25% more idropouts than are predicted using our no-evolution model.

Fig. 5.--Postage stamps in i775 z850 J160 H110 of the Weymann et al. (1998) z ¼ 5:60 object from the HDF-N (HDF4-473.0). While this object did not meet our selection criteria, it is reassuring to find a spectroscopically confirmed object at the low end of our i-dropout selection range (see x 4) just missing our Ïi775 þ z850 ÷AB > 1:5 cut to the blue. We measured an Ïi775 þ z850 ÷AB ¼ 1:2 color for this object.


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some gauge of the evolution across this redshift interval, but they provide an approximate estimate for the i-dropout selection function (assuming no evolution in the size, shape, or color distribution). It is now relatively straightforward to make three different estimates of the z $ 6 luminosity density. Our first and most direct estimate comes directly from the comparisons presented in x 4, where marginal evolution is observed from z $ 6 to z $ 5. Linking this with the result from BBI (46% drop from z $ 3 to z $ 5) yields a 20% ô 29% decrease in the luminosity density from z $ 3 to z $ 6 (a 37% decrease if the bright zAB $ 24:2 object is ignored). This relative decrease can then, in turn, be expressed as an absolute luminosity density by integrating the Steidel et al. (1999) luminosity function (LF) down to zAB $ 27 or $0:4Lö , where our i-dropouts counts are clearly becoming incomplete. The result is Ï9:8 ô 3:6÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3. Our second estimate closely follows the more standard approach pioneered by Steidel et al. (1999) in deriving the luminosity density at z $ 3. With this approach, one derives a UV-continuum luminosity function ÏM ÷ as follows:
Fig. 6.--Comparison of the number counts for the i775 -dropouts (i þ z > 1:5) observed in our two fields (histogram), corrected by 13% for possible contamination, with the no-evolution expectations based on our GOODS z $ 5 V-dropout sample (shaded regions). We also include the predictions for two different imaging depths: three orbits in i775 and five orbits in z850 (solid line), and six orbits in i775 and 10 orbits in z850 (dotted line). This illustrates how important the issue of completeness is at these depths. (Note that the shaded region above assumes that 65% of our selection area was at the shallower of these two depths and 35% of the area was at the deeper.) For reference, the thin and thick dashed lines show the z $ 3 Steidel et al. (1999) LF placed at z $ 6(mz;ö ¼ 26:1, ¼ þ1:6, 0 ¼ 0:0025 Mpcþ3) with no change in normalization (thin line) and a normalization that is 4 times lower (thick line), respectively. (An i-dropout selection volume of 800 Mpc3 arcminþ2 is assumed for both.) The observations, while slightly in excess of the z $ 5 no-evolution predictions (23% ô 25%), are consistent with no significant evolution over the redshift interval z $ 5­6.

ÏM ÷ ¼

N Ïm ÷ ; Veff Ïm÷

Ï 1÷

[Assuming that the luminosity density at z $ 6 is proportional to the light in the integrated counts, R 10þ0:4m ÏdN =dm÷dm, we infer that the luminosity density is 51% ô 29% higher at z $ 6 than it is at z $ 5. Removing the bright zAB $ 24:2 object lowers the luminosity increase to 18% ô 23%.] We include in this figure the predictions for the two depths described above (solid and dotted lines), showing the effect the assumed depth can have on the predicted numbers.17 Taking the apparent completeness into account (see also Fig. 8 and the discussion in x 5), we quote an approximate surface density of $0:5 ô 0:2 i-dropouts arcminþ2 down to zAB $ 26:5. For reference, we also include a comparison of the predicted and observed redshift distributions (Fig. 7).

° where M is the absolute magnitude at 1600 A, corresponding to some z850 magnitude m, assuming a fixed redshift of 5.9 (the average redshift for an i-dropout; see Fig. 7). The effective volumeRthen is calculated as a function of magnitude Veff Ïm÷ ¼ z pÏm; z÷ÏdV =dz÷dz, where pÏm; z÷ is the probability that an object of magnitude m and redshift z falls in our i-dropout sample and dV =dz is the cosmological volume at redshift z. The factor pÏm; z÷ contains a whole range of different selection effects that affect the inclusion of an object in our sample from the intrinsic distribution of colors to photometric scatter to the effect of the inherent surface brightnesses on the completeness of the sample. Assuming a similar distribution of surface brightnesses, shapes, and colors to that seen at z $ 5, we can use the Monte Carlo cloning simulations presented in x 4 to determine this function. [Because of the lack of V606 -dropouts to probe the selection function pÏm; z÷ at bright magnitudes, we require that pÏm; z÷ be a strictly decreasing function of magnitude.] We present our result in Figure 8. For this approach to be effective, the absolute magnitude M has to be a very tight function of apparent magnitude m. This occurs when the selection function pÏm; z÷ is a very narrow function of redshift. Since this is not the case, we rewrite the above expressions as Z ½M Ïm; z÷pÏm; z÷ÏdV =dz÷dz ¼ N Ïm÷ ; where the absolute magnitude M is a function of the apparent magnitude m and the redshift z.18 Approximating ÏM ÷ and N Ïm÷ as a series of step functions, we are able to

5. ESTIMATED LUMINOSITY DENSITY

In the previous section, we compared the i-dropouts we observe with a no-evolution projection of a wide-area z $ 5 V606 -dropout sample. Not only do these simulations give us
17 We observe a similarly strong dependence in the data, finding 65% more i-dropouts arcminþ2 in the deeper overlap regions of our RDCS 12522927 field than in regions at just half that depth (0.4 mag deeper to the same S/N). This illustrates how important a consideration incompleteness can be in the magnitude range we are considering.

18 To convert the apparent magnitudes that we measure to absolute magnitudes, it was necessary for us to take into consideration possible biases in the measurement of the z850 magnitudes. We can make an estimate for this bias by using the simulations presented in x 4. Comparing the magnitudes that we recover with those expected on the basis of an extrapolation of the original V-dropout photometry to z $ 5:5, we find an average $0.2 mag faintward offset in the measured magnitudes.


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TABLE 1 z $ 6 Sample rhl (arcsec) 0.29 0.18 0.20 0.11 0.14 0.16 0.12 0.19 0.19 0.22 0.14 0.23 0.17 0.13 0.12 0.08 0.12 0.11 0.11 0.08 0.08 0.14 0.10

597

Object ID 1252-5224-4599e .................. 1252-2134-1498 ................... 1252-2585-3351 ................... 1252-6031-966 ..................... 1252-562-2836 ..................... 1252-6798-302 ..................... 1252-4720-6466 ................... 1252-5058-5920 ................... 1252-277-3385 ..................... 1252-5377-2621 ................... 1252-7065-6877 ................... 1252-3544-3542f .................. 1252-2439-3364 ................... 1252-7005-1697 ................... 1252-3729-4565 ................... 1252-7313-6944 ................... 1252-1199-3650 ................... 1252-5399-4314 ................... 1252-3497-809 ..................... 1252-4375-1877 ................... 1252-3684-528 ..................... HDF-N 2135-3286 .............. HDF-N 4965-4355 .............. 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12

R.A. 52 52 52 52 52 52 53 53 52 52 53 52 52 52 52 53 52 52 52 52 52 36 36 56.8880 45.3816 52.2832 43.3793 50.2971 40.8435 03.8342 01.7448 52.3987 49.5122 05.4237 53.0237 52.3340 46.1876 56.7460 05.6814 53.4200 55.7957 42.7537 46.8536 41.6802 49.9368 30.7457 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 þ29 62 62

Decl. 25 28 28 25 29 24 26 26 29 25 24 27 28 24 27 24 29 25 27 26 27 13 12 55.503 27.105 04.743 17.474 43.226 39.033 20.835 03.873 57.525 47.721 26.222 16.801 12.030 28.846 07.631 13.836 11.443 46.724 18.894 37.733 09.550 55.671 53.371

z850 24.2 25.6 25.7 25.7 25.8 25.8 25.8 25.9 26.0 26.0 26.1 26.2 26.4 26.5 26.7 26.7 26.7 27.0 27.0 27.2 27.3 26.5 27.0

a

i þ zb 1.5 >2.1 2.0 2.0 2.0 1.7 1.5 >1.8 >1.6 >1.6 1.6 1.6 >1.7 >1.5 >1.8 >1.6 >1.7 >1.6 >1.6 1.6 >1.5 >1.9 >1.5

zþJ

c

V þz .. . .. . .. . . .. . .. . .. . .. .. . . .. .. . . .. .. . .. . . .. .. . . .. .. . .. . . .. .. . . .. >2.1 >1.3

I þz ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... 1.1 .. .

S/Gd 0 0.01 0 0.30 0.06 0.04 0.02 0 0 0 0.01 0 0 0 0 0.09 0 0 0 0.60 0.16 0.02 0.01

ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô ô

0.1 0.2 0.1 0.1 0.1 0.2 0.1 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.2

0.1 0.4 0.1 .. . .. . .. . .. . þ0.4 .. . <þ0.1 .. . 0.1 <þ0.2 .. . 0.4 .. . 0.1 <0.0 .. . <0.7 .. . <þ0.6g .. .

Notes.--Objects from RDCS 1252-2927 and the HDF-N that satisfy our Ïi775 þ z850 ÷AB > 1:5 i-dropout criterion. Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. a AB magnitudes. b All limits are 2 . c Here the J band alternatively refers to the ISAAC J band or the NICMOS J 110 filter, depending on the field in which the object is found. s d SExtractor stellarity parameter, for which 0 indicates an extended object and 1 indicates a point source e The prefix 1252- denotes an object from RDCS 1252-2927. f This object appears to be lensed and therefore is excluded from our sample. g This is Ïz þ J 110 ÷AB .

invert equation (1) to solve for ÏM ÷ (see Fig. 9 for a comparison of the derived LF with the Steidel et al. 1999 z $ 3 determination). Integrating this LF down to zAB $ 27 (0:4Lö ), we find Ï7:2 ô 2:5÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3 [Ï5:9 ô 1:8÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3, if the bright zAB $ 24:2 object is ignored]. This represents a 39% ô 21% drop relative to what Steidel et al. (1999) report at z $ 3toa similar limiting luminosity. Note that for z $ 6 Lö -type objects, the effective survey volume is approximately 3 á 104 Mpc. In the first two approaches presented, there is the implicit assumption that the selectability of z $ 6 objects is similar to that found at z $ 5, both in their colors and their surface brightnesses, and to a large extent this is probably true. The

TABLE 2 Number of i-Dropouts Data Set RDCS 1252-2927 .............. HDF-N ............................. Observed 18.7 1.9
a a

No-Evolution Prediction 12.1 ô 1.0 ô 3.5 4.7 ô 0.4 ô 2.2

distribution of z850 þ J colors (while perhaps a little bluer) is not that different from the low-redshift expectation (Steidel et al. 1999; BBI) and similarly for the distribution of surface brightnesses (as similarities in the fall-off of the predicted and observed number counts in Fig. 6 effectively illustrate).19 This being said, given the expectation that higher redshift objects are denser and therefore have higher surface brightness, it is useful to consider a third approach in which no completeness correction is made. This enables us to put a lower bound on the z $ 6 space density in the event these changes would have a substantial effect on the completeness of the i-dropout population. As with the previous two approaches, we use the simulations from x 4. The difference is that when computing Veff Ïm÷ we consider only objects that actually make it into our i-dropout sample, not every object from our simulations. The effective volume, Veff Ïm÷, is hence computed as an ensemble average over all inputs observed at magnitude m and selected as i-dropouts. Putting in our observed surface densities for these same magnitude intervals (Fig. 6), we derive a UV-continuum luminosity density of Ï2:7 ô 0:6÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3. We emphasize that relative to our pre-

Note.--Number of i-dropouts found in our samples vs. noevolution predictions. Two different 1 uncertainties are quoted on all predictions, the first based on the finite size of our V-dropout sample (130 objects; Bouwens et al. 1998a, 1998b) and the second based on sample variance (simple Poissonian errors). a Corrected for the expected 13% contamination rate.

19 Determining both distributions observationally would require the sort of deep optical and infrared images promised by the HST Ultra Deep Field. Lacking such, one is forced to assume a certain similarity to lower redshift dropout populations (as we have done here).


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Fig. 7.--Comparison of the estimated redshift distribution for the observed i-dropouts vs. that predicted based on our GOODS z $ 5 Vdropout sample (shaded regions). This shows that the bulk of the sample is expected to lie between z $ 5:5 and 6.2.

vious estimates, this final estimate represents a strict lower limit on the luminosity density. We converted these UV luminosity densities to star formation rate densities by using the relation L
UV

Fig. 8.--Probability pÏm; z÷ of some object of z850;AB magnitude m and redshift z being included in our i-dropout sample. This function was computed from a no-evolution projection of our wide-area V606 -dropout sample to z $ 6(x 4).

¼ const

SFR 1 M yr

þ1

ergs s

þ1

Hz

þ1

;

Ï 2÷

° where const = 8:0 á 1027 at 1500 A for a Salpeter initial mass function (IMF; Madau, Pozzetti, & Dickinson 1998). The result is 0:0123 ô 0:0045, 0:0090 ô 0:0031, and 0:0034 ô 0:0008 M yrþ1 Mpcþ3, respectively, for the three approaches just presented. Assuming a Schechter luminosity function with faint-end slope ¼ þ1:6 and extrapolating this to the faint-end limit yields a star formation rate density that is $4 times larger. This works out to an integrated star formation rate of $0:049 ô 0:018, $0:036 ô 0:012, and $0:014 ô 0:003 M yrþ1 Mpcþ3, respectively, for these three approaches. To put these estimates in context, we make a comparison with several previous determinations (Steidel et al. 1999; Madau et al. 1998; Thompson et al. 2001; Lilly et al. 1996; Stanway et al. 2003; BBI) in Figure 10, truncating the observationally derived LFs at similar faint-end luminosities.
6. DISCUSSION

In this work, the luminosity density at z $ 6 is evaluated using three different procedures. The first is strictly differential in nature. V606 -dropouts from the wide-area GOODS survey are projected to z $ 6 for comparison with the observed i-dropouts. Adopting previous results to z $ 5 (BBI; Thompson et al. 2001) then implies a $20% drop in the luminosity density from z $ 3 to z $ 6. The second and third procedures, by contrast, are more direct, relying on a derived selection function to convert the observed i-dropouts into a luminosity density at z $ 6. Relative to the

Fig. 9.--Our i-dropout LF derived from RDCS 1252-2927 and HDF-N fields (squares), using a generalized version of the Steidel et al. (1999) Veff Ïm÷ technique. The z $ 3 LF of Steidel et al. (1999) is superposed as a solid line (M1600;AB þ M1700;AB ¼ 0:14 was assumed.) We also include this same LF with a 39% lower normalization (dotted line) to match the observed evolution from z $ 6. The error bars represent 1 uncertainties.


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Fig. 10.--History of the star formation rate density assuming no extinction correction, integrated down to 0:4Lö . We include three determinations from this work (large filled red circles), the lower point assuming no incompleteness correction and providing a reliable lower limit, the slightly larger middle point based on a generalization of the Steidel et al. (1999) Veff Ïm÷ formalism, and the upper point based on the differential evolution measured from z $ 6 to z $ 5 (and linked to z $ 3 by using the results quoted in BBI; see x 5 for details). The middle point is our preferred estimate. A Salpeter (1955) IMF is used to convert the luminosity density into a star formation rate (see, e.g., Madau, Pozzetti, & Dickinson 1998). Our different estimates provide a nice illustration of the real uncertainties in the star formation rate density at z $ 6, arising from strong redshift-dependent selection effects. This topic will be explored much more extensively in R. J. Bouwens et al. (2003, in preparation). Comparison is made with the previous high-redshift determinations of Lilly et al. (1996; squares), Madau et al. (1998; open circles), Steidel et al. (1999; crosses), Thompson, Weymann, & Storrie-Lombardi (2001; open triangles), Stanway et al. (2003; pentagons), and BBI ( filled red triangles). The top horizontal axis provides the corresponding age of the universe. Note the small Dt from z $ 6to z $ 5.

luminosity density reported at z $ 3 by Steidel et al. (1999), the resulting drop is a factor of $2 and $5, depending on the two different assumptions these two procedures make about the completeness levels (and therefore the presence of low surface brightness objects at high redshift). Similarities between our first two estimates of the luminosity density point to a general consistency between those methodologies. Our three estimates have different strengths and weaknesses. Our first estimate, for example, depends on the relatively small-area BBI result (HDF-N and HDF-S) and therefore could be quite sensitive to cosmic variance. Our second estimate, by contrast, relies on the much larger area z $ 5 V-dropout population (CDF-S) to derive the z $ 6 selection function. Unfortunately, this same z $ 5 sample could be subject to similar selection effects and therefore missing light, possibly biasing the numbers low. Our first two estimates provide accurate estimates of the z $ 6 lumi-

nosity density in lieu of large amounts of size or color evolution. Our final estimate, on the other hand, is probably much too low except in cases that have had dramatic amounts of evolution in the sizes of galaxies. It therefore serves as a useful lower limit. On balance, we prefer our estimate based on a generalized version of the Steidel et al. (1999) Veff Ïm÷ formalism, given the effect of cosmic variance on our first estimate and the extreme assumptions present in the third (e.g., given the small increase in the universal scale factor from z $ 6 to z $ 5, the change in surface brightnesses should be at most modest). We will use it throughout the remainder of the discussion.20
20 Ideally speaking, we would estimate the z $ 6 luminosity density by using a completely differential procedure, scaling the sizes and colors to match the evolution observed. Such an analysis is being performed in a future paper on the dropouts in the GOODS fields where the samples are substantially larger (R. J. Bouwens et al. 2003, in preparation).


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Before getting into a comparison against previous work, we should take a more detailed look at the validity of the sample itself, particularly with regard to our use of a cluster field. Two concerns immediately arise. The first regards the effect of lensing by the cluster on z $ 6 sources. We can make a simple estimate of this effect by using the Broadhurst, Taylor, & Peacock (1995) equation for the " magnification bias, M 2:5lþ1 , where l is the slope of the number count d ½log N Ïm÷=dm. For a faint-end slope m ¼ 0:24 (a simple consequence of a z $ 6 LF with ¼ þ1:6) and an average magnification of $1.03, this works out to an expected 1% drop in the surface density of i-dropouts relative to the unlensed case. The second concern involves the possibility that z $ 1:2 cluster elliptical galaxies might get mixed up in our i-dropout sample. After all, we decided to observe RDCS 1252-2927 with the i775 and z850 filters ° because they straddled the 4000 A break. Fortunately, the mean i þ z color for bright elliptical galaxies in this cluster is $0.9 (one can see the cluster as a small overdensity in Fig. 1 at i þ z ¼ 0:9 and z þ J ¼ 1:1), and this color decreases quite markedly toward faint luminosities (Postman et al. 2002; Blakeslee et al. 2003). There is no indication that lower luminosity z $ 1:2 cluster members are being scattered into the i-dropout sample. It is interesting to compare the present results with other early work on the surface density of i-dropouts. Stanway et al. (2003), for example, report finding eight objects over 146 arcmin2, e.g., 0.05 i-dropouts arcminþ2, to zAB $ 25:6. We find only one object (%0.02 i-dropouts arcminþ2) to that same depth, a result that may not be surprising given the numbers and relative areas. In a deeper but smaller area search, Yan et al. (2003) report finding 2.3 objects arcminþ2 (27 objects) to zAB $ 28:0, subtracting at most four objects from this estimate because of contamination by stars. Since the median magnitude of their sources is z850;AB $ 27:4 and their brightest reported source has z850;AB $ 26:8, this works out to $1.2 objects arcminþ2 to our quoted magnitude limit, somewhat larger than the 0:5 ô 0:1 objects arcminþ2 we find. We are somewhat uncertain about the reliability of their identifying i-dropouts to z850;AB $ 28 (7 ) in a fiveorbit (9540 s) z850 -band exposure, given the difficulty we had in identifying i-dropouts to a much brighter limit of zAB $ 27:3 (6 ) in the deeper ($10­20 orbit) overlapping regions. For typical i-dropout sizes ($0 > 15), our analysis would tend to suggest a S/N closer to 2­3 at their stated magnitude limit. Compared with Stanway et al. (2003), who estimate a 25% contamination fraction due to elliptical galaxies or EROs in an i þ z > 1:5 sample, we estimate a smaller contamination fraction, 13%, on the basis of the measured z þ J colors for our sample. Though hardly significant given the number of objects involved, such a difference clearly follows the trend toward lower early-type fractions at fainter magnitudes. We noted similarly small contamination fractions in our analysis of the V-dropouts from the HDF-N (BBI). Down to our magnitude limit zAB $ 27:3, we find a star formation rate density at z $ 6 of 0:0090 ô 0:0031 M yrþ1 Mpcþ3, $2 times lower than similar estimates at z $ 3 from Steidel et al. (2003) and Madau et al. (1998). This estimate is nearly 14 times the quoted result of Stanway et al. [2003; Ï6:7 ô 2:7÷ á 10þ4 M yrþ1 Mpcþ3]. While a portion of this difference can be attributed to the different depths of our searches (the present census going $1.4 mag further down

the luminosity function), there are significant differences in the effective volumes we assume, the present study correcting for the significant incompleteness at z $ 6 resulting from surface brightness dimming while Stanway et al. (2003) do not make such a correction. For both this reason and our greater overall depth, the present study represents a clear improvement over the Stanway et al. (2003) estimate. From z $ 5 to 6, we find minimal evidence for dramatic evolution, consistent with the small amount of cosmic time available across this interval ($0.2 Gyr from z $ 6 to 5 and $1 Gyr from z $ 6 to 3). In general, the trends we find are consistent with the gradual decline in star formation density previously reported from z $ 3 to 5 (Madau et al. 1996; Steidel et al. 1999; Thompson et al. 2001; Lehnert & Bremer 2003; Dickinson 2002, BBI) or as found in recent work on Ly emitters, for which a deficit is claimed at z $ 5:7 relative to the z $ 3 population (Maier et al. 2003). Since recent work from absorption-line studies on z > 5:8 QSOs indicates that the universe may have been reionized near a redshift of z $ 6 (Fan et al. 2001; Becker et al. 2001; Fan et al. 2002), it is relevant to compare the star formation rate we determine here with that needed to reionize the universe at z $ 6. For the latter, we use the following relation from Madau, Haardt, & Rees (1999), correcting it for the baryon density (b h2 ¼ 0:0224) derived from the recent WMAP results (Bennett et al. 2003) and shifting it to z $ 6: 1×z 3 þ1 þ3 0:5 _ö % Ï0:052 M yr Mpc ÷ C30 ; Ï 3÷ fesc 7 where _ö is the star formation rate density, C30 is the H i
concentration factor Ï1=30÷ 2 i hH i iþ2 , and fesc is the H fraction of ionizing radiation escaping into the intergalactic medium. Given the large observational and theoretical uncertainties in the exact values of C30 and fesc , the star formation rate densities inferred here at z $ 6 ($0.0090 M yrþ1 Mpcþ3 observed and $0.036 M yrþ1 Mpcþ3 by extrapolating the LF to the faint limit) are well within the range of that needed to reionize the universe at z $ 6 (only $30% lower than the fiducial value given in eq. [3]). Whether or not the objects we observe at z $ 6 are sufficient to reionize the universe or this ionizing radiation is provided by a completely different population of objects (e.g., Madau 1998), it seems clear that this ionizing radiation does not come from z $ 5­6 AGNs (Haiman, Madau, & Loeb 1999).

7. SUMMARY

We use deep ACS WFC i+z observations of RDCS 12522927 and the HDF-N to search for z $ 6 candidates by looking for a strong Lyman break across the i and z passbands. We augment this with deep infrared imaging to derive z þ J colors for the z $ 6 candidates to help distinguish them from lower redshift interlopers if possible. We compare our findings with a no-evolution projection of a wide-area V606 -dropout sample to z $ 6 and then use these simulations to make three different estimates of the restframe continuum UV-luminosity density at z $ 6. 1. To zAB $ 27:3, we find 21 i-dropouts (i þ z > 1:5; 6 detections) over 36 arcmin2 in our RDCS 1252-2927 field (one object is lensed) and two i-dropouts over 10 arcmin2 in our HDF-N field. This is equivalent to $0:5 ô 0:1 object arcminþ2 down to our magnitude limit zAB $ 27:3, or


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$0:5 ô 0:2 object arcminþ2 down to zAB $ 26:5 if corrected for completeness. 2. Compared with an average-color (UV power-law index  ¼ þ1:3) U-dropout in the Steidel et al. (1999) z $ 3 sample, the i-dropouts we find range in luminosity from $0.3Lö to $1.5Lö [with the exception of one very bright z850;AB ¼ 24:2(6Lö ) object that also meets our selection criterion]. Our typical i-dropout has a half-light radius ranging from 0 > 09 to 0 > 29, or 0.5 to 1.7 kpc, for a M ¼ 0:3, ö ¼ 0:7, and h ¼ 0:7 cosmology. 3. Using our deep infrared data to constrain the spectral slopes redward of the break, we find that all 12 of our idropout candidates (i þ z > 1:5) for which we have IR data have blue (<0.8) z þ J colors. Using the Kaplan-Maier estimator on all extended i þ z > 1:3 sources, we estimate that only 13% of such i þ z > 1:5 sources are low-redshift interlopers. Assuming spectroscopic confirmation of the twocolor dropout technique to z $ 6 (e.g., Fan et al. 2001; Bunker et al. 2003; Dickinson 2003), this demonstrates that an i þ z selection can be an effective way of uncovering a population of high-redshift objects (see also Stanway et al. 2003). 4. Over the 21 arcmin2 for which we had infrared coverage, we identified only one red (i þ z > 1:3) pointlike object with z þ J colors consistent with being a z $ 5:5­6 AGN. Since in total we identify seven pointlike objects with zAB > 25 and Ïi775 þ z850 ÷AB > 1:3 and only one of four objects (25%) with IR coverage has z þ J colors less than 0.8, this works out to an estimated surface density of $0:04 ô 0:03 z $ 5:5­6.3 AGNs arcminþ2 down to our magnitude limit of zAB $ 27:3. 5. Comparing the number of i-dropouts with a noevolution projection of our z $ 5 V606 -dropout sample from CDF-S GOODS, we estimate the evolution in rest-frame continuum UV luminosity density from z $ 6 to 5. We find 23% ô 25% more i-dropouts ($21) than are predicted (17) once a correction for the contamination rate is made, consistent with no strong evolution over this redshift interval. After redoing this increase in terms of integrated luminosity, this increase amounts to 51% ô 29% (or 18% ô 23% if the one very bright zAB $ 24:2 object is removed). By adopting previous results to z $ 5 (BBI; Thompson et al. 2001), this works out to a mere 20% ô 29% drop in the luminosity density from z $ 3to6. 6. Using simulations based on a set of CDF-S V606 -dropouts, we estimate the selection function pÏm; z÷ for our idropout sample. Then, via a generalized version of the Steidel et al. (1999) Veff Ïm÷ formalism, we calculate the UV luminosity function for this sample and integrate it down to zAB $ 27:0($0:4Lö ). The rest-frame UV luminosity density we derive [Ï7:2 ô 2:5÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3] is 39% ô 21% lower than Steidel et al. (1999) found to a similar limiting luminosity, consistent with the above estimate. This is our preferred estimate.

7. The previous two approaches assume no large change in the selectability (color or surface brightness distribution) of dropouts from z $ 5 to 6. Given the expectations (observational and theoretical) that dropouts may have higher surface brightnesses at z $ 6 than z $ 5, it is useful to make a third estimate for the luminosity density from the simulations but this time assuming no incompleteness. Running through the numbers, we find Ï2:7 ô 0:6÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3 for the observed i-dropouts, $5 times lower than the value reported by Steidel et al. (1999) to a similar luminosity. This third approach provides a reliable lower limit to the luminosity density. 8. Converting the luminosity densities that we infer into star formation rate densities by using standard assumptions (e.g., Madau et al. 1998), we find an integrated star formation rate density of 0:0123 ô 0:0045, 0:0090 ô 0:0031, and 0:0034 ô 0:0008 M yrþ1 Mpcþ3, respectively, for the three approaches just presented (or $0:049 ô 0:018, $0:036 ô 0:012, and $0:014 ô 0:003 M yrþ1 Mpcþ3 by extrapolating the observations to low luminosities using a Schechter function with faint-end slope ¼ þ1:6). 9. Our preferred estimates for the rest-frame continuum UV luminosity density and star formation rate density at z $ 6 are Ï7:2 ô 2:5÷ á 1025 ergs sþ1 Hzþ1 Mpcþ3 and 0:0090 ô 0:0031 M yrþ1 Mpcþ3 ($0:036 ô 0:012 by extrapolating the luminosity function to the faint limit), respectively. This represents a 39% ô 21% drop from z $ 3to6. 10. The z $ 6 rest-frame continuum UV luminosity densities we infer are well within the expected range needed for reionization, for canonical assumptions about the H i clumping factor and the fraction of UV radiation escaping into the intergalactic medium. The combination of deep ACS i and z and ground-based IR imaging has been shown to be a very effective means of isolating high-redshift objects and studying their properties. We will be following up this analysis with an investigation of the shallower but larger area data in the CDF-S and HDF-N from the GOODS program (R. J. Bouwens et al. 2003, in preparation). We extend a special thanks to Mark Dickinson for providing us with his fully reduced NICMOS images of the HDF-N. We would also like to acknowledge T. Allen, K. Anderson, S. Barkhouser, S. Busching, A. Framarini, and W. J. McCann for their invaluable contributions to the ACS Investigation Definition Team (IDT). This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. ACS was developed under NASA contract NAS 5-32865. R. J. B., G. D. I., and the ACS IDT acknowledge the support of NASA grant NAG 5-7697.

APPENDIX A NOISE The drizzling and resampling procedure we employ (and generally employed with HST data sets) to produce our fully coaligned optical and infrared data set naturally introduces a certain correlation into the noise of this data set. To estimate the true amplitude of the noise, distinct from the single-pixel rms, as well as the effective noise kernel, rms fluctuations within apertures of increasing sizes are measured, after masking out detections greater than 5 , up to scales on which there is no obvious


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additional power. A noise model (amplitude and kernel) is then constructed that provides a plausible fit to the observations. This model is used throughout to estimate errors in the photometry. APPENDIX B z $ 6 AGN We found one Ïi775 þ z850 ÷AB $ 1:3, Ïz850 þ J ÷AB < þ0:1 stellar object consistent with a z $ 5:5­6 AGN identification (Fig. 11) over the area where we had infrared coverage ($21 arcmin2). Since in total we identify seven pointlike objects with zAB > 25 and Ïi775 þ z850 ÷AB > 1:3 and only one of the four objects with IR coverage (25%) had Ïz850 þ J ÷AB colors less than 0.8, this works out to an estimated surface density of $0:04 ô 0:03 objects arcminþ2 down to our magnitude limit of z850;AB $ 27:3.

z~5.8
27.92±0.22 26.62±0.14 >26.77 >26.09

i

z 1252-4950-3980

J

Ks

Fig. 11.--Images in i775 z850 JKs of a z $ 6 AGN candidate found in our RDCS 1252-2927 field. The above object is the only such candidate over the 21 arcmin2 for which we have both optical and infrared imaging. The position in i þ z, z þ J color-color space is included along with a plausible fit to the SED of an AGN.

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