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The Astronomical Journal, 128:1990 ­ 2012, 2004 November
# 2004. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE LUMINOSITY FUNCTION OF EARLY-TYPE FIELD GALAXIES AT
1 2 1 1 1 1

Z

% 0.75
2

N. J. G. Cross, R. J. Bouwens, N. Benitez, J. P. Blakeslee, F. Menanteau, H. C. Ford, T. Goto,1 B. Holden, ´ A. R. Martel,1 A. Zirm,3 R. Overzier,3 C. Gronwall,4 N. Homeier,1 M. Clampin,5 G. F. Hartig,6 G. D. Illingworth,2 D. R. Ardila,1 F. Bartko,7 T. J. Broadhurst,8 R. A. Brown,6 C. J. Burrows,6 E. S. Cheng,5 P. D. Feldman,1 M. Franx,3 D. A. Golimowski,1 L. Infante,9 R. A. Kimble,5 J. E. Krist,6 M. P. Lesser,10 G. R. Meurer,1 G. K. Miley,3 M. Postman,1,6 P. Rosati,11 M. Sirianni,6 W. B. Sparks,6 H. D. Tran,12 Z. I. Tsvetanov,13 R. L. White,1,6 and W. Zheng1
Received 2004 April 5; accepted 2004 July 29

ABSTRACT We measure the luminosity function of morphologically selected E/S0 galaxies from z ¼ 0:5 to 1.0 using deep high-resolution Advanced Camera for Surveys (ACS) imaging data. Our analysis covers an area of 48 arcmin2 (8 times the area of the Hubble Deep Field North) and extends 2 mag deeper (I $ 24 mag) than was possible in the Deep Groth Strip Survey ( DGSS). Our fields were observed as part of the ACS Guaranteed Time Observations. At ö 0:5 < z < 0:75, we find MB þ 5log h0:7 ¼ þ21:1 ô 0:3 and ¼ þ0:53 ô 0:2, and at 0:75 < z < 1:0, we find ö MB þ 5log h0:7 ¼ þ21:4 ô 0:2, consistent with 0.3 mag of luminosity evolution (across our two redshift intervals). These luminosity functions are similar in both shape and number density to the luminosity function using morphological selection (e.g., DGSS), but are much steeper than the luminosity functions of samples selected using morphological proxies such as the color or spectral energy distribution (e.g., CFRS, CADIS, or COMBO-17). The difference is due to the ``blue,'' (U þ V )0 < 1:7, E/S0 galaxies, which make up to $30% of the sample at all magnitudes and an increasing proportion of faint galaxies. We thereby demonstrate the need for both morphological and structural information to constrain the evolution of galaxies. We find that the blue E/S0 galaxies have the same average sizes and Sersic parameters as the ``red,'' (U þ V )0 > 1:7, E/S0 galaxies at brighter luminosities (MB < þ20:1), but are increasingly different at fainter magnitudes, where blue galaxies are both smaller and have lower Sersic parameters. We find differences in both the size-magnitude relation and the photometric plane offset for red and blue E/S0s, although neither red nor blue galaxies give a good fit to the size-magnitude relation. Fits of the colors to stellar population models suggest that most E /S0 galaxies have short star formation timescales ( < 1 Gyr), and that galaxies have formed at an increasing rate from z $ 8 until z $ 2, after which there has been a gradual decline. Key words: galaxies: elliptical and lenticular, cD -- galaxies: evolution -- galaxies: fundamental parameters -- galaxies: luminosity function, mass function

1. INTRODUCTION The luminosity function ( LF ) of galaxies is the number density of galaxies as a function of absolute magnitude. The shape of the LF can be used to constrain galaxy formation models. The LF is often described by three numbers: M ö , the
1 Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218. 2 UCO/ Lick Observatory, University of California, Santa Cruz, CA 95064. 3 Leiden Observatory, Postbus 9513, 2300 RA Leiden, Netherlands. 4 Department of Astronomy and Astrophysics, Pennsylvania State University, 525 Davey Lab, University Park, PA 16802. 5 Laboratory for Astronomy and Solar Physics, NASA Goddard Space Flight Center, Greenbelt, MD 20771. 6 Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218. 7 Bartko Science and Technology, P.O. Box 670, Mead, CO 80542-0670. 8 Racah Institute of Physics, The Hebrew University, Jerusalem, Israel 91904. 9 ´ Departmento de Astronomia y Astrof ´sica, Pontificia Universidad Catolica ´ i de Chile, Casilla 306, Santiago 22, Chile. 10 Steward Observatory, University of Arizona, Tucson, AZ 85721. 11 European Southern Observatory, Karl-Schwarzschild-Strasse 2, D-85748 Garching, Germany. 12 W. M. Keck Observatory, 65-1120 Mamalahoa Highway, Kamuela, HI 96743. 13 NASA Headquarters, Washington, DC 20546-0001.

magnitude at which the number of bright galaxies rapidly decreases; ö , the space density at M ö ; and the faint-end slope , which characterizes the ratio of dwarf galaxies to giant galaxies. Models of galaxy formation and evolution must be able to account for these parameters, which vary with galaxy type. Over the past few years, the LF of high-redshift (z > 0:5) galaxies have been studied extensively through the use of deep, wide-area surveys. Some of the more notable efforts include the Canada-France Redshift Survey (CFRS; Lilly et al. 1995), the Canadian Network for Observational Cosmology Field Galaxy Redshift Survey (CNOC2; Lin et al. 1999), the Calar Alto Deep Imaging Survey (CADIS; Fried et al. 2001), the Deep Groth Strip Survey ( DGSS; Im et al. 2002), the Subaru Deep Survey ( Kashikawa et al. 2003), the Classifying Objects by Medium Band Observations (COMBO-17; Wolf et al. 2003), and from a combination of Hubble Space Telescope (HST ) and Very Large Telescope ( VLT ) images, Poli et al. (2003). Most of these use deep, ground-based images with spectroscopic or photometric redshifts to construct the LF, but do not have the spatial resolution to measure the structural properties of galaxies at higher redshifts. Without information on the structural properties, groundbased surveys have resorted to using color information as a proxy for morphologies, whether this information comes in the form of a best-fit spectral energy distribution (e.g., Wolf 1990


LF OF EARLY-TYPE FIELD GALAXIES AT z % 0.75 et al. 2003), or a rest-frame color cut (e.g., Lilly et al. 1995). This can result in apparent discrepant results. For example, Wolf et al. (2003) found that the elliptical /S0 ( E/S0) galaxies that produce $50% of the current B -band luminosity density only contributed $5% at z ¼ 1. By contrast, using morphological classification, van den Bergh (2001) found that the fraction of elliptical galaxies has remained constant at $17% over 0:25 < z < 1:2, implying that either the luminosity of ellipticals has increased over time relative to other types of galaxies, or the differences in color selection and morphological selection have produced apparently inconsistent results between these surveys. Surveys using the HST, such as the DGSS ( Im et al. 2002; Simard et al. 2002) and the Medium Deep Survey (Griffiths et al. 1994) have been able to reliably morphologically classify and measure structural parameters for galaxies with IAB < 22 mag, but over much smaller areas of sky than the deep ground-based surveys. These HST surveys have discovered a population of 0:3 < z < 1 blue E/S0 galaxies (e.g., Menanteau et al. 1999; Im et al. 2001; Gebhardt et al. 2003) that have luminosities similar to standard red E/S0 galaxies. Im et al. (2001) find these make up $15% of the E/S0 sample, whereas Menanteau et al. (1999) find a much higher fraction, 30% ­ 50% of the sample. Objects such as these demonstrate the inherent weakness of using color as a proxy for morphology. At low redshifts, almost all of the bright E/S0 galaxies are red, with blue ellipticals (dwarf ellipticals) many magnitudes fainter. From the work of Menanteau et al. (2004) and Im et al. (2001), it appears that most of these blue E /S0 galaxies have blue cores and red exteriors, with the exteriors having the same colors as red E/S0 galaxies, which have constant colors at all radii. Im et al. (2001) concluded that these blue E /S0 galaxies were less massive than the red E /S0 galaxies based on the dynamical masses calculated from the velocity dispersions. However, because the velocity dispersions were measured much closer to the core of the galaxy for the low-redshift red ellipticals, the high-redshift blue ellipticals may be more massive than the measurements suggest. Even if the measurements give accurate dynamical masses, the blue E/S0 galaxies have masses equivalent to the lower mass red E/S0s, so they may still yet evolve into high-mass red E/S0s through a combination of luminosity evolution that reddens the stellar population over time and mergers that increase the mass. Luminosity evolution occurs when there is new star formation, or when the stellar population ages, and does not necessarily imply any change in the mass or number of stars in a galaxy. Structural parameters such as the size and shape are better indicators of the morphological evolution, since they are only weakly dependent on the age of the stellar population and are mainly determined by dynamical characteristics such as total mass and angular momentum. Within the half-light radius of a giant elliptical galaxy the dynamical timescale is very short, less than 108 yr, so dynamical equilibrium is reached very quickly. The size and shape of the galaxy will not change significantly unless mass is added via mergers or accretion; a close encounter changes the angular momentum; tidal forces disrupt the outer layers. Small changes in the apparent shape and size do occur when star formation is localized in the center, in bars, rings, or spiral arms, but these are much weaker changes than the variation in SED or color. Therefore morphology is a more robust indicator of the nature of a galaxy, but it requires good resolution to use. Previous studies have differed in the way they have utilized size information to make inferences about evolution. Several

1991

surveys have assumed that galaxy size and shape are constant with redshift. Schade et al. (1997) showed that cluster ellipticals evolve as à M ¼ þ2:85 log10 (1 × z), assuming they maintain a constant size, and Schade et al. (1999) demonstrated that field ellipticals show a similar evolution. Using a sample of 44 galaxies with z < 2, Roche et al. (1998) discovered that ellipticals show significant luminosity evolution but little size evolution from z ¼ 1:0 to 0.2. They found that most size evolution appears to happen at z > 1:5. Graham (2002) compared the scatter in the ``photometric plane,'' which only requires parameters measured from galaxy images, to the scatter in the ``fundamental plane,'' which requires dispersion velocities measured from high-resolution spectra. Graham showed that the photometric plane could be used to constrain distances to elliptical galaxies. In Cross et al. (2001) and Cross & Driver (2002), the effects of surface brightness selection on the z ¼ 0 galaxy LF were discussed. In this paper we look at the LF of morphological early types at 0:5 < z 1. We then examine the effect that color selection has on this LF. Finally, we use structural parameters to test whether blue E/S0 galaxies are progenitors of red E /S0 galaxies and what evolution has taken place from z ¼ 1 t o 0.5. The Advanced Camera for Surveys (ACS; Ford et al. 2002) significantly improves on WFPC2 in terms of sensitivity (a factor of 5), field of view (a factor of 2), and resolution (a factor of 2), giving well-sampled PSFs in the i and z bands. This leads to significant improvements in both the accuracy of the size measurements and the overall sample size. In this paper we use data from five fields observed as part of the ACS GTO program. The total area is over 8 times the Hubble Deep Field North ( HDFN ). These fields were selected to observe very nearby (z < 0:03) galaxies or very distant (z > 4) galaxies, so galaxies in the redshift range 0:5 < z < 1:0 should be representative of the universe at that redshift. The fields are in various parts of the sky, sampling a large volume in each redshift range ($1:6 ; 104 Mpc3 0:5 < z < 0:75 and $2:4 ; 104 Mpc3 0:75 < z < 1:0), so the effects of cosmic variance should be much smaller than in the Hubble Deep Fields. In fact, the relative independence of our fields makes this survey more competitive with larger surveys than one might think based upon the areal coverage alone. We express all magnitudes in the AB system and use a M ¼ 0:3, ö ¼ 0:7 cosmology with H0 ¼ 70 km sþ1 Mpcþ1. We define h0:7 ¼ H0 =70: 2. DATA The data were extracted from five fields observed by the ACS Wide Field Camera ( WFC) between 2002 April and 2003 June. The fields were selected to give accurate photometric redshifts (three or more filters), to not have any primary targets in the range 0:5 < z < 1:0, and to not contain any clusters at lower redshifts. While the HDFN was only imaged in two ACS bands ( F775W and F850LP), it has been imaged extensively in seven optical and near-infrared bands, and has a large amount of spectroscopic follow-up. The combined area of these fields is 47.9 arcmin2, over 8 times the area of the HDFN. The extinction values, E(BþV ), are taken from the Schlegel et al. (1998) dust maps, and the total extinction in each filter, A(Blter), is calculated using the method described in Schlegel et al. (1998). A summary of the data properties in each field is given in Table 1, which lists the ACS filters, field of view, I-band exposure time, E(BþV ), I-band extinction, I-band zero point, and the number of E/S0 galaxies in our sample.


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TABLE 1 Su mmary of Data fr om Diff erent F ield s Area (arcsec2) 7.8 10.7 11.7 11.7 5.8 Texp, (s)
a

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I

Field NGC 4676 ............ UGC 10214 .......... TN 1338 ............... TN 0924 ............... HDFN ...................
a

Filters g, V, I g, V, I g, r, i, z V, i, z i+FLY99

E(B þV ) 0.017 0.009 0.096 0.057 0.012

A(I )a 0.030 0.017 0.193 0.115 0.024

ZP(I )a,b 25.947 25.947 25.655 25.655 25.655

N( E /S0) 12 17 14 19 10

4070 8180 11700 11800 5600

The exposure time, extinction and zero point are given for the F775W or F814W filter, since this was used for measurements of the structural parameters. b This is the zero point for a 1 s exposure.

2.1. NGC 4676 NGC 4676 is a low-redshift pair of merging spiral galaxies and was observed as part of the ACS Early Release Observations ( ERO) program ( Ford et al. 2002). We mask out NGC 4676 and use galaxies in the background field. It was observed for 6740 s in the F475W ( g) filter, 4000 s in the F606W (V ) filter, and 4070 s in the F814W (I ) filter. The area remaining after masking out the two prominent foreground galaxies is 7.8 arcmin2. 2.2. UGC 10214 UGC 10214 is a low-redshift spiral galaxy that is merging with a much smaller dwarf galaxy and has an extended tidal tail as a result ( Tran et al. 2003). As with NGC 4676, it was selected as part of the ERO program. We mask out UGC 10214 and use galaxies in the background field (see Benitez et al. 2004). It was ´ observed in two separate pointings, giving a combined exposure of 13600 s in F475W ( g), 8040 s in F606W (V ), and 8180 s in F814W (I ). The area remaining after masking out the prominent foreground galaxy is 10.7 arcmin2. 2.3. TN 1338 TN J1338þ1942 ( TN 1338) is a radio galaxy at z ¼ 4:1 that was observed as part of our ACS/GTO program to study protoclusters around high-redshift radio galaxies (see Miley et al. 2004; R. Overzier et al., in preparation). It was observed for 9400 s in F475W ( g), 9400 s in F625W (r), 11,700 s in F775W (i ), and 11,800 s in F850LP (z). The total observed area is 11.7 arcmin2. 2.4. TN 0924 TN J0924þ2201 ( TN 0924), a radio galaxy at z ¼ 5:2, was also observed as part of the high-redshift radio galaxy protocluster program ( R. Overzier et al., in preparation). It was observed for 9400 s in F606W (V ), 11,800 s in F775W (i ), and 11,800 s in F850LP (z). The total observed area is 11.7 arcmin2. 2.5. HDFN The Hubble Deep Field North ( HDFN ) was observed with the ACS to find supernovae and test the ACS Grism ( Blakeslee et al. 2003b). It was observed for 5600 s in the F775W (i ) filter and 10,300 s in the F850LP (z)filter. We use theACS i-band for measurements of the structural parameters, but we do not have enough ACS filters for accurate photometric redshifts. However, there are deep seven-filter data available for the portion of the ACS image already observed by WFPC2 ( Williams et al.

´ 1996). We use the photometric catalog from Fernandez-Soto et al. (1999, hereafter FLY99), which has very deep F300W (U ), F450W (B), F606W (V ), F814W (I ), WFPC2, and Kitt Peak National Observatory ( KPNO) J, H, and K band photometry. There are 146 spectroscopic redshifts from Cohen et al. (2000). We only use ACS data coincident with the deep WFPC2 image and take our photometric redshifts and colors from the FLY99 data. The observed area is 5.8 arcmin2. 2.6. Catalogs g Each set of images was run through the ACS Science Data Analysis Pipeline ( Blakeslee et al. 2003a). The data in each field were selected from the detection images produced from combining the filter images, weighted by the inverse noise squared. This aids in the detection of extremely faint objects by combining the signal from the different filters to produce a more significant detection. SExtractor ( Bertin & Arnouts 1996) was run first on the detection image and then in dual mode on the detection image and each filter image, to produce catalogs of the same objects, with photometry in matched apertures. We use these source catalogs as the starting point for selecting our sample and measuring the photometric properties. 3. MEASUREMENTS 3.1. Photometric Redshifts We use the Bayesian photometric redshift code ( BPZ; Ben´tez 2000) to calculate the photometric redshifts of galaxies i in the fields of NGC 4676, UGC 10214, TN 1338, and TN 0924. This takes advantage of both the color information and a magnitude prior to constrain the redshift. The magnitude prior distinguishes nearby red galaxies (e.g., giant ellipticals) from distant, redshifted blue galaxies, which while having similar colors when seen through a small set of filters, will have very different magnitudes. We use the template spectra described in Ben´tez et al. (2004), which are based upon a subset of the temi plates from Coleman et al. (1980) and Kinney et al. (1996). The template set consists of El, Sbc, Scd, Im, SB3, and SB2. These represent the typical spectral energy distributions (SED) of elliptical, early/intermediate type spiral, late-type spiral, irregular, and two types of starburst galaxies. These templates have been modeled using Chebyshev polynomials to remove differences between the predicted colors and those of real galaxies. The final ``calibrated'' templates have been found to give better BPZ results on the HDFN ( Benitez et al. 2004). We use ´ extinction-corrected isophotal magnitudes to maximize the signal-to-noise ratio (S/ N ) on the color input to BPZ. In each case, the aperture is the same for each filter. The magnitude


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Fig. 1.--Filter sets used in these observations. The top panel shows the three filters used in TN 0924, the upper middle panel shows the griz filters used in TN 1338, the lower middle panel shows the gVI filters used in UGC 10214 and NGC 4676 and the bottom panel shows the HDFN, with seven bands from U to K. The dotted, short-dashed, and long-dashed curves show the ``El'' SED (N. Ben´tez et al. 2004, in preparation) at z ¼ 0:5, 0.75, and 1.0, respectively. i The arrows mark the position of the 4000 8 break at these three redshifts. The 4000 8 break is well within our filter coverage at all redshifts.

prior is based on the HDFN database ( Williams et al. 1996), which uses deep ($27 mag arcsecþ2) isophotal magnitudes. 3.2. Testing BPZ g To test our photometric redshift catalogs for completeness, contamination, and systematic and random errors, we compare them to spectroscopic data in the HDFN and to simulations. Figure 1 shows the spectral energy distribution of an elliptical galaxy against the throughput of the filters used. The bottom panel shows the HDFN filter set, consisting of the UBVI WFPC2filters andthe JHK KPNO filters. The El SED is plotted three times, at z ¼ 0:5 (dotted line), 0.75 (short-dashed line), and 1.0 (long-dashed line). The main feature of this spectrum is the 4000 8 break, which is indicated by the bold arrow at each of these redshifts. The 4000 8 break is prominent in galaxies where there is very little ultraviolet radiation produced by hot, young stars, compared to the optical flux produced by an older stellar population. This break falls within the V or I filters at every redshift in the range that we use. The drop in flux per wavelength from one side of the break to the other produces a significant change in magnitude from one filter to the next, leading to an accurate measurement of the photometric redshift. The lower middle panel of Figure 1 shows the same plot for the ACS g, V and I filters used in the UGC 10214 and NGC 4676 fields. The upper middle panel shows the g, r, i, and z filters used in the TN 1338 field. The top panel shows the V, i, and z filters used in the TN 0924 field. We use the HDFN photometric and spectroscopic redshifts to estimate the errors for three-color BPZ measurements of real galaxies seen through the WFPC2 filters and then use simulations to determine any biases in the BPZ measurements through ACS filters at the noise limits of our data. The g, V,and

Fig. 2.--Errors in BPZ derived from the HDFN. In the top panel we show the three-color BPZ redshifts plotted against the seven-color BPZ redshifts for all IAB < 25 galaxies with 0:3 < z < 1:2. The squares surround morphological elliptical galaxies that have 0:5 < zspec < 1:0or 0:5 < zBPZ < 1:0 in the sevencolor BPZ catalog. There are no outliers in our sample, and the systematic offset and error in the redshift each galaxy are small, à z=(1 × z) ¼ 0:010 and (à z=(1 × z)) ¼ 0:074, respectively. In the middle panel, we compare seven-color BPZ photometric redshifts to the smaller sample of objects with spectroscopic redshifts. We find that there is a significant offset between the seven-color BPZ and the spectroscopic redshifts. We correct for this offset (see eq. [1]) and calculate zbest , which is plotted in the lower panel.

I filters used in the UGC 10214 and NGC 4676 fields are similar in wavelength coverage to the B, V, and I filters used in the HDFN data set. Therefore we can test the accuracy of the photometric redshifts in these fields by calculating three-color photometric redshifts for ellipticals in the HDFN. In the top panel of Figure 2, we plot the three-color photometric redshifts calculated using the B, V, and I filters against the seven-color photometric redshifts. The offset, Ïz3BPZ þ z7BPZ ÷=Ï1 × z7BPZ ÷ ¼ 0:010 ô 0:074, is low and there are no outliers. We calibrate the seven-color photomþ etric redshift à þthe spectà to roscopic sample and find a deviation z7BPZ þ zspec = 1 × zspec ¼ þ0:045 ô 0:026, shown in the middle panel of Figure 2. There is one outlier, a galaxy with zBPZ ¼ 0:87 and zspec ¼ 0:67. As expected from the poor fit, this object has (V þ I ) colors that are much redder and (B þ V ) colors that are slightly bluer than one would expect for an elliptical galaxy at this redshift. The bottom panel shows the three-color photometric redshifts corrected for this offset. The correction is described at the end of this section. The quoted error in the above cases and for future BPZ measurements is for a single galaxy, so this offset is significant. Cohen et al. (2000) show that the errors in the spectroscopic data are àv ¼ 200 km sþ1, implying à z ¼ 0:0007. The final error is consistent with the typical scatter found in the overall analysis of all HDF redshifts, à z=(1 × z) ¼ 0:06. The offset between BPZ and spectroscopic redshifts implies some evolution in elliptical galaxies from z ¼ 0:2 (the redshift of the calibration cluster) and z $ 0:75. Given that all of the HDFN ellipticals have good three-band photometric redshifts, we expect that ellipticals in NGC 4676 and UGC 10214 should also have good photometric redshifts.


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Fig. 3.--Results of the four simulations, (zdetection þ zsimulation )=(1 × zsimulation ). The open represent objects with a Scd SED. The circles z ¼ 0:5, 0.75, and 1.0. The dashed lines show 2004, in preparation). There are no significant

TN 0924, TN 1338, NGC 4676, and UGC 10214, as labeled. The y axis is the difference in the redshift, squares represent objects with an El SED, the crosses represent objects with a Sbc SED, and the filled triangles with error bars represent the 3 clipped mean for the El and Sbc SEDs. The dotted lines mark out the samples at the expected mean and standard deviations based on the measurements against spectroscopic data ( N. Ben´tez et al. i systematic errors, but galaxies in UGC 10214 and NGC 4676 have large random errors for z > 0:85.

However, the noise in these fields is somewhat greater than the HDFN, so there may be some missing objects. We test the reliability of BPZ in each of the fields using Bouwens' Universe Construction Set ( BUCS; R. Bouwens et al., in preparation; Bouwens et al. 2003, 2004) simulations of r 1=4 elliptical galaxies with three different SEDs: El, Sbc, and Scd ( Benitez et al. 2004). These simulations are designed to ´ have the same noise characteristics as the observed ACS data sets and are processed in the same way as the data (x 2.6). Therefore, the UGC 10214 simulation, with double the exposure time, has 1.4 times the S/ N of the NGC 4676 simulation. We use the three SEDs to test the reliability of redshifts for early-type galaxies with a range of colors. All the simulations are made up of galaxies with elliptical morphologies (  ¼ 4) and a Schechter LF with parameters ö ¼ 0:00475, M ö ¼ þ20:87, and ¼ þ0:48. The density of galaxies was increased by a factor of 5 over the normal elliptical galaxy density to give a large sample of galaxies at each redshift. In these simulations elliptical galaxies are placed at random in four fields, each 2000 ; 2000 pixels. Each of these fields is approximately the area of a single amplifier on the Wide Field Camera.

Once the images had been processed, we compared the simulation input catalog and the catalog of detected objects. The results are shown in Figure 3. In each of the fields we find small differences between the measured redshift and the input redshift. The only major differences occur in the NGC 4676 and UGC 10214 simulations, in the zsimulation ¼ 0:95 bin. In both cases zdetection is overestimated. Figure 1 shows that at this redshift, the 4000 8 break is in the middle of the F814W filter, with no redder filter to compare to. This is also the redshift range at which there is increased scatter in three-band photometric redshifts in the HDFN, which had a similar combination of filters. The offsets are due to the increased scatter and are not a systematic effect. We find that the TN 1338 simulation has a mean scatter z ¼ 0:023, TN 0924 has z ¼ 0:028, NGC 4676 has z ¼ 0:045, and UGC 10214 has z ¼ 0:046. Since the HDFN has filters similar to those used for NGC 4676 and UGC 10214 and is deeper, we would expect z to be lower. The additional noise is due to the real galaxy spectral energy distributions varying from the ideal templates used in our simulations. There is a large increase in the scatter for all galaxy types in the HDFN, UGC 10214, and NGC 4676 fields at


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z > 0:85, with the rms in the HDFN increasing from z ¼ 0:029 (z < 0:85) to z ¼ 0:068 (z > 0:85), and the rms in the UGC 10214 and NGC 4676 fields increasing from z ¼ 0:036 (z < 0:85) to z ¼ 0:050 (z > 0:85). We can use the simulations to check for incompleteness. All of the galaxies with Bz ¼ 0 24:5 mag (Bz ¼ 0 24:0 mag at z > 0:75) were detected, apart from one or two galaxies close to the edge of each image, one or two with a nearby neighbor, and a few galaxies at z > 1:2 in TN 0924. At fainter magnitudes the errors become very large for galaxies in NGC 4676 in particular. Altogether, 15% of 0:5 < z < 1:0 objects have þ0:06 < à z=(1 × z) < 0:06, and only 6% have þ0:12 < à z=(1 × z) < 0:12. There is also around 2% contamination from lower or higher redshift objects (z < 0:3 and z > 1:2). We correct the BPZ redshift estimates to account for the difference between the spectroscopic and BPZ measurements for elliptical galaxies, z z
best best

a and b are only weakly dependent on the Sersic profile. The best-fit parameters for an exponential profile (  ¼ 1) are a ¼ 0:38 and b ¼ 0:28, whereas a de Vaucouleur 's profile (  ¼ 4) is well fitted by a ¼ 0:24 and b ¼ 0:21. Therefore, if ¼ 0:8, r ell =r cir ¼ 1:11 and 1.09 for  ¼ 1 and 4, respectively, and if e e ¼ 0:6, r ell =r cir ¼ 1:26 and 1.22, respectively. These two exe e amples demonstrate the weak dependence on . Once the bestfit parameters are found, a new total flux is calculated, and the process is iterated until the new flux is no longer larger than the old flux. We use the output from GALFIT for the rest of our analysis, since it is corrected for the PSF, which is important for galaxies with re < 0B4, but use the growth curve to identify outliers (see Fig. 4). The scatter in the two measurements is linear with size: àre ¼ 0:25re þ 0:013: Ï 3÷

¼

zBPZ × 0:045 ; (1 þ 0:045)

Ï 1÷

is plotted against zspec in the lower panel of Figure 2. This changes the input BPZ redshift range to 0:43 < zBPZ < 0:91. It also considerably reduces the errors associated with zBPZ > 0:85 galaxies in UGC 10214 and NGC 4676. We use the Benitez et al. (2004) errors (z ¼ 0:06) for our BPZ measure´ ments. We find that a few (seven) of our objects have significantly broader probability density functions. The width of these PDFs are added in quadrature to the initial z ¼ 0:06. The objects in UGC 10214 and NGC 4676 with zBPZ > 0:85 are given an uncertainty z ¼ 0:09. This takes into account both template error (errors related to mismatches between the real and assumed templates) and random errors (due to the noise). In summary, our final sample contains 72 galaxies, 10 of which have spectroscopic redshifts. The completeness is expected to be in excess of 95% (P3 ­ 4 missing galaxies), with a contamination of less than 2 ­ 3 galaxies ( from redshift uncertainties). We list the properties of all our galaxies in Table 2, in two redshift intervals (0:5 < z 0:75 and 0:75 < z 1:0). Within each interval they are listed in order of increasing restframe (U þ V )0 color (see x 5.1). 3.3. Measuring the Half-Light Radius and Total Magnitude g g g We calculate the half-light radius re of each galaxy using GALFIT ( Peng et al. 2002). In each case we assume a single Sersic profile (see eq. [2]) and allow the Sersic parameter ( )to vary between 0 and 10, ( " #) r 1= þ1 ; Ï 2÷ I (r) ¼ Ire exp þk re where Ire is the surface brightness at the half-light radius, re , and k $ 1:9992 þ 0:3271 (Capaccioli 1989). The half-light radius is defined along semimajor axis. Since the shape and size of the galaxy can be strongly affected by the background, we force the sky to the value calculated by SExtractor. An alternative way of measuring the half-light radius is through the growth curve. The growth curve analysis uses a maximum likelihood fit to the measured flux in 14 circular apertures to estimate the Sersic parameter and half-light radius. We find that the correction from circular half-light radius to elliptical half-light radius is well fitted by a Moffat profile, r ell ¼ r cir ½1 × (1=a)2 b =½1 × (=a)2 b , where the is the ratio e e of semiminor axis to semimajor axis and the Moffat parameters

Outliers are objects for which the difference between the growth curve and GALFIT is greater than 2.0 times the standard error at that size. The few outliers found had nearby neighbors that affected the growth curve analysis or GALFIT. In each case the size was checked manually. In most cases GALFIT gave the best fit, but for the largest object (number 30, in Table 2), we found that neither the growth curve or GALFIT yielded a good fit. We used the ELLIPROF task in Vista to get an ellipse fit model and IRAF PHOT procedure to continue the growth curve out to larger apertures. Both methods give an elliptical half light radius re ¼ 1B75, compared to 1B34 for the original growth curve method and 2B05 for GALFIT. Once we got our best-fit half-light radius, we ran GALFIT with this fixed half-light radius to get the Sersic parameter and total magnitude. We convert the apparent half-light radius (in arcseconds) to the intrinsic half-light radius (in kpc) using Re ¼ 4:85 ; 10
þ3

re da (z; m ; ö; H0 );

Ï 4÷

where da is the angular size distance (in Mpc) calculated from the redshift and cosmology. g 3.4. The Rest-Frame B-Band Magnitude. The rest-frame Johnson B band has a mean wavelength $4400 8, which translates to $7700 8 at z ¼ 0:75. This puts it into either the F775W band or F814W band, available for our data sets. Most of the rest-frame B-band flux falls within these bands, so the k corrections from these bands should be the smallest and most accurate, and similarly for the structural parameters. For convenience, we let the I band refer to either F775W or F814W throughout this section. Converting from these filters to the z ¼ 0 Johnson B band removes any differences particular to the passband. Correcting to total magnitudes removes any differences particular to the depth. Once these corrections have been made the data from all fields should be homogeneous, and the only differences should come from cosmic variance and the field of view. The rest-frame B-band magnitude is calculated using the k-correction of the best-fit BPZ SED from the I band to the z ¼ 0 Johnson B band, B
z ¼ 0; iso

¼I

iso

× k (SED; I ; z

BPZ

; B; 0);

Ï 5÷

where the k-correction k (SED; I ; zBPZ ; B; 0) is the difference in magnitude between the integrated flux through an I-band filter at zBPZ and the B-band filter at z ¼ 0. The SEDs fit our colors best at zBPZ rather than zbest , so we must use the zBPZ to


TABLE 2 Summary of Galaxy Pr oper ti es for All 72 E/S0s in t he Sa mple Re ( kpcþ1)

No.

R.A.

Decl. 0.5 < z

za 0.75 0.65 0.66 0.73 0.52 0.66 0.61 0.72 0.73 0.73 0.72 0.53 0.71 0.63 0.73 0.69 0.70 0.66 0.66 0.70 0.71 0.59 0.67* 0.66 0.55 0.53 0.64 0.56* 0.68 0.50* 0.53 0.55 0.68* 1.0

MB

(UþV )0



1............................ 2............................ 3b .......................... 4............................ 5b .......................... 6............................ 7............................ 8b .......................... 9............................ 10.......................... 11b ........................ 12b ........................ 13b ........................ 14.......................... 15b ........................ 16b ........................ 17b ........................ 18b ........................ 19b ........................ 20b ........................ 21b ........................ 22b ........................ 23.......................... 24.......................... 25b ........................ 26b ........................ 27b ........................ 28.......................... 29.......................... 30b ........................ 31b ........................ 32b ........................

16 16 09 16 12 13 09 09 09 12 16 09 12 09 09 12 12 13 09 09 16 12 13 12 12 09 12 13 12 09 12 12

06 06 24 06 46 38 24 24 24 46 06 24 46 24 24 46 46 38 24 24 06 36 38 46 46 24 37 38 36 24 46 36

16.9 06.5 19.1 16.5 18.1 30.0 27.4 21.4 25.4 14.7 14.9 23.2 18.3 17.4 20.0 12.3 08.6 31.5 24.5 15.7 02.0 57.1 21.8 17.3 15.2 19.2 00.2 22.0 46.2 20.1 17.8 49.9

55 55 þ22 55 30 þ19 þ22 þ22 þ22 30 55 þ22 30 þ22 þ22 30 30 þ19 þ22 þ22 55 62 þ19 30 30 þ22 62 þ19 62 þ22 30 62

26 26 01 23 42 44 01 01 02 45 26 03 43 01 03 45 41 45 00 01 24 12 44 42 43 03 12 44 11 03 43 12

53.4 50.9 28.1 44.2 53.5 20.0 37.9 15.9 46.9 32.7 52.8 04.3 25.5 38.5 15.2 21.2 52.7 05.7 42.3 33.4 51.3 10.8 31.7 28.2 57.4 00.2 35.0 38.7 51.4 11.4 38.7 46.0

þ19.14 þ18.88 þ20.44 þ19.26 þ20.75 þ19.36 þ18.81 þ20.30 þ19.33 þ18.83 þ20.51 þ20.32 þ21.26 þ19.55 þ20.23 þ22.83 þ20.75 þ20.97 þ21.37 þ21.73 þ20.97 þ21.18 þ19.62 þ19.40 þ20.45 þ21.77 þ20.32 þ20.00 þ19.43 þ21.30 þ20.87 þ21.08

0.61 0.75 0.83 0.84 0.84 0.96 0.97 1.16 1.17 1.17 1.22 1.27 1.29 1.40 1.40 1.41 1.42 1.71 1.74 1.74 1.76 1.93 1.94 1.96 1.97 1.98 1.99 1.99 2.00 2.00 2.01 2.02

2.56 2.57 2.09 2.61 7.18 3.50 2.38 5.18 2.32 2.39 2.19 2.25 5.26 4.86 9.01 5.03 4.29 5.25 4.01 6.47 3.22 4.34 10.00 3.40 3.00 2.73 3.16 5.13 3.24 6.59 3.14 5.86

0.96 1.46 2.88 1.63 2.09 0.74 1.15 1.92 1.45 1.63 1.36 2.47 4.04 1.61 2.08 3.30 2.89 1.44 2.49 2.07 2.91 2.72 1.43 0.88 2.96 6.36 2.07 1.29 0.88 11.03 1.48 4.40

0.75 < z 33.......................... 34b ........................ 35b ........................ 36b ........................ 37b ........................ 38b ........................ 39b ........................ 40b ........................ 41.......................... 42b ........................ 43b ........................ 44b ........................ 45b ........................ 46b ........................ 47.......................... 48b ........................ 49b ........................ 50b ........................ 51b ........................ 52b ........................ 53b ........................ 54b ........................ 55.......................... 56b ........................ 57b ........................ 58b ........................ 59b ........................ 60b ........................ 16 16 13 09 09 09 12 09 16 13 13 13 13 16 13 13 13 09 16 13 09 16 16 16 16 09 12 12 06 06 38 24 24 24 36 24 06 38 38 38 38 06 38 38 38 24 06 38 24 05 06 06 06 24 46 46 18.0 20.3 20.7 21.9 16.3 26.1 45.8 20.9 03.6 22.4 24.4 30.5 31.4 04.6 21.5 27.6 30.1 27.3 01.0 25.4 16.4 59.4 13.5 08.6 14.9 28.0 17.1 20.5 55 55 þ19 þ22 þ22 þ22 62 þ22 55 þ19 þ19 þ19 þ19 55 þ19 þ19 þ19 þ22 55 þ19 þ22 55 55 55 55 þ22 30 30 25 24 43 02 01 03 12 03 24 42 41 42 44 24 44 42 44 02 24 43 01 26 24 26 27 01 44 42 03.2 44.2 30.9 54.8 17.1 31.0 46.7 08.2 54.0 52.8 34.0 44.1 36.8 44.5 39.8 12.6 14.7 54.3 57.6 33.3 11.6 16.0 45.8 04.0 12.7 38.2 09.0 54.8

0.89 0.99 0.97 0.76 0.77 0.88 0.90* 0.75 0.84 0.90 1.00 0.97 0.94 0.84 0.85 0.98 0.93 0.90 0.82 0.96 0.85 0.81 0.84 0.79 0.84 0.98 0.86 0.88

þ19.80 þ21.68 þ21.23 þ21.21 þ20.52 þ20.47 þ21.52 þ20.99 þ19.78 þ20.94 þ21.17 þ22.12 þ21.21 þ21.52 þ20.07 þ20.35 þ20.68 þ21.39 þ21.52 þ21.00 þ21.52 þ22.47 þ19.68 þ20.52 þ20.78 þ20.11 þ20.25 þ21.00

1.23 1.24 1.30 1.39 1.39 1.40 1.46 1.55 1.56 1.58 1.66 1.70 1.72 1.74 1.74 1.81 1.86 1.91 1.93 1.96 1.97 1.97 1.99 1.99 1.99 1.99 2.01 2.01

2.33 3.66 5.35 2.02 9.42 2.16 6.17 4.49 4.79 2.73 8.75 7.13 4.29 2.64 9.86 2.04 3.21 6.33 5.00 3.05 5.21 8.38 2.43 2.52 4.29 4.82 2.73 2.81

2.06 1.56 1.74 1.32 2.42 2.77 2.79 3.45 3.42 4.68 2.55 7.46 1.66 2.92 0.92 3.79 1.53 1.81 3.33 1.42 3.96 5.18 1.50 1.52 1.06 1.43 3.03 4.15


LF OF EARLY-TYPE FIELD GALAXIES AT z % 0.75
TABLE 2--Continued Re ( kpcþ1) 0.89 2.42 1.21 3.72 2.35 2.03 1.64 3.82 3.48 3.67 3.55 1.27

1997

No. 61b .......................... 62............................ 63............................ 64b .......................... 65b .......................... 66b .......................... 67b .......................... 68b .......................... 69b .......................... 70b .......................... 71b .......................... 72b .......................... 12 16 12 16 12 09 12 12 12 13 12 16

R.A. 36 06 46 06 36 24 46 36 36 38 36 05 54.8 00.7 07.7 11.3 42.8 26.7 16.6 55.1 56.3 31.0 43.5 59.5

Decl. 62 55 30 55 62 þ22 30 62 62 þ19 62 55 13 24 44 27 12 01 44 13 12 44 11 26 03.9 59.5 41.7 45.3 42.3 01.7 48.2 11.5 20.4 41.9 43.0 13.3

z

a

MB þ20.26 þ19.93 þ20.03 þ22.38 þ21.64 þ20.40 þ20.13 þ21.90 þ21.39 þ21.47 þ22.09 þ20.43

(UþV )0 2.01 2.02 2.02 2.02 2.03 2.04 2.04 2.05 2.06 2.06 2.07 2.08

 2.98 2.90 3.28 5.56 4.49 4.19 4.93 3.90 5.38 6.36 5.15 3.28

0.95* 0.76 0.86 0.86 0.85* 0.97 0.79 0.97* 0.93* 0.79 0.77* 0.88

Note.--Units of right ascension are hours, minutes, and seconds, and units of declination are degrees, arcminutes, and arcseconds. a The redshifts are zbest in all cases apart from those marked with an asterisk, which are spectroscopic redshifts in the HDFN (R:A: $ 189:2, decl: $ 62:2). Within each redshift range the galaxies are in order of their (U þ V )0 color. b In the volume-limited sample MB < þ20:1, Re > 0:8 kpc.

calculate the k-correction. The terms Bz ¼ 0;iso and Iiso are the rest-frame B band and measured I band isophotal magnitudes, which have a strong dependence on the surface brightness limit and the redshift (Cross et al. 2001), so a correction must be made for the missing flux. GALFIT calculates the total flux of each galaxy in the I band, which we then trivially convert to a total I-band magnitude, IT . We can transform this to the total rest-frame B magnitude, Bz ¼ 0;T . B
z ¼ 0;T

The total magnitude is between 0.1 and 0.7 mag brighter than the isophotal magnitude, with a mean aperture correction of 0.34 mag. Finally, we convert to absolute magnitudes. Since we have already k-corrected and extinction-corrected the data, the equation is simply M
B; T ; z ¼ 0

¼B

z ¼ 0; T

þ 5log (dL ) þ 25;

Ï 7÷

¼ Bz

¼ 0;iso

× IT þ Iiso :

Ï 6÷

where the luminosity distance dL is in Mpc. The effective surface brightness of the galaxy is defined as the mean surface brightness within the half-light radius. The intrinsic effective surface brightness is calculated from the absolute magnitude and half-light radius to remove the (1 × z)4 redshift dependence: e ¼ MB × 5log10 Re × 38:57; where the constant converts from mag kpc
þ2

Ï 8÷

to mag arcsecþ2.

4. SAMPLE SELECTION We select elliptical and S0 ( E/S0) galaxies on the basis of morphology to a rest-frame B magnitude limit that gives us the largest sample with reliable redshifts and morphologies. We select over a redshift range 0:5 < zbest < 1:0, since the 4000 8 break is outside our range of filters for z < 0:25 and z > 1:25. For redshifts close to these limits it will be increasingly difficult to estimate an accurate photometric redshift. Moreover, the k-corrections between the I band and the rest-frame B band show a very weak dependence on the SED across this range and have the weakest dependence at z ¼ 0:75. At z < 0:5, the errors in the k-correction increase (the standard deviation across the range of SEDs is 0.16 mag at z ¼ 0:5 and 0.28 mag at z ¼ 0:3), and the additional volume over which galaxies can be seen is relatively small. For z > 1:0, the errors in the k-corrections increase, and the range of absolute magnitudes that can be sampled decreases. At z ¼ 1, it is possible to see MB < þ20:1galaxies; by z ¼ 1:2 , the combination of distance modulus and k-correction reduces the range to MB < þ21:6, so ö only the very brightest galaxies, $MB , will be sampled. Initially, galaxies are selected with 0:5 z < 1:0 and Bz ¼ 0;iso 25:5 mag. Stars are removed by selecting and removing objects with the SExtractor stellaricity flag >0.8. This

Fig. 4.--Comparison of the half-light radius obtained via a growth curve analysis and the two-dimensional fitting program GALFIT (Peng et al. 2002) for the ellipticals that we have selected. The PSF correction becomes important for re < 0B4. The typical error is àre $ 0B05 for each galaxy, comparable to the pixel size. The much larger errors at re ¼ 0B55 are largely the result of nearby neighbors that affect the photometry. All large outliers were checked manually to see if GALFIT or the growth curve was the source of error. All necessary changes were made.


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sample was morphologically classified using a semiautomated method. The first part of the classification was by eye. For an object to be selected as an early-type galaxy, it had to be axisymmetrical, centrally concentrated, and must not have any spiral features. This removes spiral galaxies, chain galaxies, mergers, irregulars, and most starbursts. The galaxies that were selected as early types were then run through GALFIT as described above to determine the half-light radius, Sersic parameter, and total magnitude. Objects with  < 2 or re < 0:1 were removed from the sample. The  k 2 criterion is effective at removing any residual irregular or starburst galaxies that were not caught by the first test. Removing re < 0:1 galaxies eliminates those objects for which the errors on re and  will be large, dominated by the seeing and pixel scale. These objects may not really be E/S0 galaxies, even if we measure  > 2. We find that morphological classification is easy for I < 24 mag, but becomes progressively more difficult at fainter magnitudes, until it becomes almost impossible at I > 25 mag. Since we are interested in the rest-frame B-band properties of our galaxies, our magnitude limit should be the total restframe B magnitude. The main criterion for sample selection is the magnitude at which photometric redshifts and morphological classification become unreliable. Figure 5 shows the difference between the total rest-frame Bz ¼ 0;T magnitude and the Iiso magnitude. For z < 0:75, there is a fairly constant offset of Bz ¼ 0;T þ Iiso ¼ 0:61 magwitha scatter of 0.2 mag, and the offset for z ! 0:75 is Bz ¼ 0;T þ Iiso ¼ 0:17 mag, with a scatter of 0.3 mag. Using a limit Bz ¼ 0;T ¼ 24:5 mag at z < 0:75 is equivalent to a limit of Iiso ¼ 23:89, and Bz ¼ 0;T ¼ 24:0 mag at z > 0:75 is equivalent to a limit of Iiso ¼ 23:83. The data can be used to test these limits, using the odds value that is calculated in BPZ. The odds value is the integration of the probability density function ( PDF ) between 2 standard deviations of the Bayesian redshift: Z zBPZ ×2 PDF(z) dz: Ï 9÷ odds ¼
z
BPZ

Fig. 5.--Plot of the generalized k-correction from the measured IF814W or iF775W band magnitude to the total rest-frame B magnitude for early-type galaxies in our sample. Objects in the interval 0:5 z < 0:75 have an approximate k-correction (Bz ¼ 0;T þ Iiso ) of 0.6, while for objects in the range 0:75 z < 1:0, the k-correction is closer to 0.2.

4.1. Errors The final redshift errors are calculated from the BPZ of Ben´tez et al. (2004). This gives à z ¼ 0:06(1 × z) as the final i photometric redshift error, which we use. The errors in the spectroscopic redshifts are à z ¼ 0:0007 from Cohen et al. (2000). The error bars in absolute magnitude, half-light radius, and surface brightness are calculated from the errors in magnitude, half-light radius, and redshift: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 @M àz ; Ï10÷ àMB ¼ (àB)2 × @z sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 àre 2 @ da àRe ¼ Re Ï11÷ àz ; × re @z sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ! 4:3àz 2 2: 2à r e 2 2 àe ¼ (àB) × ; Ï12÷ × (1 × z) re where àB is the final error in the rest-frame B-band magnitude. This includes the measured error in the F775W or F814W magnitude calculated in the ACS pipeline, which ranges from àm ¼ 0:002 to0.08mag,the errorinthe k-correction from the F775W/F814W to rest-frame B (àk $ 0:05 mag), the uncertainty in the zero point (àZP $ 0:02 mag), and the uncertainty in the isophotal to total magnitude correction (àmT $ 0:05 mag). For objects with photometric redshifts, the errors are dominated by the redshift error. 5. PROPERTIES OF EARLY-TYPE GALAXIES 5.1. Colors of Early-Type Galaxies An unbiased look at the colors of E/S0 galaxies is important, not only for understanding their star formation history, but also for understanding the role that color selection has in

þ2

N. Benitez et al. (2004, in preparation) determined the ´ standard deviation to be ¼ (1 × z)z where z ¼ 0:06. Thus, a galaxy with a well-defined PDF, a single peak with a small standard deviation, should have an odds value of !0.95. We find that 75% of galaxies of zbest 0:75 and 85% of zbest > 0:75 have odds !0.95. If the magnitude limits are increased by 0.5 mag, only 67% of the new 0:5 z < 0:75 galaxies have odds !0.95, and only 33% of the new 0:75 z < 1:0 have odds !0.95. Both the BPZ results from the simulations and the data suggest that the best limits are Bz ¼ 0;T < 24:5for z < 0:75 and Bz ¼ 0;T < 24:0 for z ! 0:75, both roughly equivalent to Iiso < 24:0. In summary, the final selection criteria call for morphologically elliptical galaxies, defined by a centrally concentrated, axisymmetric profile with re ! 0B1 and  ! 2. Objects in our lower redshift sample 0:5 < z < 0:75 have a rest-frame B-band magnitude limit of 24.5 mag (observed I P 23:5), while objects in our higher redshift sample 0:75 < zbest 1:0 have a B-band magnitude limit of 24.0 mag (observed I P 23:5) The 0:5 z < 0:75 sample contains 32 galaxies, and the 0:75 z < 1:0 sample contains 40 galaxies. Since our samples are morphologically selected rather than color- or SEDselected, we will be able to study the color evolution of the galaxies. In Figure 6 we show all of the galaxies in our data set, ordered in the same way as Table 2.


No. 5, 2004

LF OF EARLY-TYPE FIELD GALAXIES AT z % 0.75

1999

Fig. 6.--Three-color postage stamps for all of our galaxies. These use an asinh stretch ( Lupton et al. 2004) that preserves the colors of bright regions of thegalaxy while also showing the fainter regions of these same objects. They are divided into the two redshift samples that we use throughout the analysis and then ordered by (U þ V )0 color, going from bluest (top left) to reddest (bottom right). This is the same order as Table 2. In the case of the HDFN, we display a combination of the ACS i and z only.

isolating large samples of these objects at high redshift. Such color (or SED) selections have already been employed in the CFRS, CADIS, and COMBO-17 surveys and are relatively cheap to perform, requiring only ground-based imaging over large areas of the sky. Morphologies and structural properties are, by contrast, much more expensive to acquire, requiring the unique highresolution capabilities of HST. However, the cheaper route may not be the best, since selecting by color can result in contamination from particularly red later types (non-E/S0s) or incompleteness to blue E /S0s.

Figure 7 plots the absolute B-band magnitude against the rest-frame (U þ V )z ¼ 0 (AB) color. This is calculated in the same way as the rest-frame B magnitude: (U þ V )z
¼0

¼ ½mF1 × k (SED; F1; z

BPZ

; U ; 0) ; V ; 0); Ï13÷

þ ½mF2 × k (SED; F2; z

BPZ

where mF1 and mF2 are the magnitudes in the closest filters ( filter 1 and filter 2) to the redshifted rest-frame U and V filters. Filter 1 and filter 2 are defined in Table 3 for each field. The


2000

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z Fig. 7.--Left: Distribution of rest-frame (U þ V )0 color against MB ¼ 0 for early-type galaxies with 0:5 < z 0:75 (squares) and 0:75 < z 1:0 (crosses). The dotted lines represent the Bruzual & Charlot (2003) evolutionary tracks for a 1011 M galaxy with solar metallicity and an exponentially decaying star formation rate with decay timescales ¼ 0:1, 0.2, 0.4, 1.0, 2.0, 5.0, and 9.0 Gyr, from left to right. The filled circles represent the age of the galaxy in these models going from 1 Gyr (largest circle) to 7 Gyr (smallest circle) in steps of 2 Gyr. The short-dashed lines represent the same tracks for a 1012 M galaxy. The tracks allow us to compare the masses of blue galaxies and red galaxies. The long-dashed lines represent the selection criteria used to mimic different color selections employed in the literature. One subsample has (U þ V )z ¼ 0 > 1:38, to match the CFRS selection, and the other has (U þ V )z ¼ 0 > 1:7, to mimic the selections by the COMBO-17 and CADIS ( Fried et al. 2001) surveys. Right: Histogram in color for the combined sample. Note the significant number of E/S0s that are bluer than any of the color selections shown.

SED is the best-fit SED (or linear combination of SEDs) from BPZ, and k (SED, mF1, zBPZ , U, 0) is the k-correction between the observed filter at zBPZ and the Johnson U-band filter at z ¼ 0.
TABLE 3 Su mmary of Closest B and to Re st-Frame U and Re st-F rame V z < 0.75 Field UGC 10214 .......... NGC 4676 ............ TN 1338 ............... TN 0924 ............... HDFN ................... Band 1 F475W F475W F475W F606W F450W Band 2 F814W F814W F850LP F850LP F814W z ! 0.75 Band 1 F606W F606W F625W F606W F606W Band 2 F814W F814W F850LP F850LP JKPNO

Note.--These bands are used to give the best estimate of the rest-frame (U þ V )0 , which is used to compare to the color- or SED-selected samples of CFRS, CADIS, and COMBO-17.

We find a significant range in colors of early-type galaxies, with the majority having (U þ V )0 > 1:7. Those with (U þ V )0 > 1:9 have colors similar to the classic red ellipticals that form the red sequence seen in both clusters ( Blakeslee et al. 2003c) and the field ( Bell et al. 2004). The red colors are consistent with an old coeval population of stars. While there is a slight color-magnitude relationship for (U þ V )0 > 1:9 galaxies, the red sequence is blurred by a combination of the wide redshift range and errors in the photometric redshifts. For the remainderofthe paperwedefine galaxies with (U þ V )0 > 1:7 as ``red'' and galaxies with (U þ V )0 < 1:7 as ``blue.'' There is a set of early-type galaxies with (U þ V )0 < 1:7. These have a broad color distribution, implying a wide range in age or metallicity, with some ongoing star formation. There is also a wide range in absolute magnitude for (U þ V )0 > 1:1, þ22:5 < MB < þ18. The bottom panel of Figure 8 shows the reliability of the redshift with color. The redshift odds are good for more than 80% of the galaxies with a small dependence on color (see x 4, eq. [9]). The fraction


No. 5, 2004

LF OF EARLY-TYPE FIELD GALAXIES AT z % 0.75

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Fig. 8.--Plot showing how the redshift reliability depends on color. The bottom panel shows the odds calculated from BPZ against the rest-frame (U þ V )0 color (see x 4, eq. [9] for a definition of the odds). The squares represent z < 0:75 galaxies, and the crosses represent z > 0:75 galaxies. This shows that 80% of our objects have good odds, and that the reliability of the redshift does not vary significantly with color or redshift. The middle panel splits the distribution into eight bins of equal number and plots the number of objects with a single peak in the probability density function (dashed histogram); the solid histogram represents those with one narrow dominant peak (i.e., one peak makes up >90% of the integrated probability), and the dotted histogram includes those with multiple overlapping peaks that are in effect a wider peak with >90% of the integrated probability. While the bluer galaxies have more of the wider peaks, objects with a single dominant peak make up almost 90% of objects for (U þ V )0 > 1:2. In the top panel we show the widths of the peaks in the PDF. The open squares show the single narrow peaks, the filled squares show the multiple dominant peaks, and the filled circles show the mean from the simulations for an elliptical (U þ V )0 ¼ 1:99, an Sbc (U þ V )0 ¼ 1:40, and an Scd (U þ V )0 ¼ 1:12.

models to the colors of early-type galaxies. But instead of fitting to the radial variations in color, we use a simpler method, fitting to the overall colors. We use the Bruzual & Charlot (2003) models to calculate the expected colors for a set of exponentially decaying continuous starburst models. These models assume a Salpeter initial mass function ( IMF ) and solar metallicity. The timescales for the exponential decay ( ) were allowed to have the values 0.1, 0.2, 0.4, 1.0, 2.0, 5.0, and 9.0 Gyr. Elliptical galaxies are generally expected to have very short timescales ( 1 Gyr), while late-type galaxies are expected to have much longer timescales ( > 2 Gyr). From the models we calculate the expected magnitudes in each filter at a given redshift for a variety of galaxy ages (T ). For each field we produced the models for redshifts from 0.4 to 1.1 at intervals of 0.05. Using the set of models where the redshift most closely matches our redshift estimate zbest for each object, the model colors were compared to the measured colors, after converting from Vega to AB magnitudes. We calculated the maximum likelihood for the different values of and T using the equation ( !) X Cmod; i (; T ) þ Ci 2 2 ln (2 C; i ) × × ln p; ln L ¼ C ; i i Ï14÷ where Ci are the measured colors (e.g., [ gþV ]and [VþI ]inthe case of NGC 4676), C; i are the errors in the measured colors, and Cmod; i (; T ) are the model colors, a function of the timescale and the age T.Aprior p is used such that the combination of age and look-back time does not exceed the age of the universe in the adopted cosmology: 8 tfrm < Tuni þ 1:0 Gyr; > 1; > < T þ t þ 0: 5 G y r uni frm ; 0:5 Gyr < Tuni þ tfrm < 1:0 Gyr; p¼ > 0:5 Gyr > : 0; tfrm > Tuni þ 0:5 Gyr; Ï15÷ where tfrm ¼ T × t ½z; (M ; ö; H0 ) is the formation time of the galaxy, and Tuni ¼ 13:5 Gyr is the age of the universe in the adopted cosmology. We used the following combinations of adjacent filters for each field: ( gþV ), (VþI ) for UGC 10214/ NGC 4676; (Vþi ), (iþz) for TN 0924; ( gþr), (rþi ), (iþz) for TN 1338; and (UþB ), (BþV ), (VþI ) for HDFN. In Figure 9 we plot the star formation timescale ( ) against the galaxy age ( bottom left panel ), look-back time (bottom middle panel ), and formation time (bottom right panel ) as squares (open and filled ). The top panels show the histogram of galaxy age, look-back time, and formation time. The error bars are calculated using a Monte Carlo simulation assuming Gaussian errors in the redshift and colors. Most galaxies have 1 Gyr, suggesting an intense period of star formation that then rapidly decreased. We see a strong peak in galaxy ages of 2 Gyr, but a wide spread, with T < 1Gyr and T > 7 Gyr in some cases. The formation times show a peak at 1:5 < z < 2 (8:5 < tfrm < 10 Gyr), consistent with the star formation history seen in Heavens et al. (2004), notably a rapid falloff at high redshift and a lower limit at the look-back time of our sample. Figure 7 also shows the expected evolutionary tracks of galaxies with different masses and decay timescales. Galaxies undergoing pure luminosity evolution with an exponentially decaying star formation rate, as described above, will move along

of galaxies with just a single peak or a narrow dominant peak (total probability >90%) in the probability density function is shown by the solid histogram in the middle panel of Figure 8. The fraction is >85% for all but the bluest, (U þ V )0 < 1:12, galaxies, for which it is reduced to $60%. Some of these galaxies have a slightly wider probability density function, with a few nearby peaks that overlap. These can be used, but have a large uncertainty in their photometric redshifts. We also have two galaxies with a secondary peak at z $ 4. In the top panel of Figure 8 we show the uncertainty as determined from the PDF. The open squares denote the galaxies with a dominant narrow peak, and the filled squares represent those with overlapping peaks. The filled circles show the mean uncertainties calculated in the simulations for the three different SEDs. Galaxies with 1:4 < (U þ V )0 < 1:9 have the lowest uncertainties and the greatest chance of having a single peaked probability distribution function. Bluer galaxies have larger uncertainties and a greater chance of a multipeaked distribution. We take into account the increased uncertainty resulting from the broader probability distributions. We will use the (U þ V )0 colors calculated here to test the effect of color selection on the LF and structural properties, but note that one color by itself is not enough to set constraints on both the age and star formation timescale of these galaxies. To estimate the ages of galaxies, we use the methodology of Menanteau et al. (2001) to fit exponentially decaying starburst


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Fig. 9.--Age, look-back time, and formation time of early-type galaxies assuming a star formation model with exponential decay timescales ¼ 0: 2.0, 5.0, and 9.0 Gyr. The bottom left panel shows the best-fit vs. the best-fit age. The bottom middle panel shows the best-fit vs. the look-back time, right panel shows vs. the formation time, which is the sum of the look-back time and the age. The filled squares represent a volume-limited sample. show the histograms of the age (top left), the look-back time (top middle), and the formation time (top right). The solid histograms show all the objects, histograms show a volume-limited sample. The dotted lines in the look-back time and formation time plots show the equivalent redshift.

1, 0. and The and

2, 0.4, 1.0, the bottom top panels the dashed

these tracks from blue to red. The tracks show that these galaxies, regardless of the decay timescale, reach a maximum B-band luminosity at (U þ V )0 < 0:7 and then gradually fade as they redden. The Bruzual-Charlot models are calculated for a 1 stellar mass object, so the evolutionary tracks are calculated by scaling z MB ¼ 0 by 1011 and 1012. While most of the (U þ V )0 > 1:7 E/S0s have M > 1011 M and some have M > 1012 M , the bluer E/S0s, 1:2 < (U þ V )0 < 1:7, have 1010 < M < 1011 M and those with (U þ V )0 < 1:2 have only M < 1010 M. Note that these results should be treated with caution, given their obvious dependence on our simple exponentially decaying model. The very brightest of the blue E/S0s will end up among the red sequence that has already formed, but most will end up extending the sequence to fainter absolute magnitudes, given pure luminosity evolution. For reference, the expected color of a red elliptical at z ¼ 0 is (U þ V )0 ¼ 2:18, assuming the Coleman et al. (1980) SED, so even the reddest galaxies in the sample will undergo an additional 0.1 ­ 0.2 mag of reddening to z ¼ 0.

Galaxies at lower redshifts can be seen to fainter luminosities, so it is best to compare objects over a volume-limited sample (i.e., in which all objects are seen over the same absolute magnitude and intrinsic size ranges). The dashed histograms and filled points in Figure 9 show galaxies with MB < þ20:1 mag and Re > 0:8 kpc. The peak formation age is slightly higher at 2 < z < 2:5 (10 < tfrm < 11 Gyr). This is consistent with the Heavens et al. (2004) results that show that more massive galaxies form earlier. It is useful to compare the rest-frame (U þ V )0 colors to the Bruzual & Charlot (2003) model results, since these were calculated using very different methods. In Figure 10 we plot (U þ V )0 against the number of decay timescales (N ¼ T = ). As expected, there is a strong correlation between these numbers over the range 1 < N < 10. The strong correlation between the (U þ V )0 color and the more complicated modeling that leads to the age and decay timescale indicates that many past surveys for early-type galaxies (e.g., CFRS, COMBO-17, and CADIS) will preferentially


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Fig. 10.--Plot comparing the rest-frame (U þ V )0 color to the number of decay timescales (N ¼ T = ) derived from the Bruzual & Charlot (2003) models. For 1 < N < 10, there is a strong correlation with (U þ V )0 ¼ 1:59 log (N ) × 0:38. For N > 10, (U þ V )0 $ 2:0, the rest-frame color of the El template from Ben´tez et al. (2004). The long-dashed line indicates the besti fit linear correlation ( from a simple least-squares calculation). The dotted lines indicate the color cuts for CFRS [(U þ V )0 ¼ 1:38], and COMBO-17 and CADIS [(U þ V )0 ¼ 1:7].

Fig. 11.--Distribution of galaxies in the absolute magnitude and surface brightness plane. The size and magnitude limits are shown at both the low- and high-redshift end of each sample. All objects in the unshaded area are seen over the same volume. All objects in the cross-hatched area are outside the limits of the survey. The singly shaded region denotes parameter space where galaxies cannot be seen to the maximum redshift. The lower plot shows the 0:5 < z 0:75 sample and the upper plot shows the 0:75 < z 1:0 sample. The blue E/S0s are circled. They are not separated from the red E/S0s in MB , e space.

miss the younger versions of these galaxies. For COMBO-17 and CADIS, the (U þ V )0 > 1:7 selection eliminated objects that have undergone star formation for less than 7 decay timescales, and for the CFRS, the (U þ V )0 > 1:38 selection eliminated objects at less than 4 decay timescales. Early-type galaxies must have gone through a period of high star formation, and the youngest of these galaxies are being systematically missed by ground-based surveys that select by color or SED, rather than morphology. Menanteau et al. (2004) looked at the color gradients of galaxies in the UGC 10214 field and showed that 30% ­ 40% of field ellipticals at 0:3 < z < 1:2 are blue, and that the blue colors occur preferentially in the cores. We find that 39% of all our galaxies have (U þ V )0 < 1:7, and 33% of our volumelimited sample have (U þ V )0 < 1:7, in complete agreement. The Menanteau et al. (2004) results show that the ongoing star formation is localized to the core. 5.2. Structural Properties When we look at the structural properties of galaxies, it is important to understand the selection effects. Figure 11 shows the distribution of galaxies in absolute magnitude and surface brightness, the bivariate brightness distribution ( BBD; Cross et al. 2001). Galaxies that are in the unshaded region meet the selection criteria (in magnitude, half-light radius, and surface brightness) at all redshifts in the ranges prescribed. In this plot and most of the following plots, we use shading to highlight the visibility of galaxies. No shading is used when objects have the maximum visibility, i.e., when they can be seen right across the redshift range. Cross-hatching is used when, given our selection criteria, no galaxies can be seen (visibility is zero). Light shading denotes parts of the parameter space in which a galaxy can be seen at the minimum redshift but not all

the way to the maximum redshift. The visibility function shows us when a correlation is real or is due to a selection effect. It also helps us to properly weight our data. The absolute selection limits are calculated from the apapp parent z, re , Bz ¼ 0 ,and lim selection limits, using equations (4) app and (7), and lim ¼ lim þ 10 log10 (1 × z). The low surface brightness boundary is the limit at which the mean surface brightness of a galaxy within the half-light radius is lower than the threshold of the shallowest survey (i.e., NGC 4676, app; I ¼ lim 25:2 mag arcsecþ2), and so it becomes difficult to accurately measure the half-light radius. The following absolute selection limits are used: for the 0:5 < z < 0:75 sample (z ¼ 0:5), z MB ¼ 0 ¼ þ17:8 mag, lim; B ¼ 23:9 mag arcsecþ2, and Re ¼ z 0:61 kpc; for the 0:5 < z < 0:75 sample (z ¼ 0:75), MB ¼ 0 ¼ þ2,and R ¼ 0:73 kpc; for þ18:8mag, lim; B ¼ 23:3 mag arcsec e z the 0:75 < z < 1:0 sample (z ¼ 0:75), MB ¼ 0 ¼ þ19:3 mag, lim; B ¼ 22:8 mag arcsecþ2, and Re ¼ 0:73 kpc; and for the z 0:75 < z < 1:0sample (z ¼ 1:0), MB ¼ 0 ¼ þ20:1mag, lim; B ¼ þ2 22:2 mag arcsec , and Re ¼ 0:80 kpc. The 0:5 < z < 0:75 sample has a narrow range in surface brightness (18:5 < e < 21 mag arcsecþ2), with one outlier. This is the galaxy found earlier to have re ¼ 1B75, corresponding to Re ¼ 11:0 kpc. The 0:75 < z < 1:0 sample has a wider range in surface brightness (17:5 < e < 21:5 mag arcsecþ2). In the unshaded region, where galaxies can be seen over the whole range of redshifts, the volume over which a galaxy can be seen is constant, and so the space density is proportional to the number of galaxies. This ``volume-limited'' sample is useful for comparing galaxies over a range of magnitudes. To compare galaxies within each redshift range, we use a sample that is volume-limited from 0:5 < z 1:0, with MB þ20:1mag and


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Fig. 12.--Plot of the distribution in the Sersic parameter  for each sample (dashed histogram). The solid histogram in each panel is the distribution for equivalent volume-limited samples. The distribution of  does not change significantly with redshift. The dotted histogram is the distribution of the ``blue'' E/S0s. The thick arrow in each panel marks the mean .

Re > 0:8 kpc. Only 20 of the 32 galaxies from the 0:5 < z < 0:75 subsample makes it into this volume-limited sample, and 34 of the 40 galaxies in the 0:75 < z < 1:0 subsample ( Table 2). The ratio of galaxies in these two samples is 1: 1.7 (20 : 34), which is very similar to the ratio of comoving volume, 1:1.5. In Figure 12 we compare the histogram of the Sersic parameters in each redshift range. The bottom panel shows the 0:5 < z 0:75 sample, and the top panel shows the 0:75 < z 1:0 sample. The long-dashed line represents the full distribution at each redshift, and the solid line represents the equivalent volume-limited samples, selected at MB þ20:1mag and

Re ! 0:8 kpc. To compare each distribution, we calculate the biweight and biweight scale ( Beers et al. 1990). These are equivalent to the mean and standard deviation in the case of a Gaussian distribution and a large number of data points. The biweight is more robust in the case of a non-Gaussian distribution with small-number statistics. The biweight and biweightscale values of  in the volume-limited sample are tabulated in Table 4, for both redshift ranges and red [(U þ V ) > 1:7] and blue [(U þ V ) < 1:7] galaxies. The biweight hi $ 4:4 for the present sample and does not vary significantly with redshift or color. Redder, (U þ V ) > 1:7 galaxies have slightly lower values, closer to the de Vaucouleur 's value (  ¼ 4:0), and the bluer galaxies have larger values on average, although with a larger biweight scale, indicating a wider range of values. The larger values of  are consistent with bluer galaxies having a starburst in the cores; the central regions will be slightly brighter, making the galaxies appear more concentrated. However, at fainter luminosities, þ20:1 < MB < þ18:8, the distributions become significantly different. There is a significant increase in the number of low , blue galaxies, leading to a biweight of hi ¼ 2:7, compared to h i ¼ 4:1 for the red galaxies. Kolmogorov-Smirnov tests demonstrate that the blue and red galaxies with MB þ20:1 mag and Re ! 0:8 kpc are equivalent to each other at 85% and 55% confidence in the redshift ranges 0:5 < z < 0:75 and 0:75 < z < 1:0, respectively. At fainter magnitudes (MB ! þ18:8 mag), this probability decreases to 1% , thus implying a split in properties between red and blue early-type galaxies. This latter comparison is only possible in our lower redshift slice, 0:5 < z < 0:75, for objects with Re ! 0:73 kpc. Figure 13 shows the histogram of half-light radii. The results for the volume-limited sample are summarized in Table 4. The distribution of Re appears uneven, considering the smooth distribution of  . Again, there is no change between the two redshift ranges with the biweight size $2.6 kpc, and there is no significant difference in the biweight sizes of red or blue early types in either redshift range. The Kolmogorov-Smirnov test gives high probabilities, 73% and 79%, that the red and blue galaxies have equivalent size distributions, with MB þ20:1 mag and Re ! 0:8 kpc at z < 0:75 and z ! 0:75, respectively. At lower luminosities, the biweight size is lower,

TABLE 4 Co mparison of Structural Pr operties of Early-Type Galaxies Sample hia hReib Re vs. MBc
2

Re vs. ½ log () × 0:26e

d

2

M < þ20.1, Re > 0.8 z z z z z z < < < > > > 0.75 0.75 0.75 0.75 0.75 0.75 all ............................ red ........................... blue ......................... all ............................. red ............................ blue .......................... 4.4 4.2 4.7 4.4 4.3 4.7 ô ô ô ô ô ô 0.4 0.5 0.8 0.3 0.3 1.0 2.5 2.5 2.5 2.6 2.7 2.5 ô ô ô ô ô ô 0.2 0.4 0.3 0.2 0.3 0.3 þ0.78 þ0.74 þ0.96 þ1.32 þ1.34 þ1.29 ô ô ô ô ô ô 0.07 0.08 0.17 0.06 0.06 0.12 3.0 4.1 1.8 2.4 2.3 3.0 þ4.56 þ4.54 þ4.60 þ4.49 þ4.47 þ4.55 ô ô ô ô ô ô 0.03 0.04 0.06 0.03 0.03 0.05 1.2 0.6 1.9 0.9 0.6 1.7

M < þ18.8, Re > 0.73 z < 0.75 all ............................ z < 0.75 red ........................... z < 0.75 blue .........................
a b c d

3.7 ô 0.3 4.1 ô 0.4 2.7 ô 0.4

2.0 ô 0.2 2.0 ô 0.3 1.8 ô 0.2

þ0.72 ô 0.06 þ0.76 ô 0.08 þ0.60 ô 0.12

2.3 2.8 1.8

þ4.63 ô 0.03 þ4.61 ô 0.04 þ4.67 ô 0.04

1.4 1.6 1.1

 is the Sersic parameter; see eq. (2). The average in this case is the biweight, and the error is the biweight scale. Re is the intrinsic half-light radius in kpc. The average in this case is the biweight, and the error is the biweight-scale. Offset in the size-magnitude relation compared to z ¼ 0. Offset in the photometric plane at z ¼ 0 is þ4.85.


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Fig. 13.--Sersic parameter  distribution for each sample (dashed histogram). The solid histogram is the distribution of the volume-limited samples, and the dotted histogram is the distribution of the ``blue'' E/S0s. The thick arrow shows the mean value of Re . The shading represents the selection limits in half light radius: the single shading begins at the high-redshift limit of the sample, and the cross-hatching begins at the low-redshift limit.

and the difference between the red and blue distributions is greater, with a K-S probability of 52%. However, the discrepancy is much lower than with the Sersic parameters. Comparing samples in the same luminosity range can be misleading, since ellipticals are expected to show luminosity evolution simply as a result of passive evolution in the stars. Ideally, one would like to compare objects of the same mass, but without dynamical information we compare the luminosity of objects of a similar size, since size is expected to change more slowly. Schade et al. (1999) looked at the relationship between half-light radius and B-band absolute magnitude of field ellipticals. They used 17 ellipticals in the range 0:5 < z 0:75 (15 had spectroscopic redshifts) and 20 in the range 0:75 < z 1:0 (11 had spectroscopic redshifts). We have a larger sample, which extends to fainter absolute magnitudes, but fewer spectroscopic redshifts (4 out of 32 and 6 out of 40, respectively, for our two subsamples). Schade et al. (1997) find that cluster ellipticals are well fitted by MB ¼ þ3:33 log (Re ) þ 18:65 × à MB , where à MB ¼ s log (1 × z), and Schade et al. (1999) show that à MB ¼ þ0:56 ô 0:3 for ellipticals in the range 0:5 < z 0:75 and à MB ¼ þ0:97 ô 0:14 for ellipticals in the range 0:75 < z 1:0. In Figure 14 we measure the relationship between M and Re for our galaxies. Schade et al. (1999) used a cosmology with M ¼ 1:0, ö ¼ 0, and H0 ¼ 50 km sþ1 Mpcþ1. Converting to the cosmology used in this paper, we now have the relationship MB ¼ þ3:33 log (Re ) þ 18:56 × à MB at 0:5 < z 0:75 and MB ¼ þ3:33 log (Re ) þ 18:60 × à MB at 0:75 < z 1:0. The results are tabulated in Table 4. The solid lines in Figure 14 show our best-fit results for à MB in the volume-limited sample (i.e., the unshaded parameter space). We find àMB ¼ þ0:78 ô 0:07 (2 ¼ 3:0) for galaxies in the range 0:5 < z 0:75, and à MB ¼ þ1:32 ô 0:06 ( 2 ¼ 2:4) for E/S0s in the range 0:75 < z 1:0. Since the 2 values are so high, the fits are poor. We find poor fits for

Fig. 14.--Plot showing the distribution of absolute magnitude (MB ) vs. the logarithm of half-light radius for both E/S0 subsamples considered in this study. The light shading represents the parts of the parameter space where galaxies cannot be seen out to the maximum redshift, and the heavy shading represents the parameter space where galaxies cannot be seen at all. The dotted line is the z ¼ 0 relationship from Schade et al. (1997) corrected to our cosmology. The dashed line is the expected fit from Schade et al. (1999) for each sample, and the solid line is our best fit in the volume-limited region. The circles mark the positions of blue early-type galaxies. Neither type of galaxy shows strong evidence for a size-magnitude relationship.

both red and blue galaxies and over both redshift ranges. Furthermore, there is no obvious correlation between the halflight radius and absolute magnitude. We find many more compact luminous E/S0 galaxies ( both red and blue) than Schade found. As with the Sersic parameter, we find a significant change in à MB for fainter blue galaxies and a much greater variance in à MB for blue galaxies. One effect that is difficult to take into account is the color-selection effect. The most rapidly evolving blue galaxies at 0:75 < z < 1:0 will become red at 0:5 < z < 0:75. This could increase the evolution seen among red galaxies and decrease the evolution seen among blue galaxies. While we find a poor fit to the magnitude size relationship, we find a much better fit to the photometric plane. Graham (2002) demonstrated that the photometric plane variables Re , e,and  are correlated with an rms scatter of 0.170, compared to the fundamental plane variables Re , e , and 0 , which are correlated with an rms scatter of 0.137 for a selection of ellip´ tical and S0 galaxies in the Fornax and Virgo Clusters. Marquez et al. (2001) demonstrate that the photometric plane naturally emerges for relaxed Sersic profile systems as a scaling relation between potential energy and mass. The photometric plane log (Re ) ¼ a(log () × 0:26e ) × b Ï16÷

is plotted in Figure 15 and compared to the Graham (2002) result. The two redshift samples are fitted by constraining the slope such that a ¼ 0:86, as in Graham (2002), and then the offset b is found. We use à ¼ 0:5 in our error assessment. This is the scatter found when comparing the  from GALFIT to the  from the growth curve analysis. The values of b for each of the


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Fig. 15.--Bottom: Photometric plane for elliptical galaxies in our fields. The squares denote the 0:5 < z 0:75 sample, and the crosses represent the 0:75 < z 1:0 sample. Our best-fit lines are for 0:75 < z 1:0 (solid line) and 0:5 < z 0:75 (long-dashed line). The z ¼ 0 fit from Graham (2002) is shown by the short-dashed line. The blue galaxies are marked by circles. We find good fits to the photometric plane, although there are a few outliers among the blue E/S0 galaxies. Top: Variation in surface-brightness with redshift, calculated from this plot. Shown are points marking our results (circled squares) and those of Schade et al. (1999; crosses), Bernardi et al. (2003; squares), and Graham (2002; triangle). The solid line shows our best fit to these results, and the dashed line is the Gebhardt et al. (2003) best fit.

no significant differences between the sizes of red and blue galaxies. There is, however, some indication that the Sersic parameter is slightly larger for bright (MB < þ20:1) blue galaxies with a wider dispersion (as demonstrated by the larger biweight scale), as well as an increased variance in the sizemagnitude and photometric plane measurements for blue galaxies. When fainter galaxies (þ20:1 < MB < þ18:8) are added into the sample at z < 0:75, a significant decrease is found in the  values of blue galaxies and Re values for both samples, as well as a small decrease in  for the red sample. The fainter blue galaxies have a significant effect on the offset measured in the size-magnitude relation relative to red E/S0 galaxies, but they do not significantly affect the offset in the photometric plane. The weaker correlations among bluer galaxies could be due to three different effects: the bluer galaxies could have larger photometric variations, they may have not reached dynamical equilibrium, or the errors in photometric redshifts may be greater for the bluer galaxies. While there is a small color dependence on redshift, it only affects the very bluest [(U þ V )0 < 1:2] galaxies, and these are not particularly abundant at MB < þ20:1. The dynamical time for elliptical galaxies is very low: even if blue E/S0 galaxies are 10 times less massive than red E/S0 galaxies, as suggested by Im et al. (2001), the dynamical time would only be a few times 108 yr, much lower than the formation timescales and estimated ages. The surface brightness in these galaxies is not as tied to the Sersic parameter and half-light radii, as it is for the red E /S0s. We recalculated the above results using the geometric mean half-light radius instead of the semimajor axis, and find that this makes no significant difference to our conclusions. 6. THE SPACE DENSITY OF E/S0 GALAXIES

samples are tabulated in Table 4. There is a significant shift in the offset from the Graham (2002) result (b ¼ þ4:85) to our results, suggesting evolution in the photometric plane. There is also a small but insignificant change in offset between the different colored galaxies, and the fits for the (U þ V )0 > 1:7 galaxies are better for brighter galaxies. The increased variance in the blue galaxies at MB < þ20:1 is consistent with earlier results. Since the earlier results showed that there is no significant variation in hRe i or hi at MB < þ20:1 with redshift, the shift is caused by a change in surface brightness. At fainter absolute magnitudes, the offset changes slightly. The offset for blue galaxies with MB < þ20:1 at z < 0:75 is similar to that of red galaxies with MB < þ18:8 at z < 0:75. Unfortunately, the differences are not significant, so this does not demonstrate evolution. Solving the photometric plane equation for e , we find the evolution in surface brightness ( for MB < þ20:1) and compare our results to the change in surface brightness found in ellipticals in the Sloan Digital Sky Survey (SDSS; Bernardi et al. 2003) from z ¼ 0:06 to 0.2 and in Schade et al. (1999) at z ¼ 0:35 and 0.78. These are shown in the top panel of Figure 15. The variation is linear with redshift, à ¼ þ1:74z. Using the fundamental plane results for E/S0 galaxies in the DGSS, Gebhardt et al. (2003) find an evolution in surface brightness àe ¼ þ3:38z × 4:97z 2 þ 4:011z 3 . Our results are consistent with both the DGSS and the SDSS results. No evolution is apparent in the structural properties of earlytype galaxies over the redshift interval 0:5 < z 1:0, as shown by the lack of variation in the biweight and biweight scale of  and R e at MB < þ20:1 with redshift ( Table 4). There are also

We calculate the space density over the BBD (see Fig. 11) using the bivariate (in MB and e ) stepwise maximum likeli´ hood (SWML) method of Sodre & Lahav (1993), modified to incorporate photometric redshift errors using the method of Chen et al. (2003). The bivariate SWML takes into account limits in both magnitude and size, and outputs the correctly weighted space density of galaxies as a function of both absolute magnitude and effective surface brightness (Cross et al. 2001). The LF can be calculated by summing this distribution in the surface brightness direction. Our limits are B < 24:5 mag, re ! 0B1, and app ¼ 25:7 mag arcsecþ2 for 0:5 < z < 0:75; e and B < 24:0mag, re ! 0B1, and app ¼ 25:2 mag arcsecþ2 for e 0:75 < z < 1:0. SWML is found to give unbiased results even in very inhomogeneous samples ( Willmer 1997; Takeuchi et al. 2000). SWML gives the shape of the LF, but needs to be normalized independently. We normalize by calculating the number of galaxies in each magnitude bin (after distributing each galaxy by the probability density function in redshift) in the volume-limited region of the LF and dividing by the known volume. This is divided by the LF calculated by the SWML method to give a normalization factor in each bin, and the mean is found. 6.1. The Luminosity Function of E/S0 Galaxies Figure 16 shows the LFs of both samples, calculated by summing the two-dimensional space density along the surface brightness direction. The bottom panel shows the full morphologically selected LFs for both redshift ranges, and the middle and top panels show the (U þ V ) > 1:38 and (U þ V ) > 1:7 LFs, respectively. The squares and solid error bars show


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Fig. 16.--Luminosity functions of the 0:5 < z < 0:75 (squares with solid error bars) and 0:75 < z < 1:0 (triangles dashed error bars) samples. The bright ends are normalized to the volume-limited samples, and the lines show the Schechter function fits to each set of points. The single hatching denotes the magnitude limit of the 0:75 < z < 1:0 sample, and the cross-hatching denotes the magnitude limit of the 0:5 < z < 0:75 sample. The bottom panel shows the morphologically selected samples, the middle panel shows the two (U þ V )0 > 1:38 color-selected samples, and the top panel shows the two (U þ V )0 > 1:7 color-selected samples.

the LF for the 0:5 < z < 0:75 sample, and the triangles and dashed error bars show the 0:75 < z < 1:0 sample. The solid and dashed lines show the best-fit Schechter function to each redshift range, respectively. Since we cannot determine the LF of the 0:75 < z < 1:0 fainter than MB ¼ þ19:3 mag, the faint-end slope cannot be properly constrained. Therefore we fit the Schechter function using the faint-end slope calculated

from the 0:5 < z < 0:75 sample in each case. The best-fit parameters for all the Schechter functions are tabulated in Table 5. For the 0:5 < z < 0:75 sample, we find ö ¼ (1:61 ô 0:18) ; þ3 3 10 h0:7 Mpcþ3magþ1, M ö þ 5log h0:7 ¼ (þ 21:1 ô 0:3) mag, and ¼ þ0:53 ô 0:17, and we find that the 0:75 < z < 1:0 sample has ö ¼ (1:90 ô 0:16) ; 10þ3 h3:7 Mpcþ3magþ1, M ö þ 0 5log h0:7 ¼ (þ 21:4 ô 0:2) mag, and ¼ þ0:53 ( fixed). The evolution in the LF can be accounted for by a decrease in luminosity of 0:36 ô 0:36 mag from 0:75 < z < 1:0 to 0:5 < z < 0:75 and a decrease of (15 ô 12)% in the number density. In the 0:5 < z < 0:75 range, removing the (U þ V )0 < 1:38 galaxies significantly reduces the number of low-luminosity galaxies, changing the faint-end slope from ¼ þ0:53 to 0.24. The M ö for the 0:5 < z < 0:75 sample is 0:26 ô 0:5 mag fainter and has decreased in space density by (39 ô 11)% compared to the 0:75 < z < 1:0 sample. The MB þ 5log h0:7 ¼ þ20 point in the 0:75 < z < 1:0 sample suggests a steeper faint-end slope for this population. However, the present data are not deep enough to properly constrain it. The (U þ V )0 > 1:7 population is similar in character to the (U þ V )0 > 1:38 population, with an evolution of 0:22 ô 0:5 mag in luminosity and a (34 ô 12)% decrease in number density. In Figure 17 we compare the 0:5 < z < 0:75 LFs with each other and with other rest-frame B LFs for early-type galaxies in this redshift range. In each case, we have converted from the given cosmology to M ¼ 0:3, ö ¼ 0:7, H0 ¼ 70 km sþ1 Mpcþ1. In the case of the COMBO-17 data ( Wolf et al. 2003), we have converted from Vega to AB magnitudes by subtracting 0.13 mag (Johnson B band). All the results are summarized in Table 5. The points with error bars are those for the morphologically selected LF. The solid lines show our ACS LF, with the thick line showing the full color range, the medium line showing the (U þ V )0 > 1:38 sample, and the thin line showing the (U þ V )0 > 1:7 sample. The main difference is between the morphologically selected sample and the colorselected sample, with little difference between the (U þ V )0 > 1:38 sample and the (U þ V )0 > 1:7 sample. This difference occurs at the faint end, where most of the very blue galaxies

TABLE 5 Summary of B-Band Luminosity Function Schechte r Parameters f or Early-Type Galaxies Sample and Selection ACS, Morphological ................................ DGSS, Morphological ............................. ACS, (UþV ) > 1.38................................ CFRS, (UþV ) > 1.38.............................. ACS, (UþV ) > 1.7 .................................. COMBO-17, SED ( E+Sa) ....................... Redshift 0.5 0.75 0.6 0.5 0.75 0.5 0.75 0.5 0.75 0.4 0.6 0.8 0.5 0.75 0.5 0.5 0.75 < < < < < < < < < < < < < < < < < z z z z z z z z z z z z z z z z z < < < < < < < < < < < < < < < < < 0.75 1.0 1.2 0.75 1.0 0.75 1.0 0.75 1.0 0.6 0.8 1.0 0.75 1.04 1.0 0.75 1.0
ö MB þ 5 log h0: 7

*/10þ4 h 16.1 ô 18.9 ô 7.7 ô 12.9 ô 21.2 ô 31.5 1.9 10.3 ô 15.5 ô 9.8 ô 4.6 ô 1.6 ô 10.8 ô 4.9 ô 2.5 ô 13.9 ô 16.7 ô

3 0:7

þ0.53 ô 0.17 þ0.53 þ1.0 +0.24 ô 0.49 +0.24 þ0.37 þ2.01 +0.35 ô 0.59 +0.35 +0.52 +0.52 +0.52 þ0.05 ô 0.22 +0.63 ô 0.58 þ1.19 ô 0.15 þ0.75 ô 0.13 þ0.75

CADIS, SED ( E+Sa) ............................... ACS, (UþV ) < 1.7 ................................. ACS, SB Correlation ...............................

þ21.1 ô 0.3 þ21.4 ô 0.2 þ21.75 ô 0.15 þ20.6 ô 0.5 þ20.8 ô 0.2 þ20.74 þ22.84 þ20.6 ô 0.5 þ20.7 ô 0.2 þ20.69 ô 0.16 þ21.10 ô 0.16 þ20.96 ô 0.21 þ20.65 ô 0.27 þ20.48 ô 0.32 þ22.1 ô 0.4 þ21.3 ô 0.3 þ21.6 ô 0.2

1.8 1.6 2.2 1.5 1.8

a a a

1.4 1.5 4.1 1.2 1.4 1.1 1.0 0.5 1.8 0.5

Note.--All values have been corrected to m ¼ 0:3, ö ¼ 0:7, and H0 ¼ 70 km sþ1 Mpcþ1. a The COMBO-17 magnitudes have been corrected by þ0.13 to convert MB (Vega) to MB (AB).


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Fig. 17.--Luminosity functions of our 0:5 < z < 0:75 early types compared to that from previous surveys. The ACS LFs are plotted with solid lines, with the thickest showing the morphologically selected LF, the medium thick showing the (U þ V )0 > 1:38 LF, and the thin line the (U þ V )0 > 1:7 LF. The points and error bars are for the morphologically selected sample. The thick dashed line shows the morphologically selected DGSS LF, the medium thick dashed line shows the (U þ V )0 > 1:38 selected CFRS LF, and the thin dotted or dashed lines show the SED selected COMBO-17 and CADIS LFs. All the LFs have been converted to a öCDM cosmology with H0 ¼ 70 km sþ1 Mpcþ1.

Fig. 18.--Same as Fig. 17, but for our 0:75 < z < 1:0 early types.

are. The thin long-dashed and short-dashed lines show the COMBO-17 LFs ( Wolf et al. 2003) at z ¼ 0:5 and 0.7, respectively, while the thin dotted line shows the CADIS LF ( Fried et al. 2001). The medium thick long-dashed line represents the CFRS ( Lilly et al. 1995) LF, and the thick long-dashed line shows the DGSS ( Im et al. 2002) LF. The COMBO-17 and CADIS LFs are for objects classified as E-Sa from SED templates and should best match the (U þ V )0 > 1:7 sample. The CFRS should be compared to the (U þ V )0 > 1:38 sample, and the DGSS is morphologically selected and so can be compared to the full sample. Figure 18 shows the equivalent plot for 0:75 < z 1:0. The present study has somewhat different parameters from ö the DGSS, with a fainter MB and higher ö, but the LFs are similar (see Fig. 17), with the main differences being due to the ö ö correlations between MB and . At MB ¼ þ21:1 (MB ), our 0:5 < z 0:75 LF has a space density that is 33% larger. There is closer agreement at other magnitudes. Our LF at 0:75 < z ö 1:0 does not have such close agreement. At MB ¼ þ21:4(MB ), our LF has a space density that is 89% larger. The DGSS was not able to constrain the faint-end slope, so they used a value of ¼ þ1:0, based on the morphologically selected low-redshift LFs calculated from the Second Southern Sky Redshift Survey (SSRS2; Marzke et al. 1998) and the Nearby Optical Galaxy Sample ( NOG; Marinoni et al. 1999). Our sample goes almost 2 mag deeper than the DGSS, and hence we are able to constrain the faint-end slope to ¼ þ0:53 ô 0:17, which is shallower than the DGSS LF, but much steeper than the color-selected LFs. We can achieve this greater depth (I $ 24 vs. I $ 22) because of a combination of improved pixel scale and PSF, and images that are 1 ­ 1.5 mag deeper, giving higher resolution images with better S/ N than the DGSS.

When we compare the samples selected with (U þ V )0 > 1:38, we find that the CFRS is not a good match to the ACS LF. While both have similar values of M ö , and the values of are consistent given the shallow depth of the CFRS, the space density is about twice as high in the CFRS as in our measurement. In the higher redshift range, the CFRS LF is a closer match for MB < þ21 mag, but again overestimates the number of galaxies for lower luminosities. This suggests that there is some contamination by late-type galaxies such as Sa /Sbc spirals, which are removed by our morphological selection, as well as incompleteness to bluer early-type galaxies. The 0:5 < z 0:75 CADIS LF and 0:4 < z 0:6COMBO17 LF both closely resemble the ACS 0:5 < z 0:75, (U þ V )0 > 1:7 LF, with offsets of $0.25 mag either way, which is well within the errors. However, the 0:6 < z 0:8COMBO-17 LF has a much lower space density, which is also much lower than the ACS 0:75 < z 1:0, (U þ V )0 > 1:7 LF. In fact, all of the SED-selected LFs in the 0:75 < z 1:0 range find a much lower space density than the ACS 0:75 < z 1:0, (U þ V )0 > 1:7 LF. The ACS 0:75 < z 1:0 LFs have much better agreement with the DGSS and the CFRS surveys. The 0:75 < z 1:04 CADIS LF, the 0:8 < z 1:0COMBO17 LF, and the ACS 0:75 < z 1:0, (U þ V )0 > 1:7 LF all have a mean redshift h zi of $0.9, so it is expected that the LFs should be the same. At MB ¼ þ21:1 (M ö for the ACS LF ), the space density measured in the CADIS LF is 0.43 that of the ACS LF, and the space density measured in the COMBO-17 is only 0.13 that of the ACS LF. It appears that many more E/S0 galaxies are missing from the high-redshift COMBO-17 and CADIS LFs than expected, even considering the color selection in (U þ V )0 . However, there is an additional color selection for COMBO-17, which is the R-band selection. Galaxies were initially selected to have R < 24, so the selection is in the rest-frame UV at z > 0:75. Finally, we calculate the LF for our blue E/S0 galaxies. Since we have fewer blue, (U þ V )0 < 1:7, E /S0 galaxies, we combine all the Bz ¼ 0 24 mag galaxies together to calculate a LF from 0:5 < z 1:0 (see Fig. 19). It has a much steeper faint-end slope than the red E/S0, with M ö þ 5log h0:7 ¼ þ22:1 ô 0:4 and ¼ þ1:19 ô 0:15.


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than the 0:5 < z 0:75 sample by 0.5 mag arcsecþ2. This is consistent with the change in surface brightness measured in Figure 15. The surface brightness distributions suggest that there are no missing compact galaxies with MB < þ21. There are likely to be some missing galaxies in the range þ21 < MB < þ20, but these only make up a small fraction of the total. For MB > þ20, the missing fraction is likely to be significant. Among galaxies that were discarded, there are two additional galaxies (MB ¼ þ20:8, þ20.2) that have re < 0B1. These would increase the space density at MB ¼ þ20 by up to 10%. The low surface brightness limit also becomes important at MB > þ20. However, since this is the at which our measurements of the half-light radius begin to break down, rather than a detection limit ( E/S0s have very high central surface brightnesses), it is unlikely that we are missing any LSBGs. 7. DISCUSSION We find that ``blue'' E/S0 galaxies make up 30% ­ 50% of MB < þ20:1 E/S0 galaxies at 0:5 < z < 0:75 and 20% ­ 40% of MB < þ20:1 E/S0 galaxies at 0:75 < z < 1:0. Our results are consistent with both the Menanteau et al. (1999) sample, which found similar numbers to these depths, and the Im et al. (2001) sample, which found only $15%. Illustrating this agreement with the latter sample requires that we select galaxies to I < 22 using the Im et al. (2001) (VþI ) color criteria ( Fig. 1 from that paper). For the present sample this works out to a blue fraction of (23 ô 11)%, consistent with the above numbers. From the analysis of the colors and structural properties of E/S0 galaxies at 0:5 < z < 1:0, it is apparent that bright (MB < þ20:1), blue [(U þ V )0 < 1:7] E /S0 galaxies are not significantly different from bright, red [(U þ V )0 > 1:7] E /S0 galaxies in terms of their structural parameters. When the stellar population has aged, these galaxies will be only slightly less luminous than the current red galaxies, and there will be significant overlap (see Fig. 7). They just have higher current star formation rates, as measured by N from the Bruzual & Charlot (2003) models. However, these same models indicate that (U þ V )0 < 1:7 E/S0 galaxies are less massive than (U þ V )0 > 1:7 galaxies at the same luminosity. Fainter (MB > þ20:1) blue E/S0 galaxies are smaller, with lower Sersic parameters than their red counterparts. These galaxies often have extremely blue colors, (U þ V )0 < 1:2, andare likelytobeless massive. The evolution tracks Figure 7 suggests that these will fade by $3 mag as their stellar populations age. This is consistent with these galaxies becoming present-day dwarf ellipticals. The best fits to these models give an increasing rate of formation from z $ 8 all the way down to z $ 2, with a short star formation timescale of 1Gyr. There are only a few objects with longer timescales. The caveat in this modeling is that we have used simple, exponentially decaying star formation models at a fixed metallicity, with no internal dust corrections, since we are comparing observations in only three or four filters. With three broadband filters, there are only two color constraints that one can apply to the models, so it is impossible to test for anything beyond a simple variation in age and timescale. Observations of massive ellipticals at low redshifts and modeling support a single main burst, with a short timescale 0:1 < < 0:3 and a Salpeter IMF ( Pipino & Matteucci 2004). While there are not enough data to find the best-fit solution for a range of metallicities and dust models, it is instructive to estimate the effect that different metallicities or dust will have on the result. As a test for these effects, we recalculated the ages and timescales using metallicities Z ¼ 0:008 and 0.05 to

Fig. 19.--Luminosity functions of our (U þ V )0 < 1:7galaxies. The 0:5 < z < 1:0 LF is shown by square points, with the solid line representing the bestfit Schechter function; see also Table 5.

These results show that there is a wide variation in the LFs reported and that selection effects have a systematic effect on the results. In particular, for all color-selected samples, we note a significant underestimate of the faint end slope compared with morphologically selected samples. The space density of M ö galaxies also varied greatly from survey to survey. 6.2. The Surface Brightness Distribution g The luminosity function of galaxies can be calculated as above by summing the space density in the surface brightness direction, as long as there are no galaxies missing from the sample due to surface brightness ­ dependent selection criteria (see Cross et al. 2001; Cross & Driver 2002). Figure 11 demonstrates that we are not missing a significant population of low surface brightness ellipticals. However, the compact (re < 0B1) E/S0 galaxies that we removed from the sample do affect the faint end of the LF. The surface brightness distribution for galaxies with 0:5 < z 0:75 is shown in Figure 20, for all the galaxies and galaxies in different luminosity ranges. It is apparent that the surface brightness distribution peaks at e ¼ 20 mag arcsecþ2 for bright galaxies, and that any effects of missing galaxies are negligible for MB < þ20 mag and small for þ20 < MB < þ19 mag. However, they are important for MB > þ19. We estimate the effects by adding in all galaxies with re < 0B1, regardless of , since  will be difficult to accurately measure for such compact objects. At z < 0:75 there are three additional objects, with MB ¼ þ19:8, þ19.3, and þ18.6. The new LF parameters are shown in Table 5. The faint-end slope is steeper, ö with ¼ þ0:75; MB is slightly brighter and ö is slightly reö duced, but these effects are due to the dependence of MB on .It must be emphasized that the additional compact objects may not meet the selection criterion  > 2 ifobservedbyatelescope with better resolution, so this new LF is an upper limit. Figure 21 shows the surface brightness distributions of the 0:75 < z 1:0 sample. At bright MB the surface brightness distribution peaks at e $ 19:5 mag arcsecþ2, which is brighter


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Fig. 20.--Surface brightness distributions as a function of absolute magnitude for the 0:5 < z < 0:75 sample. The bottom left plot shows the surface brightness distribution summed to MB ¼ þ18, close to the magnitude limit of the survey. The other five plots show the surface brightness distribution in small ranges of absolute magnitude. The shading represents the limits at the midpoint of all these magnitude ranges. The light shading is the region where the sample volume decreases from the maximum, and the dark shading shows where the sample volume is zero.

contrast with the results obtained with the solar metallicities (Z ¼ 0:02). For each of these metallicities we calculated the ages and star formation timescales with no dust and using the dust model of Charlot & Fall (2000), assuming a V-band optical depth V ¼ 1 and the fraction of light contributed by the ``ambient'' interstellar medium ¼ 0:3. These values are the default values used in the Bruzual & Charlot (2003) code, and are close to the ``standard'' values discussed in Charlot & Fall (2000) and Bruzual & Charlot (2003) for objects with T > 107 yr. We recalculated models for star formation timescales of ¼ 0, 1, 0.4, and 2.0 only. We found that the addition of this dust model reduces the average age of each galaxy by $10%, depending on the metallicity. Since both age anddusttendtoreddenagalaxy,the same colors canreflectan old, dust-free galaxy or a young dusty galaxy. Age increases with decreasing metallicity and vice versa, because of the absorption of blue light by metals in the atmospheres of stars. We find that @ ln t =@ ln Z $ þ0:4, lower than the Worthey (1994) value of $þ1.5. The lower value may be due to the different assumptions. Worthey assumed a single-burst model, whereas we have a continuous exponentially decaying star formation rate. If these galaxies do have a lower metallicity (as one might expect for intrinsically fainter, likely less massive,

bluer galaxies; Tremonti et al. 2004), then they may be older than we estimate. While the structural properties (Re and  ) of bright red or blue E /S0s do not change significantly with redshift, there is a change in the photometric plane offset, the size-magnitude relation, and the LFs, demonstrating significant luminosity evolution ($0.4 mag) from 0:75 < z < 1:0 to 0:5 < z < 0:75. There are also some variations in structural properties between red and blue galaxies, with the red galaxies having a smaller variance in the Sersic parameter than blue galaxies. The luminosity evolution measured from the size-magnitude relation is 0.6 mag for red galaxies and 0.3 mag for blue galaxies. However, there is only a 0.1 mag change in the M ö point for the LFs of red galaxies, and 0.3 mag overall. While these values are quite different, the size-magnitude relation does not give a good fit, so one should be careful with the interpretation. The (U þ V )0 ¼ 2:0 galaxies are expected to fade by $0.25 mag, regardless of the star formation timescale, over the $1.5 Gyr time span that separates the median redshift in each bin. Over this same time, (U þ V )0 ¼ 1:8 galaxies are expected to fade by $0.55 mag, so $0.4 mag of evolution is expected. To complicate matters, some objects that were previously considered to be blue will have aged sufficiently to be classified as red.


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Fig. 21.--Same as Fig. 20, but for the 0:75 < z < 1:0 sample. The bottom left plot shows the surface brightness distribution summed to MB ¼ þ19.

The lower variation in the M ö point may relate to the smaller variation among the very reddest galaxies [(U þ V )0 ¼ 2:0], which are also generally the brightest. The expected variation of blue galaxies is much wider ranging, 0:2 < à M < 1:5, and shows a much greater dependence on the star formation timescale, so any offset is difficult to predict, especially given that blue galaxies will eventually evolve to become red galaxies, and other new blue galaxies may form. Since the evolutionary tracks on Figure 7 suggest that the redder galaxies are more massive than the bluer galaxies, the luminosity evolution is particularly difficult to predict, as more massive blue galaxies will become red. Indeed, the galaxies with the most rapid evolution in the rest-frame MB magnitude will also redden the most rapidly, so there is a selection effect operating that will reduce the apparent luminosity evolution observed. There is a decrease in number density for (U þ V )0 > 1:38 E/S0 galaxies of (40 ô 10)% from z ¼ 0:89 to 0.64, which is very small compared to the factor of 3 increase seen in the COMBO-17 and CADIS LFs over the same redshift range. This argues against hierarchical merging as an important evolutionary driver between z ¼ 1 and 0.5, although it could be an important feature at higher redshifts or in lower luminosity objects. Using deep high-resolution optical data we are able to measure the morphological E/S0 LF almost 2 mag deeper than the DGSS and to constrain the faint-end slope of the 0:5 < z 0:75 LF. We find a fairly flat faint-end slope of ¼ þ0:75 ô

0:13, slightly shallower than low-redshift LFs for morphologically selected E/S0s but much steeper than color-selected ö samples. Our values for MB are consistent with the DGSS, but ö our is larger by $40%. This could be due to cosmic variance, since both samples are small, or to the differences in morphological selection. To address the latter point, we note that the DGSS sample is selected using the bulge-to-total ratio (B=T > 0:4) and the residual parameter (R < 0:06). Figure 9 of Im et al. (2002) demonstrates that varying the selection criteria a little (B=T > 0:3, R < 0:08) can increase the sample size by 50%. Changing our selection criteria to  < 2:5 reduces our sample size by 15%. These changes are expected to have more of an effect at faint absolute magnitudes, where galaxies have ` flatter (i.e., lower Sersic number) profiles (Graham & Guzman 2003). Thus, different morphological selection criteria could explain the variation seen. Using purely photometric information (color and SED) to select the galaxy sample misses the bluer early types, and may lead to contamination from Sa/Sbc spiral galaxies or other red galaxies. As shown in Figures 17 and 18, there is a large variation in the measurement of the LF. Indeed, using the COMBO-17 results, one would be drawn to the conclusion that there were very few faint early-types ( ¼ 0:52) and that there is strong number evolution in the LF, suggesting that many spiral or other galaxies must have become ellipticals over time, e.g., via a high merger rate. The COMBO-17 LFs only sample


2012

CROSS ET AL. ACS was developed under NASA contract NAS5-32865 and this research has been supported by NASA grant NAG5-7697. The STScI is operated by AURA Inc., under NASA contract NAS5-26555. We are grateful to Ken Anderson, Jon McCann, Sharon Busching, Alex Framarini, Sharon Barkhouser, and Terry Allen for their invaluable contributions to the ACS project at JHU. We thank Jon McCann for his general computing support, including the development of FITSCUT, that we used to produce the color images. We would like to thank the anonymous referee for his/her useful comments.

the brightest luminosities at z $ 1, while the ACS and CADIS LFs reach 1.5 mag deeper. The LF of blue E/S0s is steeper ( ¼ þ1:19 ô 0:15), with ö a bright MB þ 5log h0:7 ¼ þ22:1 ô 0:4, but a much lower space density ö ¼ 2:5 ô 0:5 ; 10þ4 h3:7 Mpcþ3 magþ1. Low0 luminosity systems have a greater proportion of young starforming systems, suggesting that the more massive galaxies formed earlier or underwent more rapid star formation, so they now contain only older stars. These results provide a good fit to the models of Pipino & Matteucci (2004).

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