UV Luminosity Functions at redshifts z~4 to z~10: 10000 Galaxies from HST Legacy Fields

TL;DR

This paper presents the most extensive HST-based census of rest-frame UV luminosity functions from $z\sim4$ to $z\sim10$, combining CANDELS, HUDF09/12, XDF, ERS, and BoRG/HIPPIES data to build a sample of ~10^4 high-$z$ galaxies. It derives both non-parametric SWML and parametric STY Schechter fits, revealing a steepening faint-end slope $\alpha$ with redshift and only modest evolution in the bright-end characteristic magnitude $M^*$, implying that changes in $\phi^*$ and $\alpha$ drive the LF evolution. A simple conditional luminosity function model based on halo growth and a redshift-dependent mass-to-light ratio ($\propto (1+z)^{-1.5}$) reproduces the observed LF evolution from $z\sim8$ to $z\sim4$. The results have strong implications for star-formation histories and the role of galaxies in reionization, supported by updated UV luminosity and star-formation-rate densities and comparisons with theoretical models. The study also provides an empirical fitting formula to interpolate/extrapolate the LF to $z>8$, and demonstrates the LF’s Schechter-like shape across $z\sim4$–$8$, with field-to-field variation quantified across five independent CANDELS sightlines.

Abstract

The remarkable HST datasets from the CANDELS, HUDF09, HUDF12, ERS, and BoRG/HIPPIES programs have allowed us to map out the evolution of the UV LF from z~10 to z~4. We have identified 5859, 3001, 857, 481, 217, and 6 galaxy candidates at z~4, z~5, z~6, z~7, z~8, and z~10, respectively from the ~1000 arcmin**2 area probed. The selection of z~4-8 galaxies over the five CANDELS fields allows us to assess the cosmic variance; the largest variations are apparent at z>=7. Our new LF determinations at z~4 and z~5 span a 6-mag baseline (-22.5 to -16 AB mag). These determinations agree well with previous estimates, but the larger samples and volumes probed here result in a more reliable sampling of >L* galaxies and allow us to reassess the form of the UV LFs. Our new LF results strengthen our earlier findings to 3.4 sigma significance for a steeper faint-end slope to the UV LF at z>4, with alpha evolving from alpha=-1.64+/-0.04 at z~4 to alpha=-2.06+/-0.13 at z~7 (and alpha = -2.02+/-0.23 at z~8), consistent with that expected from the evolution of the halo mass function. With our improved constraints at the bright end, we find less evolution in the characteristic luminosity M* over the redshift range z~4 to z~7; the observed evolution in the LF is now largely represented by changes in phi*. No evidence for a non-Schechter-like form to the z~4-8 LFs is found. A simple conditional LF model based on halo growth and evolution in the M/L ratio of halos ((1+z)**-1.5) provides a good representation of the observed evolution.

Figures (28)

• Figure 1: (left) The expected redshift distributions for our $z\sim4$, $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ samples from the XDF using the Monte-Carlo simulations described in §4.1. The mean redshifts for these samples are 3.8, 4.9, 5.9, 6.8, 7.9, and 10.4, respectively. These simulations demonstrate the effectiveness of our selection criteria in isolating galaxies within fixed redshift ranges. Each selection window is smoothed by a normal distribution with scatter $\sigma_z \sim 0.2$. (right) Redshift distribution we recover for sources in our $z\sim4$, $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ samples using the EAZY photometric redshift code (with similar smoothing as in the left panel). Our color-color selections segregate sources by redshift in a very similar manner to what one would find selecting sources according to their best-fit photometric redshift estimate (e.g., McLure et al. 2010; Finkelstein et al. 2012; Bradley et al. 2014).
• Figure 2: An illustration of the $5\sigma$ depths of the various data sets used in this study (calculated based on the median $1\sigma$ flux errors measured for all sources found between $H_{160,AB}\sim26$ and $H_{160,AB}\sim26.5$, after correcting each of these fluxes [Kron apertures for HST, $1.2"$-diameter aperture for ground-based, and $2"$-diameter apertures for Spitzer/IRAC observations] to total). The upper leftmost panel shows the depths of the two shallower data sets available over the GOODS-S sightline, i.e., the CANDELS DEEP data set (dotted dark blue line) and the CANDELS WIDE data set (dotted blue line). The other panels show the depths of the data available over the other four CANDELS fields and those BoRG/HIPPIES fields where $z\sim8$ candidates have been identified. The blue lines indicate the depths available in the HST observations alone, while the red lines indicate the depths of all available observations, i.e., HST + ground-based. The dark blue solid lines indicate the depths of the HST observations associated with the CANDELS DEEP GN program. In 5 out of 6 cases that $z$ and $Y$ band observations exist over the CANDELS-UDS, CANDELS-COSMOS, and CANDELS-EGS fields, these data reach within 0.5 mag of that available over the CANDELS-GS+GN fields. As a result, current observations allow for the effective selection of galaxies at $z\sim6$, $z\sim7$, and $z\sim8$ over the CANDELS-UDS/COSMOS/EGS fields, if we limit ourselves to a somewhat brighter limit than we consider over CANDELS GN and GS (as we demonstrate from end-to-end simulations in §4.1 and as shown in Figure \ref{['fig:zdistsel']}).
• Figure 3: Color-color selection criteria that we use to identify star-forming galaxies at $z\sim4$, $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ over the XDF, HUDF09-1, HUDF09-2, CANDELS-GN, and CANDELS-GS field (§3.2.2). The gray-shaded regions show the regions in color-color space where we select sources. The solid, dashed, and dotted blue lines show the expected colors we would expect star-forming galaxies to have as a function of redshift, for $UV$-continuum slopes $\beta$ of $-2.3$, $-1.15$, and 0, respectively (with hashes shown every $\Delta z = 0.5)$. The red lines show the colors we would expect for various lower-redshift contaminants (using the SEDs from Coleman et al. 1980), again as a function of redshift. The black dots show the colors of individual sources found in the XDF, while the large black squares indicate the colors of sources from the XDF identified as part of the relevant high-redshift selection. The arrows indicate the $1\sigma$ upper limits on the $H_{160}-[3.6]$ colors for two $z\sim10$ candidates from the XDF. Our criteria make use of the color formed from the two bands straddling the targeted Lyman Break and the color that best constrains the spectral slope redward of the break. The criteria allow us to identify a relatively complete selection of star-forming galaxies at $z\gtrsim 3.3$, $z\gtrsim 4.5$, $z\gtrsim 5.5$, $z\gtrsim6.4$, and $z\gtrsim 7.3$, and $z\gtrsim 9.5$. To ensure a good redshift separation between these samples, we impose an upper redshift cut-off to each sample by also requiring that sources not satisfy the selection criteria of the sample just above it in redshift. In addition to the two-color criteria shown here, we also require that sources be undetected in the available HST observations blueward of the break, both on a passband-by-passband basis and in terms of a $\chi^2$ stack of all the fluxes blueward of the break (§3.2.2).
• Figure 4: The expected redshift distributions for our samples of $z\sim4$, $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ galaxies selected from the XDF+HUDF09-Ps+CANDELS-GN+GS fields with the $B_{435}V_{606}i_{775}z_{850}Y_{105}J_{125}H_{160}$ filter set (upper panel: see §3.2.2 for selection procedure), from the ERS data set with the $B_{435}V_{606}i_{775}z_{850}Y_{098}J_{125}H_{160}$ filter set (middle panel: see §3.2.2 for selection procedure), and from the CANDELS-UDS+COSMOS+EGS data set with the $V_{606}I_{814}J_{125}H_{160}$ filter set augmented by ground-based data (lower panel: see §3.2.3 for selection procedure). Each selection window is smoothed by a normal distribution with scatter $\sigma_z \sim 0.2$. We derived the redshift distributions for the $z\sim4$-10 samples shown in all four panels using the full end-to-end Monte simulations described in §4.1 (the redshift distribution for the faintest sources from the CANDELS UDS/COSMOS/EGS fields [i.e., within $\sim$0.5 mag of the limit] have a width that is only $\sigma_{z}$$\sim$0.1 greater than what is shown here.) For sources in the CANDELS EGS data set, the Spitzer/IRAC photometry is used to help discriminate between $z\sim7$ and $z\sim8$ galaxies (as $z<7$ galaxies are known to have bluer $3.6\mu$-$4.5\mu$m colors than $z>7$ given the strong high EW of [OIII]+H$\beta$: Labbé et al. 2013; Stark et al. 2013; Smit et al. 2014; Ono et al. 2012; Finkelstein et al. 2013; Laporte et al. 2014). The redshift distribution for the $z\sim8$ BoRG/HIPPIES samples should be quite similar to our $z\sim8$ ERS samples, but is based on the $V_{606}Y_{098}J_{125}H_{160}$ or $V_{600}Y_{098}J_{125}H_{160}$ filters alone (Table \ref{['tab:selcrit']}).
• Figure 5: Surface densities of candidate $z\sim4$, $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ galaxies for all the search fields considered in this analysis. Shown are the results from the CANDELS-UDS/CANDELS-COSMOS/CANDELS-EGS fields (magenta points), BoRG/HIPPIES (dark violet), CANDELS-GN-WIDE and CANDELS-GS-WIDE (black points), CANDELS-GN-DEEP and CANDELS-GS-DEEP (blue points), HUDF09-1 and HUDF09-2 fields (green points), and the XDF data set (red points). Surface densities are presented as a function of the $i_{775}$, $Y_{105}$, $Y_{105}$, $J_{125}$, $H_{160}$, and $H_{160}$ band magnitudes that provide the best measure of the rest-frame $UV$ flux of galaxies at 1600$\AA$ for our $z\sim4$, $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ selections, respectively. Surface densities for our $z\sim5$ and $z\sim6$ selections over the ERS and CANDELS-UDS/CANDELS-COSMOS/CANDELS-EGS fields are presented as a function of the $Y_{098}$ and $J_{125}$-band fluxes, respectively, due to the lack of deep $Y_{105}$-band coverage of these fields. The points have been offset horizontally from each other for clarity. The available HST + ground-based + Spitzer/IRAC observations allow for the selection of $z\sim5$, $z\sim6$, $z\sim7$, $z\sim8$, and $z\sim10$ galaxies from the wide-area CANDELS-UDS, CANDELS-COSMOS, and CANDELS-EGS fields. The HST observations available over the BoRG/HIPPIES search fields are only particularly effective for selecting candidate $z\sim8$ galaxies. The upward arrows at the bottom of each panel indicate the approximate magnitude where the efficiency of selecting galaxies at a specific redshift from some data set is just 50% of the maximum efficiency. The onset of incompleteness in our different samples is clearly seen in the observed decrease in surface density of sources near the magnitude limit. With our selection volume estimates, we can correct for the increased incompleteness at fainter magnitudes. We do not make use of the faintest sources in each search field, due to the large uncertainties in the completeness (and contamination) corrections. Table \ref{['tab:surfdens']} from Appendix C provides these surface densities in tabular form.