CLASH: Precision Photometry in Crowded Fields


We present a new method for measuring the photometry of objects around galaxy clusters, employing a novel mode-filtering technique for both detection and photometry. With this, we are able to investigate the galaxy populations inside the 25 massive clusters observed by the Cluster Lensing and Supernova survey with Hubble (CLASH). We produce multi-wavelength catalogs covering 16 bandpasses from ultraviolet (\(\sim 2360\) Å) to infrared (\(\sim 1.54\mu{\rm m}\)) including photometric redshifts. A comparison with spectroscopic values from the literature finds that \(\sim 82\%\) of our reported photometric redshifts lie within \(|z_{p}-z_{s}|\)/\((1+z_{s})<0.05\). This improvement in redshift accuracy, in combination with a detection scheme designed to maximize purity, yields a substantial upgrade in cluster member identification over the previous CLASH galaxy catalog. We find consistency between the galaxy magnitudes, colors, and photometric redshifts obtained here and from previous studies, including a deeper observation of one of the CLASH clusters. Evaluating the luminosity functions for these clusters, we find that we are able to observe galaxies down to \({\rm M}\sim{\rm M}^{*}+5\), and the values of M* we derive are consistent with that expected from published cluster galaxy luminosity functions. These clusters follow a consistent trend in mass-richness that agrees with low-mass cluster observations. We measure luminosity functions for these clusters, which we use to derive total luminosity, and, from that, stellar masses. We find stellar mass fractions of \(1.8\pm 0.7\)% of the total halo mass, in agreement with previous studies. Not only will this catalog enable new studies of the properties of CLASH clusters, but the photometric techniques we use set the stage for future surveys of galaxy clusters.

Subject headings:
galaxies: clusters: general — X-rays: galaxies: clusters


Galaxy clusters are the largest virialized structures in the Universe, although most of that mass is in dark matter and hot intracluster gas. Galaxies themselves only contribute a small (\(\approx 1\%\)) amount to the cluster mass budget (e.g. Gonzalez et al., 2013). Despite this fact, individual galaxies play a critical role in understanding the nature of cluster growth and formation of massive galaxies and of galaxies in a dense environment. Not only are individual galaxies tracer particles for the gravitational potential of their hosts, their evolution is sensitive to the conditions of their environment (Cerulo et al., 2016).

Having formed out of the same overdensity as the cluster itself (citation not found: 2012ARA&A..50..353K), the initial conditions of cluster galaxies are probes of their host’s beginnings (Voit, 2005). As galaxies accrete onto the cluster, they sample the physical properties of inner and outer regions of the system. Variations between more- and less-massive galaxies can be used to investigate the energetic scale of events such as active galactic nucleus (AGN) feedback and supernovae (e.g., Larson, 1974; (citation not found: 1987A&A...173...23A) (citation not found: 1987A&A...185...51M).

Detailed studies of cluster members are mostly conducted at low redshift (e.g., Edwards et al., 2011; Liu et al., 2011; Zhang et al., 2011; Tian et al., 2012; Ferrarese et al., 2016), as these clusters are brighter and more accessible to ground-based observations. Distant clusters offer the ability to study the evolution of cluster populations, however, by providing temporal constraints (e.g., Hilton et al., 2009; Papovich et al., 2010; Foltz et al., 2015). Due to the difficulty in observing these clusters, previous works have had limited spatial resolution, filter coverage, and/or depth (e.g. Muzzin et al., 2013).

In particular, the study of galaxy cluster luminosity functions requires precise photometry of redshifted cluster members to draw meaningful conclusions. A number of works have observed a steepening of the faint-end slope (Rudnick et al., 2009; Lan et al., 2016), but evidence for evolution is inconclusive (Crawford et al., 2009; Lu et al., 2009). Even inside a single cluster, the parameters of the luminosity function are sensitive to the galaxies included (Agulli et al., 2016), meaning that accurate membership determination is necessary to draw meaningful conclusions about any slope evolution.

In this work, we present a photometric catalog of 25 massive galaxy clusters, using mode-based filtering to select and photometer galaxies down to \({\rm M}-{\rm M}^{*}\sim 5\) (where M* is the characteristic magnitude of each cluster’s luminosity function) across 16 filters using the Hubble Space Telescope (HST). We verify the accuracy of these results with checks to spectroscopic measurements and an overlap with a cluster in the Hubble Frontier Fields. Finally, we present fits to the observed luminosity functions for these 25 clusters in rest frame \(i\) bandpass. Throughout this work, we assume a \(\Lambda\)CDM cosmology, with \(\Omega_{\rm M}=0.3\), \(\Omega_{\Lambda}=0.7\), and \({\rm H}_{0}=70\ {\rm km}\ {\rm s}^{-1}\ {\rm Mpc}^{-1}\).

Statistical Background Light Estimators

Obtaining accurate photometry – particularly color photometry – for galaxies in clusters is a longstanding problem (e.g Butcher et al., 1978). Clusters are filled with intracluster light (ICL, Vílchez-Gómez, 1999; Mihos et al., 2005; DeMaio et al., 2015), which can impact the observed colors of galaxies (Zibetti et al., 2005; Da Rocha et al., 2005; Williams et al., 2007; Rudick et al., 2010). In particular, it is difficult to disentangle the contributions of ICL from galaxy emission near the center of clusters (Krick et al., 2006). Along with the ICL, the estimate of light from a given galaxy may be affected by projected overlaps between galaxies and fore- and background contamination. While previous work has modeled and subtracted the surface brightness profiles of major galaxies such as the brightest cluster galaxy (BCG, Postman et al., 2012), this result does not scale well to measurements of the hundreds of objects visible even in the narrow WFC3 field of view. And any method to account for light contamination needs to be filter dependent – ICL, galaxy brightness, and PSF size all change with color. Here, we present a technique to determine background properties by statistically modeling the light of nearby pixels.

One of the fundamental assumptions of this work is that, for a pixel containing the light from a galaxy, the observed flux in that pixel is the sum of light from the galaxy and from the background light drawn from some unknown distribution. Lacking a complete understanding of the background light due to the limitations of our telescope’s optics and the finite observation time, our best solution is to model the background light distribution from nearby pixels.

There are three challenges that must be contended with to accurately describe the background: determining a nominal measure of the expected value of the background light, determining the range of that distribution, and performing this characterization with a limited sample of pixels, some of which may be outliers from a separate distribution (such as from the wings of a nearby galaxy). The easiest statistic to compute from a background sample, the mean, is biased by outliers. A common choice is to instead use the median, which is swayed less by skew. However, the median is still sensitive to outliers; additionally, it will always be the value of one of the measurements in the background sample (or the midpoint of two values when there is an even number of sampling points), which introduces an extra level of error in the background measurement. To avoid these issues, we instead consider the mode.

For a given probability distribution, we define the mode as the point at which the frequency is greatest. For a well-sampled distribution, this will converge with the classical definition of the mode, which is the sample value that appears most often. The mode is extremely useful as a background measure as, for a sampling of background pixels wherein two distinctly-resolved background distributions can be detected, the mode will find the central value of the dominant background distribution. In the context of this work, we use two determinations of the mode: a less-rigorous yet more computationally efficient estimator to detect galaxies and a more robust yet computationally intensive method for accurate measurements of flux and flux ratios. We first describe the former.

Pearson (1895) first noted that the mode of a distribution can be approximated through the relation

\begin{equation} M=3m-2\mu,\\ \end{equation}

where M is the mode, m is the median, and \(\mu\) is the mean. This relation, which we will refer to as the Pearson approximation in this work, has an important caveat: this is an empirically-derived relation, and it does not always find the correct mode, particularly in the case of complex backgrounds. Indeed, in the case of a background region containing light from two distributions (such as for a region consisting mostly of ICL, but with a small sub-region containing e.g. the emission of a nearby galaxy), this expression will not give an accurate representation of the mode. Due to these concerns, we will use this method for computational expediency in estimating the background for purposes of identification and detection of sources, but not for flux estimation. Since our science does not depend on teasing out detections of the faintest, smallest background sources, small errors in the mode for individual pixels do not affect detection and source definition for our scientific purposes here.

One additional input to consider when determining the background is the contribution of measurement uncertainty. A sample point with uncertain flux should not be weighted as highly as a point with more accuracy, yet it should also support background determination over a larger range. To account for all of these issues, we instead compute the mode using a kernel density estimation to derive accurate colors within fixed apertures.

Each background pixel is defined by two values: \(f_{i}\) and \(\sigma_{i}\), the flux and uncertainty, respectively. By convolving the flux in each pixel with a Gaussian kernel of width \(\sigma_{i}\), we create a probability distribution for the entire flux of the background region. The mode is then found as the peak of this distribution, which is given by

\begin{equation} \label{eqn:gaussian_sum}P(x)=\sum_{i}\frac{1}{\sigma_{i}}\exp^{-(x-f_{i})^{2}/(2\sigma_{i}^{2})}.\\ \end{equation}

To find the maximum of this function in a computationally expedient manner over a large number of points, we identify the zeroes of its derivative, given by

\begin{equation} \label{eqn:gaussian_deriv_sum}dP(x)/dx=\sum_{i}\frac{(x-f_{i})}{\sigma_{i}^{3}}\exp^{-(x-f_{i})^{2}/(2\sigma_{i}^{2})}.\\ \end{equation}

A full description of the application of this technique is provided below. Due to the limits of computational efficiency, we only employ the more accurate kernel density estimation using Equations \ref{eqn:gaussian_sum} and \ref