An Automated Cluster Finder: The Adaptive Matched Filter

Abstract

We describe an automated method for detecting clusters of galaxies in imaging and redshift galaxy surveys. The adaptive matched Ðlter (AMF) method utilizes galaxy positions, magnitudes, andÈwhen availableÈphotometric or spectroscopic redshifts to Ðnd clusters and determine their redshift and richness. The AMF can be applied to most types of galaxy surveys, from two-dimensional (2D) imaging surveys, to multiband imaging surveys with photometric redshifts of any accuracy (2.5 dimensional to three-dimensional (3D) redshift surveys. The AMF can also be utilized in the selection of [21 2 D]), clusters in cosmological N-body simulations. The AMF identiÐes clusters by Ðnding the peaks in a cluster likelihood map generated by convolving a galaxy survey with a Ðlter based on a model of the cluster and Ðeld galaxy distributions. In tests on simulated 2D and data with a magnitude limit of 21 2 D r@ B 23.5, clusters are detected with an accuracy of *z B 0.02 in redshift and D10% in richness to z [ 0.5. Detecting clusters at higher redshifts is possible with deeper surveys. In this paper we present the theory behind the AMF and describe test results on synthetic galaxy catalogs.

A Matched-Filter Analysis of the Tidal Tails of the Globular Cluster Palomar 5

“…This approach provides, statistically, the best possible measurement of a signal at any time, and it works by using the known characteristics of the expected signal and of the background noise to inform the interpretation of the incoming data. It has since become a standard technique in signal processing and is used in astronomy in the measurement of images near the sky background and when searching catalog and time-series data for objects with well-defined signatures such as clusters of galaxies (Postman et al 1996;Kawasaki et al 1998;Kepner et al 1999) and planets around other stars (Doyle et al 2000). Its application here is to finding low-level overdensities of a stellar population against the Galactic stellar background.…”

“…The expression for derived from equation (1) gives the minimum variance estimate for at low densities and, unlike a maximum likelihood estimator, an unbiased estimate at any density. Following the discussion in Kepner et al (1999), if the bins in color and magnitude are made infinitesimally small, the stars in d become a set of delta functions in color and magnitude stars (color, mag), and the binned model distributions f cl, (i,j) and n bg, (i,j) become the smooth distribution functions f cl (color, mag) and n bg (color, mag). Minimizing equation (1) …”

Galaxy Cluster Mass Reconstruction Project – II. Quantifying scatter and bias using contrasting mock catalogues

“…Friends-Of-Friends (FOF) group-finding algorithm based methods are also widely used (e.g., Berlind et al 2006;Li & Yee 2008;Jian et al 2014;Tempel et al 2014, see FOF optimisation study of Duarte & Mamon, 2014), along with methods based upon Voronoi tessellation (e.g., Marinoni et al 2002;Lopes et al 2004;van Breukelen & Clewley 2009;Soares-Santos et al 2011). Finally, the magnitudes and positions of galaxies are also used to search for over-densities via the matched filter algorithm (e.g., Postman et al 1996;Olsen et al 1999;Kepner et al 1999;Menanteau et al 2009). …”

Planck2013 results. XXIX. ThePlanckcatalogue of Sunyaev-Zeldovich sources

“…On the one hand, we run an adaptive matched filter cluster finder developed by (Aussel et al, in prep. ), similar to the one described by Kepner et al (1999), using the cluster members' luminosity function of Lin et al (2012). The background counts were determined from the neighbouring square degree in the vicinity of the Planck cluster candidate, excluding regions of fifteen arcmin centred on candidate positions.…”