Measures of galaxy environment – II. Rank-ordered mark correlations

MNRAS 429, 458–468 (2013) doi:10.1093/mnras/sts349 Measures of galaxy environment – II. Rank-ordered mark correlations Ramin A. Skibba, 1,2‹ Ravi K. Sheth, 3,4 Darren J. Croton, 5 Stuart I. Muldrew, 6 Ummi Abbas, 7 Frazer R. Pearce 6 and Genevieve M. Shattow 5 1 Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA for Astrophysics and Space Sciences, Department of Physics, University of California, 9500 Gilman Dr, La Jolla, San Diego, CA 92093, USA 3 The Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy 4 Center for Particle Cosmology, University of Pennsylvania, 209 S. 33rd St, Philadelphia, PA 19104, USA 5 Centre for Astrophysics & Supercomputing, Swinburne University of Technology, PO Box 218, Hawthorn, VIC 3122, Australia 6 School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD 7 INAF – Osservatorio Astrofisico di Torino, I-10025 Pino Torinese, Italy 2 Center ABSTRACT We analyse environmental correlations using mark clustering statistics with the mock galaxy catalogue constructed by Muldrew et al. (Paper I). We find that mark correlation functions are able to detect even a small dependence of galaxy properties on the environment, quantified by the overdensity 1 + δ, while such a small dependence would be difficult to detect by traditional methods. We then show that rank ordering the marks and using the rank as a weight is a simple way of comparing the correlation signals for different marks. With this we quantify to what extent fixed-aperture overdensities are sensitive to large-scale halo environments, nearest-neighbour overdensities are sensitive to small-scale environments within haloes and colour is a better tracer of overdensity than luminosity. Key words: methods: statistical – galaxies: evolution – galaxies: haloes – large-scale structure of Universe. 1 I N T RO D U C T I O N In hierarchical clustering models, clues about the galaxy formation process are encoded in correlations between galaxy properties and their environments. This has motivated measurements of such cor- relations. Traditional measures are intended to allow one to quantify whether galaxies in dense regions tend to be more luminous, or red- der, or older or tend to move faster than average, and so on. These conclusions depend critically on how the density N g /V is estimated: fixed-aperture (FA) measurements count the number of galaxies N g that are within volume V of an object (i.e. the numerator of the ratio N g /V varies from one object to another), whereas near-neighbour measurements find the V that contains N g nearest neighbours (i.e. the denominator is stochastic). Clearly, the size and shape of V or the choice of N g matters greatly (the Universe is homogeneous on suf- ficiently large N g or V). In addition, the choice of three-dimensional or projected surface density matters as well, as do the redshift un- certainties and sample selection. Determining which of the many observed correlations is fundamental, and which is a consequence of others, can be a subtle task, especially since the environment is often the least well determined of a galaxy’s attributes. Moreover, E-mail: rskibba@ucsd.edu the estimate of the environment is often sufficiently complicated that it cannot be modelled or interpreted analytically. Mark clustering statistics are fundamentally different in the sense that they are, strictly speaking, statements about pairs, triples, quadruples, etc., of galaxies, rather than about single objects (Stoyan & Stoyan 1994; Mart´inez et al. 2010). For example, the most com- monly used such statistic returns an estimate of how the properties of galaxy pairs (rather than of single galaxies) depend on pair sep- aration. (While this is easily extended to triples, quadruples, etc., such estimates are rarely ever made.) In essence, for each pair separation r, this statistic weights each galaxy in a pair by its own attribute (e.g. luminosity, colour, etc., expressed in units of the mean across the population) and then divides this weighted pair count by the unweighted one. Symbolically, one may write this statistic as WW(r)/DD(r), where WW and DD stand for the weighted and unweighted pair counts at separation r, respectively. Previous estimates of WW/DD have shown that close pairs of galaxies are more luminous (Beisbart & Kerscher 2000), redder (Skibba et al. 2006) and older (Sheth et al. 2006) than average (WW/DD > 1 for r less than a few h −1 Mpc). While these trends are qualitatively the same as those returned by traditional estimates, and they are also in qualitative agreement with galaxy formation models (Sheth 2005), the mark statistics are particularly interesting because a theoretical framework exists for interpreting such measurements quantitatively (Sheth 2005; Skibba et al. 2006). On the other hand, C 2012 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society Downloaded from http://mnras.oxfordjournals. org/ at University of California, San Diego on October 24, 2014 Accepted 2012 November 2. Received 2012 October 30; in original form 2012 August 16