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

TL;DR

This paper demonstrates that rank-ordered mark correlation functions effectively detect small dependencies of galaxy properties on environment, providing a robust method to compare environmental sensitivities of different galaxy marks.

Contribution

It introduces a rank-ordering technique for marks in correlation functions, enhancing the detection and comparison of environmental dependencies in galaxy properties.

Findings

Mark correlation functions detect small property-environment dependencies.

Rank ordering marks simplifies comparison of different environmental measures.

Colour is a better tracer of overdensity than luminosity.

Abstract

We analyze 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 $1+\delta$, 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-neighbor overdensities are sensitive to small-scale environments within haloes, and colour is a better tracer of overdensity than is luminosity.