Toward accurate measurement of property-dependent galaxy clustering: II. Tests of the smoothed density-corrected $V_{\rm max}$ method

TL;DR

This paper introduces an improved smoothed density-corrected $V_{max}$ method for creating random catalogs, significantly enhancing the accuracy of galaxy clustering measurements in property-dependent analyses.

Contribution

The authors develop and validate an improved density-corrected $V_{max}$ technique that outperforms existing methods in accuracy for galaxy clustering studies.

Findings

The new method yields less than 1% error in projected correlation functions.

Redshift-space correlation functions are accurate within 2%.

The approach is promising for high-precision clustering in future surveys.

Abstract

We present a smoothed density-corrected $V_{\rm max}$ technique for building a random catalog for property-dependent galaxy clustering estimation. This approach is essentially based on the density-corrected $V_{\rm max}$ method of Cole(2011), with three improvements to the original method. To validate the improved method, we generate two sets of flux-limited samples from two independent mock catalogs with different $k+e$ corrections. By comparing the two-point correlation functions, our results demonstrate that the random catalog created by the smoothed density-corrected $V_{\rm max}$ approach provides a more accurate and precise measurement for both sets of mock samples than the commonly used $V_{\rm max}$ method and redshift shuffled method. For flux-limited samples and color-dependent subsamples, the accuracy for the projected correlation function is well constrained within $1\%$ on the scale $0.07 h^{-1}\rm Mpc - 30 h^{-1}\rm Mpc$. The accuracy of the redshift-space correlation function is less than $2\%$ as well. Currently, it is the only approach that holds promise for achieving the goal of high-accuracy clustering measures for next-generation surveys.