Completeness II: A signal-to-noise approach for completeness estimators applied to galaxy magnitude-redshift surveys

TL;DR

This paper introduces an adaptive, signal-to-noise-based method for improving completeness estimators in galaxy magnitude-redshift surveys, demonstrating its effectiveness on real survey data and highlighting the importance of tailored noise considerations.

Contribution

It presents a novel adaptive smoothing approach for completeness estimators that accounts for signal-to-noise ratios, enhancing accuracy in galaxy survey analyses.

Findings

Improved estimators perform better with tailored signal-to-noise ratios.

Adaptive procedure reduces spurious completeness assessments.

Application to real surveys validates the method's effectiveness.

Abstract

This is the second paper in our completeness series which addresses some of the issues raised in the previous article by Johnston, Teodoro & Hendry (2007) in which we developed statistical tests for assessing the completeness in apparent magnitude of magnitude-redshift surveys defined by two flux limits. The statistics, Tc and Tv, associated with these tests are non-parametric and defined in terms of the observed cumulative distribution function of sources; they represent powerful tools for identifying the true flux limit and/or characterising systematic errors in magnitude-redshift data. In this paper we present a new approach to constructing these estimators that resembles an "adaptive smoothing" procedure - i.e. by seeking to maintain the same amount the information, as measured by the signal-to-noise ratio, allocated to each galaxy. For consistency with our previous work, we apply our improved estimators to the Millennium Galaxy Catalogue (MGC) and the Two Degree Field Galaxy Redshift Survey (2dFGRS) data, and demonstrate that one needs to use a signal-to-noise appropriately tailored for each individual catalogue to optimise the performance of the completeness estimators. Furthermore, unless such an adaptive procedure is employed, the assessment of completeness may result in a spurious outcome if one uses other estimators present in the literature which have not been designed taking into account "shot noise" due to sampling.