A maximum volume density estimator generalized over a proper motion-limited sample

TL;DR

This paper introduces a generalized maximum volume density estimator that corrects systematic biases in proper motion-limited samples, improving accuracy for populations with diverse kinematics, demonstrated through simulations.

Contribution

It develops a new method to remove biases in proper motion-limited density estimations by integrating the discovery fraction into the maximum volume calculation.

Findings

Biases are mitigated when the discovery fraction is incorporated.

The method performs better than traditional estimators in simulated white dwarf populations.

Applicable to any proper motion-limited sample with known kinematics.

Abstract

The traditional Schmidt density estimator has been proven to be unbiased and effective in a magnitude-limited sample. Previously, efforts have been made to generalize it for populations with non-uniform density and proper motion-limited cases. This work shows that the then-good assumptions for a proper motion-limited sample are no longer sufficient to cope with modern data. Populations with larger differences in the kinematics as compared to the local standard of rest are most severely affected. We show that this systematic bias can be removed by treating the discovery fraction inseparable from the generalized maximum volume integrand. The treatment can be applied to any proper motion-limited sample with good knowledge of the kinematics. This work demonstrates the method through application to a mock catalogue of a white dwarf-only solar neighbourhood for various scenarios and compared against the traditional treatment using a survey with Pan-STARRS-like characteristics.