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

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.

12 pages, 10 figures, 2 tables. v2: typo correction. Published in MNRAS

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• Found: The missing blue opacity in atmosphere models of cool hydrogen white dwarfs
• Velocity Shear of the Thick Disk from SPM3 Proper Motions at the South Galactic Pole
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Cited by in corpus (2)

• The Ages of the Thin Disk, Thick Disk, and the Halo from Nearby White Dwarfs
• A Deep Proper Motion Catalog Within the Sloan Digital Sky Survey Footprint. II. The White Dwarf Luminosity Function