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

References in corpus (19)

• emcee: The MCMC Hammer
• On the variation of the Initial Mass Function
• PARSEC: stellar tracks and isochrones with the PAdova and TRieste Stellar Evolution Code
• Evolutionary tracks and isochrones for low- and intermediate-mass stars: from 0.15 to 7 M_sun, and from Z=0.0004 to 0.03
• The Pan-STARRS1 Photometric System
• Kinematics of Metal-Poor Stars in the Galaxy. III. Formation of the Stellar Halo and Thick Disk as Revealed from a Large Sample of Non-Kinematically Selected Stars
• An Improved Spectroscopic Analysis of DA White Dwarfs from the Sloan Digital Sky Survey Data Release 4
• Photometric Calibration of the First 1.5 Years of the Pan-STARRS1 Survey
• A Comprehensive Spectroscopic Analysis of DB White Dwarfs
• The Pan-STARRS 1 Photometric Reference Ladder, Release 12.0
• Found: The missing blue opacity in atmosphere models of cool hydrogen white dwarfs
• The White Dwarf Luminosity Function from SDSS Imaging Data
• The Masses of Population II White Dwarfs
• A synthetic view on structure and evolution of the Milky Way
• A Survey for Cool White Dwarfs and the age of the Galactic Disc
• Velocity Shear of the Thick Disk from SPM3 Proper Motions at the South Galactic Pole
• A Schmidt-Kennicutt law for star formation in the Milky Way disk
• The Subdwarf Luminosity Function
• The white dwarf luminosity function. I. Statistical errors and alternatives

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• A Deep Proper Motion Catalog Within the Sloan Digital Sky Survey Footprint. II. The White Dwarf Luminosity Function
• The Gaia DR2 halo white dwarf population: the luminosity function, mass distribution and its star formation history
• The White Dwarf Luminosity Functions from the Pan-STARRS 1 3π Steradian Survey
• The kinematics of Galactic disc white dwarfs in Gaia DR2
• Maximizing Survey Volume for Large-Area Multi-Epoch Surveys with Voronoi Tessellation
• Exploring faint white dwarfs and the luminosity function with Subaru HSC and SDSS in Stripe 82