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

Marco C. Lam*, Nicholas Rowell, Nigel C. Hambly

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 thengood 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 showthat 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.

Original languageEnglish
Pages (from-to)4098-4108
Number of pages11
JournalMonthly Notices of the Royal Astronomical Society
Issue number4
Publication statusPublished - 24 Apr 2015


  • Methods: statistical
  • Proper motions
  • Solar neighbourhood
  • Stars: kinematics and dynamics
  • Stars: luminosity function, mass function
  • White dwarfs


Dive into the research topics of 'A maximum volume density estimator generalized over a proper motion-limited sample'. Together they form a unique fingerprint.

Cite this