Maximizing Survey Volume for Large-Area Multi-Epoch Surveys with Voronoi Tessellation

Abstract

The survey volume of a proper motion-limited sample is typically much smaller than a magnitude-limited sample. This is because of the noisy astrometric measurements from detectors that are not dedicated for astrometric missions. In order to apply an empirical completeness correction, existing works limit the survey depth to the shallower parts of the sky that hamper the maximum potential of a survey. The number of epoch of measurement is a discrete quantity that cannot be interpolated across the projected plane of observation, so that the survey properties change in discrete steps across the sky. This work proposes a method to dissect the survey into small parts with Voronoi tessellation using candidate objects as generating points, such that each part defines a `mini-survey' that has its own properties. Coupling with a maximum volume density estimator, the new method is demonstrated to be unbiased and recovered {\sim}20% more objects than the existing method in a mock catalogue of a white dwarf-only solar neighbourhood with Pan--STARRS 1-like characteristics. Towards the end of this work, we demonstrate one way to increase the tessellation resolution with artificial generating points, which would be useful for analysis of rare objects with small number counts.

10 pages, 2 tables, 8 figures, accepted by MNRAS on 10 April 2017

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Cited by in corpus (1)

• The White Dwarf Luminosity Functions from the Pan-STARRS 1 3π Steradian Survey