Characterizing the Gaia radial velocity sample selection function in its native photometry

The Gaia Data Release 2 (DR2) radial velocity sample (GDR2_RVS), which provides six-dimensional phase-space information on 7.2 million stars, is of great value for inferring properties of the Milky Way. Yet a quantitative and accurate modelling of this sample is hindered without knowledge and inclusion of a well-characterized selection function. Here we derive the selection function through estimates of the internal completeness, i.e. the ratio of GDR2_RVS sources compared to all Gaia DR2 sources (GDR2_all). We show that this selection function or 'completeness' depends on basic observables, in particular the apparent magnitude G_RVS and colour G - G_RP, but also on the surrounding source density and on sky position, where the completeness exhibits distinct small-scale structure. We identify a region of magnitude and colour that has high completeness, providing an approximate but simple way of implementing the selection function. For a more rigorous and detailed description we provide PYTHON code to query our selection function, as well as tools and ADQL queries that produce custom selection functions with additional quality cuts.