Selection Functions in Astronomical Data Modeling, with the Space Density of White Dwarfs as a Worked Example
The Astronomical Journal, vol. 162, pp. 142
Abstract
Abstract Statistical studies of cataloged object properties are central to astrophysics. But one cannot model those objects’ population properties without the sample’s selection function, the quantitative understanding of which objects could have ended up in such a catalog. As didactic introductions to this topic are scarce in the astrophysical literature, we provide one here, addressing the following questions: What is a selection function? On what arguments q should it depend? Over what domain must a selection function be defined? What simplifying approximations can be made? And, how is a selection function used in “modeling”? We argue that volume-complete samples, limited by the faintest objects, reflect a highly suboptimal selection function, needlessly reducing the number of bright and usually rare sample members. We illustrate these points by a worked example: github.com/gaia-unlimited/WD-selection-function, deriving the space density of white dwarfs (WDs) in the Galactic neighborhood as a function of their luminosity and color, Φ 0 ( M G , ( B − R )) in [mag −2 pc −3 ]. We construct a sample of 10 5 presumed WDs through straightforward selection cuts on the Gaia EDR3 catalog in magnitude, color, and parallax, q = ( G , ( B − R ), ϖ ). We then combine a simple model for Φ 0 with this selection function’s S ( q ) effective survey volume to estimate Φ 0 ( M G , ( B − R )) precisely and robustly against the detailed choices for S ( q ) . This resulting WD luminosity–color function Φ 0 ( M G , ( B − R )) differs dramatically from the initial number density distribution in the luminosity−color plane: by orders of magnitude in density and by four magnitudes in density peak location.
Authors 9
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Hans‐Walter Rix corresponding
Max Planck Institute for Astronomy
Affiliation as printed
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany; rix@mpia.de
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
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Max Planck Institute for Astronomy · Flatiron Institute · New York University
Affiliation as printed
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
Center for Cosmology and Particle Physics, Department of Physics, New York University, 726 Broadway, New York, NY 10003, USA
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany; rix@mpia.de
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
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Affiliation as printed
Magdalen College, Oxford University, Oxford OX1 4AU, UK
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Leiden University · Leiden Observatory
Affiliation as printed
Leiden Observatory, Leiden University, Niels Bohrweg 2, 2333 CA Leiden, The Netherlands
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Affiliation as printed
School of Physics and Astronomy, Monash University, VIC 3800, Australia
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Osservatorio Astrofisico di Torino · National Institute for Astrophysics
Affiliation as printed
INAF—Osservatorio Astrofisico di Torino, Strada Osservatorio 20, Pino Torinese 10025 Torino Italy
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Affiliation as printed
Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
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Max Planck Institute for Astronomy
Affiliation as printed
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany; rix@mpia.de
Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany
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Affiliation as printed
Center for Computational Astrophysics, Flatiron Institute, 162 Fifth Avenue, New York, NY 10010, USA
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