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Selection Functions in Astronomical Data Modeling, with the Space Density of White Dwarfs as a Worked Example

  • Authors: Hans-Walter Rix, David W. Hogg, Douglas Boubert, Anthony G. A. Brown, Andrew Casey, Ronald Drimmel, Andrew Everall, Morgan Fouesneau, and Adrian M. Price-Whelan

2021 The Astronomical Journal 162 142.

  • Provider: AAS Journals

Caption: Figure 6.

The effective survey volume, Veff(MG), which for our worked example is only a function of each object’s estimated absolute magnitude MG. The figure shows three regimes (thick black line) where different terms in ﹩{S}_{{ \mathcal C }}({\boldsymbol{q}})﹩ limit Veff(MG): for the most luminous objects (MG < 11), Veff is simply limited by the initial selection ϖ > 3 mas; for the least luminous objects in the volume, it is limited by the initial cut apparent magnitude, G < 20. In the intermediate regime, the volume is limited by the (subsequently) chosen cut in expected parallax S/N, ﹩{\left\langle \tfrac{\varpi }{{\sigma }_{\varpi }}\right\rangle }_{\min }﹩ (Equation (11)). For very demanding choices in ﹩{\left\langle \tfrac{\varpi }{{\sigma }_{\varpi }}\right\rangle }_{\min }﹩, this cut may dominate for all MG (green line); if such a cut is omitted or very lenient (blue line), this regime may disappear. This figure can also serve to illustrate why volume-limited samples are generally very suboptimal: if we wanted to construct a volume-limited sample of WDs covering 7 < MG < 15, it would have a volume of only Veff = 10−3 kpc−3, and we would have to discard 90% (99%) of the accessible sample members at MG = 13 (10).

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