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The cluster detection efficiency in the 400d survey was extensively calibrated by Monte-Carlo simulations. As a result, the sky coverage and volume of the survey are accurately known.
The low-level calculations are rather complex because we have to take into account the dependence of the detection efficiency on both cluster flux and angular size, the uncertainties of fluxes derived from ROSAT data etc. (see §7.1 of The Paper for details). However, for most practical purposes the sky coverage can be represented as a function of only object flux and redshift. These functions can be integrated to compute the survey volume.
- Tabulated area as a function of true flux (eq.3 in The Paper)
- Tabulated area as a function of measured flux (eq.10 in The Paper)
A (ftrue) should be used if the fluxes are accurately measured from the followup (e.g. Chandra) observations. A (fmeasured) is for the case when the raw survey fluxes are used. If you wonder why they are different, please see §7.2 in The Paper
If you need anything more accurate, please contact A. Vikhlinin or R. Burenin.
A separate set of simulations was run to derive the expected number of false detections (confused point sources). The results (more extensively discussed in §6.4 of The Paper) show that one expects 20–30 false detections. This agrees nicely with the number of unidentified sources in the 400d sample (16).