Here the situation is a little more complicated. If nothing can be assumed about the spectra of the sources, the best detection strategy appears to be as follows:
This sum over likelihoods itself follows a Poisson-like distribution. It can thus be shown that the overall likelihood for any given value of this sum being not due to chance, ie, the overall likelihood that there is a source at this position, is given by
where approximates a linear function of of slope 1. Monte Carlo studies indicate that , , and so forth; however eboxdetect at the present time assumes that ; hence that (arguably not quite correct) assumption has been built into the present subroutine as well.
subroutine minDetPoissonCountsVector(bkgCounts, likelihoodCutoff& , detectableSrcCounts, detectableSrcCountsUncert, srcCountRatios, status) real(single), intent(in) :: srcCountRatios(:),& bkgCounts(size(srcCountRatios)),& likelihoodCutoff real(single), intent(out) :: detectableSrcCounts(& size(srcCountRatios)) real(single), intent(out) :: detectableSrcCountsUncert(& size(srcCountRatios)) integer, intent(out), optional :: status end subroutine minDetPoissonCountsVector end interface minDetPoissonCounts
XMM-Newton SOC -- 2021-11-30