XMM-Newton Science Analysis System


ssclib (ssclib-4.36.1) [xmmsas_20230412_1735-21.0.0]

Parallel detection over $N$ bands (with no assumptions made about source spectrum)

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:

• Detect in each band separately.
• Calculate likelihood values according to equation 1.
• Add the band likelihoods together for each position.

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 $L_{\rm {total}}$ that there is a source at this position, is given by

$$L_{\rm {total}} = -ln\{1 - P \Big[ f(N), \sum_{i=1}^{N} L_i \Big] \}.$$

where $f(x)$ approximates a linear function of $x$ of slope 1. Monte Carlo studies indicate that $f(2) \sim 2$, $f(5) \sim 4$, $f(10) \sim 8$ and so forth; however eboxdetect at the present time assumes that $f(N) = N$; 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