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Existence of a Source - Poissonian Statistics Case


The typical HRI background in on-axis detection cells ( tex2html_wrap_inline17655 ) is of order unity or lower for most HRI observations ( tex2html_wrap_inline17657  ks), and therefore in the range where Poisson statistics are appropriate for source-detection analysis.   For example, the number of background counts expected in a detection cell for a 20 ks observation is 0.55. A tex2html_wrap_inline17659 detection of a source using Poissonian statistics would then require 7 counts, for a count rate of tex2html_wrap_inline17661  counts s tex2html_wrap_inline17663 in the detection cell, a total count rate of tex2html_wrap_inline17665  counts s tex2html_wrap_inline17667 . The count rate of the source, however, is known to less than tex2html_wrap_inline17669 . In lieu of an analytic function (of which none exists), Fig. 5.23a displays a contour plot of limiting (total) count rate for a source detection on a grid of significance (sigma) and exposure. The plot was generated for the on-axis detection cell and assumes the nominal background rate. Figure 5.23b shows the same information for a region of interest 10' off axis where the detection cell is tex2html_wrap_inline17673 and the background count rate tex2html_wrap_inline17675  counts s tex2html_wrap_inline17677 . Off axis, the same considerations of vignetting correction and larger detection cells as for the Gaussian case must be taken. The conversion between count rate and flux is the same as above.

Figure 5.23: The relation between source count rate, statistical significance, and exposure for an HRI observation using Poisson statistics is shown. The contour plots show the source count rate in units of tex2html_wrap_inline17679  counts s tex2html_wrap_inline17681 versus exposure in ks and sigma (a value for tex2html_wrap_inline17683 of 50 refers to 5 tex2html_wrap_inline17685 ). Plot a) is for the on-axis case, plot b) is for 10' off axis.

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