3.2.2 Existence of a Source - Poissonian Statistics Case

The typical HRI background in on-axis detection cells ( $\sim$ 5'' x 5'') is of order unity or lower for most HRI observations ($\lesssim$ 100 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 5$\sigma$ detection of a source using Poissonian statistics would then require 7 counts, for a count rate of 3.5 x 10^-4 counts s^-1 in the detection cell, a total count rate of 7.0 x 10^-4 counts s^-1. The count rate of the source, however, is known to less than 3$\sigma$. In lieu of an analytic function (of which none exists), Figure 29(top) 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 29(bottom) shows the same information for a region of interest 10' off axis where the detection cell is $\sim$ 12'' x 12'' and the background count rate $\sim$ 1.6 x 10^-4 counts s^-1. 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 29: 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 10^-3 counts s^-1 versus exposure in ks and sigma (a value for $\sigma$ of 50 refers to 5$\sigma$). Top plot is for the on-axis case, bottom plot is for 10' off axis.

LINK TO POSTSCRIPT FILE for Figure 29