Detection of Point Sources

The total background per SIXA pixel in a $\sim$1 ksec observation is likely to be $\mathrel{\copy\simgreatbox}$30 counts. Therefore, Gaussian statistics can be used to estimate the minimum count rate, R_min, required to detect a point source at a given count rate significance, as a function of exposure time T. For a point source on-axis, R_min is given by the solution to

$$N_{\sigma}~=~\frac{R_{min}fT}{\sqrt{R_{min}fT~+~R_BT}},$$

or

$$R_{min}fT~=~\frac{N_{\sigma}^2}{2}\left(1~+~\sqrt{1~+~\frac{4R_BT}{N_{\sigma}^2}}\right).$$

Here, $N_{\sigma}$ is the signal-to-noise ratio of the net source counts, expressed as number of $\sigma$, f is the encircled energy fraction (0.57-0.65 on-axis), and R_B is the total background rate per SIXA pixel. Results are shown in Figure 69 for a range of background rates.