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The minimum detectable count rate for the PSPC depends on the background count rate and the effective size of an unresolved source (i.e., it depends on the off-axis angle). The minimum detectable count rate, , can be estimated from the formula:
where is the required significance threshold (i.e., signal-to-noise), is the background count rate in the ``detection cell'', f is the fraction of the total source count included in the ``detection cell'', is the minimum number of photons required to constitute a detection and t is the integration time.
Note that the effective point response function of the PSPC depends on energy (cf., § 4.2.2 ) and hence on the spectrum of the considered source as well as the position of the source in the field of view. For the sensitivity calculations a circular detection cell of radius, an percent fraction of all source photons in the detect cell, a confidence level of detection as well as a minimum of number of 10 counts per source have been assumed. Because the PSPC background depends sensitively on energy (cf., § 7.8.2 ), two sets of calculations are given, one applicable to the total band (0.1 - 2.4 keV), the other to the hard band (0.4 - 2.4 keV) only, where the overall background is significantly reduced. In Figure 10.1 , the minimum detectable PSPC count rate is plotted as a function of exposure time for a low, medium and high level of mean detector background in the total band and hard band respectively. As is obvious from Figure 10.1 the PSPC becomes background-limited for exposure times around 10 ks depending on the background level (and the chosen detection cell size). However, the transition between the photon- and background limited regime is rather smooth; note that Figure 10.1 only applies to on-axis observations, for off-axis observations larger detect cell sizes and consequently larger background values must be used.