4 SXC sensitivity and localization precision

A simplified expression for the signal-to-noise ratio for a coded-aperture system with minimal slant-ray blur ([Doty 1988]) is

$$S/N = \frac{S}{\sqrt{S + \frac{f}{1-f}B}},$$ (1)

where S is the source strength, B is the contribution of the diffuse X-ray background, and f is the open fraction of the aperture. We estimate that the sensitivity of a pair of SXC modules is 520t^-0.5 mCrab for an E^-2 photon spectrum, where t is the integration time in seconds. Because HETE is always anti-solar pointing, long exposures of detected burst sources will be possible. However, most X-ray afterglows decay much more quickly than t^-1/2. Given the time histories of afterglows seen to date, we realistically expect to be able to detect most afterglows up to 100-200 seconds after burst onset.

The accuracy with which the SXC system can localize the X-ray counterpart to a GRB depends on both systematic and statistical errors. The statistical contribution to the localization precision can be estimated by the intrinsic pixel angular size (33'') over the signal-to-noise ratio of the peak in the correlation map. The SXC aspect should be precise to <5''. Sources of systematic error, including the non-parallelism of the mask slits and the CCD columns and any deformations in the mask, should be less than 10''. Using these estimates, the localization precision is strongly dominated by systematics: a 4$\sigma$ X-ray detection will be localized to 14'', while a 10$\sigma$ burst will be localized to 11'' (1$\sigma$ radius). There is a reasonable expectation that the mask/CCD alignment can be maintained to better than 5 $\mu$m, which would reduce that contribution to the blur budget to $\sim$5 $\mu$m: the resulting localization precisions would then be 12'' and 8'', for the 4$\sigma$ and 10$\sigma$ cases.

Acknowledgements

The HETE program is supported by NASA Contract NASW-4690.