The faint limit of the Hubble Space Telescope faint object spectrograph and rejection of the cosmic-ray background
The faintest object which can be observed with the Hubble Space Telescope (HST) Faint Object Spectrograph (FOS) is set by the detector cosmic-ray background and not by object flux. We use data from Beaver and Lyons to show that 48% of the background counts are from cosmic rays which each generate a near instantaneous burst of two or more counts. Setting the FOS threshold parameter REJLIM = 1, which rejects all frames with more than one count increases the ratio of signal-to-dark counts (S/D) by a factor of 1.94, regardless of the frame time or the object signal, because half of the dark counts which arrive in single counts (from either cosmic-ray bursts or thermal dark current photoemission) are rejected at the same rate as the object signal. But the signal-to-noise ratio (SNR proportional to S/square root of S + D) increases by at most a factor of 1.35, and for realistic parameters and taking into account dead time, we expect a gain in SNR of only 1.18. If a diode has failed and now emits noise, no data at all will be recorded. The chance of this occurring is approximately = 10% , and for this reason we do not recommend the use of REJLIM. The two-point correlation function of dark counts per pixel has strong peaks every four pixels, caused by the action of quarter-stepping on the counts from large bursts. The counts from such bursts spread over at least 80-100 diodes, and we show that such bursts can be rejected during data reduction if the data are recorded in RAPID mode with individual exposures of about 35 seconds. The SNR of the spectrum can also be improved by weighting each exposure by its SNR (a function ofthe mean dark count rate at that time), since dark varies by a factor of 2 around an orbit. These two procedures together increase the SNR by a factor of 1.1.3 (a 28% gain in exposure time) in regions of a spectrum where the object is much fainter than the background. We find that the Ly-alpha and O I sky emission lines give at most 4 (counts/array/s/sq arcsec), and typically half this number. With a small frame time and a small entrance aperture, these counts cause REJLIM = 1 to reject only a few percent of the data. We discuss only the HST FOS blue side detector, but the same ideas apply to any photon counter which records bursts of noise, and the calculations resemble those for the loss of signal due to coincidences in photon counters. In the ideal photon counter the dark counts are readily distinguished from photons. One way to do this is to add detectors which records only dark current, so that every cosmic ray produces more than one count and the instrument can be operated in an anti-coincidence mode.