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 Telesc ope (HST) Faint Object Spectrograph (FOS) is set by the detector cosmi c-ray background and not by object flux. We use data from Beaver and L yons to show that 48% of the background counts are from cosmic rays wh ich each generate a near instantaneous burst of two or more counts. Se tting the FOS threshold parameter REJLIM = 1, which rejects all frames with more than one count, increases the ratio of signal-to-dark count s (S/D) by a factor of 1.94, regardless of the frame time or the objec t signal, because the half of the dark counts which arrive in single c ounts (from either cosmic-ray bursts or thermal dark current photoemis sion) are rejected at the same rate as the object signal. But the sign al-to-noise ratio (SNR infinity S/square-root S + D) increases by at m ost a factor of 1.35, and for realistic parameters and taking into acc ount dead time, we expect a gain in SNR of only 1.18. If a diode has f ailed and now emits noise, no data at all will be recorded. The chance of this occurring is congruent-to 10%, and for this reason we do not recommend the use of REJLIM. The two-point correlation function of dar k counts per pixel has strong peaks every four pixels, caused by the a ction 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 reco rded 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 of the mean dark count rate at that time), since dark varies by a factor of 2 around an orbit. These two procedures tog ether increase the SNR by a factor of 1.13 (a 28% gain in exposure tim e) in regions of a spectrum where the object is much fainter than the background. We find that the Lyalpha and O I sky emission lines give a t most 4 (counts array-1 s-2), and typically half this number. With a small frame time and a small entrance aperture, these counts cause REJ LIM = 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 cou nter which records bursts of noise, and the calculations resemble thos e for the loss of signal due to coincidences in photon counters. In th e ideal photon counter the dark counts are readily distinguished from photons. One way to do this is to add detectors which record only dark current, so that every cosmic ray produces more than one count, and t he instrument can be operated in an anti-coincidence mode.