A Simple Approach to Correcting
Grating data for Pileup
Pileup is a highly non-linear effect that reduces the total counts selected for any specific grating order. Comparing the MEG and HEG spectra of the Crab pulsar shows what might happen. See also Dan Dewey's page on pileup in HETGS spectra. See the Proposers' Observatory Guide section 220.127.116.11 (particularly Fig. 8.14) for a detailed description of the effects of pileup in HETGS spectra. I use an empirical approach to apply a first-order correction for pileup that reduces the effect of the Ir-M edge to a tolerable level.
A simple correction factor is applied to the effective areas based on the observed count spectrum. The event list is binned in the spectral dimension at a wavelength interval corresponding to one ACIS pixel (which depends on the grating), giving Ci, the counts in wavelength bin i. The total number of frames, Nf, is determined from the observation length and the frametime (less the framestore transfer time), giving the rate, Ri = Ci/Nf, in counts/frame in any given wavelength bin. The effective area correction is then
A' = A exp(-a Ri) for an FI chip, or
A' = A exp(-b Ri - c Ri2 ) for a BI chip.
The coefficients a, b, and c were determined using an observation of XTE J1118-480 to be 7.5, 6.38, and 22.92. Note that the effective area is always reduced and that the correction factor drops rapidly with high count rates.
On a practical note, whenever there are few counts, the correction factor is discrete and the resultant correction factor will add noise. One way to avoid this problem is to use an averaging filter to determine the count rate for any given wavelength bin.
This approach has only been tested and seems to be effective for cases of mild to moderate pileup: rates less than about 0.1-0.2 count/frame/bin. For more extreme cases, a more detailed model is necessary. John Davis (davis at space.mit.edu) has developed an approach that may be effective when spectrum pileup is severe.
Last updated July 7, 2003