__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
8.2.1.4__ (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 C_{i}, the counts in wavelength bin i. The total number of frames,
N_{f}, is determined from the observation
length and the frametime (less the framestore transfer time), giving the
rate, R_{i} = C_{i}/N_{f}, in counts/frame in any given
wavelength bin. The effective area correction is then

A' = A exp(-a R_{i}) for an FI chip, or

A' = A exp(-b R_{i} - c
R_{i}^{2} ) 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.

__Back__

Herman Marshall

hermanm@space.mit.edu

Last updated July 7, 2003