The present recommended algorithm to fit HRC-S/LETG spectra appears to
be a "bootstrap" approach, which is necessitated by spatially
overlapping orders of the LETG and the HRC's lack of spectral
reslution, to be able to separate orders. In "bootstrapping", one
fits a spectral model (such as a power-law) at high energies (for
example, 2-6 keV), where the spectrum is dominated by the 1st order;
one extrapolates this model to lower energies, down to where the 1st
and 2nd order dominate the counts, subtracting the 1st order spectrum
from the observed spectrum. One then fits the 2nd order spectrum down
to an energy where the third order contributes counts, extrapolates,
and subtraccts; and again, for the third order. The first three
orders are the only orders for which there are presently rmf files.
This approach requires iteration if the spectral model at high
energies does not describe the spectrum at low energies (for example:
if there is galactic absorption which is important only below 1 keV,
or if there is a kT=0.75 keV thermal component). In the absence of a
tool to peform these iterations, this can be unpleasent.
Unpleasantness might be particularly accute when the source is
domianted by continuum, rather than lines.
I'm wondering if there is not an easier approach, which would require
re-calculated (and re-assigned) rmf and arf files.
In this approach, one includes the quantum efficiency not in the arf
file, but in the rmf file. For example the number of counts detected
at some off-axis angle \theta\ is a function of the input energy
spectrum I (itself a function of the photon energy E_i), the HRMA
energy-dependent Area A, the redistribution matrix R(E_i, \theta),
which includes redistribution to 1st, 2nd, 3rd and higher orders, and
the detecter quantum efficiency QE (I've ignored vignetting, assuming
on-axis source for now):
C(\theta)= \int I(E_i) A(E_i) R(E_i, \theta) QE (E_i) dE_i
Presently, QE(E_i) is included with A(E_i) in producing the arf file.
If, instead, one included QE(E_i) with R(E_i, \theta) in producing the
rmf file, and removed the QE part from the arf file, then one could
otherwise use the presently existing sherpa and XSPEC fitting packages
to fit a spectrum -- without bootstrapping. One could then use
standard chi-sqr minimization approaches to fit a spectrum.
The only difficulty I see with this scheme is potential
non-linearities in fitting spectra which have non-local counts in the
RMF. Even so, this approach seems to be more user-friendly than
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