ONe or two words on this:
The "fitting approach" for LETG+HRC-S has always been to model all the
orders at once. Bootstrapping has been mentioned in proposers' guides
as a possible approach to extracting an individual order spectrum, but
has not been slated for development in CXC software. Bootstrapping is in
principle possible for sources that have spectra that are smooth on the
scale of the instrument higher order resolution, provided the different
order effective areas are known to an accuracy that does not compound
bootstrap undertainties catastrophically. For line sources, the
problem can become intractable because of increasing resolution in
higher orders and subsequent lack of information in the 1st order
spectrum.
The hold up on the process of doing full-blown fitting
for LETG+HRC-S including all the orders at once in CIAO involves
getting the appropriate response matrices and getting fitting software
to be able to handle them. There are two possible ways to go:
1/ get SHERPA to be able to handle multiple instrument responses for the
same data set and add them up. Then the response is a sum of all the
ARF1*RMF1 + ARF2*RMF2 ... (where * is the convolution).
2/ Be able to combine the ARF1*RMF1 + ARF2*RMF2 ... into a single
response that (I think) existing SHERPA might be able to handle.
[its a bit more complicated than just taking a QE into the RMF - eg the
different grating order efficiencies vs E and QE spatial
non-uniformities need to be included].
A technical hang-up for both 1 & 2 is that the higher order RMF's that
exist for LETG are problematic and need to be re-made. A Problem for
approach 2 is that, as I understand, there is no software
in house (CXC) to combine easily ARF1*RMF1 + ARF2*RMF2 ... into a
single ARF+RMF, though I think the SDS group are working on this.
SHERPA folk could provide more details, but I understand that they
already have had the handling of multiple instrument response models in the
plan for some time.
Jeremy Drake
------- Forwarded Message
Date: Thu, 25 Jan 2001 14:54:41 -0800
From: Bob Rutledge <rutledge@srl.caltech.edu>
To: chandra-users@head-cfa.harvard.edu
Subject: LETG/HRC rmf and arf files and spectral fitting
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
bootstrapping.
Bob Rutledge
------- End of Forwarded Message
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