From: John E. Davis <davis_at_email.domain.hidden>
Date: Sun, 16 Nov 2003 14:25:28 -0500

As you probably know, a Chandra grating arf is created by using mkgarf
for each individual CCD and then summed together by, e.g., dmaddarf to
produce the final arf:

    A(E) = \sum_i A_i(E)                         (1)

This arf is related to the counts in the extracted spectrum C(h) and
the model s(E) via the standard formula:

    C(h) = T \int dE R(h,E) A(E) s(E)            (2)

Unfortunately, the above formalism works for weak sources using the
"std" kernel but does not work for the grating pileup kernel.

The validity of equation (1) for the std kernel is a result of the
linearity of the kernel, i.e., equation (2). Since the grating pileup
kernel is non-linear, individual CCD-dependent ARFs A_i must be used,

   C(h) = \sum_i K_i[A_i,R,s]  ,                 (3)

where K_i represents the CCD-dependent grating kernel, and the sum is
over the individual CCDs.

As a concrete example, suppose that I am interested in the MEG+1
spectrum, which falls on ACIS-S3, S4, and S5.  In isis, I load the pha
file for MEG+1 and then the 3 ccd-specific ARFs:

    d1 = load_data ("meg+1.pha");
    a1 = load_arf ("meg+1_s3.arf");
    a2 = load_arf ("meg+1_s4.arf");
    a3 = load_arf ("meg+1_s5.arf");

Now, where to I go from here?  I suppose that I can do:

    s = get_data (d1); s.value[*] = 0; s.err[*] = 0;
    d2 = define_counts (s);
    d3 = define_counts (s);
    assign_arf (a1, d1);
    assign_arf (a2, d2);
    assign_arf (a3, d3);
    set_kernel ([d1,d2,d3], "gpileup");
    () = combine_datasets ([d1,d2,d3]);

Will this work?  Is there a better way to do this?  I know that I can
probably load ccd-specific pha files C_i(h) and fit them jointly, but
that would require extra filtering by tgextract.  Also, I would have
to deal with the problem of low-counts for the parts of the spectra
near the chip gaps.  Using the summed pha file avoids this.

Incidently, I believe that the online help for combine_datasets has a
a couple of typos, e.g.,

    combine_datasets (1,2, weights);

should probably be

    combine_datasets ([1,2], weights);

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Received on Sun Nov 16 2003 - 15:24:35 EST

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