COMPTEL background models¶
The following section presents the model that is available in ctools for the modelling of instrumental background in COMPTEL data.
In general, the instrumental background in COMPTEL data for a given energy band E′ is specified by a so-called DRB cube:
where M(p′,E′) is given in units of eventss−1MeV−1sr−1. (χ,ψ) is the photon scatter direction while ˉφ is the Compton scattering angle.
DRB cubes¶
DRB cubes are specified as FITS files in the
observation definition file
using the DRB
parameter, e.g.
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="100001" instrument="COM">
<parameter name="DRE" file="m50438_dre.fits"/>
<parameter name="DRB" file="bgdlix_drb.fits"/>
<parameter name="DRG" file="m34997_drg.fits"/>
<parameter name="DRX" file="m32171_drx.fits"/>
<parameter name="IAQ" value="SIM2(0.75-1.00)MeV(2)deg"/>
</observation>
...
</observation_list>
DRB files are not provided by HEASARC. They may be generated from the data using the comobsback script.
DRB fitting¶
The usual way of handling the COMPTEL background model during a maximum likelihood
fit is to adjust the normalisation of each ˉφ-layer of the
DRB cube to the data. This is accomplished by using the DRBPhibarBins
model.
Below is an example model definition file for this
model.
<source name="Background(0.75-1.0)MeV" type="DRBPhibarBins" instrument="COM" id="100001">
<parameter name="Normalization" value="1" scale="1" min="0" max="1000" free="0" />
<parameter name="Normalization" value="1" scale="1" min="0" max="1000" free="0" />
<parameter name="Normalization" value="1" scale="1" min="0" max="1000" free="0" />
<parameter name="Normalization" value="1" scale="1" min="0" max="1000" free="0" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
<parameter name="Normalization" value="1" error="0" scale="1" min="0" max="1000" free="1" />
</source>
Alternatively the DRBPhibarNodes
model may be used that linearly interpolates for
the background model normalisation for ˉφ-layer that are not present
in the model. Below is an example model definition file for this
model.
<source name="Background(0.75-1.0)MeV" type="DRBPhibarNodes" instrument="COM" id="100001">
<node>
<parameter name="Phibar" scale="1.0" value="1.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="3.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="5.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="7.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="9.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="11.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="13.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="15.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="0.0" min="0.0" max="1000.0" free="0"/>
</node>
<node>
<parameter name="Phibar" scale="1.0" value="17.0" min="0.0" max="50.0" free="0"/>
<parameter name="Normalization" scale="1.0" value="1.0" min="0.0" max="1000.0" free="1"/>
</node>
...
</source>
Warning
Depending on the energy band E′, a DRB cube may be empty for a number
of ˉφ-layers, which means that the corresponding
normalisation cannot be adjusted. To avoid warnings during the ctlike
model fit it is recommended to fix the Normalization
parameters of the
corresponding layers. In the first example above, the first four layers are
fixed. In the second example, all layers with ˉφ
values below 16 degrees were fixed, the first fitted normalisation
is for ˉφ = 17 degrees.