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:

\[M(p',E') = {\rm DRB}(\chi, \psi, \bar{\varphi} | E')\]

where \(M(p',E')\) is given in units of \({\rm events} \,\, {\rm s}^{-1} {\rm MeV}^{-1} {\rm sr}^{-1}\). \((\chi, \psi)\) is the photon scatter direction while \(\bar{\varphi}\) 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 \(\bar{\varphi}\)-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 \(\bar{\varphi}\)-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 \(\bar{\varphi}\)-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 \(\bar{\varphi}\) values below 16 degrees were fixed, the first fitted normalisation is for \(\bar{\varphi}\) = 17 degrees.