Modelling CTA background¶

The standard method for modelling the CTA instrumental background makes use of background rate information that is included in the instrument response functions. For unbinned or binned analysis the background model is implemented by the GCTAModelIrfBackground class that derives from the abstract GModelData class. The XML description of the background model has the following format:

<source name="Background" type="CTAIrfBackground" instrument="CTA">
  <spectrum type="PowerLaw">
    <parameter name="Prefactor" scale="1.0" value="1.0" min="1e-3" max="1e3"    free="1"/>
    <parameter name="Index"     scale="1.0" value="0.0" min="-5.0" max="+5.0"   free="1"/>
    <parameter name="Scale"     scale="1e6" value="1.0" min="0.01" max="1000.0" free="0"/>
  </spectrum>
</source>

The type of the model is CTAIrfBackground. The tag <spectrum> allows to specify a spectral model with which the background model in the IRF will be multiplied. Any spectral model available in GammaLib can be used as the spectral component of the model. This allows to adjust the energy distribution of the background template to the data. In the above example the background rates are multiplied with a power law.

Note

In case that no background information is available in the instrument response function a first order background model can be obtained by using the effective area as a spatial template for the background. The XML model description has the following format:

<source name="Background" type="CTAAeffBackground" instrument="CTA">
  <spectrum type="PowerLaw">
    <parameter name="Prefactor" scale="1e-14" value="1.0"  min="1e-3" max="1e3"    free="1"/>
    <parameter name="Index"     scale="1.0"   value="-2.4" min="-5.0" max="+5.0"   free="1"/>
    <parameter name="Scale"     scale="1e6"   value="1.0"  min="0.01" max="1000.0" free="0"/>
  </spectrum>
</source>

For stacked analysis there is an equivalent model that makes use of the background model provided in the BkgCube parameter of the observation definition XML file:

<source name="Background" type="CTACubeBackground" instrument="CTA">
  <spectrum type="PowerLaw">
    <parameter name="Prefactor" scale="1.0" value="1.0" min="1e-3" max="1e3"    free="1"/>
    <parameter name="Index"     scale="1.0" value="0.0" min="-5.0" max="+5.0"   free="1"/>
    <parameter name="Scale"     scale="1e6" value="1.0" min="0.01" max="1000.0" free="0"/>
  </spectrum>
</source>

The structure of the XML model is identical to the one shown before, but the type of the model is now CTACubeBackground.

Another type of background model exists that assumes that the spatial and spectral component of the background can be factorised and that the spatial component is radially symmetric. This background model is rather simplistic, and is mainly still there for historic reasons. Here an example of the XML definition. The type of the model is RadialAcceptance.

<source name="Background" type="RadialAcceptance" instrument="CTA">
  <spectrum type="PowerLaw">
    <parameter name="Prefactor" scale="1e-6" value="61.8" min="0.0"  max="1000.0" free="1"/>
    <parameter name="Index"     scale="-1"   value="1.85" min="0.0"  max="+5.0"   free="1"/>
    <parameter name="Scale"     scale="1e6"  value="1.0"  min="0.01" max="1000.0" free="0"/>
  </spectrum>
  <radialModel type="Gaussian">
    <parameter name="Sigma" scale="1.0" value="3.0" min="0.01" max="10.0" free="1"/>
  </radialModel>
</source>

The spatial component of the model is a Gaussian in offset angle squared. Alternativly, a profile can be specified:

<source name="Background" type="RadialAcceptance" instrument="CTA">
  <spectrum type="PowerLaw">
    <parameter name="Prefactor" scale="1e-6" value="61.8" min="0.0"  max="1000.0" free="1"/>
    <parameter name="Index"     scale="-1"   value="1.85" min="0.0"  max="+5.0"   free="1"/>
    <parameter name="Scale"     scale="1e6"  value="1.0"  min="0.01" max="1000.0" free="0"/>
  </spectrum>
  <radialModel type="Profile">
    <parameter name="Width" scale="1.0" value="1.5" min="0.1" max="1000.0" free="1"/>
    <parameter name="Core"  scale="1.0" value="3.0" min="0.1" max="1000.0" free="1"/>
    <parameter name="Tail"  scale="1.0" value="5.0" min="0.1" max="1000.0" free="1"/>
  </radialModel>
</source>

Or a polynom:

<source name="Background" type="RadialAcceptance" instrument="CTA">
  <spectrum type="PowerLaw">
    <parameter name="Prefactor" scale="1e-6" value="61.8" min="0.0"  max="1000.0" free="1"/>
    <parameter name="Index"     scale="-1"   value="1.85" min="0.0"  max="+5.0"   free="1"/>
    <parameter name="Scale"     scale="1e6"  value="1.0"  min="0.01" max="1000.0" free="0"/>
  </spectrum>
  <radialModel type="Polynom">
    <parameter name="Coeff0" scale="1.0" value="+1.00000"   min="-10.0" max="10.0" free="0"/>
    <parameter name="Coeff1" scale="1.0" value="-0.1239176" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff2" scale="1.0" value="+0.9751791" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff3" scale="1.0" value="-3.0584577" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff4" scale="1.0" value="+2.9089535" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff5" scale="1.0" value="-1.3535372" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff6" scale="1.0" value="+0.3413752" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff7" scale="1.0" value="-0.0449642" min="-10.0" max="10.0" free="1"/>
    <parameter name="Coeff8" scale="1.0" value="+0.0024321" min="-10.0" max="10.0" free="1"/>
  </radialModel>
</source>

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