GammaLib

I added the class GCTAModelBackground to implement the general factorized CTA background model. The class does not full work so far, in particular the npred() and mc() methods need to be tested.

I added the class GCTAModelSpatial that implements the spatial part of the GCTAModelBackground model. To register all possible spatial components, a GCTAModelSpatialRegistry class was also added.

The GCTAModelRadial class now derives from GCTAModelSpatial. Still, the GCTAModelRadial::eval() and GCTAModelRadial::mc() methods need to be implemented so that the derived classes can also be used from the GCTAModelBackground class. All derived classes now also register to GCTAModelSpatialRegistry.

Finally, a unit test was added that test a XML file that is managed by GCTAModelBackground. The model type is CTABackground, the XML file is shown below. The unit test does not yet cover the test of the spatial part, that still needs to be implemented.

<?xml version="1.0" standalone="no"?>
<source_library title="source library">
  <source name="My model" type="CTABackground" 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="PivotEnergy" scale="1e6"  value="1.0"  min="0.01" max="1000.0" free="0"/>
    </spectrum>
    <spatialModel type="Gaussian">
       <parameter name="Sigma" scale="1.0" value="3.0" min="0.01" max="10.0" free="1"/>
    </spatialModel>
  </source>
</source_library>

I turns out that the H.E.S.S. data do not contain DETX and DETY information. I therefore added some code to GCTAEventList that computes the DETX and DETY information from the event direction using the pointing information. Note that DETX and DETY are defined in sky coordinates.

I also verified that the new GCTAModelBackground class produces the same result as the formal radial acceptance model. Now the code is ready for implementing more complex background models.

Note that the GCTAModelSpatial::npred method assumes that the RoI centre is the pointing direction. The same is by the way true for the GCTAModelAeffBackground and GCTAModelIrfBackground methods. At least some code should be added to these methods that throws an exception if the RoI centre is different.

I added a test to the npred() methods of GCTAModelAeffBackground, GCTAModelIrfBackground and GCTAModelBackground that verifies that the RoI centre is not significantly different from the pointing direction. In case of difference, an exception is thrown.

• GCTAModelSpatialMultiplicative implements a multiplicative spatial model, allowing to multiply spatial components to form a combined background model
• GCTAModelSpatialGradient implements a spatial gradient over the field of view

The XML format for these models is as follows:

<?xml version="1.0" standalone="no"?>
<source_library title="source library">
  <source name="My model" type="CTABackground" 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="PivotEnergy" scale="1e6"  value="1.0"  min="0.01" max="1000.0" free="0"/>
    </spectrum>
    <spatialModel type="Multiplicative">
      <spatialModel type="Gaussian">
        <parameter name="Sigma" scale="1.0" value="3.0" min="0.01" max="10.0" free="1"/>
      </spatialModel>
      <spatialModel type="Gradient">
        <parameter name="Grad_DETX" scale="1.0" value="0.0" min="-10.0" max="10.0" free="1"/>
        <parameter name="Grad_DETY" scale="1.0" value="0.0" min="-10.0" max="10.0" free="1"/>
      </spatialModel>
    </spatialModel>
  </source>
</source_library>

I tested this model on the H.E.S.S. data and it seems to describe quite nicely the background event distributions.

I added a new cscript called csbkgmodel that automatically generates background models of this format. The csbkgmodel allows to generate runwise background models, and it loops over each observation in an observation definition XML file and prefits the background model to the data. This is in particular necessary if the power law should be replaced by a node function, which seems necessary for HESS. For stability reasons, csbkgmodel first fits a power law, and then replaces the power law by a 8 nodes function and refits the new model. This procedure seems to result in quite stable results.

For the time being this is sufficient, hence close the issue.