Connecting observations to specific models

In the previous examples there was always a single background model component to describe the residual particle background in the various dataset. This implies that the spatial and spectral shape of the background distribution is assumed to be identical for all observations. This is fine in a simulation, but for a real life situation this assumption will probably not hold.

Let’s go back to the case of a joint analysis of two observations, specified by the following observation definition XML file:

<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
  <observation name="Crab" id="00001" instrument="CTA">
    <parameter name="EventList" file="events1.fits"/>
  </observation>
  <observation name="Crab" id="00002" instrument="CTA">
    <parameter name="EventList" file="events2.fits"/>
  </observation>
</observation_list>

Each observation has a unique identifier string and you can use this unique string to connect an observation to a specific model component. This is illustrated in the model XML file below that now has two background components. Both components have an id attribute that ties the model to a specific observation. Using id="00001", the first background model is tied to the events1.fits file, using id="00002", the second background model is tied to the events2.fits file.

<?xml version="1.0" standalone="no"?>
<source_library title="source library">
  <source name="Crab" type="PointSource">
    <spectrum type="PowerLaw">
       <parameter name="Prefactor" scale="1e-16" value="5.7"  min="1e-07" max="1000.0" free="1"/>
       <parameter name="Index"     scale="-1"    value="2.48" min="0.0"   max="+5.0"   free="1"/>
       <parameter name="Scale"     scale="1e6"   value="0.3"  min="0.01"  max="1000.0" free="0"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter name="RA"  scale="1.0" value="83.6331" min="-360" max="360" free="0"/>
      <parameter name="DEC" scale="1.0" value="22.0145" min="-90"  max="90"  free="0"/>
    </spatialModel>
  </source>
  <source name="Background_00001" type="CTAIrfBackground" instrument="CTA" id="00001">
    <spectrum type="PowerLaw">
      <parameter name="Prefactor" scale="1.0"  value="1.0"  min="1e-3" max="1e+3"   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>
  <source name="Background_00002" type="CTAIrfBackground" instrument="CTA" id="00002">
    <spectrum type="PowerLaw">
      <parameter name="Prefactor" scale="1.0"  value="10.0"  min="1e-3" max="1e+3"   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>
</source_library>

Note

Model components in a XML file need to have a unique name. For this reason the components are named here Background_00001 and Background_00002.

Note that both background model components distinguish in their event rate. Background_00002 has a ten times larger background rate than Background_00001. To illustrate this difference, two observations offset by +/- 2 degrees from the Crab nebulae have been simulated using ctobssim. A joint fit of the observations is then performed using ctlike and a residual map is created using csresmap.

The result is shown below. Obviously, the upper observation has larger residuals owing to the ten times larger background rate that was used in the simulation of the associated data.

Residual map of two jointly analysed observations offset by +/- 2 degrees

The scheme is even more versatile in that it allows to connect a given model component to several specific observations. This is illustrated in the model definition file below where component Background_00001 is now applicable for observations 00001, 00003 and 00004.

<?xml version="1.0" standalone="no"?>
<source_library title="source library">
  <source name="Crab" type="PointSource">
    <spectrum type="PowerLaw">
       <parameter name="Prefactor" scale="1e-16" value="5.7"  min="1e-07" max="1000.0" free="1"/>
       <parameter name="Index"     scale="-1"    value="2.48" min="0.0"   max="+5.0"   free="1"/>
       <parameter name="Scale"     scale="1e6"   value="0.3"  min="0.01"  max="1000.0" free="0"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter name="RA"  scale="1.0" value="83.6331" min="-360" max="360" free="0"/>
      <parameter name="DEC" scale="1.0" value="22.0145" min="-90"  max="90"  free="0"/>
    </spatialModel>
  </source>
  <source name="Background_00001" type="CTAIrfBackground" instrument="CTA" id="00001,00003,00004">
    <spectrum type="PowerLaw">
      <parameter name="Prefactor" scale="1.0"  value="1.0"  min="1e-3" max="1e+3"   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>
  <source name="Background_00002" type="CTAIrfBackground" instrument="CTA" id="00002">
    <spectrum type="PowerLaw">
      <parameter name="Prefactor" scale="1.0"  value="10.0"  min="1e-3" max="1e+3"   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>
</source_library>