How to compute the signifiance of a source?

What you will learn

You will learn how to compute the significance of a source detection using the ctlike tool.

To compute the detection significance of a given source you need to add the attribute tscalc="1" to the <source> tag in the model definition file and execute ctlike using the modified file. Copy the 1DC model definition file

$ cp $CTOOLS/share/models/1dc_howto.xml ts_model.xml

and modify the file by adding tscalc="1" to the <source> tag for source Src1. The first lines of the ts_model.xml model definition XML file should then look like this:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<source_library title="source library">
  <source name="Src001" type="PointSource" tscalc="1">
    <spectrum type="ExponentialCutoffPowerLaw">
      <parameter name="Prefactor"    scale="1e-18" 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="CutoffEnergy" scale="1e7"   value="1.0"  min="0.01"  max="1000.0" free="1"/>
      <parameter name="PivotEnergy"  scale="1e6"   value="0.3"  min="0.01"  max="1000.0" free="0"/>
    </spectrum>
    <spatialModel type="PointSource">
      <parameter name="RA"  scale="1" value="266.424" free="1" />
      <parameter name="DEC" scale="1" value="-29.005" free="1" />
    </spatialModel>
  </source>

Then run ctlike to compute the so-called Test Statistic, which is twice the difference between the log-likelihood value obtained for a fit that includes Src001 and a fit that excludes Src001. The Test Statistic value will follow a \(\chi^2_p\) distribution with \(p\) degrees of freedom, where \(p\) is the number of free parameters of Src001. For \(p=1\), the source significance is the square root of the Test Statistic.

$ ctlike
Input event list, counts cube or observation definition XML file [events.fits] cntcube.fits
Input exposure cube file [NONE] expcube.fits
Input PSF cube file [NONE] psfcube.fits
Input background cube file [NONE] bkgcube.fits
Input model definition XML file [$CTOOLS/share/models/crab.xml] ts_model.xml
Output model definition XML file [crab_results.xml] result.xml

An excerpt of the ctlike log file is shown below

2018-01-25T12:46:12: === GModelSky ===
2018-01-25T12:46:12:  Name ......................: Src001
2018-01-25T12:46:12:  Instruments ...............: all
2018-01-25T12:46:12:  Test Statistic ............: 7659.72844228207

The Test Statistic values are also written into the model definition file created by ctlike:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<source_library title="source library">
  <source name="Src001" type="PointSource" ts="7659.728" tscalc="1">
    ...
  </source>
  ...
</source_library>