Derive upper flux limits

What you will learn

You will learn how to use ctulimit to determine upper flux limits from Fermi-LAT data using a likelihood profile method.

Suppose there is another potential source in the field of view but you cannot see this source in a counts map, hence you want to derive an upper flux limit for the source. To do this you first have to add an additional source to the model definition file. An example for a source at \(\alpha=122^\circ\) and \(\delta=-42^\circ\) is shown below:

<?xml version="1.0" standalone="no"?>
<source_library title="source library">
  <source type="PointSource" name="Test">
    <spectrum type="PowerLaw">
      <parameter name="PhotonFlux" scale="1e-12" value="1.0"      min="1e-07" max="1e+07"     free="1"/>
      <parameter name="Index"      scale="1.0"   value="-2.0"     min="-5.0"  max="+5.0"      free="0"/>
      <parameter name="LowerLimit" scale="1.0"   value="100.0"    min="10.0"  max="1000000.0" free="0"/>
      <parameter name="UpperLimit" scale="1.0"   value="100000.0" min="10.0"  max="1000000.0" free="0"/>
    </spectrum>
    <spatialModel type="PointSource">
      <parameter name="RA"  scale="1.0" value="122.00" min="-360" max="360" free="0"/>
      <parameter name="DEC" scale="1.0" value="-42.00" min="-90"  max="90"  free="0"/>
    </spatialModel>
  </source>
  <source type="PointSource" name="Vela">
  ...
</source_library>

Now you can run the ctulimit tool. Since the tool is normally tuned for Cherenkov Telescope data analysis, energies are by default given in TeV. To specify a reference energy of the differential flux limit of 1 GeV you need to provide the hidden parameter eref=0.001. You can also set the flux interval for the intergal flux computation to 100 MeV - 100 GeV by specifying emin=0.0001 emax=0.1 (all values are given in TeV):

$ ctulimit eref=0.001 emin=0.0001 emax=0.1
Input event list, counts cube or observation definition XML file [events.fits] obs.xml
Source of interest [Crab] Test
Input model definition XML file [$CTOOLS/share/models/crab.xml] models_ulimit.xml

The results of the upper limit computation can then be extracted from the ctulimit.log file that is created by ctulimit:

2019-04-04T15:03:22: +=====================+
2019-04-04T15:03:22: | Upper limit results |
2019-04-04T15:03:22: +=====================+
2019-04-04T15:03:22:  Differential flux limit ...: 1.77270316013682e-13 ph/cm2/s/MeV at 0.001 TeV
2019-04-04T15:03:22:  Integral flux limit .......: 1.77093045697669e-09 ph/cm2/s within [0.0001-0.1] TeV
2019-04-04T15:03:22:  Energy flux limit .........: 1.96192914922622e-12 erg/cm2/s within [0.0001-0.1] TeV