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Here are example model definitions for Likelihood. Descriptions of the spectral models are described in the Workbook. See the Likelihood tutorial. An xml file containing these examples is attached.

Code Block

title	PowerLaw

  <source name="PowerLaw_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="PowerLaw">
      <parameter free="1" max="1000.0" min="0.001" name="Prefactor" scale="1e-09" value="1"/>
      <parameter free="1" max="-1.0" min="-5." name="Index" scale="1.0" value="-2.1"/>
      <parameter free="0" max="2000.0" min="30.0" name="Scale" scale="1.0" value="100.0"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	BrokenPowerLaw

  <source name="BrokenPowerLaw_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="BrokenPowerLaw">
      <parameter free="1" max="1000.0" min="0.001" name="Prefactor" scale="1e-09" value="1"/>
      <parameter free="1" max="-1.0" min="-5." name="Index1" scale="1.0" value="-1.8"/>
      <parameter free="1" max="2000.0" min="30.0" name="BreakValue" scale="1.0" value="1000.0"/>
      <parameter free="1" max="-1.0" min="-5." name="Index2" scale="1.0" value="-2.3"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	PowerLaw2

  <source name="PowerLaw2_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="PowerLaw2">
      <parameter free="1" max="1000.0" min="1e-05" name="Integral" scale="1e-06" value="1.0"/>
      <parameter free="1" max="-1.0" min="-5.0" name="Index" scale="1.0" value="-2.0"/>
      <parameter free="0" max="200000.0" min="20.0" name="LowerLimit" scale="1.0" value="20.0"/>
      <parameter free="0" max="200000.0" min="20.0" name="UpperLimit" scale="1.0" value="2e5"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	BrokenPowerLaw2

  <source name="BrokenPowerLaw2_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="BrokenPowerLaw2">
      <parameter free="1" max="1000.0" min="0.001" name="Integral" scale="1e-04" value="1.0"/>
      <parameter free="1" max="-1.0" min="-5.0" name="Index1" scale="1.0" value="-1.8"/>
      <parameter free="1" max="-1.0" min="-5.0" name="Index2" scale="1.0" value="-2.3"/>
      <parameter free="1" max="10000.0" min="30.0" name="BreakValue" scale="1.0" value="1000.0"/>
      <parameter free="0" max="200000.0" min="20.0" name="LowerLimit" scale="1.0" value="20.0"/>
      <parameter free="0" max="200000.0" min="20.0" name="UpperLimit" scale="1.0" value="2e5"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	LogParabola

  <source name="LogParabola_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="LogParabola">
      <parameter free="1" max="1000.0" min="0.001" name="norm" scale="1e-9" value="1"/>
      <parameter free="1" max="10" min="0" name="alpha" scale="1.0" value="1"/>
      <parameter free="1" max="1e4" min="20" name="Eb" scale="1" value="300."/>
      <parameter free="1" max="10" min="0" name="beta" scale="1.0" value="2"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	ExpCutoff

  <source name="ExpCutoff_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="ExpCutoff">
      <parameter free="1" max="100000.0" min="0.01" name="Prefactor" scale="1e-09" value="50"/>
      <parameter free="1" max="-1.0" min="-5." name="Index" scale="1.0" value="-2.1"/>
      <parameter free="0" max="2000.0" min="30.0" name="Scale" scale="1.0" value="100.0"/>
      <parameter free="1" max="300.0" min="1.0" name="Ebreak" scale="1.0" value="10.0"/>
      <parameter free="1" max="300.0" min="0.1" name="P1" scale="1000.0" value="100."/>
      <parameter free="0" max="1.0" min="-1.0" name="P2" scale="1.0" value="0"/>
      <parameter free="0" max="1.0" min="-1.0" name="P3" scale="1.0" value="0"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	BPLExpCutoff

  <source name="BPLExpCutoff_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="BPLExpCutoff">
      <parameter free="1" max="100000.0" min="0.01" name="Prefactor" scale="1e-09" value="1"/>
      <parameter free="1" max="-1.001" min="-5." name="Index1" scale="1.0" value="-2.1"/>
      <parameter free="1" max="-1.001" min="-5." name="Index2" scale="1.0" value="-2.1"/>
      <parameter free="1" max="10000.0" min="1.0" name="BreakValue" scale="1.0" value="1000.0"/>
      <parameter free="1" max="300.0" min="1.0" name="Eabs" scale="1.0" value="10.0"/>
      <parameter free="1" max="300.0" min="0.1" name="P1" scale="1000.0" value="100."/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	Gaussian

  <source name="Gaussian_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="Gaussian">
      <parameter free="1" max="1000.0" min="0.001" name="Prefactor" scale="1e-09" value="1"/>
      <parameter free="1" max="1e5" min="1e3" name="Mean" scale="1.0" value="7e4"/>
      <parameter free="1" max="30" min="1e4" name="Sigma" scale="1.0" value="1e3"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	ConstantValue

  <source name="ConstantValue_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="ConstantValue">
      <parameter free="0" max="10" min="0" name="Value" scale="1" value="1"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	FileFunction

  <source name="FileFunction_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum file="foo.dat" type="FileFunction">
      <parameter free="1" max="1e5" min="1e-5" name="Normalization" scale="1" value="1.0"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	BandFunction

  <source name="BandFunction_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="BandFunction">
      <parameter free="1" max="1000.0" min="1e-05" name="norm" scale="1e-09" value="1.0"/>
      <parameter free="1" max="-1.0" min="-5.0" name="alpha" scale="1.0" value="-1.8"/>
      <parameter free="1" max="-1.0" min="-5.0" name="beta" scale="1.0" value="-2.5"/>
      <parameter free="1" max="-1.0" min="-5.0" name="Ep" scale="1." value="0.1"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

Code Block

title	PLSuperExpCutoff

  <source name="PLSuperExpCutoff_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
    <spectrum type="PLSuperExpCutoff">
      <parameter free="1" max="1000" min="1e-05" name="Prefactor" scale="1e-07" value="1"/>
      <parameter free="1" max="0" min="-5" name="Index1" scale="1" value="-1.7"/>
      <parameter free="0" max="1000" min="50" name="Scale" scale="1" value="200"/>
      <parameter free="1" max="30000" min="500" name="Cutoff" scale="1" value="3000"/>
      <parameter free="1" max="5" min="0" name="Index2" scale="1" value="1.5"/>
    </spectrum>
    <spatialModel type="SkyDirFunction">
      <parameter free="0" max="360." min="-360." name="RA" scale="1.0" value="83.45"/>
      <parameter free="0" max="90." min="-90." name="DEC" scale="1.0" value="21.72"/>
    </spatialModel>
  </source>

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