FSSC: Fermi Data : Data Analysis : Analysis Threads : XML Model Definitions for Likelihood

XML Model Definitions for Likelihood

Below are example model definitions for Likelihood.

Spectral Models

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>

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>

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>

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>

SmoothBrokenPowerLaw

<source name="SmoothBrokenPowerLaw_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
<spectrum type="SmoothBrokenPowerLaw">
<parameter free="1" max="1e10" min="0.0" name="Prefactor" scale="1e-06" value="1.0"/>
<parameter free="1" max="-1.0" min="-5.0" name="Index1" scale="1.0" value="-2.0"/>
<parameter free="0" max="2000.0" min="30.0" name="Scale" scale="1.0" value="100.0"/>
<parameter free="1" max="-1.0" min="-5.0" name="Index2" scale="1.0" value="-2.0"/>
<parameter free="1" max="5e5" min="20" name="BreakValue" scale="1.0" value="1e3"/>
<parameter free="1" max="10" min="0.01" name="Beta" scale="1.0" value="0.2"/>
</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>

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>

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>

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>

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>

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>

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>

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>

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>

PLSuperExpCutoff2

<source name="PLSuperExpCutoff2_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
<spectrum type="PLSuperExpCutoff2">
<parameter free="1" max="1000" min="0" name="Prefactor" scale="1e-11" value="10.976"/>
<parameter free="1" max="5" min="-1.5" name="Index1" scale="1" value="-1.436"/>
<parameter free="0" max="1000" min="0.001" name="Scale" scale="1000" value="1"/>
<parameter free="1" max="1" min="-1" name="Expfactor" scale="1.0" value="0.001"/>
<parameter free="0" max="2" min="0" name="Index2" 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>

PLSuperExpCutoff3

<source name="PLSuperExpCutoff3_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
<spectrum type="PLSuperExpCutoff3">
<parameter free="1" max="1000" min="1e-5" name="Prefactor" scale="1e-11" value="1.0"/>
<parameter free="1" max="5" min="-1.5" name="IndexS" scale="1" value="-1.7"/>
<parameter free="0" max="1000" min="0.001" name="Scale" scale="1000" value="1"/>
<parameter free="1" max="10" min="0" name="Expfactor2" scale="1.0" value="2"/>
<parameter free="0" max="2" min="0" name="Index2" 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>

PLSuperExpCutoff4

<source name="PLSuperExpCutoff4_source" type="PointSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 -->
<spectrum type="PLSuperExpCutoff4">
<parameter free="1" max="1000" min="1e-5" name="Prefactor" scale="1e-11" value="1.0"/>
<parameter free="1" max="0" min="-5" name="IndexS" scale="1" value="-1.7"/>
<parameter free="0" max="1000" min="0.001" name="Scale" scale="1000" value="1"/>
<parameter free="1" max="5" min="0" name="ExpfactorS" scale="1.0" value="0.4"/>
<parameter free="0" max="2" min="-0.5" name="Index2" scale="1.0" value="0.66"/>
</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>

DMFitFunction

<source name="DM_Example" type="PointSource">
<spectrum file="$(BASE_DIR)/data/Likelihood/gammamc_dif.dat" type="DMFitFunction">
<parameter error="1." free="0" max="1.e+5" min="1.e-5" name="norm" scale="1.e+20" value="5.0" />
<parameter error="1." free="0" max="5000.0" min="0." name="sigmav" scale="1.e-26" value="3.0" />
<parameter error="1." free="0" max="5000.0" min="1." name="mass" scale="1.0" value="10"/>
<parameter error="0.1" free="0" max="1.0" min="0.0" name="bratio" scale="1.0" value="1"/>
<parameter free="0" max="10" min="1" name="channel0" scale="1.0" value="4"/>
<parameter free="0" max="10" min="1" name="channel1" scale="1.0" value="1"/>
</spectrum>
<spatialModel type="SkyDirFunction">
<parameter free="0" max="360" min="-360" name="RA" scale="1.0" value="128.8272"/>
<parameter free="0" max="90" min="-90" name="DEC" scale="1.0" value="-45.1762"/>
</spatialModel>
</source>

Spatial Models

To use an extended spatial model such as SpatialMap or MapCubeFunction with Unbinned Likelihood or Binned Likelihood, one must include the map_based_integral attribute in the spatialModel portion of the XML model definition. This attribute is not recommended for all-sky models (e.g. interstellar emission models) because it is too computationally intensive and provides no obvious improvements. An example is provided below:

SpatialMap

<source name="SpatialMap_source" type="DiffuseSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 sr^-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 file="$(PATH_TO_FILE)/SpatialMap_source.fits" type="SpatialMap"  map_based_integral="true">
<parameter free="0" max="1000.0" min="0.001" name="Prefactor" scale= "1.0" value="1.0"/>
</spatialModel>
</source>

MapCubeFunction

<source name="MapCubeFunction_source" type="DiffuseSource">
<!-- point source units are cm^-2 s^-1 MeV^-1 sr^-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 file="$(PATH_TO_FILES)/MapCubeFunction_source.fits" type="SpatialMap"  map_based_integral="true">
<parameter free="0" max="1000.0" min="0.001" name="Normalization" scale= "1.0" value="1.0"/>
</spatialModel>
</source>

Radial Models

Users can now model individual sources with RadialDisk or RadialGaussian models. An example is provided below:

RadialDisk

<spatialModel type="RadialDisk">
<parameter free="0" max="10" min="0" name="Radius" scale="1" value="0.2" />
<parameter free="0" max="360" min="-360" name="RA" scale="1" value="166.1138" />
<parameter free="0" max="90" min="-90" name="DEC" scale="1" value="38.2088" />
</spatialModel>

RadialGaussian

<spatialModel type="RadialGaussian">
<parameter free="0" max="10" min="0" name="Sigma" scale="1" value="0.2" />
    <parameter free="0" max="360" min="-360" name="RA" scale="1" value="166.1138" />
    <parameter free="0" max="90" min="-90" name="DEC" scale="1" value="38.2088" />
</spatialModel>

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