SPI background models¶

The instrumental background in INTEGRAL/SPI data is modelled by so-called templates that describe the variation of the background rates with time:

\[M(p',E',t') = \sum_{i=0}^{N-1} n_i(d',E',t') \times {\rm TPL}_i(d',E',t')\]

where \(M(p',E',t')\) is given in units of \({\rm events} \,\, {\rm s}^{-1} {\rm MeV}^{-1} {\rm sr}^{-1}\). \(d'\) is the SPI detector identifier, \(E'\) is the measured energy, and \(t'\) is the time that is linked via the pointing of the SPI telescope to an area of the sky.

\({\rm TPL}_i(d',E',t')\) is the \(i\) th out of \(N\) templates, and \(n_i(d',E',t')\) is a normalisation factor for this template that may depend on the SPI detector identifier, measured energy and time.

Creating a background model¶

Since the number of background normalisation factors for INTEGRAL/SPI data analysis may be large, it is not recommenced to create a model definition XML file directly, but to use the gammalib.GSPIModelDataSpace() constructor in a Python script to set up the background model. The gammalib.GSPIModelDataSpace() constructor takes four arguments:

a SPI observation group
the name you want to give to the model component
a fit method that should be used for the model component
an index that refers to the template that should be used for the model component

In the example below it is assumed that three background templates were generated using the Off-line Scientific Analysis (OSA) task spi_obs_back, which appends the templates to the SPI observation group og_spi.fits. The first template corresponds to the saturated event rates in the Germanium detectors, the second is a constant rate template, and the third corresponds to a linearly increasing rate with time.

# Load SPI observation
og = gammalib.GSPIObservation('og_spi.fits')

# Set background model components
bgm_model_1 = gammalib.GSPIModelDataSpace(og, 'GEDSAT', 'orbit,dete', 0)
bgm_model_2 = gammalib.GSPIModelDataSpace(og, 'CONST',  'dete', 1)
bgm_model_3 = gammalib.GSPIModelDataSpace(og, 'TIME1',  'dete', 2)

# Append models
models = gammalib.GModels()
models.append(bgm_model_1)
models.append(bgm_model_2)
models.append(bgm_model_3)

# Save models
models.save('model_spi.xml')

For illustration, the typical content of the resulting XML file is as follows:

<source name="GEDSAT" type="DataSpace" instrument="SPI" method="orbit,dete" index="0">
  <parameter name="GEDSAT D000 O0019" value="1" scale="1" free="1"/>
  <parameter name="GEDSAT D001 O0019" value="1" scale="1" free="1"/>
  <parameter name="GEDSAT D002 O0019" value="1" scale="1" free="1"/>
  <parameter name="GEDSAT D003 O0019" value="1" scale="1" free="1"/>
  ...
  <parameter name="GEDSAT D016 O0139" value="1" scale="1" free="1"/>
  <parameter name="GEDSAT D017 O0139" value="1" scale="1" free="1"/>
  <parameter name="GEDSAT D018 O0139" value="1" scale="1" free="1"/>
</source>
<source name="CONST" type="DataSpace" instrument="SPI" method="dete" index="1">
  <parameter name="CONST D000" value="1" scale="1" free="1"/>
  <parameter name="CONST D001" value="1" scale="1" free="1"/>
  <parameter name="CONST D002" value="1" scale="1" free="1"/>
  <parameter name="CONST D003" value="1" scale="1" free="1"/>
  <parameter name="CONST D004" value="1" scale="1" free="1"/>
  <parameter name="CONST D005" value="1" scale="1" free="1"/>
  <parameter name="CONST D006" value="1" scale="1" free="1"/>
  <parameter name="CONST D007" value="1" scale="1" free="1"/>
  <parameter name="CONST D008" value="1" scale="1" free="1"/>
  <parameter name="CONST D009" value="1" scale="1" free="1"/>
  <parameter name="CONST D010" value="1" scale="1" free="1"/>
  <parameter name="CONST D011" value="1" scale="1" free="1"/>
  <parameter name="CONST D012" value="1" scale="1" free="1"/>
  <parameter name="CONST D013" value="1" scale="1" free="1"/>
  <parameter name="CONST D014" value="1" scale="1" free="1"/>
  <parameter name="CONST D015" value="1" scale="1" free="1"/>
  <parameter name="CONST D016" value="1" scale="1" free="1"/>
  <parameter name="CONST D017" value="1" scale="1" free="1"/>
  <parameter name="CONST D018" value="1" scale="1" free="1"/>
</source>
<source name="TIME1" type="DataSpace" instrument="SPI" method="dete" index="2">
  <parameter name="TIME1 D000" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D001" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D002" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D003" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D004" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D005" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D006" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D007" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D008" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D009" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D010" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D011" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D012" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D013" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D014" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D015" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D016" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D017" value="1" scale="1" free="1"/>
  <parameter name="TIME1 D018" value="1" scale="1" free="1"/>
</source>

Fit methods¶

The fit method defines how the indices of the SPI data space are grouped into template normalisation factors. Grouping is allowed in all three data space dimensions: for pointings, detectors and energies.

In the example above, individual background normalisation factors for the GEDSAT template were assigned to each orbit and detector, while for the CONST and TIME1 template there is one normalisation factor per detector. Here some further examples:

orbit,dete,gedfail: one normalisation factor per orbit and detector and Germanium detector failure period
orbit,evtclass: one normalisation factor per orbit and event class
dete,ebin: one normalisation factor per detector and energy bin
gedanneal: one normalisation factor per Germanium detector annealing period

Pointing grouping¶

point¶

Assigns a template normalisation factor for each pointing.

orbit¶

Assigns a template normalisation factor for each orbit.

date¶

Assigns a template normalisation factor for each date interval. For example, date 4 hours assigns a normalisation factor for intervals of 4 hours, or date 1 month assigns a normalisation factor for intervals of one month. The following time units are supported: min, hour, day, week, month or year.

gedfail¶

Makes sure that there are different template normalisation factors before and after the failure of a Germanium detector. This method can either be used as a fit method, or can be used in combination with point, orbit, date and gedanneal.

gedanneal¶

Makes sure that there are different template normalisation factors before and after the Germanium detector annealing. This method can either be used as a fit method, or can be used in combination with point, orbit, date and gedfail.

Detector grouping¶

dete¶

Assigns a template normalisation factor for each detector.

evtclass¶

Assigns a template normalisation factor for event class. Event classes are either single detector events (SE), double detector events (ME2) or tripple detector events (ME3).

Energy grouping¶

ebin¶

Assigns a template normalisation factor for each energy bin.

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