Pre-computing the binned response

What you will learn

You will learn how to compute the instrument response for a counts cube. Pre-computing the instrument response will speed-up the model fitting later.

To speed-up the model fitting it is recommended to pre-compute the instrument response for the counts cube. Specifically, you should compute an exposure cube, a point spread function cube and a background cube.

The exposure cube is computed using the ctexpcube tool and provides the effective area multiplied by the livetime of the observation. You run ctexpcube as follows:

$ ctexpcube
Input event list or observation definition XML file [NONE] selected_events.fits
Calibration database [prod2]
Instrument response function [South_0.5h]
Input counts cube file to extract exposure cube definition [NONE] cntcube.fits
Output exposure cube file [expcube.fits]

This produces the FITS file expcube.fits that contains the exposure as function of sky position and energy. In the example above you extracted the binning of the exposure cube from the counts cube, which considerably reduces the number of parameters that are queried by the tool.

Note

The binning of the exposure cube does not need to correspond to the binning of the counts cube. In any case, exposure values will be determined by interpolation from the values stored in the exposure cube file. The same is true for the point spread function and background cubes that are described below.

Next, we use the ctpsfcube tool to compute the point spread function (PSF) cube for the counts cube. You run ctpsfcube as follows:

$ ctpsfcube
Input event list or observation definition XML file [NONE] selected_events.fits
Calibration database [prod2]
Instrument response function [South_0.5h]
Input counts cube file to extract PSF cube definition [NONE]
Coordinate system (CEL - celestial, GAL - galactic) (CEL|GAL) [CEL]
Projection method (AIT|AZP|CAR|GLS|MER|MOL|SFL|SIN|STG|TAN) [CAR]
First coordinate of image center in degrees (RA or galactic l) (0-360) [83.63]
Second coordinate of image center in degrees (DEC or galactic b) (-90-90) [22.51]
Image scale (in degrees/pixel) [1.0]
Size of the X axis in pixels [10]
Size of the Y axis in pixels [10]
Algorithm for defining energy bins (FILE|LIN|LOG|POW) [LOG]
Lower energy limit (TeV) [0.1]
Upper energy limit (TeV) [100.0]
Number of energy bins (1-1000) [20]
Output PSF cube file [psfcube.fits]

This produces the FITS file psfcube.fits that contains the point spread function as function of sky position and energy. You may have noted in the example that the definiton of the point spread function cube has not been extracted from the counts cube, since this would lead to a large FITS file on output. The point spread function varies in fact only slowly over the field of view of the camera, and consequently it is sufficient to sample that variation at a large spatial scale of typically one degree.

Finally, we use the ctbkgcube tool to compute the background cube. You run ctbkgcube as follows:

$ ctbkgcube
Input event list or observation definition XML file [NONE] selected_events.fits
Calibration database [prod2]
Instrument response function [South_0.5h]
Input counts cube file to extract background cube definition [NONE] cntcube.fits
Input model definition XML file [NONE] $CTOOLS/share/models/crab.xml
Output background cube file [bkgcube.fits]
Output model definition XML file [NONE] models.xml

This produces the FITS file bkgcube.fits that contains the predicted background rate as function of sky position and energy. The tool also produces the model definition file models.xml on output that will serve as input for the maximum likelihood analysis that will follow. The file is a copy of the input model definition file $CTOOLS/share/models/crab.xml where the input background model has been replaced by a background model of type CTACubeBackground. Below is the content of the models.xml file:

<?xml version="1.0" encoding="UTF-8" standalone="no"?>
<source_library title="source library">
  <source name="Crab" type="PointSource">
    <spectrum type="PowerLaw">
      <parameter name="Prefactor" value="5.7" error="0" scale="1e-16" min="1e-07" max="1000" free="1" />
      <parameter name="Index" value="2.48" error="0" scale="-1" min="0" max="5" free="1" />
      <parameter name="PivotEnergy" value="0.3" scale="1000000" min="0.01" max="1000" free="0" />
    </spectrum>
    <spatialModel type="PointSource">
      <parameter name="RA" value="83.6331" scale="1" min="-360" max="360" free="0" />
      <parameter name="DEC" value="22.0145" scale="1" min="-90" max="90" free="0" />
    </spatialModel>
  </source>
  <source name="BackgroundModel" type="CTACubeBackground" instrument="CTA,HESS,MAGIC,VERITAS">
    <spectrum type="PowerLaw">
      <parameter name="Prefactor" value="1" error="0" scale="1" min="0.01" max="100" free="1" />
      <parameter name="Index" value="0" error="0" scale="1" min="-5" max="5" free="1" />
      <parameter name="PivotEnergy" value="1" scale="1000000" free="0" />
    </spectrum>
  </source>
</source_library>