So far the same instrument response function has been used for all observations in our analysis examples. You may have recognised that we always specified the calibration database prod2 and the instrument response function South_0.5h that are shipped with ctools. When combining multiple observations in a joint analysis you may however need to specify dedicated instrument response functions for the different observations.
Let’s simulate two observations of the Crab nebula, one done with the northern array and the other with the southern array:
$ ctobssim
RA of pointing (degrees) (0-360) [83.63]
Dec of pointing (degrees) (-90-90) [22.01] 21.51
Radius of FOV (degrees) (0-180) [5.0]
Start time (MET in s) [0.0]
End time (MET in s) [1800.0]
Lower energy limit (TeV) [0.1]
Upper energy limit (TeV) [100.0]
Calibration database [prod2]
Instrument response function [South_0.5h] North_0.5h
Input model XML file [$CTOOLS/share/models/crab.xml]
Output event data file or observation definition XML file [events.fits] north.fits
$ ctobssim
RA of pointing (degrees) (0-360) [83.63]
Dec of pointing (degrees) (-90-90) [21.51] 22.51
Radius of FOV (degrees) (0-180) [5.0]
Start time (MET in s) [0.0]
End time (MET in s) [1800.0]
Lower energy limit (TeV) [0.1]
Upper energy limit (TeV) [100.0]
Calibration database [prod2]
Instrument response function [North_0.5h] South_0.5h
Input model XML file [$CTOOLS/share/models/crab.xml]
Output event data file or observation definition XML file [north.fits] south.fits
You now need to combine the information about these two observations in an observation definition XML file:
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="EventList" file="north.fits"/>
<parameter name="Calibration" database="prod2" response="North_0.5h"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="EventList" file="south.fits"/>
<parameter name="Calibration" database="prod2" response="South_0.5h"/>
</observation>
</observation_list>
Each observation now has a Calibration parameter with the attributes database and response. To see which calibration databases and response functions are available on your system you can run the cscaldb script (use the debug=yes option to get the output of the script on the console):
$ cscaldb debug=yes
Parfile cscaldb.par not found. Create default parfile.
2015-05-22T21:35:39: +============+
2015-05-22T21:35:39: | Parameters |
2015-05-22T21:35:39: +============+
2015-05-22T21:35:39: chatter ...................: 2
2015-05-22T21:35:39: clobber ...................: yes
2015-05-22T21:35:39: debug .....................: yes
2015-05-22T21:35:39: mode ......................: ql
2015-05-22T21:35:39:
2015-05-22T21:35:39: +==============+
2015-05-22T21:35:39: | Mission: cta |
2015-05-22T21:35:39: +==============+
2015-05-22T21:35:40: === Response functions in database "prod2" ===
2015-05-22T21:35:40: North_0.5h
2015-05-22T21:35:40: North_50h
2015-05-22T21:35:40: North_5h
2015-05-22T21:35:40: South_0.5h
2015-05-22T21:35:40: South_50h
2015-05-22T21:35:40: South_5h
You will see that ctools ships with one database for the CTA observatory. This is the prod2 database. Within this database there are six response functions: North_0.5h, North_5h, North_50h, South_0.5h, South_5h, and South_50h.
You now jointly fit both observations using ctlike:
$ ctlike chatter=3
Input event list, counts cube or observation definition XML file [events.fits] obs_irf.xml
Input model XML file [$CTOOLS/share/models/crab.xml]
Output model XML file [crab_results.xml]
To see the usage of the individual response functions you may inspect the log file (you need to set chatter=3 to see the details of the observations in the log file). You will notice that each observation now has a specific response function and that the filename of the response information differs for both observations.
2015-12-07T22:22:18: +==============+
2015-12-07T22:22:18: | Observations |
2015-12-07T22:22:18: +==============+
2015-12-07T22:22:18: === GObservations ===
2015-12-07T22:22:18: Number of observations ....: 2
2015-12-07T22:22:18: Number of models ..........: 2
2015-12-07T22:22:18: Number of predicted events : 0
2015-12-07T22:22:18: === GCTAObservation ===
2015-12-07T22:22:18: Name ......................: Crab
2015-12-07T22:22:18: Identifier ................: 00001
2015-12-07T22:22:18: Instrument ................: CTA
2015-12-07T22:22:18: Event file ................: north.fits
2015-12-07T22:22:18: Event type ................: EventList
2015-12-07T22:22:18: Statistics ................: Poisson
2015-12-07T22:22:18: Ontime ....................: 1800 s
2015-12-07T22:22:18: Livetime ..................: 1710 s
2015-12-07T22:22:18: Deadtime correction .......: 0.95
2015-12-07T22:22:18: User energy range .........: undefined
2015-12-07T22:22:18: === GCTAPointing ===
2015-12-07T22:22:18: Pointing direction ........: (RA,Dec)=(83.63,21.51)
2015-12-07T22:22:18: === GCTAResponseIrf ===
2015-12-07T22:22:18: Caldb mission .............: cta
2015-12-07T22:22:18: Caldb instrument ..........: prod2
2015-12-07T22:22:18: Response name .............: North_0.5h
2015-12-07T22:22:18: Energy dispersion .........: Not used
2015-12-07T22:22:18: Save energy range .........: undefined
2015-12-07T22:22:18: === GCTAEventList ===
2015-12-07T22:22:18: Number of events ..........: 8469
2015-12-07T22:22:18: Time interval .............: 51544.5 - 51544.5 days
2015-12-07T22:22:18: Energy interval ...........: 0.1 - 100 TeV
2015-12-07T22:22:18: Region of interest ........: RA=83.63, DEC=21.51 [0,0] Radius=5 deg
2015-12-07T22:22:18: === GCTAObservation ===
2015-12-07T22:22:18: Name ......................: Crab
2015-12-07T22:22:18: Identifier ................: 00002
2015-12-07T22:22:18: Instrument ................: CTA
2015-12-07T22:22:18: Event file ................: south.fits
2015-12-07T22:22:18: Event type ................: EventList
2015-12-07T22:22:18: Statistics ................: Poisson
2015-12-07T22:22:18: Ontime ....................: 1800 s
2015-12-07T22:22:18: Livetime ..................: 1710 s
2015-12-07T22:22:18: Deadtime correction .......: 0.95
2015-12-07T22:22:18: User energy range .........: undefined
2015-12-07T22:22:18: === GCTAPointing ===
2015-12-07T22:22:18: Pointing direction ........: (RA,Dec)=(83.63,22.51)
2015-12-07T22:22:18: === GCTAResponseIrf ===
2015-12-07T22:22:18: Caldb mission .............: cta
2015-12-07T22:22:18: Caldb instrument ..........: prod2
2015-12-07T22:22:18: Response name .............: South_0.5h
2015-12-07T22:22:18: Energy dispersion .........: Not used
2015-12-07T22:22:18: Save energy range .........: undefined
2015-12-07T22:22:18: === GCTAEventList ===
2015-12-07T22:22:18: Number of events ..........: 22529
2015-12-07T22:22:18: Time interval .............: 51544.5 - 51544.5 days
2015-12-07T22:22:18: Energy interval ...........: 0.1 - 100 TeV
2015-12-07T22:22:18: Region of interest ........: RA=83.63, DEC=22.51 [0,0] Radius=5 deg
...
2015-12-07T22:22:18: +=================================+
2015-12-07T22:22:18: | Maximum likelihood optimisation |
2015-12-07T22:22:18: +=================================+
2015-12-07T22:22:18: >Iteration 0: -logL=214691.468, Lambda=1.0e-03
2015-12-07T22:22:18: >Iteration 1: -logL=214679.380, Lambda=1.0e-03, delta=12.088, max(|grad|)=9.713100 [Index:3]
2015-12-07T22:22:18: >Iteration 2: -logL=214679.365, Lambda=1.0e-04, delta=0.015, max(|grad|)=0.092975 [Index:3]
2015-12-07T22:22:18: >Iteration 3: -logL=214679.365, Lambda=1.0e-05, delta=0.000, max(|grad|)=0.000749 [Index:3]
...
2015-12-07T22:22:18: +=========================================+
2015-12-07T22:22:18: | Maximum likelihood optimisation results |
2015-12-07T22:22:18: +=========================================+
2015-12-07T22:22:18: === GOptimizerLM ===
2015-12-07T22:22:18: Optimized function value ..: 214679.365
2015-12-07T22:22:18: Absolute precision ........: 0.005
2015-12-07T22:22:18: Acceptable value decrease .: 2
2015-12-07T22:22:18: Optimization status .......: converged
2015-12-07T22:22:18: Number of parameters ......: 10
2015-12-07T22:22:18: Number of free parameters .: 4
2015-12-07T22:22:18: Number of iterations ......: 3
2015-12-07T22:22:18: Lambda ....................: 1e-06
2015-12-07T22:22:18: Maximum log likelihood ....: -214679.365
2015-12-07T22:22:18: Observed events (Nobs) ...: 30998.000
2015-12-07T22:22:18: Predicted events (Npred) ..: 30998.000 (Nobs - Npred = 1.02755e-06)
2015-12-07T22:22:18: === GModels ===
2015-12-07T22:22:18: Number of models ..........: 2
2015-12-07T22:22:18: Number of parameters ......: 10
2015-12-07T22:22:18: === GModelSky ===
2015-12-07T22:22:18: Name ......................: Crab
2015-12-07T22:22:18: Instruments ...............: all
2015-12-07T22:22:18: Instrument scale factors ..: unity
2015-12-07T22:22:18: Observation identifiers ...: all
2015-12-07T22:22:18: Model type ................: PointSource
2015-12-07T22:22:18: Model components ..........: "SkyDirFunction" * "PowerLaw" * "Constant"
2015-12-07T22:22:18: Number of parameters ......: 6
2015-12-07T22:22:18: Number of spatial par's ...: 2
2015-12-07T22:22:18: RA .......................: 83.6331 [-360,360] deg (fixed,scale=1)
2015-12-07T22:22:18: DEC ......................: 22.0145 [-90,90] deg (fixed,scale=1)
2015-12-07T22:22:18: Number of spectral par's ..: 3
2015-12-07T22:22:18: Prefactor ................: 5.81237e-16 +/- 8.63534e-18 [1e-23,1e-13] ph/cm2/s/MeV (free,scale=1e-16,gradient)
2015-12-07T22:22:18: Index ....................: -2.53954 +/- 0.0137432 [-0,-5] (free,scale=-1,gradient)
2015-12-07T22:22:18: PivotEnergy ..............: 300000 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2015-12-07T22:22:18: Number of temporal par's ..: 1
2015-12-07T22:22:18: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
2015-12-07T22:22:18: === GCTAModelIrfBackground ===
2015-12-07T22:22:18: Name ......................: CTABackgroundModel
2015-12-07T22:22:18: Instruments ...............: CTA
2015-12-07T22:22:18: Instrument scale factors ..: unity
2015-12-07T22:22:18: Observation identifiers ...: all
2015-12-07T22:22:18: Model type ................: "PowerLaw" * "Constant"
2015-12-07T22:22:18: Number of parameters ......: 4
2015-12-07T22:22:18: Number of spectral par's ..: 3
2015-12-07T22:22:18: Prefactor ................: 1.01067 +/- 0.0103997 [0.001,1000] ph/cm2/s/MeV (free,scale=1,gradient)
2015-12-07T22:22:18: Index ....................: 0.0135414 +/- 0.0064452 [-5,5] (free,scale=1,gradient)
2015-12-07T22:22:18: PivotEnergy ..............: 1e+06 [10000,1e+09] MeV (fixed,scale=1e+06,gradient)
2015-12-07T22:22:18: Number of temporal par's ..: 1
2015-12-07T22:22:18: Normalization ............: 1 (relative value) (fixed,scale=1,gradient)
A more fine grained control over the response function can be achieved by specifying individual filenames for the various response components. An example for an observation definition XML file is shown below. This is definitely expert mode, to be used with utmost care.
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="EventList" file="north.fits"/>
<parameter name="EffectiveArea" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
<parameter name="PointSpreadFunction" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
<parameter name="EnergyDispersion" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
<parameter name="Background" file="$(CALDB)/data/cta/prod2/bcf/North_0.5h/irf_file.fits.gz"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="EventList" file="south.fits"/>
<parameter name="EffectiveArea" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
<parameter name="PointSpreadFunction" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
<parameter name="EnergyDispersion" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
<parameter name="Background" file="$(CALDB)/data/cta/prod2/bcf/South_0.5h/irf_file.fits.gz"/>
</observation>
</observation_list>
Finally, response information may also be provided to combine stacked observations. An example for the syntax of the observation definition XML file is given below:
<?xml version="1.0" standalone="no"?>
<observation_list title="observation library">
<observation name="Crab" id="00001" instrument="CTA">
<parameter name="CountsCube" file="cntcube1.fits"/>
<parameter name="ExposureCube" file="expcube1.fits"/>
<parameter name="PsfCube" file="psfcube1.fits"/>
<parameter name="BkgCube" file="bkgcube1.fits"/>
</observation>
<observation name="Crab" id="00002" instrument="CTA">
<parameter name="CountsCube" file="cntcube2.fits"/>
<parameter name="ExposureCube" file="expcube2.fits"/>
<parameter name="PsfCube" file="psfcube2.fits"/>
<parameter name="BkgCube" file="bkgcube2.fits"/>
</observation>
</observation_list>