How to perform spectral fitting using Xspec?¶
What you will learn
You will learn how to use Xspec to perform a spectral fitting of On/Off data.
Warning
You can reproduce this tutorial only if you have Xspec installed. You may download Xspec here.
If you are familiar with X-ray data analysis, or if you want to use a specific spectral model that is available in the Xspec package, you can use that package to fit CTA data that were prepared for an On/Off analysis.
To illustrate how you can do this, let’s simulate an observation of the Crab nebula with a pointing direction that is offset by 1 deg. We also use energy dispersion in the simulation as an On/Off analysis always
$ ctobssim edisp=yes
RA of pointing (degrees) (0-360) [83.63]
Dec of pointing (degrees) (-90-90) [22.51] 21.01
Radius of FOV (degrees) (0-180) [5.0]
Start time (UTC string, JD, MJD or MET in seconds) [2020-01-01T00:00:00]
Stop time (UTC string, JD, MJD or MET in seconds) [2020-01-01T00:30:00]
Lower energy limit (TeV) [0.1]
Upper energy limit (TeV) [100.0]
Calibration database [prod2]
Instrument response function [South_0.5h]
Input model definition XML file [$CTOOLS/share/models/crab.xml]
Output event data file or observation definition XML file [events.fits]
No use the csphagen script to generate the On/Off data using a On region radius of 0.2 deg and the reflected region model to determine the Off counts spectrum:
$ csphagen
Input event list or observation definition XML file [obs.xml] events.fits
Calibration database [prod2]
Instrument response function [South_0.5h]
Input model definition XML file (if NONE, use point source) [NONE]
Algorithm for defining energy bins (FILE|LIN|LOG|POW) [LOG]
Start value for first energy bin in TeV [0.1]
Stop value for last energy bin in TeV [100.0]
Number of energy bins [120] 20
Stack multiple observations into single PHA, ARF and RMF files? [no]
Output observation definition XML file [onoff_obs.xml]
Output model definition XML file [onoff_model.xml]
Method for background estimation (REFLECTED|CUSTOM) [REFLECTED]
Coordinate system (CEL - celestial, GAL - galactic) (CEL|GAL) [CEL]
Right Ascension of source region centre (deg) (0-360) [83.63]
Declination of source region centre (deg) (-90-90) [22.01]
Radius of source region circle (deg) (0-180) [0.2]
Now you can start Xspec for model fitting.
$ xspec
XSPEC version: 12.10.1
Build Date/Time: Mon Jan 7 12:38:07 2019
XSPEC12>
First load the On file onoff_pha_on.fits using the data command:
XSPEC12>data onoff_pha_on.fits
***Warning: Data file onoff_pha_on.fits has both POISSERR key set to 'true' and a STAT_ERR column.
XSPEC will assume Poisson errors.
***Warning: Background file onoff_pha_off.fits has both POISSERR key set to 'true' and a STAT_ERR column.
XSPEC will use assume Poisson errors.
1 spectrum in use
Spectral Data File: onoff_pha_on.fits Spectrum 1
Net count rate (cts/s) for Spectrum:1 1.619e+00 +/- 3.135e-02 (93.9 % total)
Assigned to Data Group 1 and Plot Group 1
Noticed Channels: 1-20
Telescope: CTA Instrument: PROD2 Channel Type: PI
Exposure Time: 1764 sec
Using fit statistic: chi
Using test statistic: chi
Using Background File onoff_pha_off.fits
Background Exposure Time: 1764 sec
Using Response (RMF) File onoff_rmf.fits for Source 1
Using Auxiliary Response (ARF) File onoff_arf.fits
This will load the On PHA file as well as the Off PHA``file, the ``ARF
file and the RMF file. While you specified the On file on the command line,
the file names of the other files were extracted from backfile, ancrfile
and respfile header keywords in the On file that were setup by the
csphagen script.
Now set the fit statistic to cstat using
XSPEC12>statistic cstat
Default fit statistic is set to: C-Statistic
This will apply to all current and newly loaded spectra.
and set the spectral model as well as the initial parameters of the spectral model using
XSPEC12>model powerlaw
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01( 0.01) -3 -2 9 10
1:powerlaw:PhoIndex>2.5
1 0.01( 0.01) 0 0 1e+20 1e+24
2:powerlaw:norm>500.0
========================================================================
Model powerlaw<1> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 powerlaw PhoIndex 2.50000 +/- 0.0
2 1 powerlaw norm 500.000 +/- 0.0
________________________________________________________________________
Fit statistic : C-Statistic = 727.46 using 20 PHA bins and 18 degrees of freedom.
Test statistic : Chi-Squared = 548.66 using 20 PHA bins.
Reduced chi-squared = 30.481 for 18 degrees of freedom
Null hypothesis probability = 5.939476e-105
***Warning: Chi-square may not be valid due to bins with zero variance
in spectrum number(s): 1
Current data and model not fit yet.
Note that Xspec energies are in keV, and the power law normalization is taken at a reference energy of 1 keV.
Finally, you are ready to do the spectral fitting using the fit
command:
XSPEC12>fit
Parameters
C-Statistic |beta|/N Lvl 1:PhoIndex 2:norm
96.8692 11494.2 -3 2.49807 711.693
12.0065 4626.2 -4 2.49140 735.585
10.9389 553.368 -5 2.48822 701.803
10.8978 108.533 -6 2.48774 697.592
10.8974 11.7189 -7 2.48768 697.003
==============================
Variances and Principal Axes
1 2
8.7349E-07| -1.0000 0.0001
4.6499E+04| -0.0001 -1.0000
------------------------------
========================
Covariance Matrix
1 2
2.228e-04 3.212e+00
3.212e+00 4.650e+04
------------------------
========================================================================
Model powerlaw<1> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
1 1 powerlaw PhoIndex 2.48768 +/- 1.49258E-02
2 1 powerlaw norm 697.003 +/- 215.637
________________________________________________________________________
Fit statistic : C-Statistic = 10.90 using 20 PHA bins and 18 degrees of freedom.
Test statistic : Chi-Squared = 126.30 using 20 PHA bins.
Reduced chi-squared = 7.0169 for 18 degrees of freedom
Null hypothesis probability = 2.683238e-18
***Warning: Chi-square may not be valid due to bins with zero variance
in spectrum number(s): 1
XSPEC12>
The fit results are compared in the table below to the simulated true values and the values obtained using ctlike using the same spectral model. The Xspec results are compatible with the simulated values and very close to the values obtained using ctlike.
Parameter Truth Xspec ctlike Prefactor 601.4 697.0 +/- 215.6 697.5 +/- 234.5 Index 2.48 2.488 +/- 0.015 2.488 +/- 0.017