the
XMLSource Model
The binned likelihood analysis for research in this thesis is the first step in a two-stepped approach, conducted for the purpose of determining the best-fit γ-ray properties of the target sources in the sample. The binned likelihood analysis is performed over the entire monitoring period, as defined in Table 4.3 following the pipeline shown in Figure 4.10. The selection cuts used in the binned likelihood analysis is given in Table 4.2.
In order to perform the binned likelihood analysis, the data is first selected using the event and time selection cuts as described in theGTSELECTandGTMKTIMEabove. Then
a counts map and a counts cube are created. The counts map represents all the counts summed over the photon energies while the counts cube represents the counts map this time with a z-axis representing the photon energy.
Instrument Selection Criteria ScienceTools Version v9r33p0
IRF ReprocessedPASS7 (PASS7REP)
Event Class source Zenith Angle Cuts 100◦
Rock-Angle cut <52◦
Energy Range 100 MeV - 100 GeV Radius of Interest 15◦(centred on source)
TS Threshold See Table 7.1 Likelihood Analysis Binned
Binning Timescale 5 years
Start date MJD 54682 (4 August 2008) End Date MJD 56692 (2 April 2014)
Table 4.2: Summary of Fermi-LAT instrument specification and data selection cuts for all eight sources.
Once this is complete, the ’livetime’ and exposure are computed. As with the un- binned likelihood analysis, the ’livetime’ cube is generated with GTLTCUBE. However,
unlike the unbinned likelihood preliminary analysis, the exposure map for a binned like- lihood analysis requires the generation of a complete sky exposure map for the ’livetime’ computed. This represents the predicted number of counts in a certain position over the entire sky at a certain energy. This is followed by the generation of a source map with theGTSRCMAPStool.
In order to perform the binned likelihood, theGTLIKEroutine is performed. GTLIKE
applies one of five optimisation algorithms to maximize the likelihood function as dis- cussed in Section 4.6.1. For the Fermi-LAT analysis presented in this thesis, theMINUIT29
algorithm was used. This algorithm determines the best fit to the spectral parameters in the XMLsource model. The GTLIKE tool uses output from the other tools as well as
spectral information of each source from theXMLsource model to determine the best fit to the normalisation and spectral index parameters by maximising the likelihood that the data fits the model, given by maximising the T S value (see Section 4.6.1).
29
Source Purpose Duration Date
PKS 2155-304 quiescent-state 3 mths 11/08/2012 - 16/10/2012 MRK 421 ToO Campaign 6 days 12/04/2013 - 17/04/2013 MRK 421 long-term 5.5 yrs 04/08/2008 - 04/02/2014 MRK 501 long-term 5.5 yrs 04/08/2008 - 04/02/2014 OJ 287 long-term 5.5 yrs 04/08/2008 - 04/02/2014 BL Lacertae long-term 5.5 yrs 04/08/2008 - 04/02/2014 3C 273 long-term 5.5 yrs 04/08/2008 - 04/02/2014 3C 279 long-term 5.5 yrs 04/08/2008 - 04/02/2014 3C 454.3 long-term 5.5 yrs 04/08/2008 - 04/02/2014 NGC 1275 long-term 5.5 yrs 04/08/2008 - 04/02/2014
Table 4.3: Observation periods over which light curves were analysed for this research. The purpose of the observation, i.e, short-term or long-term study, are also specified.
The output from the binned likelihood analysis provides the integrated flux and the associated T S value for each source present in the ROI over the duration analysed. This information is then used to refine the source model.
4.7.1 Refining theXMLSource Model
TheXMLsource model (see Section 4.6.5) is refined to include only sources with signifi- cant T S values above a threshold of 1030. Removing sources with T S < 10 will remove some of the noise as well as contribution from sources which may not be producing
γ-rays during the observation period31. This, will then reduce the possibility of miscal-
culating the likelihood of how well the model describes the data.
4.7.2 Generating a model map withGTMODEL
For the purpose of testing the outcome of the binned likelihood analysis and the accuracy of the refinedXMLsource model (containing only sources with T S > 10), a model map is
30A T S of 10 signifies detection at a∼ 3σ level (133). 31
Some of the sources present in the sample are variable, and as such, have periods during which they are quiet at γ-ray energies. If this occurs during the time frame used in the analysis, theXMLsource model may not reflect the accurate expected distribution of γ-rays in the ROI.
generated using theGTMODELtool. This tool provides the user with a means of assessing the accuracy of theXMLmodel. The generated model map will then be used to determine
the percentage residual between the counts map and the model map.
The GTMODELroutine produces a counts map of the region of interest based on the
fitted model. First, the fitted model is scaled based on the individual source maps pro- duced with the GTSRCMAPS tool, which are then all used to produce the final model
map.
Next, a percentage residual map (Figure 4.13) is created in order to compare the ob- served counts map (generated withGTBIN) and the expected model map (generated with
GTMODEL). The percentage residual map is produced by first subtracting the model map (Figure 4.12) from the sky map (Figure 4.11). The residual is then divided by the model map to obtain a percentage residual map (see Equation 4.16 and Figure 4.13). If there is a large difference32between both maps, then these counts must be accounted for by re- fining theXMLmodel to include the contribution of γ-ray photon counts from the source present in the counts map (which are not present in the model map). When this is com- plete, theGTLIKEroutine is carried out again. The aim is to achieve a minimal difference between the counts map and the model map (i.e. all sources observed by Fermi during the observation period have been accounted for by the XMLmodel). Once this criteria is satisfied, the source model is ready to be used in the unbinned likelihood analysis to produce source light curves.
Percentage Residual Map = Sky Map− Model Map
Model Map (4.16)