El planímetro:

Once the appropriate selection cuts are applied to the photon files, the datasets are now ready to be processed to compute the instrument exposure and γ-ray count distributions for each source. This process provides the necessary information (i.e. actual data) which the likelihood estimator uses to produce the best fit based on both model and observed data (see Section 4.6.1).

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Fermi rocks to the left and right on alternate orbits in order to enable the LAT to cover a larger fraction of the sky. The rocking angle cut will also minimise contamination from the Earth’s limb (in addition to the zenith angle cut).

Producing the Counts Map and Counts Cube withGTBIN

First, the GTI filtered datasets are used to produce a counts map under theCMAPalgo- rithm using theGTBINtool. This process provides a 2-dimensional spatial image of the

photon distribution based on the GTI filtered dataset. The output from this routine is a counts map (also referred to as a sky map) which depicts the 100 MeV and 100 GeV

γ-ray photon distribution within the chosen ROI, centred on the source.

The counts cube,CCUBE is computed using theGTBINroutine. This produces a 3-D map which bins the observed counts into an X-Y position plane with a Z photon energy axis. This counts cube is represented by a square binned-region within the circular ac- ceptance cone defined by the region of interest. The output from this is used as an input when calculating the best fit parameters during a binned likelihood analysis.

The projection method specified for the generation of both the counts map and counts cube is Aitoff [AIT] from the Hammer-Aitoff projection which represents the equatorial case of the zenithal equal area projection. This reduces distortion in the polar regions compared to other types of projections. This is the most common all-sky projection method used (254).

’Livetime’ Cubes usingGTLTCUBE

The ’livetime’ cube is created by using the GTLTCUBE tool. This essentially represents the time during which the instrument spends observing the target source at a given inclination angle. This is because the number of counts observed from a particular source is dependent on the instrument’s ’livetime’.

The ’livetime’ cube is calculated from the GTI filtered dataset over the specified time range within that dataset along with instrument pointing information obtained from the spacecraft file. This produces a three dimensional ’livetime’ cube which comprises the sky position and binned over the inclination angle (i.e. instrument z-axis). The resulting ’livetime’ cube is aFITSfile and is used as an input parameter in the likelihood analysis.

Exposure Maps withGTEXPMAPandGTEXPCUBE2

In this section, the two types of exposure maps using two different tools are presented. Exposure maps generated for the unbinned and binned likelihood analyses are done usingGTEXPMAPandGTEXPCUBE2 respectively.

Figure 4.11: The counts map (sky map) constructed using the GTBINtool. This shows the distribution of γ-ray photons over the ROI centred on NGC 1275 (green ring) for the observation period of 5.5 years (i.e. between 04/08/2008 - 04/02/2014). The colour scale shows the number of photon counts present in a given position in the counts map.

The exposure map generated by the GTEXPMAP tool shows the exposure of the in- strument as a function of position which is used to calculate the predicted number of photon counts at a given inclination angle and a given position in the sky. As such, the exposure maps are dependent on the instrument response (i.e. effective area, energy dis- persion and the PSF). TheGTEXPMAPtool uses the ’livetime’ cube to determine the time the instrument spends at a given inclination angle. The resulting map, is a total exposure map for the number of counts that could be observed for a specified position in the sky at a given energy.

The exposure cube is generated by the GTEXPCUBE2 tool for the purpose of carrying out the binned likelihood analysis. This map is generally an all sky exposure map. The difference between the exposure map and the exposure cube is that the latter generates different maps for a specified energy bin, and is not integrated over the energy band pass.

4.6.5 TheXMLSource Model

The XML source model is an input model which is needed to calculate the likelihood

that the model describes the data (see Section 4.6.1). In general, the XMLsource model consists of point sources, the galactic diffuse emission for theP7REP_V15 data,GLL_IEM

_V05_REV1.FITand the extragalactic isotropic source model,ISO_SOURCE_V05.TXT. For certain sources (e.g. BL Lacertae), which are located close to an extended source (within the ROI), contribution from the extended source must be added to theXMLfile. The anal- ysis of BL Lacertae required the addition of the Cygnus Loop source emission, obtained from the Extended Source Template Archive28in theXMLmodel.

Each point source within the XMLmodel file is given a spectral model as well as the

right ascension (RA) and declination (dec) of the source. The parameters for sources within the target’s ROI are allowed to vary, while parameters for sources outside this field of interest is fixed to the values published in the Second Fermi Source Catalog (192). For both the power-law and log parabola spectra, the normalisation prefactor as well as the spectral indices are allowed to vary. In this research, MRK 421, MRK 501 and OJ 287 use a power-law spectrum, while BL Lacertae, 3C 273, 3C 279, 3C 454.3 and NGC 1275 use a log parabola as given in the 2FGL catalogue. The functional form of both these

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spectral models is given by Equations 4.14 and 4.15. dN dE = N0 ( E E0 )γ (4.14) where N_◦is the normalisation prefactor, γ is the photon index and E_◦ is the scale.

dN dE = N0 ( E Eb )_{−(α+β log(E/Eb})) (4.15) where N0 is the normalisation prefactor, α and β are the spectral and curvature in-

dices respectively and Ebis the scaling parameter which is usually fixed near the lower

energy range of the spectrum being fit (76).

Calculating the Model Counts Map withGTSRCMAPS

This particular tool and its generated map is only used for binned likelihood analyses. The model counts maps is a product of theXMLspectral model for each source and the

exposure at the source position. This is then convolved with the effective PSF.

The result is a FITSdata structure file with each extension corresponding to a source in theXMLmodel file. Each extension then contains a counts map binned in space and

energy for the given source.