Sensaciones y Subsistencia

6.5

The Crab Nebula Analysis

As is the case with MAGIC, the rather poor angular resolution of Fermi-LAT does not enable a spatial resolution for the Crab pulsar and the Crab nebula. Therefore, the nebula emission is the dominant background of the Crab pulsar emission for Fermi-LAT data. It must be properly analyzed by using the pulse phase information and, then, must be subtracted from the Crab pulsar emission. Fortunately, the analysis of the nebula has an important by-product: one can make sure of the analysis method by checking if the obtained energy spectrum is smoothly connected to the IACT measurements (see Sect. 2.9.7).

In order to analyze the nebula component, photons with the pulse phases from 0.52 to 0.872 (see the right panel of Fig. 6.2), where no pulsed emission is seen in lower energies, are assumed to be from the nebula (and other background photons such as galactic diffuse emission). The selection of the right phase events is carried out by the Fermi-LAT analysis toolgtselet. The effective observation time and the collection area are calculated bygtltubeandgtexpmap (see [209]). The spectrum is determined by means of the likelihood method, using the official tool gtlike(see [209]). It is done in the following way: The spectral shapes with several parameters of the sources in the FoV, the galactic and extragalactic diffuse emission models and the detector re- sponse function are assumed a priori. Then, the best parameters that maximize the likelihood of the observed data sets are determined. P6 V3 Diffuse, which is officially provided by the Fermi- LAT collaboration, was used for the detector response function, A simple power law spectrum was assumed for the IC 443 while a power law spectrum with an exponential cut-off was as- sumed for Geminga. For the extragalactic and galactic diffuse emission, isotropic iem v02.txt and gll iem v02.fit, which are included in the Fermi-LAT analysis tool package as a standard model, were used. For the Crab nebula, the spectrum based on the sum of the two power laws is assumed aiming for the synchrotron and the inverse Compton emission components, which have been suggested by the previous EGRET (see [114]) and IACT measurements (see e.g. [20], [11] and Fig. 2.30).

The spectrum of the Crab nebula calculated based on the Fermi-LAT data is shown in Fig. 6.4 as a red line. One can see that synchrotron spectrum is steeply falling from 200 MeV to 500 MeV and the inverse Compton component becomes dominant above 800 MeV. They can be described as dN dEdAdTsyn = (8:61:4)10 11 (E=300MeV) 4:140:47 (6.2) dN dEdAdTIC = (7:30:710 12 (E=1GeV ) 1:680:05 (6.3) (6.4) In order to make sure that the assumption of the spectral shape of the Crab pulsar is valid, the same data sets were divided into many subsets according to the energy. Then, the likelihood analysis was applied to each subset, assuming a simple power law in each small energy range.

2_{It is almost the same as the OP (off-pulse) phases defined in Sect. 2.9.5 but not exactly. Since the official Fermi}

168 6. Analysis of Fermi-LAT public Data

The red points in the figure indicate the results for the divided subsets. Instead of showing many short truncated lines, the value at the bin center and its error are shown. All the points are very well aligned along the line, showing the validity of the assumption.

[MeV] 3 10 104 105 106 107 ] -1 s -2 F[erg cm 2 E -12 10 -11 10 -10 10 -9 10 Spectrum

MAGIC (this work) Fermi (this work) Sync. Component IC Component Fermi Publication MAGIC (A&A 674, 1037) HESS (A&A 457, 899) Spectrum

Figure 6.4: The energy spectrum of the Crab nebula. The red line and circles indicate the spectrum calculated by myself using one year of Fermi-LAT data. The green dashed line indicates the published spectrum from theFermicollaboration (see [4]). Blue circles, black open squares and black filled squares

indicate the spectrum calculated by myself with the MAGIC observation data with the SUM trigger, the published spectrum from the MAGIC collaboration before the SUM trigger was installed (see [20]) and the published spectrum from the HESS collaboration (see [11]), respectively. The synchrotron and the inverse Compton components below 100 GeV are indicated by black dotted and black dashed lines, respectively.

The spectrum published by the Fermi-LAT collaboration with smaller data samples ( 8 months of data) (see [4]) are also shown in the same figure as a green dashed line, which is consistent with my analysis. The measurements by MAGIC (the published one and the one I calculated with the data samples used for the pulsar analysis) and by HESS are also shown in the same figure. The spectra are smoothly connected from 100 MeV to above 10 TeV.3

It should be noted that the poor statistics of Fermi-LAT data in the overlapped energy region from 50 GeV to 300 GeV does not allow a relative flux scale calibration between Fermi-LAT and MAGIC with a precision better than'60%, which is larger than the systematic uncertainties of both experiments (see Sect. 4.12 and Sect. 6.2).

3_{The true spectrum should not be a simple power law from 10 to 100 GeV. Therefore, the}

'50%difference