Fermi Gamma-ray Space Telescope

Source Detection and Localization

As discussed in the overview of the likelihood method, the likelihood tool, gtlike, currently does not fit the source position parameters. Instead, the gttsmap tool runs gtlike at each gridpoint on a rectangular grid. You provide a model of all the other sources in the Source Region, and gtssmap calculates the Test Statistic (TS) for adding an additional source at each gridpoint. The livetimecube and exposure map that can be precomputed for running gtlike can also be used for gttsmap.

If you have a good approximate source location, such as the gridpoint with the maximum TS from gttsmap or a candidate source identification, then you can refine the location by running gtfindsrc, which maximizes the TS in continuous space.

The TS is -2 times the logarithm of the ratio of the likelihood for the model without the additional source (the null hypothesis) to the likelihood for the model with the additional source. Thus the TS is maximized when the likelihood for the model with the source is maximized. Thus the location with the maximum TS is the best fit source position.

But is the addition of this source significant? By Wilks' Theorem, if there is no additional source then the TS should be drawn from a χ2n distribution, where n is the difference in the degree of freedom between the models with and without the additional source. In our case the additional source is characterized by a source intensity and spectral index (the spectrum is assumed to be a power law), and thus n=2. Wilks' Theorem is valid asymptotically as the number of counts increases, and studies are underway to determine the number of LAT counts for a typical analysis is sufficiently large. If Wilks' Theorem is valid then integrating χ22 from the observed TS value to infinity gives the probability that the apparent source is a fluctuation. The resulting significance is ~(TS)1/2σ, and thus TS=25 is equivalent to 5σ.

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