## 3. Probability of chance associationIn order to make quantitative estimates of the probability of a pure chance superposition between the SNR and the gamma-ray source we have adopted the numerical code developed by Romero et al. (1999b) and used by Romero et al. (1999a) to study the positional association of unidentified EGRET sources with various populations of galactic objects. The code calculates angular distances between different kinds of celestial objects contained in selected catalogues, and establishes the level of positional correlation between them. Numerical simulations using large numbers of synthetic populations are then performed in order to determine the probabilities of purely chance associations. When generating synthetic populations of -ray sources the distribution in galactic latitude is constrained to be the same as the one actually observed for the 3EG sources. This is necessary in order to obtain reliable results since the distribution of the 3EG sources is non-isotropic, with a strong concentration towards the galactic plane. The reader is referred to the paper by Romero et al. (1999a) for further details of the simulation code. Our results for 3EG J1828+0142 indicate that the probability of finding by chance a gamma-ray source with its 95% confidence contour within the outer boundary of the SNR is . The probability of finding a variable gamma-ray source (estimated taking into account the actual fraction of variable sources in the 3EG catalog according to Torres et al. 2000) is lower: . These values are not too compelling, but if we calculate the probability of the gamma-ray source being a background AGN seen through the galactic plane and associated by chance with the SNR, we get a value of , which is significantly lower. In making this calculation we have extrapolated the isotropic population of already detected gamma-ray emitting AGNs towards the region obscured by the galactic disk emission, performing simulations with no gamma-ray source density gradient towards the plane. © European Southern Observatory (ESO) 2000 Online publication: January 29, 2001 |