γ-ray DBSCAN: a clustering algorithm applied to Fermi-LAT γ-ray data I. Detection performances with real and simulated data

Context. The density based spatial clustering of applications with noise (DBSCAN) is a topometric algorithm used to cluster spatial data that are affected by background noise. For the first time, we propose this method to detect sources in gamma-ray astrophysical images obtained from the Fermi-LAT data, where each point corresponds to the arrival direction of a photon. Aims. We investigate the detection performance of the gamma-ray DBSCAN in terms of detection efficiency and rejection of spurious clusters. Methods. We used a parametric approach, exploring a large volume of the gamma-ray DBSCAN parameter space. By means of simulated data we statistically characterized the gamma-ray DBSCAN, finding signatures that distinguish purely random fields from fields with sources. We defined a significance level for the detected clusters and successfully tested this significance with our simulated data. We applied the method to real data and found an excellent agreement with the results obtained with simulated data. Results. We find that the gamma-ray DBSCAN can be successfully used in detecting clusters in gamma-ray data. The significance returned by our algorithm is strongly correlated with that provided by the maximum likelihood analysis with standard Fermi-LAT software, and can be used to safely remove spurious clusters. The positional accuracy of the reconstructed cluster centroid compares to that returned by standard maximum likelihood analysis, allowing one to look for astrophysical counterparts in narrow regions, which minimizes the chance probability in the counterpart association. Conclusions. We found that gamma-ray DBSCAN is a powerful tool for detecting of clusters in gamma-ray data. It can be used to look for both point-like sources and extended sources, and can be potentially applied to any astrophysical field related to detecting clusters in data. In a companion paper we will present the application of the gamma-ray DBSCAN to the full Fermi-LAT sky, discussing the potential of the algorithm to discover new sources.