Evaluating the maximum likelihood method for detecting short-term variability of AGILE γ-ray sources

¹ INAF/IASF–Bologna, via Gobetti 101, 40129 Bologna, Italy
e-mail: bulgarelli@iasfbo.inaf.it
² INAF/IASF–Roma, via del Fosso del Cavaliere 100, 00133 Roma, Italy
³ INAF/IASF – Milano, via E. Bassini 15, 20133 Milano, Italy
⁴ Dip. di Fisica, Univ. “Tor Vergata”, via della Ricerca Scientifica 1, 00133 Roma, Italy

Received: 5 September 2011
Accepted: 7 January 2012

Abstract

Context. The AGILE space mission (whose instrument is sensitive to the energy ranges 18–60 keV, and 30 MeV–50 GeV) has been operating since 2007. Assessing the statistical significance of the time variability of γ-ray sources above 100 MeV is a primary task of the AGILE data analysis. In particular, it is important to verify the instrument sensitivity in terms of Poisson modeling of the data background, and to determine the post-trial confidence of detections.

Aims. The goals of this work are: (i) to evaluate the distributions of the likelihood ratio test for both “empty” fields and regions of the Galactic plane, and (ii) to calculate the probability of false detections over multiple time intervals.

Methods. We describe in detail the techniques used to search for short-term variability in the AGILE γ-ray source database. We describe the binned maximum likelihood method used for the analysis of AGILE data, and the numerical simulations that support the characterization of the statistical analysis. We apply our method to both Galactic and extragalactic transients, and provide a few examples.

Results. After checking the reliability of the statistical description tested with the real AGILE data, we obtain the distribution of p-values for blind and specific source searches. We apply our results to the determination of the post-trial statistical significance of detections of transient γ-ray sources in terms of pre-trial values.

Conclusions. The results of our analysis allow a precise determination of the post-trial significance of γ-ray sources detected by AGILE.