A NEW METHOD TO STUDY THE ORIGIN OF THE EXTRAGALACTIC GAMMA-RAY BACKGROUND AND THE FIRST APPLICATION ON AT20G

In this Letter, we introduce a new method of image stacking to directly study the undetected but possible γ-ray point sources. Applying the method to the Australia Telescope 20 GHz Survey sources which have not been detected by Large Area Telescope on the Fermi Gamma-ray Space Telescope, we find that the sources contribute (10.5 ± 1.1)% and (4.3 ± 0.9)% of the extragalactic gamma-ray background (EGB) and have a very soft spectrum with the photon indices of 3.09 ± 0.23 and 2.61 ± 0.26 in the 1-3 GeV and 3-300 GeV energy ranges, respectively. In the 0.1-1 GeV range, they probably contribute a larger fraction to the EGB, but it is not quite certain. It may not be appropriate to assume that the undetected sources have similar properties to the detected sources.