An upper limit on the cosmic-ray luminosity of individual sources from gamma-ray observations

Different types of extragalactic objects are known to produce TeV gamma-rays. Some of these objects are the most probable candidates to accelerate cosmic rays up to 10^20 eV. It is very well known that gamma-rays can be produced as a result of the cosmic ray propagation through the intergalactic medium. These gamma-rays contribute to the total flux observed in the direction of the source. In this paper we propose a new method to derive an upper limit on the cosmic-ray luminosity of an individual source based on the measured upper limit on the integral flux of GeV-TeV gamma-rays. We show how it is possible to calculate an upper limit on the cosmic-ray luminosity of a particular source and we explore the parameter space in which the current GeV-TeV gamma-ray measurements can offer a useful determination. We study in detail two particular sources, Pictor A and NGC 7469, and we calculate the upper limit on the proton luminosity of each source based on the upper limit on the integral gamma-ray flux measured by the H.E.S.S. telescopes.