Diffuse gamma-ray emission from the Galactic center - a multiple energy injection model

We suggest that the energy source of the observed diffuse gamma-ray emission from the direction of the Galactic center is the Galactic black hole Sgr A*,which becomes active when a star is captured at a rate of similar to 10(-5) yr(-1). Subsequently the star is tidally disrupted and its matter is accreted into the black hole. During the active phase relativistic protons with a characteristic energy similar to 6 x 10(52) erg per capture are ejected. Over 90% of these relativistic protons disappear due to proton-proton collisions on a timescale tau(pp) similar to 104 years in the small central bulge region with radius similar to 50 pc within Sgr A*, where the density is >= 103 cm(-3). The gamma-ray intensity, which results from the decay of neutral pions produced by proton-proton collisions, decreases according to e(-t/tau pp), where it is the time after last stellar capture. Less than 5% of relativistic protons escaped from the central bulge region can survive and maintain their energy for > 10(7) years due to much lower gas density outside, where the gas density can drop to similar to 1 cm(-3). They can diffuse to a similar to 500 pc region before disappearing due to proton-proton collisions. The observed diffuse GeV gamma-rays resulting from the decay of neutral pions produced via collision between these escaped protons and the gas in this region is expected to be insensitive to time in the multi-injection model with the characteristic injection rate of 10(-5) yr(-1). Our model calculated GeV and 511 keV gamma-ray intensities are consistent with the observed results of EGRET and INTEGRAL, however, our calculated inflight annihilation rate cannot produce sufficient intensity to explain the COMPTEL data.