2013ApJ...775L..20F

In this study, we treat Fermi bubbles as a scaled-up version of supernova remnants (SNRs). The bubbles are created through activities of the super-massive black hole (SMBH) or starbursts at the Galactic center (GC). Cosmic-rays (CRs) are accelerated at the forward shocks of the bubbles like SNRs, which means that we cannot decide whether the bubbles were created by the SMBH or starbursts from the radiation from the CRs. We follow the evolution of CR distribution by solving a diffusion-advection equation, considering the reduction of the diffusion coefficient by CR streaming. In this model, gamma rays are created through hadronic interaction between CR protons and the gas in the Galactic halo. In the GeV band, we can well reproduce the observed flat distribution of gamma-ray surface brightness because some amount of gas is left behind the shock. The edge of the bubbles is fairly sharp owing to the high gas density behind the shock and the reduction of the diffusion coefficient there. The latter also contributes the hard gamma-ray spectrum of the bubbles. We find that the CR acceleration at the shock began when the bubbles were small, and the time scale of the energy injection at the GC was much smaller than the age of the bubbles. We predict that if CRs are accelerated to the TeV regime, the apparent bubble size should be larger in the TeV band, which could be used to discriminate our hadronic model from other leptonic models. We also present neutrino fluxes.