Fermi Gamma-Ray “Bubbles” from Stochastic Acceleration of Electrons

Gamma-ray data from Fermi Large Area Telescope reveal a bilobular structure extending up to $\sim 50°$ above and below the Galactic Center. It has been argued that the gamma rays arise from hadronic interactions of high-energy cosmic rays which are advected out by a strong wind, or from inverse-Compton scattering of relativistic electrons accelerated at plasma shocks present in the bubbles. We explore the alternative possibility that the relativistic electrons are undergoing stochastic 2nd-order Fermi acceleration by plasma wave turbulence through the entire volume of the bubbles. The observed gamma-ray spectral shape is then explained naturally by the resulting hard electron spectrum modulated by inverse-Compton energy losses. Rather than a constant volume emissivity as in other models, we predict a nearly constant surface brightness, and reproduce the observed sharp edges of the bubbles.

Figure 1

Relevant time scales (top) and the electron spectrum (bottom), at various distances $x=\xi L$ from the shock.

Figure 2

The average gamma-ray flux $J_{\gamma }$ from the Fermi bubbles [1] compared to the spectrum from our model (the contributions from inverse-Compton scattering on the CMB, FIR, and optical/UV backgrounds are shown from left to right as dash-dotted lines). The spectra from a hadronic [6] (dashed line) and a leptonic DSA model [7] (dotted line) are also shown.

Figure 3

The gamma-ray intensity as a function of distance from the bubble edge [1] is compared with our model predictions at 2 GeV (solid line), 10 GeV (long dashed line), and 500 GeV (dash-dotted line). The dotted line indicates the expected profile for both the hadronic model [6] and the leptonic DSA model [7].

Figure 4

Our model prediction for the synchrotron flux at $(\ell ,b)=(0°,25°)$, for two assumed magnetic field values, compared to the inferred spectrum of the WMAP haze [4].