Neutrinos from stochastic acceleration in black hole environments

Abstract

Recent experimental results from the IceCube detector and their phenomenological interpretation suggest that the magnetized turbulent corona of nearby X-ray luminous Seyfert galaxies can produce ∼1 − 10 TeV neutrinos via photo-hadronic interactions. We investigate the physics of stochastic acceleration in these environments in detail and examine the conditions under which the inferred proton spectrum can be explained. To this end, we used recent findings on particle acceleration in turbulence and paid particular attention to the transport equation, notably for transport in momentum space, turbulent transport outside of the corona, and advection through the corona. We first remark that the spectra we obtained are highly sensitive to the value of the acceleration rate, for instance, to the Alfvénic velocity. Then, we examined three prototype scenarios, one scenario of turbulent acceleration in the test-particle picture, another scenario in which particles were preaccelerated by turbulence and further energized by shear acceleration, and a final scenario in which we considered the effect of particle backreaction on the turbulence (damping), which self-regulates the acceleration process. We show that it is possible to obtain satisfactory fits to the inferred proton spectrum in all three cases, but we stress that in the first two scenarios, the energy content in suprathermal protons has to be fixed in an ad hoc manner to match the inferred spectrum at an energy density close to that contained in the turbulence. Interestingly, self-regulated acceleration by turbulence damping naturally brings the suprathermal particle energy content close to that of the turbulence and allowed us to reproduce the inferred flux level without additional fine-tuning. We also suggest that based on the strong sensitivity of the highest proton energy to the Alfvénic velocity (or acceleration rate), any variation in this quantity in the corona might affect (and in fact, set) the slope of the high-energy proton spectrum.