Diffusive Cosmic Ray Acceleration at the Galactic Centre

The diffuse TeV emission detected from the inner $\sim2^\circ$ of the Galaxy appears to be strongly correlated with the distribution of molecular gas along the Galactic ridge. Although it is not yet entirely clear whether the origin of the TeV photons is due to hadronic or leptonic interactions, the tight correlation of the intensity distribution with the molecular gas strongly points to a pionic-decay process involving relativistic protons. But the spectrum of the TeV radiation---a power law with index $\alpha\approx -2.3$---cannot be accommodated easily with the much steeper distribution of cosmic rays seen at Earth. In earlier work, we examined the possible sources of these relativistic protons and concluded that neither the supermassive black hole Sagittarius A* (identified with the HESS source J1745-290), nor several pulsar wind nebulae dispersed along the Galactic plane, could produce a TeV emission profile morphologically similar to that seen by HESS. We concluded from this earlier study that only relativistic protons accelerated throughout the inter-cloud medium could account for the observed diffuse TeV emission from this region. In this paper, we develop a model for diffusive proton acceleration driven by a turbulent Alfv\'enic magnetic field present throughout the gaseous medium. Though circumstantial, this appears to be the first evidence that at least some cosmic rays are accelerated diffusively within the inner $\sim300$ pc of the Galaxy.