Magnetic field dissipation in converging flows

Converging flows (e.g., gas accreting on to compact objects) are often ionized and magnetized. As the gas in these systems compresses towards smaller radii, flux conservation acts to intensify the magnetic field B , which can attain superequipartition values. (Throughout this paper, equipartition is meant to imply a comparison between the energy density in the field and that of the particles only, not including turbulence.) Since such a field probably cannot remain anchored in the gas, it is often assumed that the field intensity in excess of equipartition (i.e., B eq ) is dissipated as heat, and that B therefore saturates at its B eq value – the so‐called ‘equipartition assumption’. In this paper we make an attempt at developing a model for magnetic field dissipation based on resistive magnetic tearing, in order to provide a more realistic means of determining the evolution of B in cases where the contribution to the spectrum from magnetic bremsstrahlung is important. We find that the violation of equipartition can vary in degree from large to small radii, and in either direction. Thus the spectrum predicted on the basis of the equipartition assumption is not always an adequate representation of the actual state of the system. However, several major shortcomings remain in our formulation. For example, our approach in this paper is to consider the turbulence as being initiated primarily by hydrodynamic processes. Arguing that the magnetic field is frozen into the highly ionized plasma, we therefore adopt a magnetic field spatial distribution that mirrors that of the gas. This may be valid only when the field is subequipartition, for otherwise the turbulent cascade may be influenced primarily by magnetic dissipation, rather than the hydrodynamics. In the application of this work to systems such as Sgr A* at the Galactic Centre, our approach may therefore break down at small radii (i.e., several Schwarzschild radii) where the magnetic field can in fact become superequipartition, for which a complete treatment of magnetic turbulence would need to be considered. However, the dominant emission mechanism in sources such as this appears to be magnetic bremsstrahlung over the full extent of the accreting region, so that even with these limitations, the bulk of the spectrum is influenced significantly by the qualitative results presented here.