The statistical mechanics of reconnecting flux loops and consequences for massive star formation

We present a simple model that describes the reconnection process for a collection of magnetic flux loops in an astrophysical system. We derive and solve the master kinetic equations for reconnecting flux loops in a plasma with β ≤ 1 (where β is the ratio of the gas pressure to the magnetic field pressure). The solution is a similarity solution for the distribution, N(Φ, M, t) , of flux loops as a function of magnetic flux Φ, mass M, and time t, and it is given by N(Φ, M, t) ∼ t^-1Φ^-2M^-1, where the power-law indices are determined by the cross-sectional interaction and the physics of the flux loops. We discuss applications to star formation. In particular, we find that this reconnection process can lower the flux-to-mass ratio in portions of the system and can thereby provide sites for massive star formation. In addition, kinetic models such as those considered here may provide a means of calculating the distribution of clump masses (and fluxes) within molecular clouds.