Stochastic Heating, Differential Flow, and the Alpha-to-Proton Temperature Ratio in the Solar Wind

We extend previous theories of stochastic ion heating to account for the motion of ions along the magnetic field. We derive an analytic expression for the ion-to-proton perpendicular temperature ratio in the solar wind for any ion species, assuming that stochastic heating is the dominant ion heating mechanism. This expression describes how this temperature ratio depends upon the average velocity of the ions along the magnetic field direction and the ratio of the parallel proton pressure to the magnetic pressure. We compare our model with previously published measurements of alpha particles and protons from the WIND spacecraft. We find that stochastic heating offers a promising explanation for these measurements when the fractional cross helicity and Alfven ratio at the proton-gyroradius scale have values that are broadly consistent with solar-wind measurements.