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 B. We derive an analytic expression for the temperature ratio T-perpendicular to i/T-perpendicular to p in the solar wind assuming that stochastic heating is the dominant ion heating mechanism, where T-perpendicular to i is the perpendicular temperature of species i and T-perpendicular to p is the perpendicular proton temperature. This expression describes how T-perpendicular to i/T-perpendicular to p depends upon U-i and beta(parallel to p), where U-i is the average velocity along B of species i in the proton frame and beta(parallel to p) is the ratio of the parallel proton pressure to the magnetic pressure, which we take to be less than or similar to 1. 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 the dependence of T-perpendicular to alpha/T-perpendicular to p on U-alpha and beta(parallel to p) when the fractional cross helicity and Alfven ratio at the proton-gyroradius scale have values that are broadly consistent with solar-wind measurements. We also predict how the temperatures of other ion species depend on their drift speeds.