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 ₀/T _0p in the solar wind assuming that stochastic heating is the dominant ion heating mechanism, where T _0i is the perpendicular temperature of species i and T _0p is the perpendicular proton temperature. This expression describes how T _0i/T _0p depends upon U _i and β_p, where U _i is the average velocity along B of species i in the proton frame and β_p is the ratio of the parallel proton pressure to the magnetic pressure, which we take to be ≲ 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 _0α/T _0p on U _α and β_p when the fractional cross helicity and Alfvén 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.