Nature of stochastic ion heating in the solar wind: testing the dependence on plasma beta and turbulence amplitude

The solar wind undergoes significant heating as it propagates away from the Sun; the exact mechanisms responsible for this heating are not yet fully understood. We present for the first time a statistical test for one of the proposed mechanisms, stochastic ion heating. We use the amplitude of magnetic field fluctuations near the proton gyroscale as a proxy for the ratio of gyroscale velocity fluctuations to perpendicular (with respect to the magnetic field) proton thermal speed, defined as ${ϵ}_p$. Enhanced proton temperatures are observed when ${ϵ}_p$ is larger than a critical value ($\sim 0.019-0.025$). This enhancement strongly depends on the proton plasma beta (${\beta }_{\mathrm{\mid }\mathrm{\mid }p}$); when ${\beta }_{\mathrm{\mid }\mathrm{\mid }p}\ll 1$ only the perpendicular proton temperature $T_{\perp }$ increases, while for ${\beta }_{\mathrm{\mid }\mathrm{\mid }p}\sim 1$ increased parallel and perpendicular proton temperatures are both observed. For ${ϵ}_p$ smaller than the critical value and ${\beta }_{\mathrm{\mid }\mathrm{\mid }p}\ll 1$ no enhancement of $T_p$ is observed while for ${\beta }_{\mathrm{\mid }\mathrm{\mid }p}\sim 1$ minor increases in $T_{\parallel }$ are measured. The observed change of proton temperatures across a critical threshold for velocity fluctuations is in agreement with the stochastic ion heating model of Chandran et al. (2010). We find that ${ϵ}_p>{ϵ}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}$ in 76% of the studied periods implying that stochastic heating may operate most of the time in the solar wind at 1 AU.