Alfven Wave Turbulence and Perpendicular Ion Temperatures in Coronal Holes

Low-frequency Alfven-wave turbulence causes ion trajectories to become chaotic, or "stochastic," when the turbulence amplitude is sufficiently large. Stochastic orbits enable ions to absorb energy from the turbulence, increasing the perpendicular ion temperature even when the fluctuation frequencies are too small for a cyclotron resonance to occur. In this paper, an analytic expression for the stochastic heating rate is used in conjunction with an observationally constrained turbulence model to obtain an analytic formula for the perpendicular ion temperature as a function of heliocentric distance r, ion mass, and ion charge in coronal holes for values of r between 2 and 15 solar radii (Rs). The resulting temperature profiles provide a good fit to observations of protons and OVI ions at 2Rs < r < 3Rs from the Ultraviolet Coronagraph Spectrometer (UVCS). Stochastic heating also offers a natural explanation for several detailed features of the UVCS observations, including the preferential and anisotropic heating of minor ions, the rapid radial increase in the OVI temperature between 1.6Rs and 1.9Rs, and the abrupt flattening of the OVI temperature profile as r increases above 1.9Rs.