Thermodynamic constraints on stochastic acceleration in compressional turbulence

Recent observations in the solar wind have revealed an important phenomenon. In circumstances where stochastic acceleration is expected, a suprathermal tail on the distribution function is formed with a common spectral shape: the spectrum is a power law in particle speed with a spectral index of -5. This common spectrum occurs in the quiet solar wind; in disturbed conditions downstream from shocks; and, in particular, throughout the heliosheath downstream from the termination shock of the solar wind currently being explored by Voyager 1. In this article, simple thermodynamic principles are applied to stochastic acceleration in compressional turbulence. The unique spectral index results when the entropy of the suprathermal tail has increased to the maximum allowable value. Relationships for the pressure in the suprathermal tail are also derived and found to be in agreement with observations. The results are shown to be consistent with the suprathermal tail arising from a cascade in energy, analogous to a turbulent cascade. The results may be applied broadly, because stochastic acceleration in compressional turbulence should be common in many astrophysical settings.