Empirical Measurement of Diffusive Heating across Earth’s Bow Shock

We use high cadence observations of velocity distribution functions (VDFs) from the Magnetospheric Multiscale Mission (MMS) to empirically estimate diffusion coefficients and heating rates in a crossing of the Earth’s bow shock. We approximate the observed VDFs using non-parametric representations and evaluate the gradients of the modeled VDFs (GPR-VDF) to empirically estimate diffusion coefficients. This allows us to have a better representation of the non-thermal features of the distribution functions. We invert the proton guiding center equation to get estimates of diffusion coefficients and proton heating rates. We compare these results with theoretical models and simulations of stochastic heating, heating via cyclotron or Landau damping, and other heating methods to constrain the heating mechanism(s) at work across the shock. Our approach allows for an estimate from observations of collisionless heating rates within a kinetic framework and discussion of the mechanism(s) at work. This methodology could be applied to future multipoint measurements in the magnetosphere (e.g. Plasma Observatory) to study heating across shocks and other regions of interest.