On the thermodynamics of MHD wave-heated solar wind protons

Abstract

It has been clearly observed by the NASA deep-space probes that the solar wind protons do not adiabatically cool as expected towards larger solar distances, but appear to be heated by non-collisional energy sources. In some papers these heating sources were directly or indirectly ascribed to pick-up ions incorporated as suprathermal ions into the background solar wind. Neutral interstellar H-atoms penetrate into the inner heliosphere and at ionization they are converted into pick-up ions. Here we do not consider how the magnetized solar wind flow incorporates these ions into the plasma bulk when enforcing their co-motion. We simply take the first step of their incorporation for guaranteed, namely the fast redistribution of pick-ups from an initially unstable toroidal to a quasistable bi-spherical distribution. The free energy lost by pick-ups during this redistribution goes into the turbulent MHD waves, and as such cascades down to the proton dissipation scale and finally is absorbed by solar wind protons. Here we investigate the thermodynamics of solar wind protons being heated by absorption of this free energy of pick-ups. In addition we also consider as a relevant and competing proton heat source the heating due to absorption of wave energy of convected MHD turbulences, showing that the latter source always dominates inside some critical solar distance, whereas the first one dominates in the outer heliospheric regions. We then solve the resulting differential equation for the solar wind proton temperature and show in the solutions obtained that a quasipolytropic behaviour of the solar wind protons with a distance-dependent polytropic index is found. The expression for the pressure clearly shows the change from an adiabatic to a quasipolytropic behaviour with a decreasing polytropic index at increasing distances as observed by the VOYAGERs. The quantitative run of the temperature and the polytropic index with solar distance thereby is strongly influenced by the interstellar H-atom density. The (pick-up ion)-induced heating also evidently leads to a wind-asymmetric solar wind temperature distribution with higher temperatures occuring in upwind direction compared to downwind direction.