Reproducing the Solar Wind proton temperature profile via DNS of MHD turbulence
Résumé
Context: The Solar Wind proton temperature Tp shows a radial profile R-0.9 significantly shallower than the adiabatic R-4/3 profile [Totten et al 1996]. This temperature profile has been attributed to turbulent heating, which requires a dissipation rate equal to Q = 3.610-5TpU/R[J/(kg s)] (1) [Vasquez et al 2007]. The possibility of a turbulent heating large enough to modify the radial profile of the temperature has not been verified yet via direct numerical simulations. Aim: We want to test if MHD turbulence developing in the range [0.2,1] AU is able to reproduce the observed R-0.9 temperature profile. Method: We use the expanding box model (EBM) [Grappin & Velli 1996] which incorporates the effects of expansion into the compressible MHD equations, and so allows to follow the evolution of the plasma advected by the solar wind between 0.2 and 1 AU. In the absence of turbulence, the R-4/3 temperature profile is obtained. We start at 0.2 AU with mean field almost aligned with the radial and k⊥-1 spectrum perpendicular to the mean field [Verdini, Grappin 2016]. Simple phenomenology (Kolmogorov) suggests that the ratio between turbulent heating and the required heating (1) is close to M2/ε, where M is the Mach number of the large eddies and ε is the nonlinear time normalized by the transport time of the plasma by the wind. We thus explore the (M,ε) parameter space and examine whether a large enough value of M2/ε indeed allows to recover the temperature profile observed by Totten et al (1996). Results: We have obtained significant slowing down of the adiabatic cooling by considering increasing Mach numbers and/or decreasing ε and approach in some cases the R-0.9 temperature profile. The role of the compressibility in the cascade is examined.