The Steady Global Corona and Solar Wind: A Three-dimensional MHD Simulation with Turbulence Transport and Heating

We present a fully three-dimensional magnetohydrodynamic model of the solar corona and solar wind with turbulence transport and heating. The model is based on Reynolds-averaged solar wind equations coupled with transport equations for turbulence energy, cross helicity, and correlation scale. The model includes separate energy equations for protons and electrons and accounts for the effects of electron heat conduction, radiative cooling, Coulomb collisions, Reynolds stresses, eddy viscosity, and turbulent heating of protons and electrons. The computational domain extends from the coronal base to 5 au and is divided into two regions: the inner (coronal) region, 1-30 R☉, and the outer (solar wind) region, 30 R☉-5 au. Numerical steady-state solutions in both regions are constructed by time relaxation in the frame of reference corotating with the Sun. Inner boundary conditions are specified using either a tilted-dipole approximation or synoptic solar magnetograms. The strength of solar dipole is adjusted, and a scaling factor for magnetograms is estimated by comparison with Ulysses observations. Except for electron temperature, the model shows reasonable agreement with Ulysses data during its first and third fast latitude transits. We also derive a formula for the loss of angular momentum caused by the outflowing plasma. The formula takes into account the effects of turbulence. The simulation results show that turbulence can notably affect the Sun's loss of angular momentum.