V. Usmanov, 1,2 W. H. Matthaeus, 1 M. L. Goldstein, 2,3 and R. Chhiber 1

1. Three-dimensional MHD Simulation of the Solar Corona and Solar Wind with Turbulence Transport and Heating • V. Usmanov,1,2 W. H. Matthaeus,1 M. L. Goldstein,2,3 • and R. Chhiber1 • 1 Department of Physics and Astronomy, University of Delaware • 2 NASA Goddard Space Flight Center • 3 Space Science Institute, Boulder, CO Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

2. Model Outline • Global 3D MHD solar corona and solar wind (and global heliosphere) model with turbulent transport and heating • Takes into account effects of turbulence on the flow and vice versa. • Boundary conditions are specified at the coronal base (just above the transition region) • Mean-field (Reynolds-averaged) MHD equations are solved simultaneously with turbulence transport equations • Turbulence model: three scalar equations for turbulence energy, normalized cross-helicity, and correlation length • The computational domain is split into sub-regions: corona and near solar wind (two-fluid: thermal protons and electrons), distant solar wind (three-fluid: thermal protons, electrons, pickup protons), heliospheric interface (four-fluid: thermal protons, electrons, pickup protons, interstellar hydrogen) • Predictions and context for upcoming Parker Solar Probe and Solar Orbiter missions Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

3. Reynolds Averaging Parker Solar Probe SVG Meeting, JHU/APL, Laurel, MD, October 6, 2017

4. Two-Fluid Reynolds-Averaged MHD Equations with Turbulence Transport Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

5. Coupled Governing Equations: Mean Flow + Turbulence mean flow turbulence Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

6. Model Assumptions Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

7. Two-Fluid Coronal Model with Turbulence Transport 1-20 R, Meridional Plane, Solar Dipole Tilted by 10o Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

8. Two-Fluid Solar Wind Model with Turbulence Transport 20 R- 5 AU, Meridional Plane, Solar Dipole Tilted by 10o Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

9. Comparison with Ulysses observations in 1994-1995 Solar Dipole Tilted by 10o Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

10. Applications • Location of sonic, Alfvén, and β=1 surfaces • Collisional and turbulent dynamical ages of the solar wind plasma • Comparisons with remote imaging of the corona • Azimuthal velocity and angular momentum loss rate • Diffusion coefficients • … (Rohit Chhiber’s talk) Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

11. Mach, Alfvén Mach, and Plasma β Surfaces Meridional Plane, Solar Dipole Tilted by 10o 1-20 R 1-20 R 1R - 1 AU Heavy white lines: M = MA = β = 1 Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

12. Azimuthal Velocity Weber & Davis (1967) Simulation results Pizzo (1978) Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

13. WSO Magnetogram Scaling by Comparison with Ulysses Observations in 1994-1995, CR1898, 1x Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

14. WSO Magnetogram Scaling by Comparison with Ulysses Observations in 1994-1995, CR1898, 3x Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

15. WSO Magnetogram Scaling by Comparison with Ulysses Observations in 1994-1995, CR1898 Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

16. WSO Magnetogram Scaling by Comparison with Ulysses Observations in 2007-2008, CR2078, 1x Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

17. WSO Magnetogram Scaling by Comparison with Ulysses Observations in 2007-2008, CR2078, 4x Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

18. WSO Magnetogram Scaling by Comparison with Ulysses Observations in 2007-2008, CR2078 Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

19. WSO Magnetogram Scaling • Zhao and Hoeksema (1995): “As the inner boundary condition, the observed photospheric magnetic field is corrected by a factor of 1.8 and 3.6.” • Riley et al. (2014): “Wilcox Solar Observatory (WSO) synoptic maps must be multiplied by a factor of 3 – 4 to match Mount Wilson Observatory (MWO) estimates.” Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

20. Untilted Dipole: Meridional Plane, 0.3-100 AU Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

21. Contour plots of computed parameters in the meridional plane from 40 to 600 AU for “solar minimum” conditions s Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

22. Planned Development • Add upper chromosphere and transition region into the coronal model • Include eddy viscosity/turbulent resistivity into the coronal models • Include compressibility of fluctuations and an evolution equation for energy difference • Time-dependent simulations: time-dependent coronal and solar wind evolution, CMEs Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017

23. Summary • A fully 3D MHD model of the solar corona, solar wind (and global heliosphere) that incorporates turbulence transport and heating. • Turbulence transport equations are coupled and solved simultaneously with mean-flow solar wind equations. • Using the model, we compute the distributions of plasma, magnetic field, and turbulence quantities from the coronal base to the outer heliosphere. • The model takes into account effects of turbulence on the flow and vice versa. • The model can be applied to the problems of solar modulation of galactic cosmic rays and propagation of solar energetic particles (SEPs). • The model can make predictions for the Solar Probe Plus and Solar Orbiter projects. Parker Solar Probe SWG Meeting, JHU/APL, Laurel, MD, Oct 6, 2017