Modeling/Inferring Coronal And Heliospheric Field From Photospheric Magnetic Field

1. Modeling/Inferring Coronal And Heliospheric Field From Photospheric Magnetic Field Yang Liu – Stanford University yliu@solar.stanford.edu KIPAC Workshop on Magnetism

2. Outline • HMI/SDO observables; • HMI science with vector magnetograms; • Modeling the coronal and heliospheric field from the photospheric magnetic field. KIPAC Workshop on Magnetism

3. HMI observables • Continuum intensity; • Full disk with a CCD of 4096×4096 pixels; • resolution is 0.5’’/pixel; • Cadence less than 1 minute. • Doppler velocity; • Full disk with a CCD of 4096×4096 pixels; • resolution is 0.5’’/pixel; • Cadence less than 1 minute. • Line-of-sight magnetic field; • Full disk with a CCD of 4096×4096 pixels; • resolution is 0.5’’/pixel; • Cadence less than 1 minute. • Vector magnetic field. • Full disk with a CCD of 4096×4096 pixels; • resolution is 0.5’’/pixel; • Cadence less than 2 minute. More information KIPAC Workshop on Magnetism

4. HMI Science (Magnetic Field) • Sources and drivers of solar activity and disturbances; • Evolution of small-scale magnetic elements (coronal heating); • Emergence of magnetic flux and solar transient events; • Magnetic configuration and mechanisms of solar flares and CMEs. • Links between the internal processes and dynamics of the corona and heliosphere; • Complexity and energetics of solar corona; • Coronal magnetic structure and solar wind. • Precursors of solar disturbances for space-weather forecast. • Determination of magnetic cloud Bs events. KIPAC Workshop on Magnetism

5. Modeling the coronal and heliospheric field. • Potential field source surface model (PFSS); • Hybrid model; • Non-linear force-free field model; • MHD simulation. KIPAC Workshop on Magnetism

6. Potential Field Source Surface Model where, j = 0 Coefficients Alm and Blm are determined from the boundary conditions. Schatten, Cosmic Electrodynamics, 2, 232, 1971. KIPAC Workshop on Magnetism From Arge 2005.

7. Solar Boundary: Magnetic Field KIPAC Workshop on Magnetism

8. Potential field source surface model PFSS KIPAC Workshop on Magnetism

9. Validation of PFSS KIPAC Workshop on Magnetism Zhao and Webb (2003)

10. Validation of PFSS Current Sheet plasma sheet KIPAC Workshop on Magnetism

11. Current Sheet Type 1 Type 2 Plasma Sheet Type 3 KIPAC Workshop on Magnetism

12. 3D MHD simulation shows that type 2 and 3 CMEs are faster than type 1. KIPAC Workshop on Magnetism

13. Data • We looked for the halo CMEs from the CMEs list of Gopalswamy’s group. 91 halo CMEs in the period from 2000 to 2004 were chosen. The solar sources were identified by that group, and were confirmed by other groups/works. KIPAC Workshop on Magnetism

14. Speed distribution for type 1 and types 2&3 CMEs. The types 2 & 3 CMEs are significantly faster than type 1 CMEs. KIPAC Workshop on Magnetism

15. Distributions of flare class for type 1 and 2 & 3 CMEs. They have very similar distributions. This suggests that the difference of the CMEs speed is not biased by flare importance. KIPAC Workshop on Magnetism

16. Long-Term Comparison of Observations and Solar Wind Speed Predictions Using the PFSS Wang & Sheeley (1990) simulate the solar wind speed at Earth for ~20 year period (1967-1988). i) Test hypothesis that Vsw and fs = (R/Rss)2[BP(R)/BP(Rss)]are inversely correlated. ii) Correlation between observed and simulated wind speed found. Simulated speed Observed Speed From Arge (2005) Wang & Sheeley, ApJ, 355, 726, 1990.

17. MWO CR1988 CR1987 CR1986 750 650 550 450 350 250 NSO 750 650 550 450 350 250 de Toma and Arge (2004)

18. Measurements Model Calculation Validation of PFSS Wang et al. 2000 KIPAC Workshop on Magnetism

19. Global Coronal Field: Extrapolations and Observations Photospheric field extrapolation (MWO) White light (pB) data HAO/MLSO/Mk3 Comparison of photospheric field extrapolations (left) to white light (pB) image (right) indicate a degree of qualitative correlation between closed field lines and streamers Gibson and Arge

20. Hybrid models • Potential field-current sheet model (PFCS model, Schatten 1971); • Horizontal current-source surface model ( HCSS model, Zhao & Hoeksema, 1992); • Horizontal current-current sheet model (HCCS model, Zhao & Hoeksema, 1994); • Current sheet-source surface model (CSSS model, Zhao & Hoeksema, 1995). KIPAC Workshop on Magnetism

21. Current-sheet source surface model KIPAC Workshop on Magnetism From Zhao & Hoeksema 1995.

22. Validation of CSSS model KIPAC Workshop on Magnetism From Zhao, 1999.

23. Non-linear force-free field model Wiegelmann, Solar Physics, in press, 2007. Case 1: use boundary data on both photosphere and source surface in 30<theta<150; Case 2: use boundary data on both photosphere and source surface in delta_theta<theta<180-delta_theta Case 3: use boundary data on both photosphere and source surface. Case 4: only use boundary data on photosphere. Magnetic field on the source surface is replaced by the initial potential field. KIPAC Workshop on Magnetism

24. MHD simulation Solar eclipse on March 29, 2006. Simulation was done by Linker et al at Science Application International Corporation (SAIC) at San Diego. Magnetic Field Lines (MHD Model) Polarization Brightness (MHD Model) Eclipse (Williams College)* & SOHO LASCO C2 Images KIPAC Workshop on Magnetism

25. HMI simulation • Extra boundary data help improve simulation results. KIPAC Workshop on Magnetism Hayashi et al 2006

26. Comparison of MHD and PFSS MHD PFSS From Riley et al, 2006, ApJ. KIPAC Workshop on Magnetism