1. Effect of solar chromospheric neutrals on equilibrium field structures - T. Arber, G. Botha & C. Brady (ApJ 2009) 太陽雑誌会ー 22/01/10

2. From T. Matsumoto

3. Coronal Field believed to be a force free field, or more precisely a nonlinear force free field (NLFFF) Extrapolation from the boundary requires the boundary to have a NLFFF But photospheric fields, where observations of magnetic field are most accurate, are not NLFFF Extrapolations of photospheric fields give a good approximation of the coronal field – Somewhere in the upper photosphere / chromosphere the field becomes a NLFFF Motivation

4. What mechanism allows this to happen – Chromospheric neutrals may be important (as well as gravitaional stratification or plasma becoming low β) – This is a study of how Cowling resistivity affects chromospheric equilibrium fields (As Cowling resisitivity (Ambipolar diffusion) is known to produce Nonlinear force free fields - NLFFF) α is a measure of the parallel current, they studied the evolution of α under Cowling resistivity for a 1 2/2 D current sheet where the amount of shear is varied Motivation

5. Model From K.A.P. Singh MHD equations (including Spitzer, Cowling and viscous terms) Define height in atmosphere through density and temperature These values also determine the value of the cowling resistivity (greatest in upper chromosphere) b gives the amount of shear of the magnetic field. 0 is a Harris current sheet and 1 is a NLFFF (aka Yokoyama-Shibata current sheet) Looking at an area of the atmosphere where Cowling resistivity dominates Spitzer resistivity (so Spitzer resistivity can be ignored)

6. Harris Current Sheet (J || =0) Lorentz force is balanced by pressure gradient in a fully ionized plasma If there is a neutral component in the plasma, this will flow along the lines of hydrodynamic force The force on the ions (still frozen to the magnetic field) from the gas will decrease, meaning the ions move in the direction of the Lorentz force The current sheet will collapse into a singularity. N ++ + N N N + Pressure Gradient Lorentz Force

7. Current Sheet with Shear (J || ≠0) Cowling resistivity cannot work on the component of J that acts parallel to the magnetic field Therefore only perpendicular current is dissipated This leaves a current sheet that is force free, as the Lorentz force now balances inside the current sheet The parallel current has increased.

8. Current Sheet with Shear (J || ≠0) The smaller the initial shear, the larger and thinner profile of α created Implies that accuracy of observational estimate of α is heavily dependent on the initial field structure

9. Time dependence Characteristic time scale for force free field to be created was found to be: Takes about 10~20 minutes for a field above 800km to relax to a force free state.

10. Conclusion & Summary Maximum value and decrease in FWHM of α more pronounced for small b (small amount of shearing of field) Any shear in the initial field and Cowling resistivity is able to create a force free field – Estimated to take about 10~20 mins This work studies a highly simplified setting and ignores the complex chromospheric dynamics and so only provides a handle on how Cowling resistivity would really affect flux emergence

11. Application to my work Study of how the Kippenhahn-Schlueter prominence model evolves under Cowling resistivity

12. Bx/Bz= Black: 0.1 Green: 0.2 Blue: 0.3 Magenta: 0.4 Magenta-ish: 0.5 Red: 0.7 Purple: 1.0