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太陽雑誌 会ー 22/01/10

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. From T. Matsumoto. Motivation. Coronal Field believed to be a force free field, or more precisely a nonlinear force free field (NLFFF)

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太陽雑誌 会ー 22/01/10

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  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. Motivation • 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

  4. Motivation • 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

  5. Model • 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 aNLFFF (aka Yokoyama-Shibata current sheet) • Looking at an area of the atmosphere where Cowling resistivity dominates Spitzer resistivity (so Spitzer resistivity can be ignored) From K.A.P. Singh

  6. Harris Current Sheet (J||=0) Lorentz Force Lorentz Force • 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

  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

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