太陽雑誌 会ー 22/01/10
DESCRIPTION
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) - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/1.jpg)
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
![Page 2: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/2.jpg)
From T. Matsumoto
![Page 3: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/3.jpg)
0
)(
Bj r
• 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
![Page 4: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/4.jpg)
• 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
perpr jBj 0
)(
Motivation
![Page 5: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/5.jpg)
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)
![Page 6: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/6.jpg)
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
++
+
NN
N+
Pressure Gradient
Lorentz Force Lorentz Force
zB
P
![Page 7: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/7.jpg)
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.
![Page 8: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/8.jpg)
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
![Page 9: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/9.jpg)
Time dependence
• Characteristic time scale for force free field to be created was found to be:
20
20
)()(2hBhL
• Takes about 10~20 minutes for a field above 800km to relax to a force free state.
![Page 10: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/10.jpg)
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
![Page 11: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/11.jpg)
Application to my work
Study of how the Kippenhahn-Schlueter prominence model evolves under Cowling resistivity
![Page 12: 太陽雑誌 会ー 22/01/10](https://reader036.vdocuments.mx/reader036/viewer/2022081417/56816124550346895dd07e0e/html5/thumbnails/12.jpg)
Bx/Bz=Black: 0.1Green: 0.2Blue: 0.3Magenta: 0.4Magenta-ish: 0.5Red: 0.7Purple: 1.0