Physics 681: Solar Physics and Instrumentation – Lecture 22

1. Physics 681: Solar Physics and Instrumentation – Lecture 22 Carsten Denker NJIT Physics Department Center for Solar–Terrestrial Research

2. The Magnetic Force • Lorentz force (non-relativistic Ohm’s law = magnetohydrodynamic approximation) • The volume force can be divided into a magnetic pressure gradient and a magnetic tension • Magnetic flux tube applies a lateral pressure to the gas into which it is embedded • Typical pressure 104 Pa can be balanced by B ≈ 0.15 T • In sunspots we see at deeper layer  2  104 Pa  B ≈ 0.3 T • Magnetic tension is the tendency of lines of force to shorten themselves  restoring force to perturbations Center for Solar-Terrestrial Research

3. Magnetic Flux Tubes • Converging plasma motion is capable of concentrating magnetic flux • Cellular flows (granulation, mesogranulation, supergranulation, and giant cells) • Kinematic approximation (the flow v is given, the Lorentz force is neglected) • 2D, stationary flow consisting of rolls • Magnetic Reynolds number Rm = ul / η = 250 • Boundary conditions: field is vertical at all times at all boundaries • Field lines become deformed  diffusion term in the induction equation is no longer negligible  field line reconnection  magnetic flux is expelled from the interior and accumulated in sheets near the cell edges Center for Solar-Terrestrial Research

4. Clark and Johnson (1967) Galloway and Weiss (1981) Center for Solar-Terrestrial Research

5. Steady state: time scale of field decay d 2 / η equals time scale of advection l / u • Final flux after field concentration • Field amplification is rapid l / u (turnover time) • Expulsion of flux is slower 5( l / u ) and depends on Rm • Flux sheets may exist (chain-like crinkles) • Equipartition between kinetic and magnetic energy densities (dynamic regime) • Regions of motion and regions of fields mutually exclude each other • Critical flux • Field BP corresponds to an equilibrium between magnetic and gas pressure Center for Solar-Terrestrial Research

6. Galloway and Weiss (1981) Center for Solar-Terrestrial Research

7. Surface density ρ = 3  10-4 kg/m3, velocity of granules u = 2.0 km/s  equipartition field Be = 0.04 T • Observed fields are a factor 3 larger  convective collapse (convective instability in the presence of a magnetic field) • Stable flux tube exist for a minimum field of 0.1 T capable of suppressing the convective instability • The magnetic field is very weak for the major fraction of the solar surface • Locally stronger fields of >0.1 T in flux tubes • Solar magnetic fields are intermittent • Pores are sunspots lacking a penumbra (B ≈ 0.15 T, lifetime ≈ 1 day, size ≈ 5 arcsec) • Magnetic knots (B ≈ 0.1-0.2 T, “line gaps” in spectra, lifetime ≈ 1 hour, size 1-2 arcsec, IR observations, abundant near sunspots, ≈ 10 knots per 100 granules, knots have predominantly the opposite field of sunspots, flux is balanced) • Unresolved fields  filling factor (d ≈ 100-200 km) Center for Solar-Terrestrial Research

8. http://www.kis.uni-freiburg.de/~steiner/ Center for Solar-Terrestrial Research

9. Lin and Rimmele (1999) Center for Solar-Terrestrial Research

10. Wang et al. (1998) Center for Solar-Terrestrial Research

11. http://nsosp.nso.edu/dst/images/fill1.gif Center for Solar-Terrestrial Research

12. Center for Solar-Terrestrial Research

13. Center for Solar-Terrestrial Research

14. Langhans et al. (2002) Center for Solar-Terrestrial Research

15. http://dotdb.phys.uu.nl/DOT/Showpiece/movies.html Center for Solar-Terrestrial Research