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

2. November 15, 2005Center for Solar-Terrestrial Research 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 10 4 Pa can be balanced by B ≈ 0.15 T  In sunspots we see at deeper layer  2  10 4 Pa  B ≈ 0.3 T  Magnetic tension is the tendency of lines of force to shorten themselves  restoring force to perturbations

3. November 15, 2005Center for Solar-Terrestrial Research 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 R m = 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

4. November 15, 2005Center for Solar-Terrestrial Research Galloway and Weiss (1981) Clark and Johnson (1967)

5. November 15, 2005Center for Solar-Terrestrial Research  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 R m  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 B P corresponds to an equilibrium between magnetic and gas pressure

6. November 15, 2005Center for Solar-Terrestrial Research GranulesSupergranulesGiant Cells Depth [10 6 m]0.510150 l [10 6 m]115100 ρ [kg/m 3 ]10-3110 u [m/s]200040070 Φ c [Wb] 7  10 8 3  10 11 2  10 13 B e [T]0.070.450.9 B P [T]0.5502500 RmRm 10300350 Galloway and Weiss (1981)

7. November 15, 2005Center for Solar-Terrestrial Research  Surface density ρ = 3  10 -4 kg/m 3, velocity of granules u = 2.0 km/s  equipartition field B e = 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)

8. November 15, 2005Center for Solar-Terrestrial Research http://www.kis.uni-freiburg.de/~steiner/

9. November 15, 2005Center for Solar-Terrestrial Research Lin and Rimmele (1999)

10. November 15, 2005Center for Solar-Terrestrial Research Wang et al. (1998)

11. November 15, 2005Center for Solar-Terrestrial Research http://nsosp.nso.edu/dst/images/fill1.gif

12. November 15, 2005Center for Solar-Terrestrial Research

13. November 15, 2005Center for Solar-Terrestrial Research

14. November 15, 2005Center for Solar-Terrestrial Research Langhans et al. (2002)

15. November 15, 2005Center for Solar-Terrestrial Research http://dotdb.phys.uu.nl/DOT/Showpiece/movies.html