Physics 681: Solar Physics and Instrumentation Lecture 22 Carsten Denker NJIT Physics Department Center for SolarTerrestrial Research November 15, 2005Center for Solar-Terrestrial Research The Magnetic Force Lorentz force (non-relativistic Ohms 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 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 / = 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 November 15, 2005Center for Solar-Terrestrial Research Galloway and Weiss (1981) Clark and Johnson (1967) November 15, 2005Center for Solar-Terrestrial Research Steady state: time scale of field decay d 2 / 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 November 15, 2005Center for Solar-Terrestrial Research GranulesSupergranulesGiant Cells Depth [10 6 m] l [10 6 m] [kg/m 3 ] u [m/s] c [Wb] 7 B e [T] B P [T] RmRm Galloway and Weiss (1981) November 15, 2005Center for Solar-Terrestrial Research Surface density = 3 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 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 km) November 15, 2005Center for Solar-Terrestrial Research November 15, 2005Center for Solar-Terrestrial Research Lin and Rimmele (1999) November 15, 2005Center for Solar-Terrestrial Research Wang et al. (1998) November 15, 2005Center for Solar-Terrestrial Research November 15, 2005Center for Solar-Terrestrial Research November 15, 2005Center for Solar-Terrestrial Research November 15, 2005Center for Solar-Terrestrial Research Langhans et al. (2002) November 15, 2005Center for Solar-Terrestrial Research