Physics 681: Solar Physics and Instrumentation Lecture 22

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Physics 681 Solar Physics and Instrumentation
Lecture 22

• Carsten Denker
• NJIT Physics Department
• Center for SolarTerrestrial Research

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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 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

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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 / ? 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

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Clark and Johnson (1967)
Galloway and Weiss (1981)
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• 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 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

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Galloway and Weiss (1981)
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• Surface density ? 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 gt0.1 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)

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http//www.kis.uni-freiburg.de/steiner/
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Lin and Rimmele (1999)
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Wang et al. (1998)
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http//nsosp.nso.edu/dst/images/fill1.gif
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Langhans et al. (2002)
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http//dotdb.phys.uu.nl/DOT/Showpiece/movies.html