Heliosphere: Solar Wind

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Heliosphere Solar Wind
CSI 662 / ASTR 769 Lect. 05,
February 27 Spring 2007

• References
• Gombosi Chap. 12, P236 P252 (main reference)
• Tascione Chap. 3, P31-P40 (supplement)
• Prolss 6.1 6.2, P277-P314 (supplement)
• Update on 2007/03/15

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Ideal MHD Frozen-in effect

• Reference
• Prolss A.14, P484-P487
• The magnetic flux passing through a closed curve
  that moves with the plasma flow velocity remains
  constant
• Plasma elements connected at any point in time by
  a common magnetic field line remain connected by
  a common field line

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What is Solar Wind?

• Solar wind is the continuous flow of plasma
  outward from the Sun through the solar system
• It was recognized in 1950s by observing the tails
  of comets the straight blue tail could be driven
  by plasma flow

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What Causes Solar Wind?

• High thermal pressure in hot corona overcomes the
  gravitational constraints, resulting in coronal
  expansion
• Extremely low pressure (10 orders of magnitude
  smaller) in interstellar medium can not contain
  the coronal pressure
• Expansion becomes supersonic

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More on solar wind
Solar Wind Solution
If you neglect the effect of heat conduction and
magnetic fields
Aassuming isothermal corona so pnpkTnekT
2kT/mp?
Ref Gombosi 12.1, P236
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Problems with Static corona
Solar Wind Solution (cont.)
If we assume stationary solar atmosphere (u0)
Where the index B indicate the Base of the corona
As r??
For TB 106 K
p? 3 x10-4 pB gtgt any reasonable
interstellar Pressure!!! So a Hot Static Corona
cannot exist
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Solar Wind Solution (cont.)
Parker Solution (neglecting electromagnetic
effects) (1958)
The momentum equation
is the local sound speed.
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Solar Wind Solution (cont.)
Critical distance where kinetic energy equals
gravitational energy
Type V solution gives the right solar wind sonic
speed at the critical distance
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lachzor page 239 T. Gombosi
Solar Wind Solution (cont.)
Parkers solution for different coronal
temperatures
For example, for T106K, and coronal density of
2x108cm-3, rc6Rs. The solar wind accelerates to
up to 40RS, and afterwards propagates to a nearly
constant speed of 500km/s
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Solar Wind Structure
Archimedean Spiral

• Garden Sprinkler Analogy
• Jetlines that connect the flow elements from the
  same differentially small source region form an
  Archimedean spiral
• However, the streamline, along which an
  individual flow element is flowing, is strictly
  radial

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Solar Wind Structure

• F the azimuth angle of magnetic field line at r
• F0 the azimuth angle of magnetic field footpoint
  at the source surface
• Rs source surface, e.g., 3 Rsun
• Usw solar wind speed, e.g., 400 km/s
• O solar rotation, 2.7 X 10-6 radians/sec
• At the Earth, r 1 AU, F0 45
• When the plasma flow arrives at the Earth, the
  solar source has rotated 45

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Interplanetary magnetic Field (IMF) structure

• Frozen-in theorem Plasma elements connected at
  any point in time by a common magnetic field line
  remain connected by a common field line
• Since the plasma flow in a single spiral
  jet-line originates from a common source, the IMF
  should follow the jet-line, thus also display an
  Archimedean spiral pattern.
• Magnetic field is rooted in the photospheric
  surface of the Sun
• At certain height in the corona (e.g., 3 Rs), all
  magnetic field lines open and point radially. A
  surface of this is called source surface
• The spiral pattern can be traced back to the
  source surface

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IMF

• Frozen-in Theorem The magnetic flux passing
  through a closed curve that moves with the plasma
  flow velocity remains constant

• Because magnetic field along the jetline

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IMF

• Bs magnetic field at the source surface
• T polar angle

(fall more slowly!)
As we go outward in the solar system the magnetic
field becomes more and more azimuthal
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IMF
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The End