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

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

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

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

Solar Wind Solution More on solar wind If you neglect the effect of heat conduction and magnetic fields: Aassuming isothermal corona: so p=npkT+nekT = 2kT/mpρ Ref: Gombosi 12.1, P236 More on solar wind

Problems with Static corona Solar Wind Solution (cont.) If we assume stationary solar atmosphere (u=0) Where the index B indicate the Base of the corona As r For TB ~ 106 K p ~ 3 x10-4 pB >> any reasonable interstellar Pressure!!! So a Hot Static Corona cannot exist Problems with Static corona

Solar Wind Solution (cont.) Parker Solution: (neglecting electromagnetic effects) (1958) The momentum equation: is the local sound speed.

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

Solar Wind Solution (cont.) Parker’s solution for different coronal temperatures For example, for T=106K, and coronal density of 2x108cm-3, rc=6Rs. The solar wind accelerates to up to 40RS, and afterwards propagates to a nearly constant speed of 500km/s lachzor page 239 T. Gombosi

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

Solar Wind Structure Φ :the azimuth angle of magnetic field line at r Φ0: 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 Ω: solar rotation, 2.7 X 10-6 radians/sec At the Earth, r = 1 AU, Φ0 = ~ 45° When the plasma flow arrives at the Earth, the solar source has rotated 45°

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

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

IMF Bs: magnetic field at the source surface Θ: polar angle (fall more slowly!) As we go outward in the solar system the magnetic field becomes more and more azimuthal

IMF

The End