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Lecture 18: The solar wind

Lecture 18: The solar wind . Topics to be covered: Solar wind Inteplanetary magnetic field. The solar wind. Biermann (1951) noticed that many comets showed excess ionization and abrupt changes in the outflow of material in their tails - is this due to a solar wind?

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Lecture 18: The solar wind

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  1. Lecture 18: The solar wind • Topics to be covered: • Solar wind • Inteplanetary magnetic field PY4A01 - Solar System Science

  2. The solar wind • Biermann (1951) noticed that many comets showed excess ionization and abrupt changes in the outflow of material in their tails - is this due to a solar wind? • Assumed comet orbit perpendicular to line-of-sight (vperp) and tail at angle  => tan = vperp/vr • From observations, tan  ~ 0.074 • But vperp is a projection of vorbit => vperp = vorbitsin ~ 33 km s-1 • From 600 comets, vr ~ 450 km s-1. • See Uni. New Hampshire course (Physics 954) for further details: http://www-ssg.sr.unh.edu/Physics954/Syllabus.html PY4A01 - Solar System Science

  3. The solar wind • STEREO satellite image sequences of comet tail buffeting and disconnection. PY4A01 - Solar System Science

  4. Parker’s solar wind • Parker (1958) assumed that the outflow from the Sun is steady, spherically symmetric and isothermal. • As PSun>>PISM => must drive a flow. • Chapman (1957) considered corona to be in hydrostatic equibrium: • If first term >> than second => produces an outflow: • This is the equation for a steadily expanding solar/stellar wind. Eqn. 1 Eqn. 2 PY4A01 - Solar System Science

  5. Parker’s solar wind (cont.) • As, or • Called the momentum equation. • Eqn. 3 describes acceleration (1st term) of the gas due to a pressure gradient (2nd term) and gravity (3rd term). Need Eqn. 3 in terms of v. • Assuming a perfect gas, P = R  T /  (R is gas constant;  is mean atomic weight),the 2nd term of Eqn. 3 is: Eqn. 3 Isothermal wind => dT/dr 0 Eqn. 4 PY4A01 - Solar System Science

  6. Parker’s solar wind (cont.) Eqn. 5 • Now, the mass loss rate is assumed to be constant, so the Equation of Mass Conservation is: • Differentiating, • Substituting Eqn. 6 into Eqn. 4, and into the 2ndterm of Eqn. 3, we get • A critical point occurs when dv/dr  0i.e., when • Setting Eqn. 6 PY4A01 - Solar System Science

  7. Parker’s solar wind (cont.) • Rearranging => • Gives the momentum equation in terms of the flow velocity. • If r = rc, dv/dr -> 0 or v = vc, and if v = vc, dv/dr -> ∞ or r = rc. • An acceptable solution is when r = rcand v = vc(critical point). • A solution to Eqn. 7 can be found by direct integration: where C is a constant of integration. Leads to five solutions depending on C. Eqn. 7 Eqn. 8 Parker’s “Solar Wind Solutions” PY4A01 - Solar System Science

  8. Parker’s solutions • Solution I and II are double valued. Solution II also doesn’t connect to the solar surface. • Solution III is too large (supersonic) close to the Sun - not observed. • Solution IV is called the solar breeze solution. • Solution V is the solar wind solution (confirmed in 1960 by Mariner II). It passes through the critical point at r = rcand v = vc. v/vc Critical point r/rc PY4A01 - Solar System Science

  9. Parker’s solutions (cont.) • Look at Solutions IV and V in more detail. • Solution IV: For large r, v 0and Eqn. 8 reduces to: • Therefore, r2v  rc2vc = const or • From Eqn. 5: • From Ideal Gas Law: P∞ = R  ∞ T /  => P∞ = const • The solar breeze solution results in high density and pressure at large r =>unphysical solution. PY4A01 - Solar System Science

  10. Parker’s solutions (cont.) • Solution V: From the figure, v >> vcfor large r. Eqn. 8 can be written: • The density is then: =>   0 as r  ∞. • As plasma is isothermal (i.e., T = const.), Ideal Gas Law => P  0 as r ∞. • This solution eventually matches interstellar gas properties => physically realistic model. • Solution V is called the solar wind solution. PY4A01 - Solar System Science

  11. Observed solar wind • Fast solar wind (v~700 km s-1) comes from coronal holes. • Slow solar wind (v<500 km s-1) comes from closed magnetic field areas. PY4A01 - Solar System Science

  12. Interplanetary magnetic field Bor v  • Solar rotation drags magnetic field into an Archimedian spiral (r = a). • Predicted by Eugene Parker => Parker Spiral: r - r0 = -(v/)( - 0) • Winding angle: • Inclined at ~45º at 1 AU ~90º by 10 AU. Br or vr B r (r0, 0)  PY4A01 - Solar System Science

  13. Alfven radius • Close to the Sun, the solar wind is too weak to modify structure of magnetic field: • Solar magnetic field therefore forces the solar wind to co-rotate with the Sun. • When the solar wind becomes super-Alfvenic • This typically occurs at ~50 Rsun (0.25 AU). • Transition between regimes occurs at the Alfven radius (rA), where • Assuming the Sun’s field to be a dipole, PY4A01 - Solar System Science

  14. The Parker spiral • http://beauty.nascom.nasa.gov/~ptg/mars/movies/ PY4A01 - Solar System Science

  15. Heliosphere PY4A01 - Solar System Science

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