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PY4A01 - Solar System Science Lecture 18: The solar wind oTopics to be covered: oSolar wind oInteplanetary magnetic field

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PY4A01 - Solar System Science The solar wind oBiermann (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? oAssumed comet orbit perpendicular to line-of-sight (v perp ) and tail at angle => tan = v perp /v r oFrom observations, tan ~ oBut v perp is a projection of v orbit => v perp = v orbit sin ~ 33 km s -1 oFrom 600 comets, v r ~ 450 km s -1. oSee Uni. New Hampshire course (Physics 954) for further details:

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

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PY4A01 - Solar System Science Parker’s solar wind oParker (1958) assumed that the outflow from the Sun is steady, spherically symmetric and isothermal. oAs P Sun >>P ISM => must drive a flow. oChapman (1957) considered corona to be in hydrostatic equibrium: oIf first term >> than second => produces an outflow: oThis is the equation for a steadily expanding solar/stellar wind. Eqn. 1 Eqn. 2

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PY4A01 - Solar System Science Parker’s solar wind (cont.) oAs, or oCalled the momentum equation. oEqn. 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. oAssuming a perfect gas, P = R T / (R is gas constant; is mean atomic weight), the 2 nd term of Eqn. 3 is: Eqn. 3 Eqn. 4 Isothermal wind => dT/dr 0

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PY4A01 - Solar System Science Parker’s solar wind (cont.) oNow, the mass loss rate is assumed to be constant, so the Equation of Mass Conservation is: oDifferentiating, oSubstituting Eqn. 6 into Eqn. 4, and into the 2 nd term of Eqn. 3, we get oA critical point occurs when dv/dr 0 i.e., when oSetting Eqn. 6 Eqn. 5

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PY4A01 - Solar System Science Parker’s solar wind (cont.) oRearranging => oGives the momentum equation in terms of the flow velocity. oIf r = r c, dv/dr -> 0 or v = v c, and if v = v c, dv/dr -> ∞ or r = r c. oAn acceptable solution is when r = r c and v = v c (critical point). oA 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. 8 Parker’s “Solar Wind Solutions” Eqn. 7

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

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PY4A01 - Solar System Science Parker’s solutions (cont.) oLook at Solutions IV and V in more detail. oSolution IV: For large r, v 0 and Eqn. 8 reduces to: oTherefore, r 2 v r c 2 v c = const or oFrom Eqn. 5: oFrom Ideal Gas Law: P ∞ = R ∞ T / => P ∞ = const oThe solar breeze solution results in high density and pressure at large r =>unphysical solution.

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PY4A01 - Solar System Science Parker’s solutions (cont.) oSolution V: From the figure, v >> v c for large r. Eqn. 8 can be written: oThe density is then: => 0 as r ∞. oAs plasma is isothermal (i.e., T = const.), Ideal Gas Law => P 0 as r ∞. oThis solution eventually matches interstellar gas properties => physically realistic model. oSolution V is called the solar wind solution.

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

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PY4A01 - Solar System Science Interplanetary magnetic field oSolar rotation drags magnetic field into an Archimedian spiral (r = a ). oPredicted by Eugene Parker => Parker Spiral: r - r 0 = -(v/ )( - 0 ) oWinding angle: oInclined at ~45º at 1 AU ~90º by 10 AU. B or v B r or v r B r (r 0, 0 )

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PY4A01 - Solar System Science Alfven radius oClose to the Sun, the solar wind is too weak to modify structure of magnetic field: oSolar magnetic field therefore forces the solar wind to co-rotate with the Sun. oWhen the solar wind becomes super-Alfvenic oThis typically occurs at ~50 R sun (0.25 AU). oTransition between regimes occurs at the Alfven radius (r A ), where oAssuming the Sun’s field to be a dipole,

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

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PY4A01 - Solar System Science Heliosphere

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