Lecture 17: The solar wind

Transcription

1 Lecture 17: The slar wind Tpics t be cvered: Slar wind Inteplanetary magnetic field

2 The slar wind Biermann (1951) nticed that many cmets shwed excess inizatin and abrupt changes in the utflw f material in their tails - is this due t a slar wind? Assumed cmet rbit perpendicular t line-f-sight (v perp ) and tail at angle => tan = v perp /v r Frm bservatins, tan ~ But v perp is a prjectin f v rbit => v perp = v rbit sin ~ 33 km s -1 Frm 600 cmets, v r ~ 450 km s -1. See Uni. New Hampshire curse (Physics 954) fr further details:

3 The slar wind STEREO satellite image sequences f cmet tail buffeting and discnnectin.

4 Parker s slar wind Parker (1958) assumed that the utflw frm the Sun is steady, spherically symmetric and isthermal. As P Sun >>P ISM => must drive a flw. Chapman (1957) cnsidered crna t be in hydrstatic equibrium: dp dr = ρg dp dr + GM Sρ r 2 = 0 Eqn. 1 If first term >> than secnd => prduces an utflw: dp dr + GM Sρ + ρ dv r 2 dt = 0 Eqn. 2 This is the equatin fr a steadily expanding slar/stellar wind.

5 Parker s slar wind (cnt.) As, dv dt = dv dr dr dt = dv dr v dp => dr + GM Sρ r 2 + ρv dv dr = 0 r v dv dr + 1 dp ρ dr + GM S = 0 Eqn. 3 r 2 Called the mmentum equatin. Eqn. 3 describes acceleratin (1st term) f the gas due t a pressure gradient (2nd term) and gravity (3rd term). Need Eqn. 3 in terms f v. Assuming a perfect gas, P = R T / (R is gas cnstant; is mean atmic weight), the 2 nd term f Eqn. 3 is: dp dr = Rρ dt µ dr + RT dρ µ dr Isthermal wind => dt/dr 0 1 dp ρ dr = $ & RT % µ ' ) 1 dρ ( ρ dr Eqn. 4

6 Parker s slar wind (cnt.) Nw, the mass lss rate is assumed t be cnstant, s the Equatin f Mass Cnservatin is: dm = 4πr 2 ρv = cnst r 2 ρv = cnst dt Eqn. 5 Differentiating, d(r 2 ρv) = r 2 ρ dv dr dr => 1 dρ ρ dr = 1 v dv dr 2 r + ρv dr2 dr + r2 v dρ dr = 0 Eqn. 6 Substituting Eqn. 6 int Eqn. 4, and int the 2 nd term f Eqn. 3, we get v dv dr + RT # % µ 1 $ v dv dr 2 & ( + GM S = 0 r' r 2 # v RT & % ( dv $ µv ' dr 2RT µr + GM S = 0 r 2 A critical pint ccurs when dv/dr 0 i.e., when 2RT µr = GM S r 2 Setting v c = RT /µ => r c = GM S /2v c 2

7 Parker s slar wind (cnt.) Rearranging => v 2 2 ( v c ) 1 v dv dr = 2 v 2 c r (r r c) Eqn. 7 2 Gives the mmentum equatin in terms f the flw velcity. If r = r c, dv/dr -> 0 r v = v c, and if v = v c, dv/dr -> r r = r c. An acceptable slutin is when r = r c and v = v c (critical pint). A slutin t Eqn. 7 can be fund by direct integratin: " $ # v v c % ' & 2 " ln v % $ ' # v c & 2 " = 4ln r % $ ' + 4 r Eqn. 8 c # r c & r + C Parker s Slar Wind Slutins where C is a cnstant f integratin. Leads t five slutins depending n C.

8 Parker s slutins Slutin I and II are duble valued. Slutin II als desn t cnnect t the slar surface. Slutin III is t large (supersnic) clse t the Sun - nt bserved. v/v c Slutin IV is called the slar breeze slutin. Critical pint Slutin V is the slar wind slutin (cnfirmed in 1960 by Mariner II). It passes thrugh the critical pint at r = r c and v = v c. r/r c

9 Parker s slutins (cnt.) Lk at Slutins IV and V in mre detail. Slutin IV: Fr large r, v 0 and Eqn. 8 reduces t: # ln v & % ( $ v c ' 2 # 4ln r & % $ r c ' ( v v = # r & % $ r ( ' c c 2 Therefre, r 2 v r c2 v c = cnst r v 1 r 2 Frm Eqn. 5: ρ = cnst r 2 v = cnst r c 2 v c = cnst Frm Ideal Gas Law: P = R T / => P = cnst The slar breeze slutin results in high density and pressure at large r =>unphysical slutin.

10 Parker s slutins (cnt.) Slutin V: Frm the figure, v >> v c fr large r. Eqn. 8 can be written: " $ # v v c % ' & 2 " 4 ln r % $ # r c & ' v v 2 ln " r % $ c # r ' & c The density is then: => 0 as r. ρ = cnst r 2 v cnst r 2 ln(r /r c ) As plasma is isthermal (i.e., T = cnst.), Ideal Gas Law => P 0 as r. This slutin eventually matches interstellar gas prperties => physically realistic mdel. Slutin V is called the slar wind slutin.

11 Observed slar wind Fast slar wind (>500 km s -1 ) cmes frm crnal hles. Slw slar wind (<500 km s -1 ) cmes frm clsed magnetic field areas. Figure frm McCmas et al., Gephysical Research Letters, (2008).

12 Interplanetary magnetic field B r v Slar rtatin drags magnetic field int an Archimedian spiral (r = a ). B r r v r Predicted by Eugene Parker => Parker Spiral: r - r 0 = -(v/ )( - 0 ) B r Winding angle: tanψ = B φ B r = v φ v r = Ω(r r 0) v r Inclined at ~45º at 1 AU ~90º by 10 AU. (r 0, 0 )

13 Alfven radius Clse t the Sun, the slar wind is t weak t mdify structure f magnetic field: 1/2ρv 2 << B2 8π Slar magnetic field therefre frces the slar wind t c-rtate with the Sun. When the slar wind becmes super-alfvenic This typically ccurs at ~50 R sun (0.25 AU). 1/2ρv 2 >> B2 8π Transitin between regimes ccurs at the Alfven radius (r A ), where 1/2ρv 2 = B2 8π Assuming the Sun s field t be a diple, B = M r 3 $ M 2 ' => r A = & ) % 4πρv 2 ( 1/ 6

14 The Parker spiral

15 Helisphere