SOLAR WIND

VRIJE UNIVERSITEIT

BRUSSEL INSTIlUT O' AERONOMIE SPATIAlE OE BHGIQU£

. venu~ Circu!wr~ 3 1180 8PUXELLES

THIRD CYCLE IN ASTRONOMY PROGRAM OF TH E POST

GRADUATE LECTURES

T H E SOLAR WIND ^{(15 H)}

U itgav en van de Vrije Universlteit Brussel

Waaglaan 13 1050 Brussel

C. De Loore J. Lemaire

Hiets uit dele uitgove mag wordt.'n verveelvuldi!Jd zonder toestemming van de schrilver.

Aile vertoolrechten, overdr"kken en bewerk ingen worden voorbehouden in 0 lie londen.

•

Third Cycle 1n Astronomy Program of the post graduate lectures

THE SOLAR WIND (15 h)

Lectures at the

C.

De

Loore - J. Lemaire

Institut d'Aeronomie Spatiale, 3 Avenue Circulaire, Uccle, Instituut voor Ruimte-Aeronomie,Ringlaan 3, Ukkel

October 21 at ISh 30

1) Introduction (general description of the atmosphere of the Sun, the corona, the interplanetary and interstellar medium; history of the solar wind discovery and subsequent controversies).

1 h. - J. Lemaire

2) Methods of observations of the corona and the solar wind (measurement of the densities, bulk velocities, temperatures, heat fluxes, ionic composition, magnetic fields).

3) The physical properties of the solar wind medium (Debye Length; mean free path; Larmor radius; thermal and electrical conductivities;

Prandtl, Reynolds, Knudsen numbers; state of ionization; magnetic sector structures).

2h. - J. Lemaire

November 4 at 9h 30

4) Model calculations for the solar transition reg10n and the corona;

heating mechanism; mechanical fluxes; energy balance.

2h. - C. De Loore

UI

76/8/002

-2-

~2Y~ . '~§

at 9h

30

5) Theoretical models for the steady corona and the solar wind (one fluid multi fluid models; static. convective, hydrodynamic models).

2h. -

J.

Lemaire.

November 25 at 9h

30

---

6) Theoretical models for corona and solar wind (kinetic models).

2h. - M. Scherer

December 2 at 9h

30

---

7) Effects of rotation, viscosity, conductivity, heating, magnetic forces and waveS on the solar wind expansion; angular momentum transported by the solar wind.

2h. - J. Lemaire

8) The disturbed solar wind (observations and theory of the high-speed streams, discontinuities, shocks and Alfveen waves).

·

2h. -

J.

Lemaire

December 16 at 9h

30

9) Interaction of the solar wind with the planets (observations and theory of the bow shock and magnetopause of the Earth, other planets and the Moon; correlation between the geomagnetic activity and the solar wind velocity and interplanetary magnetic field direction).

2h. - M. Roth.

-3-

Third Cycle 1n Astronomy TIlE SOLAR WIND (21 October 1975) - J. LEMAIRE

1.- Some historical steps 1n coronal and solar wind SC1ences

After 1840 the corona was considered as extension of atmosphere of sun.

- 1869

- 1875

- 1896

Spectroscopic observation of f.reen coronal line A 5303 )\ (YOUNG)

Streamers associated with sunspots (SECCHI)

correlation between SUNSPOTS NUt~ER and ellipticity of coronal isophotes .- distinction bet\veen K (polarized) and F (unpolarized) coronae. - Reflexion of photospheric light by free electrons

(T ~ 5000 K) produce K cont inum spectrum

- hy 1930 : 18 coronal emlSSlon lines observed - they are attributed to

- 1930

- 1942

- 1945

- 1964

CORONIU11 (!?)

LYOT develops the coronograph - t!A5303i\ = {'-.9 )1.., is indication for high temperature, but atomic mass, of coronium unknoun ! v

=

V2leT 1m .

corona coronlum

EDLEN, identifies red line (A = 7892 )1..) as forbidden transition of FeXI - New indication of hi~h temperature: T. . . = 0,5 -

lOlllZatlon 1.1 x 106

K

T

=

1.5 - 1.8 x 10 h K, \v/1en deduced from observed electron corona

density gradient

new recombination process found by BURGESS - As a consequence,

.~ 6

T - T - 1.5 - £.0 x 10 K

(ionization) - (L'lA Doppler)-

- 1903

- 1931

- 1943

- 1931

-4-

BIRKELAHD and STOR~lE~ consider that sporad ic charged particle emission propagates from SUN to EARTH and generate AURORAE

magnetic storm effect also explained by sporadic solar corpuscular radiation (CHAPNAN and FERRARO).

aherration angle of comet tails indicate existence a mOVIng interplanetary medium (f!OFPIEISTER)

acceleration of irregularities In comet tails also indicate continous outward streaming of solar corpuscular radiation

(H IE R'1:\NN)

- 1938 - 1960 : Anti correlation of solar activity and cosmIC ray Forbush decrease also indicates presence beyond the corona of, streaming solar

(magnetized) material. (GOLD, 1960)

- 1957

- 1958

- 1960

- 1969

CHAPl'IMI shows importance of heat conduction by free electrons in corona, he extends hydrostatic model of corona beyond 1 A.U.

PARKER shm·;s that hydrostatic models are convectivcly unstahle (poo too large) - he proposes hydrodynamic supersonic expansion (solar wind)

CHM18ERLAIN, suggest an evaporative (subsonic) type expansion (solar breeze)

A controversy develloped.

Recent spacecraft observations confirmed PARKER supersonic velocities at 1 AU. Evaporative model fel into discredit.

It is found that with a correct exospheric electric field evaporative models also. lead to supersonic velocities at lAU. JOCKERS and

LL~~IRE - SCHFRER.

- 1959

.., 1961

- 1962

-5-

Lunik III, Venus I, detect charged particle fluxes of ~

9 -2 -1 P

10 cm sec (GRINGJ\UZ)

Explorer 10 1 2 108 -2 -1 -

280 km/sec

; ¢

= -

^{x cm sec v}

=

^;

3 8 -3 P lOS _{or.LT. ;::roup)} questionable ! ?

n

r = -

^cm T ^p '" ^K

Hariner 2 .: solar wind detected at all times ; v '" 300 - 860 km/sec

-3 -5

v =

500 km/sec ; n

=

5 cm : B

=

5 10 Gauss ...

r

After 1962 an over whelming amount of data came in.

These observations Hill be presented in the next lesson 1n a non-historic order.

-6-

lHBLI0GRAPHICAL p.EFEnENCES

BIERMANN,L., (1951), Comet tails and solar corpuscular radiation, Z. Ap., 29,

~

274.

BOWEN, I.S., and EDLEN, B., (1939), FeVII 1.n Nova Pictoris, Nature, 143, )74.

BURGESS, A., (964), Dielectronic recombination and the temperature of the solar Corona, Ap. J., 139, 776.

CHMtBERLAIN, J.I;I., (960), Ap. J., 131, 45.

CHJ\Pr-W~, S., and FERRARO, V.C.A., (931), Terrest. Nagnetism and Atmospheric Elec., 36, 77, 171.

CHAPMAN, S., (957), Notes on the solar corona and the terrestrial ionosphere, Smithson. Contr. Astrophys., 2, 1-12.

DESSLER, A.J., (1967), Revs. Geopbys., 5, l . FORBUSH, S.E., 0938a), Phys. Rev., 5/~, 975.

FORBUSH, S.E., STINCHCOHtI, T.B., and SCBEH1, H., (950), Phys. Rev., 79, 501.

GOLD, T., (1960), Astrophys. J. Suppl., 4, 406.

GROTRIAN, \'1., (931), 7.. Ap., 3, 199.

HOFFMEISTER, C., (1943), ~s. f. Astrophys., 23,265.

HUNDHAUSEN, A.J. (1972), Coronal expansion and solar wind, Springer-Verlag, B Berlin.

JOCKERS, K., (970), Solar Hind models based on exosplleric theory, Astron.

Astrophys., 6, 219-239.

LYOT, B., (1932), Study of the solar corona in the ahsence of an eclipse,

z.

^{Ap., 5, 73.}

LEMAIRE, J., and r'L SCHERER, Le champ electrique de polarisation dans l'exosphere ioni~ue polaire, C;H. Acad. Sc. Paris, 269, 666-669,

LEHAIRE, J. and H. SCHERER, (1971), Kinetic Hode Is of the Solar ~'!ind, JGR, 76, 7479.

-7-

LEt1AIRE, J., and t1. SCHERER, (1973), Kinetic Models of the Solar and polar h·inds, Rev. Geophys. and space physics, 11, 427-468.

MACKIN, R.J. and M. NEUGEBAUER, Eds., (1966), The Solar Ivinci, Pergamon Press, New York.

PARKER, E.N., (1963), Interplanetary Dynamical Processes, Interscience Publishers, New York.

PARKER, E.N., (1969), Theoretical Studies of the solar "lind phenomenon, Space Sci. Rev., 9, 325-360.

PARKER, E.N., (1971), Recent Developments ln Thcor:r of Solar Hind, Rev. Geophys. and Space Physics, 9,825-835.

SECCHI, Le P.a., (1875), Early history of eclipses in "Lc Soleil", 2nd ed. Gauthers-Villars, Paris, pp. 330-369.

STamlER, C., (1955), The Polar Aurora, Clarendon Press, Oxford.

van de HULST, H.C., (1953), in The Sun, G.P. Kuiper, Ed., University of Chicago Press, Chicago, p.306.

WALD~mIER, M. (1945)) Mitt. der harg. Natur. Gcs., 22. 185.

YOUNG, C.A. (1896), "The sun", pp. 237-276, Apllcton, New York.

-8

Astronomy THE SOLAR WIND (28 October 1975) -

J.

LEMAIRE

2

and

3.-

of the corona and Solar Wind

1)

- Separat of K continuum (photospheric 1 scattered by free electrons polarized) from the F cont (photospheric

1

scattered by dust particles

observat

not significantly ized near Sun) by photopolarimetric of corona during eclipses.

- Assuming radially symmetric and homogenous electron density model.

N (r) e

deduce theoretical br correct

N

r) model

[

n

toess distribution. - deduce new theoretical br

r -n

cm -3 - F . 1

Alpha icle concentration (not , ... ell known)

N + z 0.1 (?)

with observations sses ••. etc ..•

- Proton particle concentra (from quasi-neutrality eq.)

N + 2 N

P a

(r ^J 8 ^J

\f) •

broadening of

x

N e ^N _P

0.83

on colatitude

8

and heliocentric longitude 4 (Streamers diameter of Radio Source; Radio source scintillation)

/<N > 2

e

X(l,S Rei

~

1.6 r

- 0.7

-9-

2) Determination of temperature in corona - From isothermal harometric law

T e

10

7 ^j1

dlog N /d(l/d

e

- dlog N /d(l/r) determined from N (r) (see above)

e e

- 11 mean mo 1 e cuI a r rna s s (

0.1)

T (r) depends as

N

(r) on solar activity

e e

T (r) very sensitive toassumoovalue of X(r)

e

- Te (1.5 Rd ^{= 2 x 10 6} K (confirmed by other methods: line broadening - degree of ionization - radio brightness temperature - Type III burst observations)

3) Determination of bulk velocities in corona

- By Radar Echos (38 Mc/S) at 1.6 RO in corona; Doppler shifts showed slow expanSion (16 Km/sec) and erratic ("turbulent") motions

(+

100 km/

sec)

4) Density measurements in interplanetary space

- with Faraday cups or/and curved surface electrostatic ana1ysers, Energy per charge spectra are obtained (e.g. Fig. 2)

- f(E)

V ~E

6 E ' J(>Et/Q) - J(>E/Q)

- Nand N _P

_e

=f ^{f(~) d ~}

-10-

N Eo [ 0.4 ^{- )}

eo

^{- )}

-

^tl _{e :t p} ^{cm cm}

-

<r\ > =8.7 !4 cm ^{- )} p

- Alpha particle distribution (e.g. Fig. )

N /N

=

0.045 (comparable to photospheric abundance; higher values a p

of N /N are usua ly observed in high speed streams (~o. 25)

(l p

5) Velocities In interplanetary space

E /Q value for which f(E/Q) IS maXImum (in energy spectra) max

\-.' CO;

I

200 krn/ sec; 900 km/ sec] (e.g. Fig. 4)

- w approximately In -+ radi~l direction (+ 10° - IS°)

- Quiet solar wind average: <w> 325 km/sec

- w ++ :t w +

a p /(w - w )/w <15% (e.g. Fig. 5)

(l p p

6) Tempcrature~ In interplanetary space

- T P

T

" ,.1.

m 2,k

-+ -+ ')

« v - <w»- >

\I ,.1.

...

Temperature anisotropy In direction parallel to magnetic field B (e. g. Fig. 6)

- T correlated with proton bulk sreed <w >

p p

-11-

~

^{__ 11_-10}

^(K)

^{3 = 0.036 <~] p > (kml sec) - 5.54}

(Burlaga ond Ogilvie's relation) (Fig. ])

- < T >

P

- <T >

e

1.5 x 10 5 K

- T '" 4 T (v '" v )

a p ^a p

1.1

- 3 types of mar,netometers (spin coil; flux r,3te magnetometer; nuclear spin precession magnetometer)

- 1131 E: [ 0.2') y - 40 y

1

(Fig. 8)

(ly

=

10 -5 Gauss) (N.F. Ness)

- <ih II

to ecliptic plane; along /\rchemedian sratial direction,

<t+, >

til 135° or 315°; (e.g. Fig. 9)

- 1131 a 4.13 ^_r (i\U_)]-l. 25

- - (obs. radial dependance) 1.5

- Ness and Wilcox ohservcd persistent sector structure during 3 solar rotations (Fig. 10)

- B at lAU is correlated with B at photosphere (Fig. 11)

IO~

^d

)0 1

Ud ^'}

c ~

....

)-

I!f

f

ID ⁶

~ Q:

...

~d .J w

12-

e ATHAV. ""[NUL. I"(CJ([R. AND TItOIIIAS

• VAN Of: HUl.5T

o IIIICHAI/O .. kACPI1lll£LL

0,0 I ¹⁰

^IDO

IO~

^{~rL-______ ~+-}

__________

^~

__________ -+ __________

^~

__________

^~~

0010 O~ 10

•

HEIGHT AIIOY£ 1.'1118 ISOljllll AADII)

FIG.

1. -The electron density is plotted as a function of the height ahove the solar limb. The meas

ures refer to the solar equator about

th~

time of sunspot minimum.

200

--> 100

<D

·1,

~ ^C SO

:0

u 0

20

10 100

-13-

o He"

xW

I I

1000 2000 Energy! unit chorge

I I

5000 10000

Fig . 2 Tyrical Fxrlorcr 34 energy-rer-charge srectra at the rna,s til charge ratios MiQ= 1 alld 2 alOmic mas, ullits rer ciLctronic charge. The first or tllese.

corresronding to ^I H'. is indicated by the x·s. while the sewnd. corre'ronding to

"He· +. is indicated oy the (l's

V1 z

0 1= §!

a: w

V1 CD 0 lL 0

a: w CD ::<

:::>

z 300

250

200

150

100

50

ooL----o-oL5----0-L,o----o~,-5--~O~2~O-c~025

HELIUM - HYDROGEN DENSITY RATIO

Fig .. ~ The distrioutioll nr the ratios or helium alld hyuwgell numher densities observed hy the H EOS-l satellite'

I- Z

\.U U a::

~ 20 ...J

;;

a::

\.U I- Z

~

>- u Z

\.U ::J

10

13,976 VELA 3 MEASUREMENTS JULY 1965 TO NOV. 1967

AVERAGE fLOW SPEED' 400 km sec·1 MEDIAN FLOW SPEED'

380 km sec·¹

8

^{OL-__ ~ __ ~ __ -L __ _L __ ~ __ ~L-__ L_~±=~dL} __ ~

a: 250

u. ^{~50 450 550 650}

FLOW SPEED, km sec-I

750

fig.

It /\

hi,togr;lnl or the nllw 'pced, oh,erved hy Vela .1 ,p<l(en;111

20

10

-10

-14-

~(%) _Up

Fig.

5

/lislograrns of normalized hulk speed. (Top panel) All observalions. (Bnrtom panel) Ail observations exccpt for those laken in inlervals A, 8, and C of Figure L

c:

t.I

i:: u

"-

270⁰

fiGURE 6

VclaJB R.·S/65 4.759 hrs.

The temperature T(4)) as defined by equation (5.1) is shown in the V, V2 plane for the distribution measured in Figure 5.5; the projecled field B, is also shown.

12

\0 8 0 4

2

o

Median

l

2 4 6

IMP-I 20.4R second data n = 161.738

(F) = 60 ± 0.051 Median = 5.50 ± 0.25¹

II 10 I~ 14 10 III ~O

Gammas

Fl0URt: .8

The di~lribulion of inlerplanclary magnelic field magnilude as observed by IMP-I from 1963 to 1964. -

50~1 ---~---~---~

"

N

40

~30

o

It)

I

o

X

-

~

²⁰

'"

'"

'"

'"

'" -

^."..

^,..

10 f-y _____ ^W

0 150

2-FLUJD

MODEL

X I

250

;<;~~~~,,\..

\SO

\ _ ~\...D\'O

._____N' ...

~O'O~'-S ^~\\~

),)c-.; \'.J\-';'<

C. S CO~O

· 0

~~~\S

~~"SIJ~~

350 450 550 650

V (km/sec)

Figure, 7

•

750

t-' U1 I

-16-

S,t;6min Averages

North

KhptK~ Normal 10 ecliptic plane

Ectiplic plorw

~~~~~L---~--~8:~

8:-90"

Fig

9

Histograms of the interplanetary magnetic field orientatiun obscrlied on Imp 1 in 1963 " The angle rP is the solar ecliptic longitude of the \'ector field (\\'ith rP =0 the direction toward the sun) and the angle (I is the solar ecliptic latitude of t he vector field

Dec 20

0300

.

• • + • .-;:::::"..:::. . .

,-

...

_ .

.,., . ...

r ••

!

:::;

... .

^..:..

:..:.: ^{. .}

^{.... ::-~}

Dec J2

I~OO

n(;URI

'0

--

\

nee I 0,\00

SlOrrn

The sector structure of thc'inlcrplanet:lry magnetic field obserlied hv IMP-I. The plus or minus plliarities correspond to the positi\'~ and negati\'e directions indicated in figure 5,11.

Polarities in parentheses c(>rresl'(lIlll t(l a lll(lVCnll'nt inll> the shaded area of I"igure 5.11 for a fl'\\' hours in a SI11<",th and continuous manner.

~

'J

-- c: ','

:L

c_

~

c:

'J

c.

'J -

~

if)

I I

r / /

3 I 2

\ 5ou'c~ iud (f! -..:.. \

K - Si

--

-17-

1 PhOI V5phC'uc .-nOQn~"c ~1~ld ob~61ryed 0' !Aouni VI· s n 2 MognCIi( I.dd (ul(uIOit!d hom ;»Ol~nlto' !:"\'='CHY V'4> =-0

\.

~'-\ AU

3 Mngn~"( held ',on,p=,'ed by ,010' _on,~ riR = -B(V V) , iO

'nv

(ob,e,v.d • ,po(ecr~h 01 1 AU! dl

:.

Fig. 1/ 1\ sl(eleh i!lustrali:lg the wmrllialion of '.'"le eorClal fTlasncli( licld conli~urali()n in the "source Slirfaee" m0lkl

Electroll-ProtO:l tCllll/~ra:u;~, uen<ty, ;li:C: hulk sreed ,11 the solar wind

I

I

OclIH)

dlHtmitl.1 ('oK I

;, I1d 'lli 11.1 ( k: I

__ L -_ __ _ ~ __ __ _ ~ ____ .~ ____ ~ _ _ _ _ _ ~ ~\-,~----~ ___

()~O() (lI,'W) 07fKl 1l')fKl IIK~I

Sun declinalicll .15°

Solar cllirtic co()~Jillates: J,"n~iludc Y L"i,udc .. ''.l' - ! I

'Ihc pInion and c-lcclrPIl p'(lrL"rli(~(,' "rille sll!:lr wine for:t s'.ll\rl ktl~th nf lil'.l"", rlw :I ... ·n~ilil'" ;tHO ,d, ",it ics of PI nllll" ;11 .1 clct:IItlIlS a I c equal ;" wi I hi" the erl"cl:'S (,f IIIl'" 'mCIIICI't, btl I I he ,elllf'<"ra lure rfilfcrcnccs arc significant.

3d Cycle Astronony The Solar (Hnd (3d lesson

J.

LEMAIRE 28 oct. 1975)

Some characteristic distances, times and dimensionless nUQbers in the corona and solar \vind

Heliocentric distance Electron concentration p.elium abundance

Electron temperature Proton temperature Alph3 temperature Bulk speed

~gnetic

field Thermal speed

(p ) +

Thermal speed (e-)

~ac":1

number Alfven speed

~agnetic ~ach

number P1asna oscillation period Larmor period (p+)

(e )

Close collision time (p+)

r [ RO = 6.96

10 10

crr.

]

N e

N _Cl ++H: p + T e

T

? T Cl

w B

v = 12 k Tim

T 0.128

VTTJITI

A

[kml s]

A~ \.J/v~8.5

^W

^{[km/sl lIT}

⁺

^{T [KJ}

v

A⁼

R/4

^{71P =} 21.5 x

10

⁵

rt

^C)

I%,-e-"--b-'l.-...,..~-

^[km/s

U -7 ^f -3

.;1{0 ..

\V/

^{V =} 4.5

17.,

^{'vi (kml s) v"1}

^[cm

^J

^{18 [}

^{G J}

m .,A 2 I_ e / 3

_ _ 71_ 1T

me _

F,-4/t. [ - ][

tpl - w -

^{2 1/2 - ..}

1\

^Cr:l

^sec

? (417 N e ) e t = 21Tl"C

L 6

10 -{~

^{A/z B [C}

1 [ sec] .

t c

Ze B

ml/

2 (3 k T) 3

I

2

l2

^{1T e} 4 ^N

46 Al/2 T3/2/N

[cm- 3 ]

e

[secl

1.5 10 7 (10) 2.10 6 2.10

⁶ (2.106

)

(15) 0.5

182 7800 .06 330 .05

3

10~

10-3

7 1(,-7 104

215

5 5

1.5 10 5

4. 104

16. 10 4 325 5

10-

5

25 2130

9

48

6

5

10-

⁵

13 7

10-

3

7

10 7

RC ctr.

-3

% K K K

km/s Gauss km/s km/s km/s

sec

sec sec sec

I I-' 00 I

TT 2/4

2 3 TTm v

2.6 10-2 T3/2/N

Deflection colI. time (e-) e e

[sec]

[

7 3 105

tD 2 4 sec

<X > 32 N c In I\. e

e . (+

t P 1m

1m

t;1I2

. I

¹⁰⁶

Deflection colI. tlrne p) _{D p} e 220 sec

3/2 3/2

3 In m 1 k

( T + Tl )

I

^{3 103 108}

Energy equipartition time (e p) t _eq

=

_{1/2 2 2 4 sec}

8(2TT) n

l 2 Zl e In I\. m T1

" " "

^{(p+ a++)} 100 106

sec

"

"

(e - a ++)

3 103

108

sec

Interparticle distance r

2 (2:l )-1/3.

I

^{3 10-3 0.5 cm I-'}

e

'"

I

Debye length

jk

^T 6.9 T [ K ]

[ cm ] 3 103

r D = \ 4-rr e 2 N -3 Cm

N [cm

e e

Larmor radius (e ) ^{r L}

P- ^{- -}

^{ZeB c 3.5 10-2 Tl/2/2}

^~

^{[C 1 [ em 1}

^I

^{100 3 105 cm}

+ [km/seel/Z B [y

1

[ cm ] ₁ 4 103

6 106

Larmor radius (p ) r

L 10 v

T cm

h'l

²

.1 5 109

6 1013

~fean free path (e ) 1

=

^t _D ^{H~ + V} _T

_.

_cm

t~ean free ';:lath (r> ) +

I

4 109

5 1013

cm

Density seale height

Knudsen number (e-)

"

^{" (p +)}

Beta (e )

(p+)

~~gnetie Reynolds nu~ber

Reynolds nU1r.ber

Prandt1

Jeans nu!':':be r

Poche nu~ber

k(T ⁺ T )

H .. e

p

_or

H

r/2 (at

1 Al')

2~ ~ g

J.C .. ~

B ,.

~

_In

..

~ ..

e H

~ k T B2

/81T

L W (J

- - 2 - e L 0 ,,,

n

:: 3.5 10-

¹⁵

-3

T [ K J N [em J

"82

[ Gauss J

; cr

=

2

10

⁷

T3/2

_{[ see} ^-1 ) . . . . .

n = 1.2 10- 16 TS/2

. . . .

I ^{3 10 10}

. I

^o.~

0.15

0.3 0.3

3

10 12

1

cp

" , - p -^{e n}

r ^K:

-7

5/2 I

K =

8.2

10

T . . . 1/43

A

^a

GJ/.,""R 1.14

10

7

2 rk T T [ K ]

R C ( - )

r

(,) ~ 2 r -5 3

Ji.. = - - 2 ^1£

1.8

10 (r/!L) . . . .

o

cJl,tr

CJ

3.B

I ^{6 10- 5}

I

^{7 10Z0}

8 6

1 0.3

3 10 14

2

1/~ '3

0.56

182

I err.

I N

o

I

-21-

Third Cycle in Astronomy THE SOLAR WIND (18 November 1975) -

J.

LEMAIRE

5.-

Theoretical models for the steady corona and the solar wind

A. Hydrostatic spherically symmetric

1. Isothermal models dn

kT ---.£.

-

^{n m g}

+

e n E

dr p p p

dn kT e

dr - n m g-e n E

e e e

dn dn Since n n (quasi-neutrality) _ _ e

== ---.£.

e p dr dr

m - m

e E p e

2 g

(Pannekoek - (1922) Rosseland (1924) , polarisation field)

n e

A o

(r) exp [

m ^I

U~0

G

n p .

e,o 2kT r

0

"

m .

'r

G p 0

3.8 for T 2kT r

o

dr ] o

-3 J

n [cm e

1.5

(~ r

-

r

]

(barometric dens ity 1)

1 AU

r o

2.29xlO 5

distribution)

1.5 R0

00

2.23xlO 5

Remarks

a) n (00) and n (1

AU)

are much too large (zoodical light n ( 1

AU) <

^{500 cm} -3

e e e

b . n (1

AU) 5

cm-3

space 0 servatlons ) e

ct, questionable since T 125 K in interstellar medium

(Xl

-22-

2. Conductive models

d(p + p )

e p

dr 1 d

[r2 (

r 2 dr

<p

2

-

-

^){

_e

(fie dT dr

- p

+

»

r 2

(fI ) ]

p

<p

p 0

){

e

Solution of energy transport equation :

r

2/7

T(r) T [I: +

-E

(1 -

1:)]

o r

Remarks

r

2/7

-7 T5/2

==

8.2 x 10 thermal conductivity coefficient

a) When I:

== 0

, T (r)

^{T (-E )}

o r

Chapman's (1957) conductive solution is recovered.

b) When I:

⁼⁼

¹ , ^T(r)

c)

When T

==

125

K

00

T : isothermal model

o T

7/2

I:

⁼⁼

(~

^{) = 2 10-}

¹⁵

^{rv 0}

T o

d) Fig. 1 temperature distribution for different values of 1:.

Solution of hydrostatic equation : nCr)

In - - n o

7 - - A-

5 0

1 -(T/T ) 5/2

o 1 -

I:

In(

T )

T o

-23-

Remarks

a) Fig. 2 density distribution for different values of ~

b) n (r) has a minimum value at r

e m

(dT / dr) 1 r m r m

.5RO

o

- 6.6

- 3 K/km [Billings 1960] for ~ - 6.6

c) n (r) increases to ⁰⁰ when r -

=.

This means that the model is convcctively e

unstable !

d) The temperature gradient becomes superadiabatic at rAe

<

rm) i.e.

9 ~ 9 for r

>

r cd ad A

9 cd

9 ad

rA

dIn T 2 dIn p

n

0

I - 1 I 2/5

34 R for

1:

o

1.5 RO for

c:

r -5/7

0 - 0 [c: +

r

0 (1-E)]

o

- 6.6

Conclusion: The hydrostatic conductive models (including Chapman's model) are convectively unstable beyond the radial distance r

A.

-24-

3. Convective model Beyond r

A the previous model is convectively unstable. This means that convective heat transport (upward and downward motions of hot and cool elements "turbules") will help conductive heat transport to carryall the energy outwardly. A mixing length theory (Vitense, 1953) has been developped.

The result is that convection in a hydrostatic model is "dry" as a consequence of the inhibition of heat transfer perpendicularly to the field lines. The

convection velocity of the elements becomes rapidly supersonic. As a consequence an other type of equilibrium state is required to carryall the energy out

of the corona: the hydrodynamic expansion achieves this goal.

B. HYDRODYNAMIC, SPHERICALLY SYMMETRIC MODELS

1. One-fluid_J conductive model

eq. of transport :

1 d 2

2 (r vn ~) 0 r dr

dv d(2 n kT) ^{G ':,} 0 n~ v dr

+

_dr ^{= - n m} _{H 2}

r '"

1 d

[ / n

2 5kT G ^it

(Y-

+

⁰ ) 2

m v

-

^r

r2 dr ^H 2

~

^r

4n: n 2

2 1012

gr/sec =

I,d' ^/1013

~v r I ,..

0

2 G ^{( m}

J -

^4n:

4n: n v 2

[

^{1 '0}

r ²

"11

^v

⁺

^{5kT - r}

(v2 _ 2kT ) dv

~ dr

4kTv

~r

G ,

"

r r

0 v

2 k v aT

2

dr

]

T5/2 dT

K 0

0 dr

years ⁽¹⁾

K T5/2

10

²⁷

_10

²⁸

2 dT

dr F

0

erg/sec

~ 10

-5

'10 (2)

(3)

-25- Remarks

a) When x is very

o

large dr must be very small dT Parker's

(1958)

isothermal model is then recovered. (Fig.

3)

b)

variables nCr), v(r), 'fer),

dT

dr the solutions are determined

by 4

boundary conditions :

n., V , 'I' , F iJl. r •

I> 0 (l 0

v :~ k'i

/111 .

II

per " ) I' I'r'·'~'''lI[(.' ill iIiLt:r~l,'llur Hledi,""

d) Fill' V

<) " Lh,' gnldi .. ,l1l 01 tilt' l)tl!.k spe,>d dv/dr l,\,conw::;" at a

I II I i i ,

ill.;I"II<I' sflIdtl"r Ulil,l'- , the IUC;ltjul. pi I ltv " (ritic.al i,!)ill!.!!

(uliJthemalical

III

:,iJI).',lIldl'ir.v ',JIII'I" t.llt' ",h,';, 01 (''I. (II ,111.1 ,c(;\"lli,i"111 oj dvld!' b"l:ome both

"'llld I I. () ~~(: 1(') ,'I'll(', sulut j 011:1 ~vj til \f

I I

V

\1( I i ( i l l " 111'1 v,ll i i) \vhell

dv/ dr

h('! UlIll':; (no I.dlg'.' Ihe Vis,'Obity 10[,\<.: HIiISL be iiH:l.utled ill eq (2) ;

ii)

the

, - I

dt;,m;lLy :,c,III' Ilt;ll.',hl

II '"

(JIll il/dd blCC()H1e

rapidly smaller than the mean

l,d till

(jilly

!:;otlltion which

gives

i)

a subsonic velocity in the inner corona and

i.i)

a

^{I I} 2el'O"

pt'cssure or temperature at infinity is the

^{I '}

critical

suluLion" lor which v = v "

o o,cr1t

u(r

⁴ 'n) -

u (supersonic velocity)

_2⁰⁰

n( r - (0) a r

o (arbitrary small pressure)

o

f) total mass of solar wind

j ^rmax

4

^1t

r o

r

max

^{00 (!)}

( 1 0 ) ^{n '}

However rmax < uooX 10 years ,and therefore

01({oo)

< ,if/3000.

Self-gravitational effect unimportant in Solar Wind

!

g) The different' assymptotic behaviors of hydrodynamical conductive models,

F

T

4 2 T5/2 dT

nr >t -

o dr

2 G

4n n v r ~ r

4 n n v r 5kT 2

2 1 2 4 n n v r "2mv

v

n

p .-E. 1 H n

Parker 1964 Noble and Scarf

1963

>

0 -2/7

r F

Coo

r -1

-2 17

r

F-F

Coo

J

^{2 CF-F )}

v

=

^Coo

0:> I

r -2 -16/7

r

{ r

4/7

0:>

hThang Chanb 1965

>

0

_::> 1=

r - 1-

-2/5

r r -1

-2/5

r F

v

= I

^2F

0:> \i I

-2

r

-12/5

r

2/5

r

0:>

Durney

1971

>

0 -4/:3 r

-11 /3 r

-l r

-i..;'1

r ,-

f

; ~F

\ I

-2

r

-10/3

r

r o

cst

Konyoukov

1974

>

⁰

T-

-X!

ln r r -1 r o

1n r

(In r)1/2

-?

r -(In r)-1/2

-?

r - (In r) -1/2

r ln r

"',;.:,

Chamberlain

=

⁰

r -1 1960

-5/2

l:'

r -1 r -1 r -1

-1/2

r

-3/2

r

-5/2

r

-4/3 r

o

I N 0'\

I

-27-

Conclusion

I) There are 5 different types of solutions depending on the 5 different asymptotic behaviors of the temperature at r = = or on the boundary conditions in the corona (See Roberts and Soward, 1972)

2) The mean free path of the protons 1 becomes much larger than the

p

density scale height H in Parker's, Whang-Chang's and Konyoukov's models.

n

Asa consequence the assumptions, p .. = isotropic, and q

= -

^K T 5/2 dT/dr,

1J 0

become untenable or unjustified. What is then the meaning of these

solutions at large distances ? Why should the solution in the collision dominated region i.e. r < 6 - 10 R ) be determined from the asymptotic

o

behavior of T(r) at infinity where the plasma is collisionless and where the Chapman-Enskog's approximations used in eq. (2) and (3) fail to be appropriate.

A suggestion : calculate new hydrodynamic conductive models with all boundary conditions specified at the maximum of coronal temperature.

-28-

1200

4 ^y Ill"K

((~J()

3 ⁾⁽ 10" "K ^I

I

::;

Ji.

2 ^{)( 10" ~K I} 1.5 ^{)( 10" 'K'}

c

~ 1 y ((lh"K:

"

_o,~

x 10" ~K I

200 Orhil Qr earlh

20 40 1>0 SO 100 120 140 11>0

'-,(1((1 = 10" em)

-29-

'.

.. ", '"

F i (Jure ,i.t> I~is tr i ',',ion 1 adiale d,~ t€:lnt

">e

["a ture dans trois moaeles ,conductiis ; ,;1) ': ::: . ,, 2 ; 2) !", ::- (',,0 : G modele de Chapman; a) t:

=-

- r:, P. ; To (l~5 R

0)

=-

1 ~4J JO OK.

I

Z ^d'

I '

'+l

l - -

1 ^.~

--- ^{--- ~ :+0,2}

\

0.4 ~ ⁼⁰⁰ _•

~

^{== -}

^0,2

~---.----r--...__yl,--

... , - - - .

^{J T} ·~i --r--~--r---r..-.

1 2 4 6 810 20 40 60 100 200 400

r/ _R

\.:. ':')

-30-

Figure :2 I - Distribution radiale de densitcs dans trois modeles conductifs I}

~

= 0,2 ; 2}

~6=

0:

mod~le

de Chapman;

, , ) (. ::!!

'7

0 ^L 2 i 3 T ⁰ (1 ~ ¹⁾ Re )

= 1,

·1,"1, lOoK : n e ( 1., 1) Raj

=

1.,81 10

e lam.

9 rO'

log ne (cm-3 ) 8

,7

6

5

~=+02

"I

4

1 2 ^{, 6 10 20} 40 60 100 200 400

Third Cycle in Astronomy THE SOLAR WIND (4 November 1975) - C.De Loore

4

and

^{5 -}

Model calculations for the solar transition region and corona

1.

Introduction

The ocourence of a hot corona around the cooler sun seemed to be in contradiction with the second law of t.hermodynamics.

~~E1~!!~!!2!!§

:

- accretiun

⁰¹ (iU:31~

dnd meteorite::;

(ldt.':Iillclllll,

tell

B1Ul3(lCllcdLe)

- mechan

iCdl t..:IH:r'JY (L! l.c.fBldnll, Sc Ilwarzbc!l j ttl)

'L'huy sU9gesLed that.

the grannJes

WO\lld del 1 tkt~

pistons and

~lene:rdlt~ a fiE~lcl

of

pressu.n.:

waves

in Lht~

photosphere. They lound

Uldl.

the

fLux

of

m(!cild.nical

energy carr-ied by these

v/dve::; I"JUU 1d lid

ve

Ihe r-igll L

order of magnitude. The dissipation

o

t ent:L!JY l)ecoJiles i

lnflortan t as soon as the velocity amplitudes

dCe uf

the

^ordt~r

of the sound velocity.

'fhese are the fundamentals of all modern theories of chromo- spheric and coronal heating.

The study of the generation of sound by isotropic turbulence in a compressible medium (Lighthill,1955) led to an estimate of the acoustic power for the solar atmosphere.

2. Generation of mechanical energy in convection zones

Turbulent motions in the convective region are sources of pressure fluctuations, going outwards.

The amount of energy radiated in a unit volume by isotropic

homogeneous turbulence is, according to Proudman(1952)

-32-

a is related to the correlation between energy in the wave number region and the wave number itself.

a - 40 for a Heisenberg correlation

£

is the turbulent energy dissipation per unit-volume

pv

³

£

=

^L

- v is the averge turbulent velocity of the convective elements.

L gives the dimension: in stellar atmospheres L is generally

assurn.ed

to be of the order of a scale height H.

As energy contained in the turbulent velocity field we take

hence

1 pv2

2 conv (i.e. the entire energy of the convective motion is converted into turbulence)

£

=

^pv

³ /L

conv

^(L=H)

M is the flow Mach number of the convective velocities

M

₌

- _c v

with c

² = yRT

~

The integrated flux can then be determined by integrating the Po-value at each level over the total convection zone.

F m

1 upper

= 2

^{J p(z) dz}

lower

-33-

3. Computation of an atmosphere including convection (grey

RAD •••..• 1t"."..

Computation of atmosphere Hydrostatic equilibrium

T4

³

T 4 4" ^e

(-r

dPg

dT

= g

K

3

RAD

+ ^q 6) )

L

r

KP9:

V =

rad 16 ^nacGT4

M

r

'lad tables

V < V -+

radiation

rad ad

> -+

convection

T -

0.001

T

= ⁴⁰⁰⁰

^K

o

log g = 4.45

Teff :: 5800 K

-34-

4.

Equations for convective regions

1.

F _conv + F _ra d = _{F tot} =

^a

2.

F c

^p

v

^l'IT

conv

p

V

= ^{(d log}

^T

^>

d log Pg surra with

^l'IT _T

=

¹ _2H (V-V')

V'

= (d log _{d log}

^T

_Pg>

el.

F rad

V

3.

_F =

tot

^V

rad

4. v

² = ¹

S.

_12(V-V')

"2

H

5. F

= ^{16 a T4} V

rad

3xpH

V

and

V'

can be evaluated by equalling the total radiation loss of the element during its lifetime

and the change of the average con- tent in energy by radiation losses.

Solution gives v,V', v

and

-+

T

Pg

1.0

0.8

0.6

0.4

0.2

o

1 ²

Figure 1

Ratio (F

elF

t) max

-35-

3

Curves labeled with Teff-values 4

4760 7130

5940 8320

5350

9130 5 log g

Convective energy important for stars with Teff

^<

8300K

bO tiD o

r l

1

2

3

5

Figure 2

TABLE 1

o

o

0'\

co

N

0

~ V

-36-

~

J

^J

r~ ^I

^~

: ) rt. ^{~ /}

-0 0

I ' i ^~5

o

r<'\

r l

['-.

0

I

10

oS

o

⁰

~ l!'\

0'\ r<'\

l!'\ LC"\

numbers give this value in %

N

Extent of convective regions (in km) for stars determined

by

Teff and log g.

~ff

log g

^{4760 5350 5940 7130 8320}

2 200000 80000 80000 75000 140000

3 400000 70000 16000 6000 12000

4 400000 480000 1200 140

5 1500

9510

1200 90

-37-

TABLE 2

Solar atmosphere.

T log T log Pg

0.001 3.609 3.54

0.003 3.617 3.86

0.007 3.631 4.02

0.028 3.670 4.27 RAD

0.055 3.692 4.41

0.108 3.711 4.54

0.517 3.767 4.87

0.808 3.792 4.95

1.010 3.80 4.981

\j <

ad ^V rad

log 1"

0.37 3.87 5.14

1.05 4.07 5.43

3 4.52 7.58 _CONV

6 5.27 9.63

-

-38-

,

:r ,

Figure 3

Convective velocities in the solar atmosphere, as a function

of temperature.

~

3.,

I

J&r I

,

I

I

log T

:s.tl-

I !

,

39 ^1_

It

Figure 4

.,_. - ----^{,.~ ~}

f. ~t"\

'f. ~ v

c-

1"" ... 1 .:._ , : , _ •• ~_

'-- .... ^'-" -

-

^--'.-

--<- ~-.. ~-

--

⁾

Comparison of our computed m o del (A) with the Bilderberg- model

(B).

~=-= :="DERBERG

I r,r

""":'"'>f/"

I ~-1 -.~

~

,.

I!

ss"

f LV 1.0 f

-40-

1 ~---~---.

V

f.r ,

^I-

Figure 5

The behavior of the different

gradients as a function of depth

in the solar atmosphere.

-41-

Figure 6

The mechanical fluxes for various types of stars in the Hertzsprung- Russell diagram.

MS :

main sequence stars

G: giants

SG: supergiants

-42-

5. Model calculations for coronae

Bird 1963 constant shock strength Uchida 1963

Kuperus 1965 inwards

without solar wind Ulmschneider 1970 outward

+ s.w.

De Loore 1970

1975

outward + s.w.

+ reflection

+ stellar coronas starting at 1800 km

6. Computation of transition zone and corona

~----.----^.. ----.-.. ---~

/

'rZ

DF

TZ transition zone DZ dissipation zone DFA : dissipation free

area

WAVES

Principle

Fmech

⁺

outwards (sound waves)

~

amplitude

~

-43-

Subsonic ~ - no dissipation when v = c

=>

dissipation starts

F P v ² c m

At shock height v=c

and

now :

~ L3

dh

=

^{Hd in}

hence : h

=

^{H (in}

-t P Pg -

*

^F m

(H scale in P)

-t

pc y p p

height

reference at shock level

Energy balance

Balance term

Eguations -

l . Motion av

+ (v

-at

2. Continuity ^~ at

level

input

dissipated

radiated wind

F cond

grad) v

+

div ( pv)

Fluxes F mech

Fd_lSS ·

F rad

F . d Wln

1 grad p

0

local)

p

+

g

-44-

1) is transformed into an for the of

the flow velocity

dM

x f(T,x)

2) the variation of the pressure is

dP

_{f , T, M}}

The absorption coefficient

4

_(M

=

shock numbe

IC

=

There exists so a relation between the flux and the shock Mach number

2 M

so that the can be calculated

fluid energy:in I-volume fixed in space-matter is flowing

1

+

^pE

E: =

2"

^p

-} -}

kin. internal en. en.

o

-45-

Worked out

_ 1 2

x

2

Ed' - E d= div pV(-2 v

+

H - g ~) - div K grad T

lSS ra 0 x

1. low temperatures

+

low velocity E , d - 0

Wln

E - E ⁷ converted into heat diss rad

2. higher levels : Erad

+

E

wind ^» Ediss and conduction necessary.

In that case

x

F _Wln , d

+

f (E ra d - Ed' lSS ) dx

dT

dx

o

=

^{6.105 T-5/ 2 F}

cond

F cond