[1968], we shall take the following as typical values of the solar wind temperature at i AU;. Tf -- 4.0 X 10*øK, Tâ¢* -- 2.0 X 10*øK (so that Tf/Tp ⢠-- 2.0), and Te -- 1.2 ...
JOURNAL OF GEOPHYSICAL RESEARCH, SPACEPHYSICS
VOL. 74, NO. 21, OCTOBER 1, 1969
Letters
ThermalState and EffectiveCollisionFrequencyin the Solar Wind Plasma ATSUHIRO •NISHIDA
Institute of Space and Aeronautical Science University of Tokyo, Komaba, Meguro-ku Tokyo, Japan
As in many plasmasystems,the rate of energy dissipationin the solar wind plasma is much higher than what is expectedfrom the binary Coul.ombinteractionsalone. A typical mani-
ing, we shall assumethat the nonthermal heating is practicallynegligibleat I AU. On the other hand, the electrontemperature predicted by the Hartle-Sturrock model is
festation of the strong dissipationis the formation of the thin bow shock front upstream to
comparablewith the observationat i AU, suggestingthat the (normal) heat conduction is the predominant source of the electron thermal energy. Since the observed value of Te/T• is considerablylarger than 1, there is a
the magnetosphere. Sincethe empiricalvalue of
the strength of such 'collisionless'interaction mechanismsetsa goalfor a theoreticalapproach to explainthe abnormaldissipation,an attempt possibility that the proton temperature is is made to derive this quantity from the ob- raisedto the observedvalue by the interaction served degreeof the thermal nonequilibriumof with electrons, if there exists an interaction the solarwind plasma.Accordingto Hundhausen sufficientlystronger than the binary Coulomb [1968], we shall take the followingas typical interaction. To estimate the expectedstrength values of the solar wind temperature at i AU; of such interaction,we write the energy equaTf -- 4.0 X 10*øK, T•* -- 2.0 X 10*øK (so tion in the steady state ((•T/•t) ---- 0) using that Tf/Tp • -- 2.0), and Te -- 1.2 X 105øK the effective collision frequency v as follows
(so that Te/Tf -- 3.0), wheresuffixesp and e denote protons and electronsand prefixes _]_
dT•
dn •n
and [[ designate temperatures perpendicular and parallel to the magneticfield. Temperature anisotropyof electronsis ignored since it is muchlessthan that for protons. The theoretical study of the thermal state of the solar wind was made by Hartle and Sturrock [1968]. They assumedthat the heat conductionand the proton-electroninteraction are governed by the binary Coulomb interactions and found that the predicted proton temperatureis an order of magnitudelessthan the observed value. The discrepancy was ascribedto the nonthermalheatingmechanism
ß(3T,-
2T•• -- T•II)-]- 3Q•
(1)
TXdB nvk dT•x dr -- nvkt•--•rr-["nkv•,(T, -- T,•')
•-nla%(T•" -- T••) •- 2Q•
(2)
«nvk dT•11 dr - «nvkn• dr
in the solar wind. The need for such nonthermal
n
+
+ Q,
(3)
heating at high solar altitudes (namely, afterburning) has been recognizedalso from the interpretation of the density and velocity of the solar wind [Dessler, 1967]. However, it is
where r is the r•dial distancefrom the sun, and Q, and Q. representheat depositedby conduction to each degreeof freedomof protonsand
not known how far above the solar corona such
tive, rather than Coulomb,collisionfrequency, •nd the •bove equations•re more relevant th•n
heatingmechanismis operative.In the follow5155
electrons in • unit volume. v now means effec-
LETTERS
5156
equations2-4 and 2-5 of Hartle and Sturrock model as also in that (a) proton temperatureanisotropy is taken into account,and (b) the adiabatic
decreaseof temperatureis estimatedusingthe CGL approximation, taking account of the presenceof the magneticfield. Density n, velocity v, and magneticfield B in the solarwind dependon r approximatelyas
v-
constant
(5)
tiT.. --1 (12) dr -• --0.97X 10-søKcm
(They derived severalmodelscorresponding to differentconditionsof the corona,but the above ratio at 1 AU is practically the same for all models.)Sincethe heat flux carriedby protons is about 10' times less than that carried by electrons[Hundhausen, 1968], q• will be ignored in comparisonwith q,. From equations7 through 12 it followsthat
vw - 9.5 X 10-s sec-1 •
where 9 is the angular velocity of the solar rotation.Taking the spiral angle of the inter-
= 5.2 X 10-7 sec-•
In comparison, reciprocalsof energyexchange planetarymagneticfieldto be 45ø (correspond- times due to binary Coulomb interactionsare ing to v -- 400 Inn sec-•),equations I through 3 can be written as • = 1.0 X 10-s sec-1
7.1 X 10-7 sec-'
v dT• 10• dr
:
Therefore,
x
_9.3•,,,,-[- q,
(7)
v dT•,i 104 dr
Thus, the temperaturesof the solar wind protonsat 1 AU can be explainedif the effec10.O•q,, q- 2.0•q,•, q- q•, (8) tive collisionfrequencybetweenprotons and electronsis about 10 times larger than the v dT•" valuo due to binary Coulomb interactions. 104 dr Althoughthe presentdiscussion involvesseveral assumptionsthat have not yet been examined observationally,the result representsa possible solutionthat is compatiblewith data availwhereq = 2Q/lO'nk. able at present.It is noteworthythat the degree It is assumed then that at r -- 1 AU the of anisotropy of the proton temperature dedegreeof thermal nonequilibriumof the solar pends on the nature of the heat sourceto wind has come to a steady state. Namely, we protons.In the present model in which the assume that the 'collisionless' interaction mechaproton thermal energy is supplied from deenism works to maintain the ratios TJTf and trons with the efficiencyv•,, which is the same T•"/T, • at constantlevels and to imposethe for kT' and kT", the observedvalue of the conditions ratio T,"/T,' can be explainedeven when v, is not raisedabovethe value v, ø due to binary Coulombinteractions.'Collisionless' pitch-angle dr scatteringmechanismsas discussed by Scar[ et al. [1967] and Kennel and Scar[ [1968] becomevital in the explanationof T//T• • only dr \T• i whenthe energyinput into kT•• muchexceeds dTo/dr is estimated from the Hartle-Sturrock that into kT, •.
=--4.0(•-r)q-8.0V, o-4.0v,, q-% (9)
d(T,')=0
(11)
LETTERS REFERENCES
Dessler,A. J., Solar wind and interplanetary magnetic field, Rev. Geoph•s., 5, 1, 1967. Hundhausen, A., Direct observations of solarwind particles, Space $c•. Rev., 8, 690, 1968. IIarfie, R. E., and P. A. Sturrock, Two-fluid model of the solar wind, Astroph•s. J., 151, 1155, 1968.
5157
Kennel, C. F., and F. L. Scarf, Thermal anisotropies and electromagnetic instabilities in the solar wind, J. Geoph•ls.Res., 73, 6149, 1968. Scarf, F. L., J. H. Wolfe, and R. W. Silva, A plasma instability associatedwith thermal anisotropiesin the solar wind, J. Geoph•ls.Res., 7•, 993, 1967.
(Received May 29, 1969.)
