The solar wind H and He+ content

Planet.

Space Sci. 1972, Vol. ZQ, pp. 841 to 847. Pergamon

Press.

Printed in Northern

Ireland

THE SOLAR WIND H AND He+ CONTENT Department

C. T. GREGORY of Physics, University of California, San Diego, La Jolla, California 92037, U.S.A. (Received 6 December

1971)

Abstract-Charge exchange collisions between interplanetary neutral H atoms and solar wind protons may lead to fluxes of neutral H atoms and He+ ions in the solar wind. Photoionization of interplanetary helium atoms may also contribute to the He+ flux. The expected fluxes of He+ ions and neutral H atoms in the solar wind are computed. A simple model is used to compute the intensity of resonantly backscattered solar He11 (i304 A) and Lyman ccradiation. 1. INTRODUCTION It has been suggested that charge exchange collisions between interplanetary H atoms and solar wind Hea+ ions (Hundhausen et al., 1968) or photoionization of interstellar helium atoms (Holzer and Axford, 1970, 1971; Holzer, 1970) may explain Vela 3A satellite observations (Bame et al., 1968) which suggest that the solar wind He+ content is at times of the order of 1O-3 times the He2+ ion content. It has been further suggested that a sensitive means of detecting He+ ions in the solar wind is through observations of the resonantly backscattered He11 (1304 A) sunlight (e.g. Holzer and Axford, 1970, 1971; Tohmatsu, 1970; Ogawa and Tohmatsu, 1971; Johnson et al., 1971). Also, charge exchange collisions between interstellar neutral hydrogen atoms and solar wind protons would be expected to yield a solar wind neutral H atom content which could possibly be detected through observations of the resonantly backscattered HI (11216 A) (Lyman a) sunlight. In this paper we will compute the expected fluxes of He+ ions and neutral H atoms in the solar wind as well as the intensity of backscattered solar He11 (1304 A) and Lyman a radiation resulting from the presence of these particles in the solar wind. 2. THR FLUXES

OF He+ IONS

AND H ATOMS

IN THR SOLAR

WIND

Several authors have examined the flow of neutral interstellar gas past the Sun (e.g. Fahr, 1968a, b, 1969, 1970; Blum and Fahr, 1970; Holzer, 1970; Holzer and Axford, 1970, 1971; Semar, 1970; Johnson, 1972). According to the treatment of Holzer (1970) and Johnson (1972), if the thermal velocities of the interstellar atoms are small compared to the bulk velocity of the gas relative to the Sun (V w 20 km see-I), then the possible trajectories for each atom are hyperbolae with the Sun as focus lying in the plane determined by the velocity vector at infinity and the Sun. The number density (n) of an atom in interplanetary space is obtained by solving a continuity equation which takes into account losses due to charge exchange collisions between interstellar atoms and solar wind ions and photoionization of interstellar atoms by solar radiation, and treats the trajectories as streamlines. In this manner it is possible to show (Holzer, 1970; Johnson, 1972) that the number density n is given by 2 NPi2 n(r’

”

=S

r

exp

{-8,re2ei/lPil)

sin B[r2 sin2 8 + 4r(l - cos

e)/c]l/2

’

(1)

where 8 is the polar angle measured from the axis of symmetry, (0 < f3 I II), N is the number density of the incident particles at infinity, angular momenta for the two allowed trajectories are given by pl, p2 = gV{r sin

e

f

[r2 sin2 841

8 +

4r(l -

cos

eycly’2

(2)

842

T. GREGORY

C.

where the plus and minus signs go with p1 and pe respectively, C = P/(1 - ,u)GM’,, V being the velocity of the incident particle at infinity, G the gravitational constant, M, the mass of the Sun, re the Earth-Sun distance and ,u a parameter which takes into account solar radiation pressure. The parameter p arises from the assumption that solar radiation pressure produces a radial force varying as the inverse square of the distance from the Sun. The radial pressure that results is taken into account by defining an ‘effective’ gravitational constant (1 - p)G. Thus p is the ratio of the force on an atom due to radiation pressure to that of gravity. In Equation (1) @, is a loss coe~cient at 1 A.U. associated with charge exchange and photoionization losses. Cross sections used in evamating j3, are given in Table 1 (Holzer, 1970). In Equation (1) Br = 8 if p, > 0 and 8$ = (2, - 8) if pj < 0. The contribution must be ignored for trajectories which strike the Sun before intersecting at (r, 8). We note that n(r,

e = 0) =

z(1 + 4V2exp (--lo/ Tu,,I) r(l

where the flow velocity u = V(1 + ~/C’P)~‘~and r, is the penetration depth defined by r, = @,re2/V. It is apparent from Equation (1) that n(r, 8 = V) = co. This is a consequence of the assumption that the thermal velocity of the interstellar atoms is negligible compared with the interstellar flow velocity Y for all 8 (e.g. Danby and Camm, 1956; Feldman et al., 1971). TABLE

I. CROSS-SECTIONS AND

RATES

TO THE

OF THE

THE REACTION RATES ARE CALCULATED FOR ZERO OPTICAL

Reaction H

Hee+ +

(Y,~~

AT

4OOkm

+ He’-

x x x x

+ He*+ ZHe+ He+ He+-tHe++ He + He NC++

2

(cm2) set-l)

lo-‘8 lo-‘6 10-l’ lo-‘* lo-‘6 lo-‘5

A.U.

Reference

Fite al. (1962) Afrosimov al. (1969) Hertef and Koski Nagy et (1969) Nikolaev et (1961) Fite al. (1962)

Reaction rate (r

H+hv=H”-t-e + hv He+ 4

As Holzer (1970) has exchange

the main with solar

x 10-1 1.0 x

Nicolet et al. Nicoiet et al.

processes for interstellar hydrogen atoms are protons and

THE SOLAR

WIND

H AND

He+ CONTENT

843

where the bulk flow velocity of the solar wind V,, is assumed to be radial, lzne is given by Equation (1) and fl = ,9,re2/r2 is a loss coefficient evaluated from cross sections given in Table 1 and a radially symmetric solar photon flux is assumed. Equation (4) is readily integrated to yield the He+ ion flux in the solar wind. In Fig. 1 we plot contours of constant He+ flux in the solar wind normalized to the solar wind Hf flux for an interstellar penetration depth of r, z 1 A.U., a solar wind flux of 2 x lo8 cm-2 set-l at 1 A.U., an interstellar flow velocity V = 20 km/set, ,u = 0 and an interstellar number density of 0.008 cm-3 which corresponds to an interstellar number density for hydrogen of 0.092 cm- 3. The plane of the figure contains V. The sharp maximum in the antapex direction (parallel to V) is due to the neglect of temperature effects.

Fm. 1, C~TOURS OF CONSTANT He+ ION FLUX [&He+)] IN THE SOLAR WIND (NORMALIZED TO THBSOLARWIND H+ IONFLUX [&H+)] FORDS = lA.U.; A SOLAR WIND FLUX OF 2 X lOa Cm-*SK-' AT 1A.U. IS ASSUMED AND THE INTERSTELLAR HELIUM NUMBER DENSITY Is TAKEN TO BE 0908 cm+. THE PLANE OF THE FIGURE CONTAINS V.

An equation similar to Equation (4) may be written for hydrogen and integrated to yield the neutral hydrogen flux in the solar wind. In Figs. 2a-d we plot contours of constant H flux in the solar wind in the plane containing V normalized to the solar wind H+ flux for an interstellar hydrogen penetration depth of 4 A.U. and ,D= 0.0, O-4, 0.8 and 1-O respectively. The other parameters are the same as those for Fig. 1. The elongation of the contours in the antapex direction which increases with increasing values of ,u is due to the fact that the solar radiation pressure tends to lessen the effects of gravitational focussing. 3. THE BACKSCATTER

It may be by observing suggested in He+ ions and

OF He11 (2304 A) AND

HI (21216&

SOLAR

RADIATION

possible to detect the He+ ion and the neutral H atom solar wind components the resonant backscatter of He11 (2304 A) and HI (11216 A) radiation as Section 1. To compute the intensity of backscattered solar radiation from neutral H atoms in the solar wind it is convenient to make several simplifying

C. T. GREGORY

844

+#W

30

jizi i

FIG. 2a. CONTOURSOF CONSTANT

1

I

40

30

30 R IA.U.1 Q p=o.o

FIG. 2b. As FOR FIO. 2a BUT WITH ‘u = o-4.

40

H

FLUX IN THE SOLAR WIND (NORMALIZED TO THE SOLAR WIND H+ FLUX) FORro =4.&U.; ASOLARWINDFLUX OF 2 X lo8 cm-2 see-l AT 1 A.U. IS ASSUMED AND THE INTERSTELLAR ~YDROGENNUMBERDEN~IS TAKEN TOBE O-092 cm-‘. TSE PLANEOFTHE FIGURE CONTAINS v, AND@ = 0.0.

--x---

30

A (A.&l Q

8’0.4

30 t

#(HI

q-iii-5

FIG. 2~. As FOR FIN. 2a BUT wrm p=O%.

THE SOLAR WIND

H AND He+ CONTENT

30

845

i

FIG. 2d. As FOR FIG. 2a BUT WITH ,u = 1.0.

assumptions. We take the flux J(r, 0; v) of solar photons with frequency between Y and v + dv to be J(r; v) = G J(r,; v). r2

(5)

If r and r’ are the position vectors of a point in space relative to the Sun and the Earth respectively, then the intensity of singly-scattered photons in a lixed direction is given by

J’b) =

k s _(r;v)n(r)J(r;

v) dr’

(6)

where a(r, 13; v) is the absorption coefficient, n is the number density of He+ ions.or neutral H atoms in the solar wind and multiple scatterings have been neglected (cf. Johnson, 1972). The integration in Equation (6) is carried out along the line of sight from the Earth. Also, v is the frequency before scattering and absorption of scattered photons is ignored. The total intensity of singly-scattered photons from a given solar emission line is then given by m I = 47r x 1o-6 J’(V) dv (Rayleighs). (7) s -co If we assume that the natural broadening of the solar line is small compared to the Doppler width, the absorption coefficient is given by (Allen, 1963; Aller, 1963) a =

72e2fabs 1 exp -

-

me Av,, Jrr

where v,, is the frequency of the line at line center, f& is the oscillator strength, c is the velocity of light, e is the electron charge, m is the electron mass and A

vo,Il_o

c

2

J

XT M

(8)

846

C.T.GREGORY

where k is the Boltzmann constant, T is the temperature and M is the mass of the He+ ion or hydrogen atom in the solar wind. The temperature T for He+ ions was taken to be 40,OOO”Kat the Earth’s orbit (Holzer and Axford, 1970b) and assumed to vary as r4i3 which corresponds to adiabatic cooling beyond 1 A.U. For hydrogen, a temperature of 50,OOO”K at the Earth’s orbit was assumed. The results are not very sensitive to these values. Values off& are given in Allen (1963) and V,, was taken to be 400 km/set. The effects of Doppler shifts have been taken into account since the solar emission lines are not broad. The solar line intensities at 1 A.U. appearing in Equation (5) were taken to be gaussian in shape for the He11 (1304 A) case and the sum of two gaussians for the Lyman c( case (e.g. Tohmatsu and Fujita, 1964; Hall et al., 1965; Ogawa and Tohmatsu, 1966; Hall and Hinteregger, 1970; Tohmatsu, 1970). For the case of He11 (1304 A) the solar line width was taken to be 0.06 A and the solar flux used was 5 x lo9 photons/cm2-sec. These numbers are consistent with those reported by Hall and Hinteregger (1970) and Timothy and Timothy (1970) to within a factor of two. Gaussian parameters for the Lyman a line were taken from Morton and Widing (1961).

I

60

I

90

I

120

I 150

0 (degrees) FIG. 3. CALCULATEDTOTALINTENSITY PROITLE FOR BACKSCA~ERED

SOLAR He11 (A304A) RADIATION AS A FUNCITON OF POLAR ANGLE 8. PARAMETERS ARE AS IN FIG. 1.

We have evaluated Equation (7) for the intensity of backscattered He11 (1304 A) and HI (A1216 A). Th e results for He11 (i1304 A) are shown in Fig. 3 as a function of 8 measured from the solar apex direction (antiparallel to V). The divergence at 8 = rr is due to the neglect of temperature effects. The results appear to be consistent with measurements made by Ogawa and Tohmatsu (1971) and Johnson et al. (1971). The result for Lyman c( is Z N 3.5 Rayleighs at 8 = 0; this is probably masked by Lyman GCof galactic origin (Blamont and Berteau, 1971; Thomas and Krassa, 1971) and is certainly negligible compared to the solar Lyman a radiation backscattered resonantly from interstellar hydrogen which has been computed by Johnson (1972). Acknowledgements-I would like to acknowledge helpful discussions with Dr. W. I. Axford who also suggested the problem. This work was supported under NASA grant NGR-05-009-081. REFERENCES AFROSIMOV,V. V., MAMALEO,Y. A., PANOV, M. N. and FEDORENKO,N. V. (1969). Charge-exchange proton-inert gas interactions. Sov. P/y+Tech. Phys. 14, 109.

in

THE SOLAR

WIND

H AND He+ CONTENT

847

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