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Planet. Space Sci., Vol. 40, No. 4, pp. 439~i45. 1992 00324)633/92 $5.00+0.00 Printed in Great Britain. ~ 1992 Pergamon Press pie

ANISOTROPY OF THE ENERGETIC NEUTRAL FLUX IN THE

MICHAEl, A. GRUNTMAN Space Sciences Center, SHS-274, MC-1341, University of Southern California, Los Angeles, CA 90089, U.S.A.

(Received 18 October 1991)

Abstract--Characteristics of the energetic neutral born at the heliospheric interface are considered for flow structure resulting from a two-shock model of the interaction between the and the . The energy distributions of heliospheric energetic neutral atoms (HELENAs) are calculated and it is shown that the HELENA flux is highly anisotropic at the 's . The charac- teristics of the HELENA flux are highly sensitiveto the size of the heliosphere. This supports the conclusion that measurements of HELENAs from the Earth's orbit would give us an efficient tool to remotely study the heliosphere.

tribution of the , and some of them would be INTRODUCTION directed "back" towards the Sun. Therefore HEL- The interaction of the Sun and the local interstellar ENAs are probably the only messengers born beyond medium (LISM) is manifested by the build up of the solar wind termination shock and capable of a heliosphere (e.g. Axford, 1990). The heliosphere reaching the inner solar system with a minimum dis- provides a unique opportunity to study in detail the turbance. At present the imaging of the heliosphere only accessible example of a commonplace astro- in the HELENA fluxes seems to be the only means to physical phenomenon--the formation of an astro- remotely study, from the Earth's orbit, the distant sphere. From a practical point of view, the heliosphere boundaries of the heliosphere. Remote study will is our natural "environment" and knowledge of its remain important even if a spacecraft, e.g. , characteristics is important for the interpretation one day crosses the termination shock. Only a remote of space experiments, e.g. measuring cosmic rays technique can provide a global view of the heliosphere (McKibben, 1990). on a continuous basis. Direct experimental data on the heliosphere are The measurement of HELENA particles, which has quite limited. Direct proofs of the adequacy of our yet to be demonstrated, presents a challenging exper- concepts of the heliosphere are not available, and its size imental task. A discussion of all the relevant exper- and shape are not accurately known. A self-consistent imental problems is beyond the scope of this paper. model of the heliosphere has still to be built and many It only has to be mentioned here that the instru- important parameters such as pressure mentation, developed initially for the study of the and in the LISM are known with poor neutral solar wind (Gruntman and Morozov, 1982; accuracy. Gruntman et al., 1990), is capable of measuring and The solar wind is a highly supersonic plasma flow performing energy analysis of very weak fluxes of low into the LISM which is characterized by a certain energy atoms (< 1000 eV) in the presence finite pressure. It is believed that this supersonic of the dominant u.v./e.u.v, background . The plasma flow terminates at a solar wind shock front use of similar instrumentation for the measurement beyond which its kinetic energy is largely converted of the HELENAs, and thus of the heliosphere itself, into thermal energy in the subsonic plasma. Details was first suggested by Gruntman and Leonas (1983) of this interaction depend essentially on the assumed and the first attempt to perform such measurements parameters of the LISM. Neutral interstellar gas is planned on the Relikt-2 mission (Gruntman et al., atoms penetrate relatively freely through the interface 1990). The development of recently suggested novel region, but there is a certain probability for "hot", e.u.v, photon suppressing filters (Gruntman, 1991) energetic (> 100 eV) to charge exchange there may make the measurements less difficult in the newly with interstellar gas atoms and give rise to heliospheric proposed instrumentation. Requirements for a dedi- energetic neutral atoms (HELENAs). The velocities cated space experiment and instrumentation to per- of these particles would reflect the velocity dis- form the imaging of the heliosphere in HELENA 439 4411 M. ,\ (il<~ XiMA\

ttuxcs from the Earth's orbit wore discussed re- I1o\~ is described bv the Ikn-ano~ ~lmiomn-\ two> qlo,:k cently by Hsich el a/. (1990), ('urtis cl a/. (1990) and inodcl (Baranov, 1990a.hl. This model sccn> Io hc (]runtnl:Jn (1990). the most quantitati\.cly de',eloped at the m~m+cnt Expected characteristics of the HELENA Jltix have though it has :_1 ntunber el" inherent deliciencies. ~n never been previously presented in detail. The value important feature is. however, thai the Barano\ model of the total expected HELENA llux (10 ~ cm " s ~) provides plasma Ilow characteristics in a form which and the average atom velocity were just mentioned by allo\~s one to scale them for ditl'crcnt parameters of Bleszynski (1987) as a by-product of his Monte Carlo the LISM and solar v,ind plasmas. Tllc latter iL'alurc study of the filtering of" interstellar gas at the hello- Makes it a con\,enielll tool l]]l makillg the semiquan- pause. Such flux values can also bc obtained easily titativo estimates. Hox~,exer. one has to keep in mind from rather simple qualitative considerations (Grunt- thai the derivation of the hcliosphere parameters from nlan. 1990). However, the discussion of a dedicated the measurements requires a detailed undersiandm? space experiment and optimization of lhe relevant of the physical processes involved and extensive com- instrurnentation require knowledge of the expected puter simulation. In the garanov model, both thc HELENA flux characteristics in much more detail. interstellar phisma llow. and the solar wind lloxx are The HELENA flux should also bc responsible l\n- supersonic and hence lyre shocks, bo,a shock and some of the noise count rates 01" tl.V. photometers on solar v;iIld lermination shock, arc fornled (t:ig. I1. board the Pioneer 10/1 I spaceeral'l which measure the The plasma flow is cylindricall}, synlnletric and angle interplanetary glow at the hydrogen (1216 /~) and is nlcastlrod 1toni the direction ~.iutipaiailcl to the (584/~) resonance lines (Carlson aud Judge. vector of lho relative velocity of the interstellar plasma 1974). This source of noise may become important as flow. Only the plasma parameters in llle region ~ here the intensity of backscattered radiation decreases with the ttELENAs are born. i.e. bciwecn the holiopause Pioneer 10 moving away from the Sun (the spacecraft and termination shock, are of interest for the scope is now at 50 a.u.). of the present work. Mosl of the kinelic energy of the The present work is devoted to the calculation of solar wind ph.isma transl\~rnls into energy oi" therlilal the energy distributions and the anisotropy of the nlolion of the plasnla ions and beyond the HELENA l]ux at the Earth's orbit. All calcuhllions iernlination shock. are performed for plasma flow parauletcrs determined by a two-shock model of thc interaction of the solar wind and the LISM plasmas.

MODEl.

Various scenarios of the interaction between the expanding solar wind and the LISM are possible 8 // depending on the solar wind plasma and the LISM 7 parameters (e.g. Parker, 1961: Axford, 1972). For example, it is not known whether interstellar plasma ltow is subsonic or supersonic. Similarly, the strength and the direction of the magnetic field in the LISM "~ 5 are not accurately known, nor is the cosmic ray press- BS ure. A self-consistent model of the stationary hello- sphere has not yet been built and there are good reasons HP LISM to think that the heliosphere is "'breathing", changing its size and shape during the . All these factors can have a substantial effect on the inor- :/ phology of the heliospheric boundary and parameters I i l I I of the hot plasma which is a source of the HELENAs. 4 3 2 I 0 I 2 However, the motion of the Sun relative to the LISM -V'K"~.u. should result in an anisotropic heliosphere, com- pressed on the upwind side and extended in the wake FIG. I. W~&'o SHOCK MOI)I~L ()I THE INFERA("II(IN O1, IHI INTERSTELLAR PLASMA FI.OW WITH THE SOLAR WIND. direction. BS is a bow shock, HP is a heliopause and TS is a termination It is assumed in this work that the interaction of shock. All dimensions are in the units of x,iK a.u., and the the solar wind plasma flow and the interstellar plasma definition of the factor K is given in the text. Anisotropy of the ENA flux in the heliosphere 441

Neither cosmic rays nor an interstellar magnetic where VA is the velocity of a HELENA particle and field are included in the model which results in an ~(VA) is the charge exchange cross-section. The increased size of the heliosphere. In this model, the dependence of the charge exchange cross-section characteristics of plasma flow in the interface region, a(VA) on the relative velocity of the colliding particles i.e. the region between the bow shock and the ter- is approximated by the formula of Maher and Tinsley mination shock, are calculated for a particular Mach (1977). The distribution function (per unit solid angle) number of the interstellar plasma flow. For a constant of plasma protons is given by Mach number all linear distances, i.e. the distances - M ]3,2 from the Sun to the bow shock, the heliopause, and ,q(VA) = Ne L2~kbTd VA2 the termination shock, are scaled by a certain factor, x/K. The factor K is equal to N~,,,V,w/N~p 2 V~-~p,where V~w and Nsw are the bulk velocity and the number M(VA-V.) 2 MV ] density of the solar wind at the Earth's orbit and V~p × exp 2kb Tp 2kh T d and Ni~ p are the bulk velocity and the number density and corresponds to a shifted Maxwellian distribution, of the unperturbed interstellar plasma, respectively. where kh is the Boltzmann constant, M is the Both the solar wind and the interstellar plasma are mass, Np = Np(R) and Tp = Tp(R) are the number assumed to consist only of protons and electrons. This density and temperature of the plasma protons, and possibility of scaling the plasma flow structure for U R = UR(R ) and UN = UN(R) are the proton velocity different parameters of the solar wind and interstellar components in the radial and azimuthal directions, plasmas makes the Baranov model a convenient tool respectively. The plasma flow parameters Np, Te, UR, for semiquantitative estimates. and UN depend on both R and ® and were computed The characteristics of plasma flow used in this work by Baranov, V. B. (pers. comm). The function S(VA) were computed by Baranov (Baranov, V. B. pers. is a survival probability for a neutral hydrogen atom comm.) for an interstellar plasma flow Mach number with a given velocity to reach the observation point, equal to 1.6. The influence of neutral interstellar gas i.e. the Earth's orbit (RE = 1 a.u.), moving radially on plasma flow structure was neglected. towards the Sun. It can be shown that Let us assume that the entire interface region is filled with a neutral interstellar hydrogen gas with a S(VA) = exp(--floR2o/VARE), uniform number density N O. Hot plasma protons may where fl0 is the hydrogen atom ionization rate (photo- charge exchange with neutral atoms and give rise to ionization plus charge exchange with solar wind ions) energetic hydrogen atoms, the HELENA flux. We will at the distance R0 from the Sun. The dependence of S only consider the HELENA flux coming back to on the hydrogen atom energy is presented in Fig. 2 the Sun along the radial direction and reaching the Earth's orbit. HELENA particles are considered to move freely and effects of solar gravitation and solar radiation pressure are disregarded. Such an assump- tion seems to be justified because (i) for high velocity 08 atoms the effect of acceleration in the gravitational field is relatively small compared with an atom's in- itial velocity and (ii) for low velocity atoms solar gravi- 06 tational attraction is approximately counterbalanced s by solar radiation pressure. Let us consider HELENA flux coming sunward to O4 the observation point at the distance of 1 a.u. from the Sun and situated at angle ® (Fig. 1). HELENA 0.2 particles are born in the charge exchange process along this direction in the region between the hclio- pause and the termination shock. Only those atoms O I I I I with their velocity vector directed towards the Sun 0 400 800 ~200 16oo 2000 would reach the observation point. The velocity dis- E A ( ev ) tribution of HELENA flux (per unit area), which FIG. 2. ENERGY DEPENDENCE OF THE PROBABILITY S OF A is born in a unit volume at a distance R from the NEUTRAL HYDROGEN ATOM TO REACH A POINT ] a.U. FROM THE observation point, is SUN FOR DIFFERENT ATOM IONIZATION RATES: (1) flo= 4.5×10 7 s ~; (2) flo=6.0×10 7 s '; (3) flo= .1(VA) = Noa(YA) rag( VA)S( VA)/R 2, 7.5×10 7s i. 442 M. /\. (iRI',IMAX

Ibr different ionization rates. Wc will assume that Ioo I the average ionization rate at ii~e Earth's orbil is 6x10 ~s j 80 The velocity, distribution of the total HELENA l]ux T 2- (per unit area and per unit solid angle) reaching thc ~6o observation point is given by' the integral over the line of sight between the termination shock and the P~ ~ 40 4 heliopa use la_ 2O .5 F(V,~) = I'( V~)R-" dR.

0 Making translbrmation from the velocities of HEL- 400 800 1260 1600 2000 ENAs to the corresponding energies, which is more E (eV) convenient for the presentation of the present results, k](;. 3. ENI!R(;Y I)ISTRIB[;II(INS OF I';IE tIELENA Fi I.:X I,()R one finally obtains the expression for the energy dis- I)IFFERt NI AN(;I,ES 0 : SOLAR WIND VELO(TFY (AT 1 a.U. FROM IHtCSt:N) ISCONSI'ANTI',, 500kms ~;(I)0 ;(2)I~ :(3) tribution of HELENA particles (era :s ~ sr ~ erg ~) 36 ;(4) 54 :(5) 72 ;(6) 90 .

,<'~E,,) = 2MX,,E,,~(E,,)S(&) ('~.... ,¥,> (2~zM)''~ J/~,~ (kh Ti,) ~" number of 1.6. The intensity of HELENA ttux is ( E.,+E,,+-e(E, ER) '~) scaled by the interstellar hydrogen atom number den- xexp k~, T,, dR, sity. The dependence of the total HELENA flux. F.. on O is shown in Fig. 4. The dependence of the flux where Eo M(U~+U~),'2 = Eo(R) and ER = of HELENA with an energy greater than 400 eV is k4U~,.'2 = FR(R) tire proton energies correspond- also presented in Fig. 4. The detection efficiency of ing to the plasma total bulk velocity and the velocity neutral atoms is about 0.01 at Ex - 600 eV and it component in the radial direction (the negative sign @creases rapidly with decreasing atom energy in the argument of the exponential corresponds (Gruntman and Morozov. 1982: Gruntman el al., to a radial velocity directed towards the Sun, and the 1990). An atom energy. E\ = 400 eV could probably positive sign corresponds to the anti-solar direction). be considered as an energy threshold lbr the neutral Total HELENA flux, /:. (per square centimeter per particle detection as currently envisaged. Therefore second per sterodian), would consequently be equal Ihe value of F.(E A > 400 eV) is useful for lhc assess- to the integral over the cnerg 3, distribution ment of the feasibility of an experin-rent to measure the HELENA fux. F<, = J'~' f'( k'~ ) dE. x. Not only does the total flux intensity diminish with

It is also convenient, as discussed later, to use the total flux of HELENAs with energies greater than 400 eg. i.e. 60 - I 50 \ ,,,,, 41~oc\ ,o 40 v

30-- 2 RrSt;urs AND DISCt sSnON 2o The calculated HELENA energy distributions arc ro presented in Fig. 3 for different angles ®. Parameters used in the present calculations are: N,>--0.1 em ~: o V,,~=500kms ':N~= 5cm '. Solar wind charac- 0 30 60 teristics (correspond to the conditions 1 a.u. from the 8 ° Sun. The interstellar plasma velocity is l/,~p = 20 km lq(i.' 4. "I'OTAL (tNTEGRAitiL) OVER I~NJ:Rt;YJ | |ELENA tl[x /:. (c[ RVt~ 1) AS A 1,[ N('IION ()1. IHE AN(HA(~172). s ~, number density N~p = 0.04 cm ~, and the tem- ('urve 2 is flux of HELENAs wilh atom energy greater than perature is 11,275 K, which corresponds to a Mach 400 cV. Anisotropy of the ENA flux in the hell®sphere 443 increasing ® (towards the wake), but also the energy 300 distributions shift to smaller energies. This happens because both the radial and angular components of the plasma bulk velocity increase and, simultaneously, T 200 the plasma temperature decreases as the angle ® T increases. It is important to note that a change of the interstellar plasma velocity and/or number density ~E lO0 would result in a change of the size of the heliosphere u_o and the total HELENA flux. However, the shape of the HELENA energy distribution would remain unchanged for the Baranov plasma flow model. The HELENA flux coming from the wake region b of the Sun is virtually non-existent. The Pioneer 10 spacecraft is moving away from the Sun in the wake 300 region, its u.v. photometer is looking in the anti-solar direction, and for all practical purposes the effect of the HELENA flux on detector count rate can be 200 neglected. 13c For the parameters of the interstellar plasma and the solar wind used in this work, the distances from I00 the Sun to the termination shock and heliopause are Rrs = 264 a.u. and RH~ = 352 a.u., respectively, for O = 0. There are indications that the size of the helio- I [ I sphere should be substantially smaller than that given 0 0.2 0.4 0.6 by the Baranov model (e.g. Webber, 1987). The inter- Nisp(Cm-3) stellar plasma number density used was N~p -- 0.04 FIG. 5. (a) DEPENDENCE OF THE TOTAL FLUX OF HELENAs cm 3, and one way to simulate a high "outside" press- (1) AND FLUX or HELENAs W1TH THE ENERGY GREATE~ ure of cosmic rays and an interstellar magnetic field THAN 400 eV (2) ON NUMBER DENSITY OF THE INTERSTELLAR is to increase the value of N~p. Strictly speaking, such PLASMA FOR O = 0. (b) Dependence of the position of the heliopause (I) and an increase is not equivalent to the actual outside the termination shock (2) on the number density of the pressure because the pressure of cosmic rays has to be interstellar plasma ions for O = 0. is®tropic and the pressure of the interstellar plasma flow is highly directional. However, one can expect that at least in the upwind direction, the conditions at high, one could expect that the two shock model gives the interface region would be similar to those expected conditions in the heliospheric interface similar to for the presence of an additional outside is®tropic those expected for a more realistic number density pressure. Figure 5b demonstrates the dependence of (say, Nis p = 0.04 cm 3) and additional pressure of the the size of the heliosphere in the upwind direction cosmic rays and the interstellar magnetic field. For (® = 0) on the interstellar plasma number density. As the termination shock located at a distance of 100 a.u. has already been mentioned, in the two shock model from the Sun the total expected HELENA flux is the shape of the HELENA energy distribution has equal to 150 cm 2 s ' sr ~ and approximately half of to remain unchanged for different interstellar plasma the atoms would have an energy greater than 400 eV. flow parameters and consequently for different sizes Figure 6 demonstrates the dependence of the of the heliosphere. The total HELENA flux, F0, would HELENA energy distributions on the solar wind vel- be different for different values of Nisp, and the depen- ocity at 1 a.u. from the Sun for ® = 0. The solar wind dence of F0 on the interstellar plasma number density number density is maintained constant. The bulk of is shown in Fig. 5a for O = 0. One can clearly see that the energy distributions shifts towards higher energies the closer the solar wind termination shock is to the with an increase of the solar wind velocity and the Sun, the higher the expected HELENA flux. The ter- high energy tail of the distribution grows rapidly. mination shock located at a realistic distance of about HELENAs are born in the heliospheric region con- 100 a.u. from the Sun in the upwind direction cor- taining hot plasma and they are expected to reach responds to an interstellar plasma number density an observer at 1 a.u. from the sun with negligible equal to 0.3 cm ~ in the model used. Though such disturbance. Measurement of the HELENA flux and interstellar plasma number density is unrealistically its energy distribution should provide information on 444 ~,l. A. (.~R[ \IMAX

400

-- 300 T> \ m 200 %

u_ I00

0 0 400 800 1200 1600 2000

E (eV) ["I(L (~. ~NER(~Y I)]STRII{[ IIONS ()I [Hli HELENA FlUX FOR I)]l'|:t RINT SOLAR Vv'INI) VI{LO('ITIIS IAI I ~I.U. FROM THE SUN) J',,,: AN(',LI O 0: (I) 400 km s L: (2) 450 km s ~: (3) 500 km s ~: (4) 550 km s ~' (5) 600kms 1:(6) 650kms i.

the parameters of the hot plasma beyond the ter- field strength and direction m the L1SM. It takes mination shock. How much one can learn from such different time interwds For HELENA particles with measurements about the properties of the LISM and different energies to reach the Earth's orbit. Eor exam- the heliosphere boundary morphology remains an pie, it takes two and a hail'years lk~r a HELENA with open question. A definitive answer requires extensive 200 km s ~ velocity to travel from hot plasnla at a computer simulation supported by the development distance of 100 a.u. from the Sun, and it takes only of a self-consistent model of the heliosphere, including one and a half years for a HELENA with 300 km s non-stationary effects. However, some conclusions velocity. Therelk)re even a single measurement of the can be made now on the basis of the semiquantitative energy distribution of the HELENA flux may yield estimates presented here. information about the heliosphere "'history", i.e. Detection of the HELENA flux would provide an heliosphere -breathing" and the corresponding tem- unambiguous signature of the existence of the ter- poral variations at the fietiospheric interface. Feasi- mination shock, which has yet to be proved exper- bility of the extraction o1" physical inl\wmalion from imentally. HELENA flux intensity measurements such measurements, which involves non-trivial decon- should give us the distance between the termination volufion, could be determined only on the basis of the shock and the Sun, and HELENA energy distribution self-consistent heliosphere model which has yet to be data could provide the value of plasma temperature developed. in the interface region. Asymmetry of the HELENA The energy distributions of the HELENA flux pre- flux could elucidate a number of questions. Depen- sented here are highly sensitive to tt]e size of the hello- dence of HELENA flux characteristics on the angle sphere and parameters of the interstellar plasma and O may provide an answer as to whether the interstellar solar wind, and we have shown that the HELENA plasma flow is subsonic or supersonic as well as to the characteristics are highly anisotropic. This justifies the value of the isotropic pressure outside the hcliosphere. optimism that measurements of HELENA from the Variations of the HELENA flux in latitude, i.e. the Earth's orbit would give us an efficient tool 1o difference between HELENA parameters in and out remotely study the distant boundaries of the hello- of the ecliptic plane, would contain information on sphere. the large scale, global anisotropy of the solar wind. .4vlwl~wlud,qenzeHl,~' 1 would like to thank Prol'. Vludimir Asymmetry of the HELENA flux parameters relative Baranov who provided the results of calculations ol" the to the vector of the solar system motion through the plasma flow parameters. This work was partially supported LISM could provide information on the magnetic by NASA grant NAG 2-146, Anisotropy of the ENA flux in the heliosphere 445

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