with two-component circumsolar interstellar cloud: Mutual influence of thermal plasma and galactic cosmic rays

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. A3, PAGES , MARCH 1, 2000 Self-consistent model of the solar wind interaction with two-component circumsolar interstellar cloud: Mutual influence of thermal plasma and galactic cosmic rays Artyom V. Myasnikov Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow Vladislav V. Izmodenov Lomonosov Moscow State University, Department of Aeromechanics, Faculty of Mechanics and Mathematics, Moscow Dmitrii B. Alexashov and Sergei V. Chalov Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow Abstract. The interaction of the solar wind with the two-component interstellar medium consisting of thermal plasma and galactic cosmic rays is studied numerically using a soft fitting technique based on the high-resolution Godunov scheme and the physical process splitting method. Mutual influence of plasma and cosmic ray components on the solar wind termination is considered. It is shown that cosmic rays can considerably modify the shape and structure of the solar wind termination shock and the bow shock, and change the positions of the heliopause and bow shock if no H atoms are taken into account. 1. Introduction important physical effects such as heliospheric and interstellar magnetic fields, solar cycle variations, helio- It is currently believed that the local interstellar cloud latitudinal variations of the solar wind, etc. During the (LIC), surrounding the solar system, is a partially ionlast several years a great effort has been made to study ized gas, which moves supersonically with respect to influences of these processes on the heliospheric interthe Sun. The LIC interacts with the supersonic solar face structure. Solar cycle effects have been studied by wind (SW). A complex interaction region (heliospheric interface) including shock waves and tangential discon- Karmesin et al. [1995], Barahoy and Zaitsev [1998], and tinuities is formed in this interaction. In the last decade, Wang and Belcher [1999]. Solar wind latitudinal variation influence has been considered by Pauls and Zank considerable progress has been achieved in the theoretical modeling of the LIC - SW interaction. The struc- [1997]. The effects of interstellar and heliospheric magnetic fields have been studied by Barahoy and Zaitsev ture of the heliospheric interface has been studied by Barahoy and Malama [1993, 1995, 1996] and Barahoy [1995], Myasnikov [1997], and Linde et al. [1998]. For a recent review of the heliospheric interface models, see et al. [1998]. These authors have developed a selfconsistent model where two interstellar components, Zank [1999]. plasma (protons and electrons) and hydrogen atoms, Cosmic rays (CRs) are coupled with the solar wind and LIC through random magnetic fields frozen in the interact with the solar wind plasma. The main advanplasma flows. Thus one can expect that the plasma tage of the Baranov-Malama model is a rigorous kinetic structure of the heliosphere is affected by the pressure description of interstellar atoms in the heliosphere. At gradient of cosmic rays. The problem of the dynamthe same time, this model does not take into account ical influence of cosmic rays on the solar wind flow in the outer parts of the heliosphere in the spherically sym- 1Now at Department of Aerospace Engineering, University of Southern California, Los Angeles. Copyright 2000 by the American Geophysical Union. metric approximation has been studied by Ko and Webb [1987, 1988], Ko et al. [19881, Lee and Axford [1988], Ziemkiewicz [1994], and Banaszkiewicz and Ziemkiewicz [1997] within the framework of two-fluid models, and by Paper number 1999JA /00/1999JA le Roux and Ptuskin [1995a,b] and le Roux and Fichtnet [1997a,b] by solving the kinetic transport equation <1

2 5180 MYASNIKOV ET AL.' TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL for the cosmic ray distribution function. Modifications of the termination shock structure and prediction of its location as a function of the cosmic ray diffusion coefficient have been explored in these papers. The deceleration of the solar wind upstream of the termination shock (TS) by anomalous cosmic rays (ACRs) has been considered by Fahr et al. [1992], who took into account a possible upwind-downwind asymmetry of ACR pro- duction at the TS. A realistic heliosphere significantly differs from a spherically symmetric cavity embedded in a uniform, motionless interstellar cloud. To reach the termination shock, P-{O, Op galactic cosmic rays (GCRs) pass through a complex Oz' Or' v.vp,v.vp } r, interaction region between the solar wind and LIC, the where p, v, and p are the density, velocity, and pressure region of the heliospheric interface. The properties of of the plasma, respectively; e- plv]2/2 + )is GCRs could change considerably in this region. Izmode- the plasma component energy density per unit volume; nov [1997] investigated the effect of GCR modulation on pc is the GCR pressure; Fc - (7cpcV- kwpc)/(7c- 1) the plasma flow properties in the heliosphere on the ba- is the cosmic ray energy flux; k is the isotropic energysis of the Baranov-Malama model. It was shown that averaged diffusion coefficient, and 7 is the cosmic ray GCRs can have a significant effect on the structure of the plasma flow, in particular, at the bow and termination shocks. Therefore an accurate model of the SW- LIC interaction requires a self-consistent description of plasma and cosmic rays. This paper focuses on studying self-consistently the effects of the galactic cosmic rays on the heliospheric interface plasma structure. GCRs are considered to be a hot gas of low density, with negligible mass flow. The influence of GCRs on the structure of the interaction region for different diffusion coefficients is studied. LIC is assumed to be a fully ionized plasma. Therefore our results can not be directly applied to the heliospheric interface and should be considered as preliminary. However, this simplified model allows us to clearly understand plasma- GCR coupling before it is incorporated into the complete model of the heliospheric interface. The problem considered can be applied to astrospheres of other stars, the properties of the heliosphere in the past or future (when the Sun is not immersed in the LIC), or binary star systems. A more complicated and realistic model of the threecomponent LIC (plasma, H atoms, and GCRs) interaction with the solar wind is presented in the companion paper [Myasnikov et al., this issue] (hereafter paper 2). Figure 1. A supersonic flow of the solar wind plasma terminates at the termination shock (TS), beyond which 2. Gasdynamical Model its kinetic energy is largely converted into thermal en- We consider a two-dimensional (2-D), axisymmetric ergy of the subsonic plasma. The TS reflects from the model of the solar wind and LIC interaction. The sym- axis of symmetry and forms a Mach disk. The bow metry axis is assumed to be parallel to the LIC ve- shock (BS) terminates a supersonic flow of the interlocity vector. LIC is assumed to be a two-fluid mix- stellar plasma. The heliopause (HP), a contact or tanture consisting of thermal plasma and GCRs. GCRs gential discontinuity, separates the interstellar and solar are considered as a hot gas of negligible mass density wind plasmas. but nonnegligible energy density. The system of two- To explore a possible cosmic ray influence on this fluid. governing equations that includes the cosmic ray structure, let us consider a one-dimensional (l-d) strucconvection-diffusion equation in the cylindrical coordi- ture of a planar cosmic ray modified shock. In general, nate system is a diffusive shock wave in a mixture of a thermal gas with Ot -'l- z-z-'l- r-r- H-'I- P (1) P U- {p, pvz, pv,., e,, 7c - 1 r - {P z, P+ P, P z, z (* +P), r,z, G - {pv, pv v, p + pv, v (e + p), F, }T, adiabatic index. In fact, the diffusion coefficient and adiabatic index of GCRs are spatial]y dependent because of the cosmic rav modulation in the he]iosphere. However, the fuji solution would require a kinetic description of GCRs. We simplify the model by assuming the values of k and 7c to be constant. The radial GCR gradients are small in the inner he- liosphere [e.g., Toptygin, 1983]. Since we are interested here in the global distribution of GC in the SW - LIC interaction region, it is a good approximation to assume that in some vicinity of the Sun the condition Vp - 0 if R Rs is satisfied, where R is the heliocentric distance and Rs - 1 AU. In our calculations we used the dimensionless form of equations (1). This form coincides with the dimensional form when all linear dimensions are normalized to the density and velocity are normalized to the undisturbed LIC density p and velocity V, respective]y, the gasdynamic and GCR pressures are normalized to p V, and the diffusion coefficient k is replaced by the dimensionless diffusion coefficient - k/r V. 3. Schematic Structure of the Flow A possible LIC-SW interaction structure is shown in

3 MYASNIKOV ET AL.' TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL 5181 Figure 1. A schematic diagram of the solar wind (SW) interaction with the local interstellar cloud (LIC}. TS denotes the termination shock; HP denotes the contact discontinuity (heliopause); BS denotes the bow shock, which can be split into the subshock (SS) and precursor (PC}; SL denotes the slip line; RS denotes the reflected shock; f denotes plasma streamlines; and t denotes some of the possible trajectories of cosmic ray particles. LISM denotes local interstellar medium. specify as the distance from the Sun to the shock). We place an upstream "free escape boundary" at the point z t = L. This means, for our purely hydrodynamical model [ Chalov and Fahr, 1994], that p½(z'=l)=p½,. (3) The solutions of equations (2) with boundary condition (3) and conservation requirements at the subshock are presented in Figure 2 in the case of a spatially independent diffusion coefficient, 7½ = 5/3, and M = 2. This figure shows the total compression ratios across the shock and the subshock as functions of the ratio of the diffusion length and characteristic size of the shock ( S) - One can see from Figure 2a that the compression across the shock is almost independent of c for small (< 0.1) and large (> 5) values of,c. In the 0.1 < < 5 region, there is a transition from small to large compression rates. The smallest compression value 2.4 I I... I I... '' and cosmic rays consists of a dissipative gas subshock = and a smooth precursor; the latter is formed when en- ' ergetic particles scatter upstream of the subshock [e.g., 1.6 Axford et al., 1982]. The spatial extension of the pre- cursor is determined by the diffusion coefficient. The equations (1) can be written for a 1-D stationary state ' in the following dimensionless form: pu - const, Pu 2 + P + Pc -- const, u(e + p) + Fc -- const, (2) dfc dpc dz dz 2.0 o 1.2 " 2.4., '''''''!... I... I ; dimensionless diffusion coefficient i The cosmic ray pressure and energy flux density are conserved across the subshock, and one can obtain the conservation relations for plasma mass, momentum, and energy fluxes at the subshock. Considering the structure of the bow shock, it is convenient to introduce a new displaced z' axis directed along the z axis so that z - z'+ ZBS, where ZBS is the position of the BS at the axis of symmetry in the upwind direction. The LIC moves in the negative direction of the z' axis, and the subshock is placed at z t - 0 in this new system of coordinates. The degree of modification of a shock by cosmic rays would essentially depend on the relation between the spatial size of the shock and the diffusion length of the energetic particles. To model the finite size of the shock, we consider the escape of cosmic rays diffusing upstream from the subshock. Let us introduce L, the characteristic dimensionless (normalized to RE) size of the shock (which we dimensionless diffusion coefficient Figure 2. The dependence of (a) the total compression across the BS and (b) compression across the subshock (b) on the dimensionless diffusion coefficient and Pc,oo obtained from the simple 1-D model. Curves 1 denote the case with/ c,oo - 0.4, curves 2 denote the case with Pc,oo , and curves 3 denote the case with/ c,oo = 0.1. Dashed lines in Figure 2a correspond to the cases when subshock is absent.

4 5182 MYASNIKOV ET AL.: TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL (for small diffusion coefficients) corresponds to the case interface flow can not be predicted prior to the selfwhen the flow structure is determined by the effec- consistent solution. Therefore the shock-fitting methtive Mach number(1 /Meff, o - 1/M + 1/M,OO, where ods are not useful. This is why we used in the present M = pu /%pc). The characteristic diffusion length is study the soft fitting technique [Godunov et al., 1979]. much smaller in this case than the characteristic size The technique allows to combine the advantages of the of the shock, and cosmic ray particles are "frozen" in the plasma flow. For the chosen set of Moo and the LIC flow is supersonic and the effective Mach number Meff,oo > 1 and, therefore, the bow shock exists if Eulerian and Lagrangian approaches. When coupled with the method of physical processplitting [e.g., Yanenko, 1967], the soft fitting technique allows us to take into account different physical processes and study their i5c,oo < If the condition Pc,oo < 0.45 is satisfied influence on the gas flow. The numerical algorithm can but/5,oo is larger than 0.1, the BS has a pure diffusive be briefly described by the following. The results of incharacter and the subshock is absent for small diffusion tegration of equation (1) over the volume of a grid cell coefficients (Figure 2b, also Figure 2a, dashed lines). and time step r are written in the form The cosmic ray influence on the flow is negligible at (, n+lcn+l large values of t. Although the precursor always exists, i,j _ S.n.C,,3 n )It - (4) its intensity decreases rapidly when increases (Figures 2a and 2b). For large the total compression is equal to the compression across the subshock as in the pure gasdynamic case. In this case the compression can be determined by Rankine-Hugoniot relations assuming M = Moo. Thus one can see that depending on the - n+l/2 q- (/..In q- pn)s, l/2 ' Here S/,j is the volume of (i,j) cell; ll - - i-1/2,j q- - i+l/2,j q- - i,j_l/2q- - i,j+l/2 where - i+l/2,j-- (rile+ n2g)i+l/2,j; n -- (hi, n2) is an outward normal vector to the cell surface; and U, E, and G are defined in dimensionless parameters, and/5,oo, the bow shock section 2. may be pure "gasdynamical", may be split in the precursor and subshock, may have a pure diffusive nature, or, finally, may disappear. Semiquantitative estimates can also be made for the termination shock. An accurate numerical 1-D solution According to the physical process splitting method, solving equation (4) is equivalento solving the following three equations: (Sn+Iu* - SnUn)/T- - - g(u n) q- H;S n+l/2, (5) is difficult because (1) the boundary condition (3)is not accurately known and (2) the flow behind the TS sn+l(u ** -U*)/t- (6) may be rather complicated, essentially two-dimensional. - - c(u') q-(l-lc* q- P )S n+l/2, Therefore a simple 1-D model may fail in predicting the compression at the TS. However, again, the smaller values of (TS) - Voo/Vs L s (here L s is a charac- S n+l(u n+l -- U* *)IT-- rg, (7) teristic size of the TS in AU) would correspond to the stronger influence of GCRs on the flow in the vicinity where E s - {pvz, p+ pvz 2, pvz vr, vz (e + p), O} T, of the TS. It was seen in the previous section that cosmic ray modified shock structure strongly depends on the dimensionless parameter, which is determined by the diffusion coefficient } and the characteristic size of the shock. The characteristic sizes of the TS and BS can not be determined without solving the problem selfconsistently. Thus the structure of the hellospheric % - {pv, pvv, p + pv, + p), 0} pv, pv, v, +p), Pg = { O, -Opt/Oz, -Opt/Or, -v. Vp, 0} T, {0, 0, 0, 0, {0, 0, 0, 0, = {0, 0, 0, 0, 1)}T/r, P = {0, O, O, O,-p V. v} T. Equation The stagnation point at the HP presents another complication. In a pure diffusive transition the effective Mach number downstream is less than 1, while the gasdynamical Mach number M > 1. However, both Mach numbers are equal to zero at the stagnation point. Thus set the transition of the flow behind the pure diffusive BS (5) is a finite difference analogue of pure gasdynamior TS passes through the point where M = 1. Forcal equations, and it is possible to solve it by the Gomation of an additional dissipative shock may occur at dunov scheme. To increase the resolution properties this point since the flows are supersonic with respect of this scheme (first-order accuracy), we introduced a to short-wavelength sonic disturbances. It is difficult piecewise-linear distribution of the parameters inside to treat this problem analytically because the flow is the cells to define values on their boundaries. Slope two-dimensional in the vicinity of the stagnation point. limiters have been used to achieve the total variation diminishing (TVD) property [Myasnikov, 1997; Hirsch, 4. Numerical Method 1990]. This part of the code has been tested by comparisons with the results of the Baranov-Malama model in the case of a pure ionized interstellar medium. Equation (6) describes evolution of GCR pressure and can be also split into convective and diffusive equations. To solve the former equation, we used the second-order TVD Roe's scheme [e.g., Hirsch, 1990] with the linear cosmic rw pressure distribution inside the cell, similar to the

5 MYASNIKOV ET AL.' TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL 5183 distribution used for equation (5). The diffusiv equation was solved using the implicit scheme described in (plasm and H atoms) heliospheric interface model [Izmodenov et al., 1999]. A range of possible values is 0.04 detail by Myasnikov and Zhekov [1998]. The solutions cm -3 < np,oo 0.07 cm -3. were additionally tested by comparing with the results of the explicit scheme on the spherical immovable grid and with the kinematic solution [Izmodenov, 1997]. The pressure of GCRs was estimated from the interstellar spectra for GCR protons [e.g., Webber et al., 1987; Reineck et al., 1993]: Equation (7) is solved by an explicit scheme. To calculate Pg, we use solutions of equations (5) and (6). We used a flow-adaptive Malama-type grid in our ja" / (T + 0.5E0) -2'6, (S) calculations. The difference of our grid from the orig- where ja"is the differential particle intensity in units of inal Malama grid [Barahoy and Malama, 1993, 1995, m-esr-ls-lmev-lnucleon -1, T is the kinetic energy, 1996] is in capturing the slip line if the triple point oc- and E0 is the rest energy of particles in units of GeV. curs in the flow (Figure 1) instead of fitting it. The soft It follows from (8) that the pressure of unmodulated fitting method introduces spreading of the discontinu- GCRs with energies less than I - 2 GeV/nucleon is ities to one or two grid points instead of the zero-point about 0.18 ev cm -3. Since particles with larger enerspreading in Barnnov and Malama's [1993, 1995, 1996] gies have a weak coupling with the plasma LIC comporesults. However, the comparison of the calculations nent, we adopt in our calculations the value of the inwith those based on an immovable polar mesh showed terstellar cosmic ray pressure pc,oo=0.18 ev cm -3 and that the positions and shapes of the discontinuities are the dimensionless pressure /5c,oo The value of determined correctly. In addition, the soft fitting of the the energy-averaged diffusion coefficient k is uncertain discontinuities makes it possible to determine whether the solution is convergent in a simple way. We considered the solution to be steady state if the maximum in the outer heliosphere and in the LIC, and we assume here that k is spatially independent. We consider k varying in the wide range from 3.75 x 1019 to 3.75 x 102 absolute value of all dimensionless velocities of disconcm 2 s -1. The cosmic ray adiabatic index is assumed to tinuities was less than For each set of the flow be 4/3 _< 7c _< 5/3, with the lower and upper limits parameters we ran series of calculations where the to- corresponding to ultrarelativistic particles and nonrelatal number of grid points was doubled subsequently in tivistic particles, respectively. The value of 7c that can order to be sure that the grid resolution is sufficient to be obtained from the spectrum (8) is approximately 1.5. treat properly diffusive shocks. In our experience, five Let us start the description of the results with their or six points are necessary per diffusive wave to resolve dependence on for fixed value 7c - 5/3. Figure 3 the shock structure [Myasnikov et al., 1997; Myasnikov presents the dimensionless plasma density and GCR and Zhekov, 1998]. pressure distributions along the axis of symmetry in The described high-resolution soft fitting technique the upwind direction (see Table 1). The pure gasdyhas been successfully applied to the description of flows namical solution/5,oo - 0 (run 5) is also shown in Figin various astrophysical objects [Myasnikov, 1997; Zhekov ure 3a. The curve number in the figure corresponds and Myasnikov; 1998, Myasnikov and Zhekov, 1998; to the run number. In run i the BS is located approxi- Myasnikov et al., 1998]. mately at 1500 AU (not shown in Figures 3a but seen in Figure 3b) and the compression across the BS is equal to 5. Results The structure of this flow differs strongly from the gasdynamical flow (run 5); in particular, the distance We assumed the following parameters in our simu- between the HP and BS increases approximately by a lations' 7-5/3, np,z - 7 cm -3, Vz km s -i, factor of 7, and the BS intensity dramatically decreases. Tz - 73,600 K, np,oo cm -3, Voo - 25 km s -i, Such behavior can be easily explained by the use of reand Too = 5680 K, where np,is, Vls, and Tls are the suits presented in section 3. Actually, as is shown in solar wind proton number density, velocity, and tem- this section, the total compression at the BS depends perature at the Earth orbit; and rtp,oo, Voo, and Too on the dimensionless parameter,c(bs) (Table 1). One are the proton number density, velocity, and tempera- can see that g(bs) << 1 for / - 1, and therefore the ture in the undisturbed interstellar medium. The parameters of the interstellar velocity and temperature are close to those recently determined from interstellar He measurement by Witte et al. [1996] with the shock transition corresponds to a small-compression, subshock-free part of curve i in Figure 2a. Therefore the properties of the shock transition are defined completely by the effective Mach number MefLoo Interstellar Neutral-Gas (GAS) instrument on Ulysses. This explains why the position of the BS at the axis of The interstellar proton number density np,oo is the upper limit obtained from the analysis of the Solar Wind symmetry is much farther from the Sun and its intensity is much smaller than those in the pure gasdynami case. Ion Composition Spectrometer (SWICS) Ulysses pickup The compression rate at << 1 (/5c,oo - 0.4) is equal ion data, Ly c measurements, and low-frequency radio to 1.07 (Figure 2a), that is, exactly the same as in 2-D emissions on the basis of the two-shock, two-component calculations. Since the value of the diffusion coef cient

6 , ß 5184 MYASNIKOV ET AL- TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL IE+I I I i 1 HP BS IE+0 8 d. IE-I IE-2 IE-3 I I I R(AU) ,,.,.-.'-,, r I r r r, r - ',, ['3 i l! O R(AU) Figure 3. The distributions of (a) the plasma density, and (b) GCR pressure in the upwind direction as functions of/c. The curve numbers correspond to run numbers, namely, curves 1 correspond to /c- l, curves 2 correspond to /c- l0 2, curves 3 correspond to /c- l0 a, 4 correspond to /c- 104, curves 5 correspond to the pure gasdynamical solution. AS denotes locations of the additional shock on curve 2. is comparatively small, cosmic rays can not penetrate through the heliopause deeply into the shocked SW region because they are swept out by convection and concentrate in the vicinity of the HP (curve 1 in Figure 3b). The additional pressure of cosmic rays pushes the HP and TS closer to the Sun. The calculated value of n(bs) in run 2 corresponds to the beginning of the steep transition zone (Figure 2a) between small and large compressions. In this case the compression increases when compared with the case / - 1, but subshock-free transitions still take place with more effective smoothing for larger. The diffusion Table 1. Parameters of Runs k, cm2s - n(b$) n(t$) / / / / x X x X x x x x x 10-4

7 MYASNIKOV ET AL.' TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL 5185 length of cosmic rays is comparable with the size of the BS, and the structure of the flow changes qualitatively. Curves 2 in Figures, 3a and 3b show that the plasma density and CR pressure vary smoothly from the LIC toward the HP. Diffusion is large enough in this case to allow CRs to penetrate into the region between the HP and TS. However, diffusion is insufficient for their penetration further, inside the TS, where the SW velocity is higher by a factor of 4. The calculated value of t (TS) in run 2 is very small (see Table 1), so CRs are accelerated at the TS and modify the shock structure effectively. One can see (Figure 3a) that instead of a sharp deceleration of the SW at the TS, a smooth transition takes place, indicating a diffusive nature of the TS. The cosmic rays are convected out and concentrated in the region between the TS and HP. More precisely, cosmic rays are concentrated at the additional shock (see section 3), where they are accelerated as well. We did not see the additional shock between HP and diffusive BS in runs 1 and 2. Instead, our calculations indicate a smooth transition through the point M = 1 there. Although it may be a result of grid selection, we do not exclude the possibility of a shock-free deceleration of the gas-rays mixture. Further numerical and analytical study of this phenomenon is needed. The increase of leads to the weakening of the cou- pling between the plasma flow and CRs and resulting decrease of the cosmic ray influence on the flow structure. The estimated value of n(bs) for run 3 corre- sponds to the end of the steep transition zone (Table 1 numerical model is based on the soft fitting technique and Figure 2a) between small and large compressions. and the physical process splitting method. The main The total compression therefore is very close to the lim- results of this study are the following. iting compression, which takes place in the gasdynam- 1. GCRs with the pressure 0.18 ev cm -a exert ical case (run 5), and that is clearly seen in Figure 3a. strong influence on the plasma flow in the SW-LIC in- However, the cosmic ray pressure gradient between the teraction region in the case when their energy-averaged diffusion coefficient k < l0 2a cm2s -. In the case BS and TS still exists (Figure 3b), and cosmic rays have an effect on the plasma flow. Namely, the effect is in the k < 4 x l0 2ø cm2s -, GCRs have a strong influence shifts of the HP and TS. As the diffusion coefficient increases further, the pressure gradient of CRs decreases in runs 3 and 4. The downwind part of the TS is a very effective "accelerator" of cosmic ray particles in run 3 (Figure 4c): The GCR pressure increases there and its maximum exceeds the value of Pc,oo. The concentration of GCRs leads to the increase of their influence on the plasma flow, and, as a result, TS consists of an extensive precursor and subshock in the downwind direction. Our calculations, carried out for 7c = 1.5 (run 6), showed a strong influence of 7 on the BS position (Figure 3b). Namely, the smaller 7 is, the closer to the Sun the BS is situated. Such dependence is expected since the structure of the flow is determined by the effective Mach number for small diffusion coefficients. Decrease of 7 leads to increase of Meff,oo. Thus the BS is closer to the Sun and it is stronger. The variation of 7 has no strong influence on the flow structure and TS, HP positions. At the same time the GCR pressure distribution essentially depends on 7c. The effect of cosmic ray pressure increase at the TS is more pronounced for larger 7c (Figure 3b; see also Figure 7 in paper 2). In fact, this is in accordance with the results of analyti- cal models of diffusive shock acceleration [Axford et al., 6. Conclusions We have presented here a new axisymmetric model of interaction between the SW and a two-component (thermal plasma and GCRs) interstellar medium. The on the plasma flow between the BS and HP but can not penetrate through the HP in the region occupied and the HP, TS, and BS shift from the Sun, approaching by the SW. In comparison with the pure gasdynamitheir position in the pure gasdynamicase (see curves cal case the HP and TS shift toward the Sun, and the 4 and 5 in Figure 3a). BS shifts away from the Sun and its intensity decreases The spatial distributions of the GCRs (the contours dramatically. Increasing of the diffusion coefficient up of the constant GCR pressure) and the approximate to k - 4 x l0 2 cm2s - leads to a qualitative change in the flow structure. In this case both the BS and TS positions of TS, BS, and HP are presented in Figure 4. One can see that the cosmic ray distributions are have a smooth structure, the additional shock appears strongly asymmetric for small diffusion coefficients. The between them, and the HP is located at the smallest GCR pressure growth is most pronounced in the up- distance from the Sun. Further increasing of k results wind direction, exists in the entire region between the in smooth displacement of the TS, HP, and BS to their BS and HP, but is weaker than at the axis of symmetry positions in the pure gasdynamical case. for/ - 1. GCR do not penetrate through the HP any- 2. The region of interaction between the LIC and where (Figure 4a) if diffusion is small. As the diffusion SW has a strong modulation effect on GCRs. Our calcucoefficient increases, the pattern becomes more symmet- lations indicate that the degree of GCR penetration into ric (Figures 4b and 4c); however, even for/ - 10,000, the heliosphere is very sensitive to the value of the difasymmetry is noticeable. The TS has a more spheri- fusion coefficient. Strong GCR pressure depletion takes cal shape than in the pure gasdynamic case under the place for small diffusion coefficients, k _< l0 2ø cm2s -. influence of GCRs for small diffusion coefficients. The For k m 4 x l0 2 cm2s - we found a strong GCR prestriple point disappears in runs 1 and 2, but it remains sure increase in the region between the TS and HP, namely, at the additional shock, which is found numer-

8 5186 MYASNIKOV ET AL.: TWO-COMPONENT (PLASMA AND GCR) LIC/SW MODEL O , 300 4* "ø.,i o.s o.e o.? o. o.o 20, -coo -oo.. oo.- oo O. 1 0, O. 15 0,21 0, Figure 4. The spatial distribution of the GCR pressure for the cases with (a) - 1, (b) - 100, and (c) Solid white lines in Figures 4a and 4b and black lines in Figure 4c denote softly fitted shocks and contact discontinuity. ically in the present study. For k m 4 x 1022 cm2s -1 the strong GCR pressure increase takes place at the TS in the downwind direction. We have used here the simplest model of the CR transport to show how GCRs can influence the structure of the interaction region between the SW and LIC. The region can also influence considerably the penetration of GCRs into the heliosphere. We believe that the simplest model is good enough to study the GCR effect on the plasma flow, but the problem of GCR modulation in the SW - LIC interface must be solved in the frame of a more complex model in which the kinetic approximation rather than the hydrodynamic one is used. To understand the effects of plasma- galactic cosmic rays interaction clearly, we ignored here the effect of interstellar atoms, which are probably a major component of the LIC. The self-consistent model of the three-component (plasma, atoms, and GCR) interstel- lar medium with the solar wind is studied in the com- panion paper (paper 2). Acknowledgments. We would especially hke to thank V.B. Baranov for stimulating this research and for useful discussions. This work was supported by the Russian Foundation of Basic Research under grants and , INTAS-CNES grant 97512, "The heliosphere in the local interstellar cloud," partly supported by the Interna-

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