from Ulysses to Voyager 2

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. A2, PAGES 2337-2344, FEBRUARY 1, 2000 A numerical study of the evolution of the solar wind from Ulysses to Voyager 2 C. Wang and J. D. Richardson Center for Space Research, Massachusetts Institute of Technology, Cambridge J. T. Gosling Los Alamos National Laboratory, Los Alamos, New Mexico Abstract. Voyager 2 continues to explore the outer hellosphere as Ulysses studies the latitudinal dependence of the solar wind. During the year 1991 these spacecraft were within 2 ø latitude and their radial separation was larger than 30 AU. This alignment presents a good opportunity to investigate the evolution of the solar wind and, in particular, the effect of pickup ions, which are an important component of the solar wind in the outer heliosphere. A numerical simulation study is used to model the evolution of solar wind structures from the location of Ulysses (1-5 AU) to Voyager 2 (33-36 AU) in 1991. The Ulysses observations were used as input into the numerical models and the theoretical predictions were compared with the Voyager 2 observations. The model produces profiles and magnitudes of the plasma parameters (e.g., flow speed and density) which are in reasonable agreement with the observations. The inclusion of pickup ions slows the solar wind, reduces the amplitudes of the speed variations and density spikes, and changes the speed of shock propagation. However, within 35 AU, pickup ions do not change the solar wind structures dramatically. Our calculations favor a low interstellar neutral hydrogen density, i.e., n -0.05 cm -a, for this time period (1991). 1. Introduction Multispacecraft observations over the past 35 years have yielded a detailed description of the solar wind throughout the heliosphere. Theoretical models have been developed to establish connectivity between these observations and help us to understand the data in a global context. The radial alignment of two or more spacecraft is seized upon as a propitious opportunity to study the radial evolution of the solar wind using a simple one-dimensional model. The first attempts to compare a model for the evolution of a corotating stream and the formation of shock pairs with observations beyond I AU were made by Hundhausen and Gosling [1976] and Gosling et al. [1976]. Their onedimensional (l-d) gas-dynamic model was successful in describing the evolution of the speed profile between I and 5 AU, but was less successful in modeling the shock pairs, probably a consequence of neglecting the effects of the magnetic field. A 1-D MHD code was used to simulate the evolution of a solar wind corotat- ing stream from Pioneer 11 at 2.8 AU to Pioneer 10 at 4.9 AU [Dryer et al., 1978]. The authors were suc- Copyright 2000 by the American Geophysical Union. Paper number 1999JA900436. 0148-0227/00/1999 J A900436509.00 cessful in explaining major details of solar wind stream structures. A similar approach was employed by Smith et al. [1981] to simulate the evolution of corotating interaction regions between the positions of Pioneers 10 and 11 out to 6.2 AU. Pizzo et al. [1995] developed a 2-D MHD model to do a radial alignment simulation of solar wind streams observed by these two spacecraft in 1974. A radial alignment study of three solar wind stream structures observed by IMP 7 and 8 (at 1 AU) and Voyager 1 and 2 (in the range 1.4-1.8 AU) in late 1977 was carried out by Burlaga et al. [1985]. They demonstrated that several important aspects of the observed dynamical evolution can be both qualitatively and quantitatively described with their MHD model. However, all the above studies (and others of this type) were limited to cases of small radial displacement (1-4 AU) and to heliocentric distances of less than 5 AU. No such studies have previously been performed for the outer hellosphere, beyond 6-10 AU, to our knowledge. The dynamics of the outer heliosphere are expected to be fundamentally different from those of the inner hellosphere. One important factor is the introduction of pickup ions in the outer hellosphere. The interstellar neutrals can penetrate into distances well within the solar wind regime and charge exchange with solar wind protons, producing pickup ions [Ax/ord, 1972; Holzer, 1972; Isenberg, 1986]. Their inclusion in a propagation 2337

2338 WANG ET AL.- EVOLUTION OF THE SOLAR WIND model should cause the temperature to increase with distance beyond the ionization cavity, and consequently play a significant role in the propagation of shock waves in the outer heliosphere [Zank and Pauls, 1997; Rice and Zank, 1999]. While Ulyssestudies the latitudinal dependence of the solar wind in the inner heliosphere, Voyager 2 continues to explore the outer heliosphere. During the year 1991 these spacecraft were within 2 ø latitude and their radial separation was larger than 30 AU. Figure 1 shows the trajectories of Ulysses and Voyager 2 in 1991. During this time period, Ulysses moved from 1.6 to 5.1 AU, and Voyager 2 moved from 33.6 to 36.2 AU. Both spacecraft were near the solar equatorial plane, and their latitudinal separation was very small. Although they are at different longitudes, their large radial separation affords us a good opportunity to investigate the evolution of the solar wind in the outer heliosphere and to investigate the effect of pickup ions. We use a one-dimensional MHD model (with and without pickup ions) to carry out a numerical study of solar wind evolution in the equatorial plane. We feed data from Ulysses observations into our numerical models, map the evolution of solar wind to the location of Voyager 2, and compare theoretical predictions with the Voyager 2 observations. The outline of this paper is as follows' the basic equations and the initial boundary conditions are described in section 2, the evolution of the solar wind structure is described in section 3, the effect of pickup ions is examined in section 4, and we summarize our results in section 5. 2. Basic Equations and Initial Boundary Conditions 2.1. Basic Equations The computations are confined to the solar equatorial plane of a spherically symmetric flow. This assumption is reasonable as both spacecraft are within 6 ø of the equatorial plane. The basic equations can then be written as follows: ot Oh + Oq (r2 pvr )-- 0 (1) o 1 o B.B, Ot (pv,) + ; [r 2 (pwv, )] OB Ot r 10 + - - - o (2a) (2b) (3a) -5 -lo 850 800 150 100 50 40 5 30 go 10 0 91.0,,, I,,, I,,, I,,, I,,, 91.2 91.4 91.6 91.8 92.0 Time (Year) Figure 1. The trajectories of Voyager 2 (dotted lines) and Ulysses (solid lines) during 1991. Shown are the heliolatitude, inertial heliolongitude, and heliocentric distance from the top to bottom panel. where I a OE --q- Ot 7 7, 2 0 Or (r B ) - 0 (3b) rr {[r2 Vr ( 7-1 I 2 7p + p(v +v})] - + - (4) E - P + pv B 2 7-1 2 q--. 21 The dependent variables are the density p, radial velocity vr, azimuthal velocity v, thermal pressure p, radial magnetic field Br, and azimuthal magnetic field B. These variables are functions of the radius r and time t. The quantity / is the magnetic permeability, G is the gravitational constant, M is the solar mass, and 3' = 5/3 is the adiabatic index for an ideal fluid. The terms QM, Q o and QE are the momentum and energy source terms for charge exchange when pickup ions are included. In the MHD model without pickup ions, they are taken to be 0. 2.2. Numerical Model The computational domain is 1 AU _ r _ 45 AU with a uniform mesh of Ar- 0.02 AU. Equations (1)-(4) are

_,, WANG ET AL' EVOLUTION OF THE SOLAR WIND 2339 solved by the piecewise parabolic method (PPM)[Col- lela and Woodward, 1984; Dai and Woodward, 1995], which possesses a formal accuracy of the third order in smooth flow regions and can capture shocks and other discontinuities within 1-2 grid points. All quantities can be specified independently at the inner boundary (r - 1 AU) based on the Ulysses observations (an adiabatic atmosphere with a constant radial velocity solar wind model is used to calculate the plasma parameters at 1 AU from Ulysses observations), since it belongs to an inflow boundary with the radial flow velocity larger than the fast magnetoacoustic speed. At the outer boundary (r = 45 AU) the radial magnetic flux (r2br), the proton flux (nr2vr), v, v½, and the temperature T are evaluated by linear extrapolation, and Be is determined by the condition vllb in the corotating coordinate system, i.e., B, = (u,- f r) B, 700 600 500 400 300 100 10 1 ' ' ' i,, ' i, ß ' i. ' ' i, ' ' i ß, ' Observation _ '... Model B - A,,,',:,:".. - _,,,,,, ', : : : ', : '. '. I.' I : : : ',-.. _ where f is the solar rotation rate. 120 160 200 240 280 320 360 The initial solar wind conditions at the inner bound- Time (DOY) ary are set equal to the average values observed by Figure 3. Direct comparison of the Voyager 2 obser- Ulysses during 1990. A numerical calculation is then vations at 33-36 AU (one-hour averages) with the precarried out until a steady state solution is reached. This dicted radial velocity and scaled number density. The initial steady state corresponds to the Weber and Davis solid lines and dotted lines denote the observations and [1967] solution for "/- 5/3. The time-dependent flow model results, respectively. is then initiated by introducing Ulysses 1-hour average data from 1991. 800 ' ' 700 A B 600 400 O0 0 0 ]00 200 300 Time (DO'f) Figure 2. Ulysses plasma observations (1 hour averages). Shown are the (top) radial velocity and (bottom) scaled number density. These data were used as input for our numerical models. 3. Evolution of the Solar Wind Figure 2 shows the Ulysses hourly averages of the radial velocity V and scaled proto number density nr 2 (r is the heliocentric distance) for 1991, which were used as input into the pure MHD model (without pickup ions). We will focus on two events: the sharp increase in the solar wind speed at the end of March (labeled A in the figure) and the stream structures from day 140 to 210 (labeled B). They correspond to the two major series of solar activity during March and June 1991. After an initial steady state has been reached, these observations are introduced into the numerical model. The initial quiet solar wind is characterized at I AU by the following parameters: the radial velocity V = 400 km S --1, number density n = 5 cm -3, temperature T = 1.6 x 105 K, and magnetic field strength B = 9 7. The numerical calculation was continued until all of the solar wind observed by Ulysses (--,1.6-5 AU) had traveled beyond the location of Voyager 2 (--,33-36 AU). The solar wind propagation time from Ulysses to Voyager 2 was --,4 months. The model results were recorded at the location of Voyager 2 so that we can compare plasma parameters with Voyager 2 observations. Figure 3 shows comparisons of the observed velocity and number density (solid lines) with those simulated by the MHD model (dotted lines). The model results agree well with the observed large-scale profiles of the plasma parameters and with the observed magnitudes. The lo-

2340 WANG ET AL' EVOLUTION OF THE SOLAR WIND Voyager 2 Solar Equatorial Plane (February) ß SUN Ulysses 0 o Figure 4. The solar equatorial projection of the location of Ulysses and Voyager 2 are plotted for February 1991. The solar activity which caused the large shock on day 146 at 34.6 AU by Voyager 2 is indicated by the dotted loops. Ulysses did not directly observe that activity due to the longitudinal difference. cations of the shocks and the finer-scale density structure do not match well. One big difference between the observations and the calculated results is the large shock observed by Voyager 2 near day 146. The arrival time of the shock in the model, which evolves from the sharp speed increase (event A) shown in Figure 2, lags about I month behind the observations. We think this discrepancy is an effect of the longitudinal separation of the spacecraft. McDonald et al. [1994] show that the shock observed by Voyager 2 on day 146 was likely associated with activity on the Sun in late February. Owing to the difference in longitude, Ulysses did not directly observe that activity, as illustrated in Figure 4, which shows the positions of Ulysses and Voyager 2 projected onto the solar equatorial plane in February 1991. We conclude that the large shock observed by Voyager 2 on day 146 was not associated with the event observed by Ulysses at the end of March. In order to model the development and evolution of this shock, we need information about the disturbance driving it. We assumed that properties of this disturbance are identical to those which caused the event A observed by Ulysses in March and we moved this sharp speed increase to the end of February for the purpose of modeling the leading shock observed by Voyager 2, as an exercise. These "modified" Ulysses observations were put into our numerical model as before. The results are shown in Figure 5, using the same format as in Figure 3. The leading shock time of arrival matches the observations, but the shock strengths differ, most likely due to the assumption that the solar disturbance causing this shock was identical to that in late February. The MHD model still reasonably describes the the dynamical processes in the solar wind over a radial distance of 30 AU. In order to examine the evolution of the solar wind structures in detail, we pay close attention to the stream structures from day 140 to 220 in the Ulysses data. We choose this time period to avoid artificially shifting the Ulysses observations (i.e., event A). The radial development of these stream structures predicted by the model are plotted in Figure 6 at successive distances of 10, 15, 20, 25 AU and the position of Voyager 2. The dotted line in the bottom panel shows the Voyager 2 observations. The interaction and evolution of the stream structure observed by Ulysses produces a quite different solar wind structure at Voyager 2. The evolution at large distances is such that the stream structure beyond 25 AU has little resemblance to that observed at 3 AU by Ulysses. The amplitude of the biggest speed peak decreases with distance as expected. However, the strength of the first shock does not always decrease with distance due to the shock interaction. For example, the first shock at 20 AU has a compression ratio p2/pl ---- 3.2 (Pl and P2 representhe density in the upstream and downstream of the shock, respectively). By 25 AU, the leading two shocks appearing at 20 AU merge to form a stronger forward shock (p2/p = 3.8). The comparison of the model results with the Voyager 2 observations at 35 AU is illustrated in the bottom panel of the figure. The phasing and magnitude of the two strong, fully developed forward shocks (labeled F in Figure 6) are predicted well by the model, although the model shock arrival time is later than that observed, a deficiency which is not considered to be serious in view of the long total propagation time, complex interactions and the longitudinal effects. In summary, the model predicts the main features at Voyager 2 satisfactorily. 700 600 500 400 3OO 100 o 10 120 160 200 240 280 320 360 Time (DOY) Figure 5. Direct comparison of the Voyager observations (solid lines) with the model results (dotted lines) based on the "modified" Ulysses observations. See text for details.

WANG ET AL.' EVOLUTION OF THE SOLAR WIND 2341 45o Ulysses ( -, 3 AU) 650 ' 550 45o,, 650 550 450 650 140 160 180 200 220 10 AU 160 180 200 220 240 550 450 J'... 650 550 15 AU 180 200 220 240 20 AU 200 220 240 260 We follow the approach of Zank and Pauls [1997] to treat the interaction of the solar wind protons with the interstellar neutral hydrogen. The cold neutral density distribution nil(r) is taken as [Vasyliunas and $iscoe, 1976] nil(r) -- nh e -x/r TH -- THoo UH -- UH, (5) where - 4 AU, THoo = 104 K, nhc = 0.1 cm -3, and u - 20 km/s. The subscript infinity indicates the parameter value at infinity. The source terms for charge exchange (QM, QE) we adopt here were derived by McNutt et al. [1998] and summarized in our previous work [Wang and Belcher, 1999]. The effects of photoionization have been ignored in the calculation. Keeping the same computational mesh, boundary conditions and parameters for the plasma component, we plug the neutral hydrogen H distribution equation (5) into our numerical model. The MHD model now includes the effect of pickup ions (hereafter referred as the PI model). The calculation was carried out until a steady state solution was obtained. This solution therefore represents a pickup ion-mediated ambient solar wind solution. Using the same procedure as before, we introduced the "modified" Ulysses observations as described for Figure 5 and followed the evolution of the solar wind out to Voyager 2. Figure 7 shows the model results at the location of Voyager 2. The solid lines correspond to the the PI model. For comparison, the 650 550 450 25 AU 220 240 260 280 Voyager 2 ( 35 AU) 650 ß ' ß I 550 450 > 260 280 300 320 Time (DOY) PI 550 600... I 500 450 400 : I,,, I,,, I,,, I,,, t _ loo Figure 6. Evolution of the velocity profile from that observed by Ulysses during days 140-220 at - 3 AU, to various heliocentric distances out to the location of Voyager 2 at - 35 AU. The dotted line in the bottom panel denotes the Voyager 2 observations. 1 i i 4. Effect of Pickup Ions Pickup ions play an important role in the outer heliosphere. In this section we discuss the effect of pickup ions on the evolution of the solar wind structures. 120 160 200 240 280 320 360 Time (DOY) Figure 7. The model results at the location of Voyager 2. The solid lines show the results from the MHD model including the effect of pickup ions (PI model). For the purpose of comparison, the results from the MHD model without pickup ions are plotted as dotted lines.

2342 WANG ET AL.' EVOLUTION OF THE SOLAR WIND results from the MHD model without pickup ions are shown by the dotted lines. The pickup ions slow down the solar wind speed as a result of the mass-loading effect. Their inclusion increases the solar wind tempera- ture in the outer heliosphere and consequently increases t he Pressure as well as the sound speed. The inertial s ock speed will change. Even though the shocks propagate faster in the presence of pickup ions, the increase in propagation speed is offset by an increased magnet0sonic speed. The shock Mach numbers therefore tend to b e smaller, so the shock strength is less. This decrease in shock strength results in a reduction of speed and density variations. The drag force acting on the solar Wind plasma acts to further reduce these variations. From the plasma momentum equation, the source term can be expressed as [Wang and Belcher, 1998] --m(y71p71h(¾p ¾H)U*, where is charg exchange cros section, n is the number density, v is the velocity, U* represents a characteristic velocity and the subscripts p and H denote protons and neutral hydrogen. This drag term thus acts as an effective force to inhibit the variations of the solar wind density and speed. However, overall the inclusion of pickup ions does not change solar wind structures at Voyager 2 dramatically. This conclusion would be quite different a pure hydrodynamic model was used (the results of the hydrodynamic model are not presented here). The hydrodynamic code does not reproduce the observations as well as the MHD code, and the inclu- sion of the pickup ions into the hydrodynamic model significantly changes the evolution of the solar wind. This difference between MHD and gas dynamics codes demonstrates the important role that the magnetic field plays in the solar wind. To study the effect of pickup ions quantitatively, we plot histograms of the frequency of occurrence of various speeds for both the Voyager 2 observations and model results in Figure 8 for days 120-365 in 1991. Day 120 is is when solar wind observed by Ulysses at the beginning of 1991 first arrives at Voyager 2. The top three panels show histograms of the speeds from Voyager 2 observations, the MHD model and the PI model (with nj - 0.1 cm-3). All the histograms peak around 450 km s -, but the Voyager 2 observations are more sharply peaked than the model results. The average speed for this period is 460 km s -1. The MHD model gives a higher "right shoulder" (high-speed region) than "left shoulder" (low-speed region) with an average speed of 466 km s -. The PI model gives a higher "left shoulder," demonstrating that pickup ions slow the solar wind. Speeds over 550 km s- have virtually disappeared. The average speed is 446 km s -1, - 20 km s -1 less than the MHD result and 14 km s -1 less than observed. Compared with the Voyager 2 observations, the model overestimates the effect of the pickup ions, which dampen the solar wind speed too much. Note that we took the interstellar neutral hydrogen den- 0.50 0.40 0.30 0.20 0.10 0.00 0.50 0.40 0.30 0.20 0.10 0.00 0.50 0.40 0.30 0.20 0.10 0.00 0.50 0.40 0.30 0.20 0.10 Voyager 2 ObservatiOn...,...,..., 400 450 500 550 600 MHD model 3{,0 400 450 500 550 600 PI model (n,h. = 0.1 cm -3)... i... J... i,,..,... 400 450 500 550 600 PI model (nil.= 0.05 cm -3)...,...,...,.... 0.00... 400 450 500 550 600 Velocity (km s-1) Figure 8. Comparison between the distribution of solar wind speeds observed by Voyager 2 and the distributions predicted by the numerical models. The data sets run from day 120 to 365 of 1991 with a bin size of 50 km s-1. sity nhoo to be 0.1 cm -3 in our calculation. However, the estimates of the interstellar neutral hydrogen density vary greatly from study to study, ranging between 0.03 and 0.3 cm -a (see Geiss and Witte [1996 and references therein]). We thus halved the the interstellar neutral hydrogen density n/ oo from 0.1 to 0.05 cm -a

WANG ET AL.' EVOLUTION OF THE SOLAR WIND 2343 in an attempt to better match the observations. The n o, 0.05 cm -3, gives better agreement with the data. model results using n o - 0.05 cm -a are given in the Of the values for n quoted in the literature, which last panel of Figure 8. The solar wind speed from this range from 0.03 to 0.3 cm -3, our calculations favor the model better matches the observations. The average so- lower end of this range for this time period (1991). lar wind speed is 458 km s -1, very close to the observed The MHD model with pickup ions used in this pavalue (460 km s-i). For this time period, our calcula- per is a one-fluid model and can not be used to detion favors a fairly low value for the interstellar neutral termine the coupling of the pickup ions and the therhydrogen density 0.05 cm -a. This value is comparable mal plasma. The temperature measured by Voyager 2 to the density of 0.077+0.015 cm -a derived from Solar is, moreover, only the temperature of the core of the Wind Ion Composition Spectrometer (SWICS) obser- solar wind protons and does not include the contrivations on board Ulysses during a 15-day period in the bution from the pickup ions. The temperature profile same year (November 24 to December 9, 1991) [Gloeck- predicted by this MHD model therefore cannot be relet et al., 1993]. garded as accurately describing the total temperature variation. Nevertheless, the pur e MHD model with- 5. Discussions and Conclusions out pickup ions gives a much slower temperature decay with radial distance than the classical adiabatic atmo- During 1991, both Ulysses and Voyager were near sphere. For "7-5/3 and a structure-lessolar wind, the solar equatorial plane and their radial separation the temperature T would decrease as R -4/3 For the was larger than 30 AU. In spite of their difference in time period shown in figure 6 where the stream struclongitude, they provide a good opportunity to inves- ture evolution is well predicted from the model, if we tigate the evolution of the solar wind from the inner compare the Ulysses temperatur e T with the Voyager heliosphere to the outer heliosphere and to investigate 2 temperature T and assume a power law dependence, the effect of pickup ions. The data from Ulysses in the T/To - (R/Ro) p, we find a valhe for p of-0.8, coninner heliosphere (1-5 AU) were used as input for a one- sistent with the value of-0.7 reported by Gazis and dimensional MHD model with and without the inclusion Lazarus [1982], but lower than the value of-0.5 reported of pickup ions. The predictions of the numerical models by Richardson et al. [1995]. Our MHD model with no at the location of Voyager 2 (33-36 AU) were compared pickup ions gives a decrease in the average T which with Voyager 2 observations. corresponds to an exponent of-0i5, a larger value than The MHD model was successful in predicting the the observed. This non-adiabatic behavior of solar wind profiles and magnitudes of the plasma parameters ob- temperature may be the result of shock heating, as served by Voyager 2. By comparing plasma observa- previously studied by Goldstein and Jokipii [1977] and tions from both Ulysses and Voyager 2, we found that S mith et al. [1985]. Other work [see Williams et al., the sharp increase in the solar wind speed observed by 1995; Matthaeus et al., 1999], hbwever, suggests that Ulysses at the end of March and the large shock ob- this behavior is due to turbulent heating of the core of served by Voyager 2 on day 146 are not related. The the solar wind distribution by shear driven turbulence numerical model was also used to describe the evolution in the inner heliosphere and wav e excitation by pickup of the stream structures observed by Ulysses on days 140-220 to the location of Voyager 2. The model results gave a clear picture of how the solar wind structures ions in the outer heliosphere. A two-fluid model needs to be developed in order to separa te the temperature of the core solar wind distribution and that of the pickup evolve to produce quite different structures at Voyager ions. Finally, it should be pointed out that a 2-D (prob- 2. The overall agreement between the numerical models ably 3-D) model is needed to allo TM for the difference in and the observations is satisfactory. Although the timing of the shocks and other minor details differ between the theoretical predicts and observations, these should not be regarded as serious problems, considering the longitudinal separation between the two spacecraft and the complicated interactions of solar wind structures during their long journey from 3 AU to 35 AU. Pickup ions play an important role in the outer heliosphere. We thus employed a MHD model allowing for the effect of pickup ions. The pickup ions slow down the solar wind, reduce the solar wind speed and density variations, and change the speed of shock propagation. However, within 35 AU, the inclusion of pickup ions into our MHD model does not change the solar wind structures dramatically. The PI model with a interstel- lar neutral hydrogen density n of 0.1 cm -3 slows the solar wind speed more than observed. A lower value of longitude between Ulysses and VoYager 2. The effect of longitudinal and latitudinal gradients on the propagation of the solar wind structures, which is neglected in the 1-D model, may also play an important role. Acknowledgments. This work was supported under NASA contract 959203 from the Jet Propulsion Laboratory to the Massachusetts Institute of Technology and NASA grant NAG5-6472. Work at LANL was performed under the auspices of the U.S Department Of Energy with support from NASA. The authors thank the referees for their helpful comments. Janet G. Luhmann thanks W. K. M. Rice and Murray Dryer for their assistance in evaluating this paper. References Axford, W. I., The interaction of th e solar wind with the interstellar medium, in Solar Wind, NASA Spec. Publ., NASA SP-308, 609, 1972.

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