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Evidence for a Solar Wind Slowdown in the Outer Heliosphere?

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J. D. Richardson, K. I. Paularena, A. J. Lazarus, and J. W. Belcher
Center for Space Research, M.I.T., Cambridge, Massachusetts, USA

Table of Contents:

Abstract.

Voyager 2 and IMP 8 plasma data are used to look for the predicted slowdown of the solar wind with heliospheric distance. Decreases of roughly 7% in the radial velocity and of the same order in the flux are found if the Voyager 2 and IMP 8 velocities are normalized to agree in the inner heliosphere. This decrease is consistent with a pickup ion density equal to 8% of the total ion density, similar to predictions and other determinations of this density. Comparison with published model results allows us to infer an interstellar neutral density of 0.05 cm-3.

Introduction

The Parker solution to the solar wind predicts a nearly constant radial velocity from several hundred solar radii until the termination shock is encountered. Spacecraft data confirm that this prediction holds to first order from 0.3 to 43 AU [Barnes et al., 1992; Belcher et al., 1993]. A small deviation from the constant velocity solution is expected due to pickup of interstellar neutrals. These neutrals drift into the heliospheric cavity and are ionized by charge exchange, photoionization, or electron impact. The pickup process imparts to these newly created ions an initial energy equal to twice the local solar wind energy. This energy comes from the bulk motion of the solar wind plasma. Thus the pickup of interstellar plasma could be detected, in theory, by a slowing of the solar wind flow.

Solar wind velocities are highly variable on time scales ranging from minutes to solar cycles, and vary with heliographic latitude and longitude as well. Thus detection of even fairly substantial decreases of the solar wind speed with heliographic distance is not possible with one spacecraft since time, distance, and latitude effects cannot be deconvolved. In this paper we use data from the IMP 8 and Voyager 2 spacecraft to look for changes in the solar wind velocity as Voyager 2 moves from 1 to beyond 40 AU. IMP 8, in Earth orbit, provides a stable monitor which is used to distinguish changes in the solar wind radial velocity due to the increase in Voyager 2's heliospheric distance from latitudinal and temporal effects. After 1992, Voyager 2 is always at more southerly latitudes than those sampled by IMP 8; thus the data now in hand probably provide the best chance of detecting a solar wind slowdown that will be available for the foreseeable future.

We find that the radial velocities observed at Voyager 2 decline relative to those observed by IMP 8 as Voyager 2 moves from 1 to 40 AU. The magnitude of the velocity decrease is approximately 30 km/s, consistent with theoretical predictions. This change is much greater than the uncertainties in the velocity measurements from either spacecraft; however, IMP 8 and Voyager 2 velocities had to be normalized to bring them into agreement in the inner heliosphere.

The Instruments and Trajectories

The plasma parameters used in this paper are derived from observations obtained using the MIT Faraday cup detectors on the IMP 8 and Voyager 2 spacecraft. The IMP 8 instrument has a split collector which provides information about the out-of-ecliptic flow angle; the complete velocity vector can be obtained from the spacecraft rotation. This instrument measures protons with energies up to 6.9 keV with an energy resolution (DELTA V / V, where V is voltage) of 10%. A non-linear least squares fitting routine assumes a convected, isotropic Maxwellian proton distribution to find the proton velocity, density, and temperature which best fit the data. Typical 1-sigma errors in the radial velocity are less than 0.5%, or less than 2 km/s for a typical 400 km/s solar wind speed.

The Voyager 2 plasma experiment has three Faraday cups which detect solar wind ions [see Bridge et al., 1977]. Protons with energies up to 6 keV are measured with an energy resolution of 3.6%. A non-linear least squares fitting routine is used to derive plasma parameters from the Voyager 2 data. The 1 sigma uncertainties in the radial velocities derived by fitting Maxwellian distributions to the data are generally 1 km/s or less.

IMP 8 is in Earth orbit and thus traverses 360 degrees in heliographic longitude each year and while moving between plus and minus 7.26 degrees heliographic latitude. Approximately 62% of IMP 8's orbital period is spent in the solar wind; the remainder of the time IMP 8 is in Earth's magnetosheath and magnetotail. Voyager 2 moves relatively slowly in longitude and latitude compared to IMP 8. The trajectories of the two spacecraft in heliospheric latitude are shown in Figure 1. Voyager 2 remained within the latitude range sampled by IMP 8 until 1992; it then moved to more southerly latitudes than those traversed by IMP 8. Thus comparison of future data from IMP 8 and Voyager 2 will be more difficult since the (unmonitored) latitudinal variation of solar wind parameters will add to the complexity of the analysis.

Figure 1: (GIF format (8K)) or (PS format (47K)): The trajectories in latitude of Voyager 2 and IMP 8 since the launch of Voyager 2 in 1977.

Observations

Figure 2 shows 1-year running averages of the radial velocity, the density-weighted velocity, and the flux of the solar wind determined by IMP 8 and Voyager 2. The Voyager 2 parameters are time-shifted to 1 AU by dividing the radial distance from 1 AU by the 50-day running average of the radial velocity measured by Voyager 2. A 50-day average is used to smooth solar rotation effects. Voyager 2 densities and fluxes are normalized to 1 AU by multiplying by R squared. The IMP 8 velocities in the top panel are shifted upward by 20 km/s; this shift gives good agreement between IMP 8 and Voyager 2 in the inner heliosphere. The IMP 8 density-weighted velocity and flux are also shifted to give agreement with Voyager 2 data in the inner heliosphere. The data from time period near solar minimum (1985.5-1988) are not shown since strong latitudinal gradients are present in the velocity at this time [Gazis et al., 1994].

Figure 2: (GIF format (11K)) or (PS format (185K)): The velocity, density-weighted velocity, and flux of the solar wind from Voyager 2 and IMP 8. The quantities shown are 1-year averages to emphasize long-term trends. Voyager 2 data are time-shifted back to 1 AU.

The top panel of Figure 2 shows that the Voyager 2 velocity decreases relative to that observed by IMP 8 as Voyager 2 moves into the outer heliosphere. The deviation of Voyager 2 from IMP 8 velocities becomes noticeable near the beginning of 1983 when Voyager 2 was at 15 AU. The difference increases to about 30 km/s after 1988.

The density-weighted velocity (sum over nv /sum over n, summed over the 1 year averaging interval, where v is velocity and n is number density) results shown in the middle panel of Figure 2 are similar, with the Voyager 2 velocity decreasing relative to IMP 8 as Voyager 2 moves away from the Sun. This quantity is roughly equivalent to momentum flux, and shows that the velocity decrease is not an artifact caused by velocity differentials between more and less dense regions. We do not understand why the normalization constant between spacecraft is larger for this velocity. Comparison of the proton fluxes at IMP 8 and Voyager 2 (bottom panel of Figure 2) is complicated by the less than ideal correspondence between features detected by IMP 8 and Voyager 2, but the trend seems to be for the flux to decrease with radial distance. After 1988 (about 30 AU) this decrease is roughly 10%. The IMP 8 flux is adjusted downward by a factor of 20%, roughly comparable to the systematic difference in densities detected by these two spacecraft.

Figure 3 shows 1-year running averages of the difference between IMP 8 and Voyager 2 velocities versus time and heliospheric distance. The solar minimum period is not shown. The differences were obtained by interpolating time-shifted Voyager 2 velocities to the times for which IMP 8 data were available. The best linear fit to these data is shown by the dashed line. This figure illustrates that in the inner heliosphere Voyager 2 velocities are greater than those observed by IMP 8, but that the Voyager 2 velocities are less than those observed by IMP 8 after 1983.

Figure 3: (GIF format (8K)) or (PS format (58K)): One-year running averages of the difference in velocity measured by IMP 8 and Voyager 2.

Discussion

Offsets

The interpretation that the solar wind velocity and flux decrease with heliospheric distance depends on the assumption that these quantities should be normalized to agree in the inner heliosphere. The discrepancies between long-term averages of parameters obtained by Voyager 2 and IMP 8 in the inner heliosphere are not understood. Comparison of IMP 8 and Voyager 2 data in the two weeks after the launch of Voyager 2 in 1977 show that the velocities from these two spacecraft match each other to within a few percent. IMP 8 densities are, on average, about 15% higher than those reported by Voyager 2 at those same times. Calibrations performed periodically aboard each spacecraft show the calibrations have not changed. Thus much of the difference between IMP 8 and Voyager 2 parameters which lead to the normalizations used in Figure 2 is introduced by the averaging process. Numerous selection effects may contribute. The Voyager 2 instrument can measure much lower densities than the IMP 8 instrument. Extremes of velocity and density which may be outside IMP 8's observational range will be moderated by the time the plasma reaches Voyager 2. The times of entry of IMP 8 into the magnetosheath and magnetotail are dependent on the solar wind parameters. If bow shock crossings are not picked correctly on IMP 8 then slower, denser magnetosheath plasma can contaminate the solar wind parameters.

Near Earth, the solar wind can be influenced even outside the bow shock by upstream waves which can slow the solar wind (and thus make it more dense by flux conservation). We believe that interaction with diffuse ions and upstream waves is a significant contributor to the decrease of IMP 8 velocities relative to Voyager 2 velocities in the inner heliosphere. Formisano and Amata [1976] show that the proton velocity decreases by 30 km/s when upstream waves are present. Bame et al. [1980] document the decrease in velocity of the solar wind when diffuse ions and long-period waves are present; they look at regions where the solar wind speed is slow (less than 450 km/s) and find an average deceleration of 7-10 km/s, although changes as large as 25-40 km/s were observed. Bonifazi et al. [1980] confirm the Bame et al. [1980] results, and find an average slowdown of 10 km/s, and also establish a velocity dependence for the slowdown; the slowing varies from 5 km/s for solar wind speeds less than 300 km/s to 30 km/s for solar wind speeds between 400 and 450 km/s, the fastest speeds used in their study. Bonifazi et al. [1983] show that the slowdown is greatest (30-40 km/s) near the shock and decreases away from the shock. Zhang et al. [1994] find that the deceleration is largest for quasi-parallel shocks, within 5 RE of the shock (where RE is an Earth radius), and 10 RE from the foreshock boundary. The average deceleration is roughly 20 km/s when the shock normal is less than 45 degrees. IMP 8 is in the foreshock only a fraction of its orbit; a rough estimate that 1/4 of its orbit is in the foreshock region would give a slowdown of 5 km/s based on the Zhang et al. [1994] study. We compared the average undisturbed IMP 8 solar wind speed (far in front of the Earth (> 20 RE) and near the Earth-Sun line, where speeds are least likely to have been reduced by connection of field lines to the bow shock) to the speed in other regions and find an average slowdown of 5 km/s, with the greatest decrease (8 km/s) in the quadrant where the foreshock is most likely to reduce the speed (X < 0, Y < 0 in GSE coordinates). This effect explains only one-fourth of the correction factor needed to bring IMP 8 velocities into agreement with Voyager 2 velocities in the inner heliosphere. [Any reduction due to bad picking of the boundaries would be detected in the quadrant analysis and is small.] The correlation between solar wind velocity and pressure is small but positive, so the effect of the moving boundaries should skew the IMP 8 velocities to higher values, but probably not significantly higher. This leaves the possibility that IMP 8 misses high velocity regions either because the protons are above the 6.9 kV instrument energy threshold or because the fluxes in these regions are below the IMP 8 threshold. Such an error is difficult to quantify because the solar wind evolves a great deal in terms of the observed velocity and density distributions between IMP 8 and Voyager 2.

Although we are able to only roughly determine the relative importance of each of these effects, it is not surprising that they influence the long-term averages of solar wind parameters. The important consideration is that none of these effects should vary systematically with time; thus, if we normalize IMP 8 and Voyager 2 average parameters when Voyager 2 is in the inner solar system, this normalization should remain valid in the outer solar system, as the spacecraft calibrations do not change.

Another possible cause of systematic discrepancies between the observed velocities is the difference in latitude of the two spacecraft. The solar wind velocity increases with with heliographic latitude (actually, with distance from the heliospheric neutral sheet [Hakamada and Akasofu, 1981; Zhao and Hundhausen, 1981]). Until 1992 the Voyager 2 and IMP 8 latitude ranges overlap. Thus we can use the yearly traversal by IMP 8 of latitudes +-7.26 degrees to look for systematic variations of velocity with latitude. A rough idea of the variation is obtained by finding the slope of the linear regression of radial velocity versus latitude for each year of data. Figure 4 shows that the only clear correlation is at solar minimum where, as pointed out by other authors [i.e., Miyake et al., 1989], the velocity increases with latitude. At other times in the solar cycle the tilt of the current sheet is large compared to the latitudinal variations of the spacecraft, effectively washing out latitudinal variations.

Figure 4: (GIF format (6K)) or (PS format (12K)): The slope of the radial velocity of the solar wind versus latitude obtained by performing a linear regression on each year of IMP 8 data. The only consistent correlation of the radial velocity with the latitude is near solar minimum in 1986-1987.

Finally we mention the possibility that latitudinal transport of solar wind plasma may affect the velocity profile. A decrease of velocity from this mechanism is suggested by the 3-D MHD model of Pizzo [1994], but his model also predicts a density increase which is not observed.

Pickup ions

Since we find no convincing alternative, we proceed under the assumption that the normalization procedure is reasonable and thus that the solar wind flux and velocity decrease with radial distance. Interaction of the solar wind with interstellar neutrals should slow the solar wind [Holzer, 1972; Isenberg, 1986]. Interstellar pickup ions (interstellar neutrals which are ionized in the solar wind and accelerated to the solar wind speed by the E=-v cross B electric field) were detected in the solar wind inside 5 AU [Mobius et al., 1986; Gloeckler et al., 1993]. In the outer heliosphere, Burlaga et al. [1994] deduce that the pickup ion density averages 6% of the total ion density based on observations of pressure-balanced structures at 35 AU.

Momentum flux conservation is used to deduce the percentage of pickup ions in the solar wind from the decrease in solar wind velocity. We neglect the alpha particles, which comprise 4% of the solar wind by number, in this analysis. Lee [1995] shows that the solar wind velocity change resulting from pickup of interstellar H

delta v = [(beta (3 gamma - 1)) / (2 (2 gamma - 1))] r (1)

and the pickup ion density

npu = [(beta n0) / v0] 1/r (2)

where

beta = nH (sigma v0 n0 + nuH) / n0 (3)

where v0 is the unperturbed solar wind velocity, gamma the ratio of specific heats, r the distance from the Sun in AU, nH the density of interstellar H, n0 the solar wind density at 1 AU, sigma the charge exchange cross section for H and H+, and nuH is the photoionization rate of H at 1 AU. Combining (1) and (2), we obtain

npu / nsw = [(3 gamma -1) / (2 gamma -1)] [delta v / v0] (4)

where nsw is the solar wind density. For gamma = 5/3,

npu / nsw = 7/6 delta v / v0 (5)

The average solar wind speed is about 440 km/s (averaging all the Voyager 2 data), so the observed velocity decrease of 30 km/s implies that 8% of the solar wind protons are pickup ions.

Pickup ions do not thermalize with the solar wind plasma but remain hot [Isenberg, 1986]. Since densities derived from Voyager 2 data include only the thermal portion of the solar wind distribution, the replacement of thermal ions with pickup ions through charge exchange reduces the observed plasma density. The changes in the density profile due to the removal of (observable) ions via charge exchange are offset almost exactly by changes resulting from the velocity slowdown. Mass conservation requires that a change in velocity [delta v / v] results in a change in number density n of [-{delta n} / n]. Including the addition of ion density via photoionization (nPH), the density n(r) = n0 r**(-2) (1 + delta v / v0) + nPH. The PLS instrument on Voyager does not detect the pickup ions, so the observed density is n(r) - npu. But the velocity change delta v / vsw = 6/7 npu/nv and the ratio of photoionized pickup ions to total pickup ions is about 1/7 [see rates in Lee, 1995], so the increase of density due to the slowdown and addition of photoionized H is almost exactly balanced by the decrease in the percentage of plasma detected by the PLS instrument. Thus, we expect Voyager to detect a simple R**(-2) density decrease with distance. The observed density profile does decrease as roughly R**(-2) [Belcher et al., 1993].

The observed solar wind flux should decrease, due to the replacement of thermal ions by pickup ions, by roughly 6% (the percentage of pickup ions created by charge exchange minus the percentage created by photoionization, which add to the flux). A 6% reduction is consistent with the decrease in flux shown in Figure 2.

The effect on the temperature profile of adding interstellar neutrals to the solar wind depends on the amount of thermalization which occurs between the pickup ions and the thermal plasma. Early theoretical papers [i.e., Holzer and Leer, 1973] predicted rapid thermalization and an increase in temperature with radial distance. This has not been observed, and more recent papers predict that wave-particle interactions spawned by the pickup process cannot assimilate the pickup ions into the solar wind [Vasyliunas and Siscoe, 1976; Isenberg, 1986]. Voyager 2 temperatures decrease as R**(-0.5) [Richardson et al., 1995], much less quickly than adiabatic, but this may result from stream-stream interactions and subsequent shock heating [Gazis and Lazarus, 1982]. Thus the observed temperature profiles reveal little about the pickup ion population.

The average solar wind density at 40 AU is approximately 0.004 cm-3; thus for npu / n = 0.08 the average interstellar pickup ion density would be 0.00032 cm-3. Isenberg [1986] gives profiles of the solar wind velocity and pickup ion density for different values of the interstellar H density. Interpolation of these model results using a 30 km/s velocity decrease at 40 AU gives a density for interstellar neutrals on the order of 0.05 cm-3, close to recent determinations of this density which appear in the literature [Chassefiere et al., 1986; Gloeckler et al., 1993].

The other measurement which could be used to corroborate these results are the magnetic field observations. A 7% decrease in the velocity of the solar wind should result in a compression of the magnetic field which would give a 7% rise in the average magnetic field strength (unless latitudinal transport is important). When analysis of the magnetic field data are complete these data may provide a test of this result.

Acknowledgements

The authors thank P. Isenberg and C. Smith for helpful comments. This work was supported by NASA under contract 959203 from JPL to MIT (Voyager) and by NASA contracts NAGW-1550 (SR&T) and NAG5-584 (IMP) to MIT.

References

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Richardson, J. D., J. W. Belcher, K. I. Paularena, and A. J. Lazarus, Radial evolution of the solar wind from IMP 8 to Voyager 2, Geophys. Res. Lett., 22, 325-328, 1995.

Vasyliunas, V. M., and G. L. Siscoe, On the flux and the energy spectrum of interstellar ions in the solar system, J. Geophys. Res., 81, 1247, 1976.

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J. W. Belcher, A. J. Lazarus, K. I. Paularena, and J. D. Richardson, Center for Space Research, Cambridge , MA 02139 USA (email: jdr@space.mit.edu)

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For more information contact John Richardson at MIT (e-mail: jdr@space.mit.edu).