1 1 The heliosphere-interstellar medium interaction: One shock or two? John D. Richardson M.I.T. Abstract. The issue of whether a shock forms in the interstellar medium as it approaches the heliopause has not been settled. Observations generally show that the local interstellar medium is slightly supersonic with respect to a stationary (constant distance from the Sun) heliopause. The solar wind dynamic pressure varies over the solar cycle, causing the heliopause distance to move inward and outward. This work shows that the heliopause speeds may be large compared to the speed of the interstellar medium. This leads to the scenario where the interstellar medium is supersonic with respect to the heliopause when the heliopause moves outward (the declining phase of the solar cycle) and subsonic the rest of the time. A shock would form when the heliopause moves outwards and dissipate when the heliopause moves inwards. The heliospheric radio emission is shown to occur at times when the heliopause moves outwards and thus may be related to the formation of the shock in the interstellar medium. This work leads to two testable predictions: 1) the heliospheric radio emissions will intensify when the solar wind pressure increases and 2) the temperature of the interstellar neutrals will fluctuate over a solar cycle with larger temperatures when there is a shock in the interstellar medium.
2 2 Introduction The interaction of the heliosphere with the interstellar medium has engendered much interest of late as the Voyager spacecraft reach distances where crossing of the termination shock may be imminent. In and again in intense heliospheric 2-3 khz radio emissions were observed by Voyager 1 and 2 [Kurth et al., 1984; Gurnett and Kurth, 1993]. One interpretation is that these emissions are triggered by the passage of a strong interplanetary shock through a region near the heliopause [Gurnett et al., 1993]. These emissions are the first direct evidence of the approach to the interstellar medium. Recent work on anomalous cosmic ray gradients provides evidence that the shock location is at roughly AU and that the shock is a weak shock [Stone et al., 1996]. Since the solar wind pressure is expected to decrease as solar maximum approaches [Richardson et al., 1996], the Voyagers may cross the termination shock in the next few years. The impending reconnaissance of this long-postulated boundary and the heliosheath beyond have driven a recent surge in both theoretical modeling of the solar wind - interstellar medium interaction and in efforts to pinpoint the properties of the local interstellar medium. The first models were formulated by Wallis  and Holzer . Since then increasingly sophisticated Monte Carlo [Baranov and Malama, 1993; 1995] and fluid [Pauls et al., 1995; Zank et al., 1996] models have been developed to self-consistently treat the various neutral and plasma populations. A major question concerning the topology of the solar wind-interstellar medium interaction is whether the interstellar medium is supersonic with respect to the heliopause. Figure 1 shows a schematic picture of the heliospheric interaction with the local interstellar medium; the arrows show plasma flow directions. If the local interstellar medium is supersonic a shock (indicated by the? s) forms upstream of the heliopause, resulting in what is called the twoshock model (the other shock being the termination shock). If the second shock exists, the inflowing local interstellar medium plasma would slow, heat, and become more dense upon crossing this shock. The coupling of the interstellar plasma to the interstellar neutrals would lead to heating of the neutrals as well. Zank et al.  show that a major difference between 1 and 2-shock models is that the 2-shock models predict upstream neutrals will be heated by a factor of 2 over their temperature in the local interstellar medium, whereas the 1-shock model predicts no heating. In theory, observation of the temperatures should discriminate between these models based on temperature, but the observations are not conclusive. Properties of the local interstellar medium have been recently reviewed [Frisch, 1995; Axford, 1996]. The Sun is moving through the local interstellar medium at about 26 km/s. Frisch  estimates the sound speed is on the order of 10 km/s and the magnetosonic velocity km/s, although considerable uncertainty is present in these numbers. (The flow is supersonic if the Mach number M, the ratio of the flow speed to the magnetosonic speed, is greater than 1.) Zank et al.  point out that cosmic ray pressure or a larger magnetic field could, using reasonable parameters, give a subsonic flow. In this paper, we suggest that since the interstellar medium flow is very close to M=1, the movement of the heliopause driven by solar wind dynamic pressure changes can determine whether a 1- or 2-shock topology is present. Since the solar wind dynamic pressure changes over the solar cycle, we can predict when each topology is most likely. Solar Wind Dynamic Pressures and Heliopause Distance The solar wind dynamic pressure varies on time scales of seconds to solar cycles. Since only long-duration changes are likely to affect heliopause motion, we plot 300-day running averages
3 of the solar wind dynamic pressure observed by IMP 8 (dotted line) and Voyager 2 (solid line) in the top panel of Figure 1. The sunspot number is shown in the bottom panel. The solar wind dynamic pressure is a minimum at solar maximum and a maximum in the declining phase of the solar cycle. The IMP 8 increase in pressure is over 50% from 1980 to 1982 and almost 50% from 1991 to The Voyager 2 pressure changes are comparable. Since IMP 8 remains in the same orbit whereas Voyager moves in heliolatitude with time, IMP 8 data should provide a more consistent picture of the change of solar wind pressure with time and are used throughout the rest of this paper. The solar wind will evolve as it moves outward, but, since the averaging times used in this paper are comparable to the transit time of the solar wind through the heliosphere, this evolution should not affect the results. The distance to the heliopause is calculated following Belcher et al.  and using the smoothed IMP 8 pressure profile in Figure 1 to give the instantaneous equilibrium distances shown in Figure 2. Although the heliopause does not instantaneously achieve its equilibrium position, this does give a sense of its motion. For 2-3 years after solar maximum the heliosphere rapidly expands, then follows a slow contraction until the next solar minimum. Figure 3 shows the 300-day average velocities of the heliopause again assuming it remains at its equilibrium position. The heliopause velocities derived in this manner clearly dwarf the 26 km/s speed of the interstellar medium. The actual rate of motion of the termination shock and heliopause in response to changes in solar wind pressure is of course not known, although several models have been used to estimate the speed of the termination shock. Analytical studies of a planar 1-D hydrodynamic shock find the shock can move up to 100 km/s [Barnes, 1993; Naidu and Barnes, 1994]. Whang and Burlaga  found that solar wind pressure changes cause the termination shock to move 14 AU over a solar cycle with speed of up to 100 km/s. The 2-D hydrodynamic model of Karmesin et al.  predicts 15 AU range of termination shock values but an average velocity of only 12 km/s; they use a sinusoidal pressure variation, whereas the observed pressure increase is much faster than this. The best observational analogies are probably the planetary magnetospheres; although much smaller than the termination shock, the bow shocks of the planets presumably respond to solar wind variations in a manner similar to the termination shock. Bow shock motions of km/s are common in response to solar wind pressure changes. Given the uncertainty in how the termination shock will respond, we use the velocities shown in Figure 3 in our discussion of the termination shock and heliopause response to solar wind variations. For the gross effects discussed here, if the response is only half as fast our results will not be affected. The dotted line in Figure 3 shows a reasonable estimate of the difference between the velocity of the local interstellar medium and its magnetosonic velocity (6 km/s). If the heliopause is moving inwards at greater than 6 km/s, then the local interstellar medium is subsonic with respect to the heliopause and a bow shock will not form. If the heliopause is moving inwards less rapidly or moving outwards, then the local interstellar medium is supersonic with respect to the heliopause boundary and a bow shock must form. Figure 3 shows that there are two times when velocities are strongly outward for long periods (1-2 years). The first is from to about , the second is double-peaked and lasts from 1989 to We can estimate when the increase in pressure will affect the heliopause position. If the termination shock is at 80 AU, the pressure increase at must travel about 79 AU at the average solar wind speed of 440 km/s, or roughly 300 days. The heliopause distance is about 110 AU; the speed across this distance depends on the shock strength which recent evidence suggests is 2.4 [Stone et al., 1995]. This would imply an initial post-shock speed of about 150 km/s which would decrease as the heliopause is approached. An average speed from termination shock to heliopause of 100 km/s would give a transit time of 480 days for a total time 3
4 from Earth to the heliopause of 780 days or 2.1 years. After this amount of time the heliopause should begin to accelerate outward. The details of the transition from a one-shock to two-shock heliosphere are beyond the scope of this paper, but some time lag must occur at this step also. When the heliopause begins to move outward the plasma density and temperature across the heliopause will increase, first by compression as the heliopause moves outward, then due to the shock when it forms. One obvious speculation is that the onset of the radio emission could be related to the change in plasma conditions when the heliopause moves outwards. Possibilities are that the emissions come from the vicinity of the shock itself, or that the increased densities and temperatures caused by the outward motion are conducive to generation of the radio emission. Figure 4 shows the spectral density of emission frequency and speed of the heliopause. The outward motion increases sharply to a plateau starting at and the first radio emissions were observed near The second strong outward motion of the heliopause reaches a plateau at , whereas the second radio emission event starts in In each case the time delay is roughly 3.5 years; given the relatively slow sound speeds and large distances between the heliopause and the probable location of an upstream shock an additional 1.5 year lag (compared to the 2-year lag calculated above) is not implausible; MHD modeling is required to better determine the time scales. A current suggestion [Gurnett et al., 1993] is that the passage of very strong interplanetary shocks (observed at the Voyagers in 1981 and 1991 and associated with very large Forbush decreases) through the plasma beyond the heliopause. The radio emissions begin each time about 400 days after the solar wind shock passes Voyager. An advantage of the mechanism proposed here is that it can qualitatively explain the double peak in the radio emissions, which diminish for a few month in early 1993 before intensifying again. The decrease in radio emissions can be interpreted as due to the cessation of outward motion at about , with the intensification of the emissions occurring when the heliopause again moves outwards starting near One prediction of this hypothesis is that the radio emissions will begin roughly 3.5 years after the solar wind pressure begins to increase as the next solar cycle begins. Another prediction is that the temperature of the interstellar neutrals upstream of the heliopause will change over the solar cycle. At times when the heliosphere is expanding, such as the descending phase of the solar cycle, we expect two shocks will be present and thus that the interstellar neutrals will be hotter [Zank et al., 1995]. When the heliosphere is contracting, the local interstellar medium will not be shocked before encountering the heliopause and the interstellar neutrals will be cooler. In the two-shock case, the heating at the shock depends on the strength of the shock; thus we expect variation of interstellar neutral temperature depending on the speed of the heliopause even when there are two shocks. As summarized by [Zank et al., 1995], the temperature of the interstellar neutrals can be measured with current techniques but results are so far inconclusive. 4
5 5 Summary The location of the heliopause is determined by a balance between the solar wind dynamic pressure and the pressure of the interstellar medium. Changes in the solar wind pressure over a solar cycle should cause the heliopause to move; the velocity is probably large enough that the interstellar medium alternates between being subsonic and supersonic with respect to the heliopause. This may result in the formation and dissipation of the heliospheric bow shock over the course of a solar cycle. Since the heliospheric bow shock would heat the plasma when present, the plasma temperature and, through coupling, the neutral temperature should vary, an effect which can be observed from Earth. Acknowledgments. The Voyager plasma wave data was taken from the PWS WWW page. This work was supported by NASA under contract from JPL to MIT (Voyager) and NAGW-1550 (SR&T).
6 6 References Adams, T. F., and P. C. Frisch, High-resolution observations of the Lyman alpha sky background, Astrophys J., 212, 300, Axford, W. I., The heliosphere, Sp. Sci. Rev., 78, 9 14, Baranov, V. B., and Y. G. Malama, Model of the solar wind interaction with the local interstellar medium: Numerical solution of self-consistent problem, J. Geophys. Res., 98, 15,157, Baranov, V. B., and Y. G. Malama, Effect of local interstellar medium H fractional ionization on distant solar wind, J. Geophys. Res., 100, 14,755, Barnes, A., Motion of the heliospheric termination shock, 1, a gas dynamic model, J. Geophys. Res., 98, 15,137, Belcher, J. W., A. J. Lazarus, R. L. McNutt, Jr., and G. S. Gordon, Jr., Solar wind conditions in the outer heliosphere and the distance to the termination shock, J. Geophys. Res., 98, 15,166 15,183, Bertaux, J-.L., R. Lallemont, V. G. Kurt, and E. N. Mironova, Characteristics of the local interstellar hydrogen determined from Prognoz 5 and 6 interplanetary Lyman α line profile measurements with a hydrogen absorption shell, Astron. Astrophys., 150, 1, Clarke, J. T., R. Lallemont, J-.L. Bertaux, E. Quemerais, HST/GHRS observations of the interplanetary medium downwind and in the inner solar system, Astrophys J., 448, 893, Frisch, P. C., Characteristics of nearby interstellar matter, Sp. Sci. Rev., 72, , Gurnett, D. A., and W. S. Kurth, Radio emissions from the outer heliosphere, Sp. Sci. Rev., 78, 53 66, Gurnett, D. A., W. S. Kurth, S. C. Allendorf, and R. L. Poynter, Radio emission from the heliopause triggered by an interplanetary shock, Science, 262, , Holzer, T. E., Interaction of the solar wind with the neutral component of the interstellar gas, J. Geophys. Res., 77, , Karsemin, S. R., P. C. Liewer, and J. U. Brackbill, Motion of the TS in response to an 11 year variation in the solar wind, Geophys. Res. Lett., 22, , Kurth, W. S., D. A. Gurnett, F. L. Scarf, and R. L. Poynter, Detection of a radio emission at 3 khz in the outer heliosphere, Nature, 312, 27-31, Naidu, K., and A. Barnes, Motion of the heliospheric TS, 4, MHD effects, J. Geophys. Res., 89, 17674, Pauls, H.L., G.P. Zank, and L.L. Williams, Interaction of the solar wind with the local interstellar medium, J. Geophys. Res., 100, 21595, Richardson, J. D., J. W. Belcher, A. J. Lazarus, K. I. Paularena, P. R. Gazis, and A. Barnes, Plasmas in the outer heliosphere, Proceedings of the Eighth International Solar Wind Conference, Dana Point, CA, D. Winterhalter, J. T. Gosling, S. R. Habbal, W. S. Kurth, M. Neugebauer, eds., , AIP Conference Proceedings 382, Stone, E. C., A. C. Cummings, and W. R. Webber, The distance to the solar wind termination shock in 1993 and 1994 from observations of anomalous cosmic rays, J. Geophys. Res., 101, 11017, 1996 Wallis, M., Shock-free deceleration of the solar wind, Nature, 233, 23, Zank, G.P., H.L. Pauls, L.L. Williams, and D. Hall, Interaction of the solar wind with the local interstellar medium: A multifluid approach, J. Geophys. Res., 101, 21,639, 1996.
7 7 Figure Captions Fig. 1. A schematic drawing of the configuration of the heliosphere-interstellar medium interaction. The termination shock is where the solar wind becomes subsonic, the heliopause is the boundary between solar wind and interstellar plasma, and the heliospheric bow shock may form if the interstellar plasma is supersonic with respect to the heliopause. Fig. 2. The top panel shows 300-day running averages of the solar wind dynamic pressure observed by IMP 8 (dotted line) and Voyager 2 (solid line, normalized to 1 AU). The bottom panel shows the sunspot number. The pressure increases rapidly just after solar maximum. Fig. 3. The location of the heliopause assuming equilibrium between the solar wind and interstellar medium pressures. Fig. 4. The speed of the heliopause in response to the observed solar wind pressure variations. Fig. 5. The spectral density of radio emission in the Voyager 1 plasma wave subsystem 3.11 khz channel (top panel) and the rate of motion of the heliopause (bottom panel).