Planetary Bow Shocks

C. T. Russell

  Department of Earth and Space Sciences and Institute of Geophysics and Planetary Physics
University of California, Los Angeles, California 90024

Originally published in:
Collisionless Shocks in the Heliosphere: Reviews of Current Research, Geophysical Monograph 35, 1985.

 

Planetary bow shocks provide insight into both the behavior of collisionless shocks and the nature of the planetary obstacle responsible for creating those bow shocks. This review paper first presents a survey of the microstructure of planetary bow shocks using data obtained at Mercury, Venus, the earth, Mars, Jupiter, and Saturn. Then it examines the correspondence of the behavior of the shock jumps with that predicted by theory, and the differences between gas dynamic and magnetohydrodynamic solutions. Finally, it examines the information available from observations of the location of the bow shock about the nature of the solar wind-planetary interaction.

 

Introduction

The study of planetary bow shocks provides important insight both into the behavior of collisionless shocks and into the nature of the planetary obstacle to the solar wind flow. Since the flow velocity of the solar wind at each of the planets exceeds the velocity of compressional waves in the solar wind plasma, i.e., exceeds the fast magnetosonic velocity, a shock wave must form in front of each planet if it does not absorb the incoming flow. The shock wave slows the flow and heats it and deflects it. This layer of deflected and heated flow we call the planetary magnetosheath. The properties of the planetary obstacles vary from planet to planet. Also, the properties of the solar wind change markedly with heliocentric distance. Thus when we compare the bow shocks of Mercury, Venus, the earth, Mars, Jupiter, and Saturn, we find differences in shape, structure, and strength.

It is the purpose of this review to compare the location and structure of the bow shocks of the planets and to infer from these properties both differences in the nature of the interaction and changes in the properties of collisionless shocks with location in parameter space, e.g., Mach number and beta. We also wish to demonstrate, by comparing observations with theory, that we understand the basic behavior of collisionless shocks. To do so, we will compare the expected changes of properties across planetary bow shocks with the observed changes. In this process we must be careful to distinguish two different problems: the local solution and the global solution. The former problem has an analytic solution; the latter problem is amenable only to computer simulation. Unfortunately, these computer solutions lack spatial resolution if they include all the physics.

Another complication in attempting global solutions is the nature of the obstacle. There are three different types of obstacles that deflect the solar wind flow: planetary magnetospheres, planetary ionospheres, and cometary and planetary atmospheres. A fourth interaction, that of the moon and most asteroids, in which most of the solar wind is absorbed, causes sufficiently little deflection that shocks do not appear to form. However, there still may be some deflection, as we discuss below.

The most prevalent obstacle to the solar wind flow is the planetary magnetosphere, which stands off the flow well away from the planet. Such an obstacle occurs at Mercury, the earth, Jupiter, and Saturn. Second, planetary ionospheres can deflect the flow, since the magnetized solar wind does not diffuse rapidly into the highly conducting ionosphere. This certainly occurs at Venus and possibly at Mars. However, if the solar wind is deflected by a planetary ionosphere, the solar wind also penetrates the tenuous outer atmosphere of the planet. The solar wind can charge exchange with the neutral atmosphere, losing momentum and gaining mass, if the neutral atom is heavier than the solar wind ion with which it charge exchanges. Photoionization of the neutral atmosphere can also take place, further adding mass to the solar wind plasma. These processes add complexity to the ionospheric interaction. Third, the solar wind can be deflected solely by mass addition. Since the solar wind can readily absorb only so much mass, it will be deflected about a region of sufficiently strong mass addition, leading to the formation of a shock above a critical mass addition rate. While this process does not seem to be responsible for the Venus shock, it can perhaps lead to bow shocks around comets.

The plan of this review is as follows. First, we present an overview of the bow shocks of the solar system, visiting first the moon, which absorbs most of the incident solar wind but still deflects a little, then Mercury, Venus, the earth, Mars, Jupiter, Saturn, and finally comets. Next we examine the macroscopic behavior of shocks by comparing the shock jumps expected from the Rankine-Hugoniot equations with those observed. Finally, we examine the location of planetary bow shocks and the information to be gleaned from these locations. Those interested in the theory of collisionless shock waves in general are referred to the book by Tidman and Krall [1971] and the reviews by Biskamp [1973] and Galeev [1976]. Two more observationally oriented reviews with emphasis on the terrestrial bow shock are the papers by Formisano [1977] and Greenstadt and Fredricks [1979].

 

A Tour of Planetary Bow Shocks

Planetary bow shocks are expected to have both similarities and differences. They should be similar because the physical processes occurring at the bow shocks should remain the same at each of the planets. However, there should also be differences because the average properties of the solar wind vary with heliocentric distance. Since the sound velocity and the Alfven velocity both decrease with heliocentric distance, while the solar wind flow speed remains fairly constant, the Mach number of the flow past the planet increases away from the sun [cf. Russell et al., 1982]. The beta of the solar wind, i.e., the ratio of thermal to magnetic energy density, increases to the orbit of Mars and then decreases again. Other parameters of the solar wind also change. While the parameters in the solar wind fluctuate a great deal, so that a wide range of parameter space is sampled at each of the planets, the time spent at the extremes is brief. Thus bow shock observations from especially the distant planets are quite useful. There should be differences due to variations in scale size. The planetary obstacles vary in size from being only a few thousand to about 10,000 km across for Mercury, Venus, and Mars to about 200,000 km across for the earth and several millions of kilometers across for Jupiter and Saturn. Finally, the possible interactions of the solar wind with the planets' neutral atmosphere is a factor.

 

The Moon

Fig. 1. Schematic of orbits of Explorer 35 and the Apollo 15 subsatellite together with sample of magnetic field strength measured along the Explorer 35 orbit, illustrating the effects associated with the passage of the spacecraft through the lunar wake (shaded). Most of the incident solar wind is absorbed by the moon, leaving a plasma void and a magnetic enhancement in its wake.

The terrestrial moon does not have a bow shock, although this was not realized until the measurements from Explorer 35 became available [Colburn et al., 1967; Ness et al., 1967]. It was difficult to anticipate the nature of the interaction, since the moon differs in many ways from the earth. It is much smaller, has no atmosphere or ionosphere, and has little intrinsic magnetic field. The reason for this lack of a bow shock became understood from the analysis of the Explorer 35 data and then later the Apollo surface measurements. The solar wind is almost totally absorbed by the lunar surface [Lyon et al., 1967]. Figure 1 shows the Explorer 35 orbit and the Apollo 15 subsatellite orbit to scale. As Explorer 35 orbited the moon in the solar wind, it encountered a variety of regions labeled I to IV. Region I is the undisturbed solar wind. Region IV is the lunar wake, which is devoid of flowing ions. The thermal pressure of the plasma is less in the wake because of the absorption of the solar wind by the moon, and the field pressure is greater here, as shown in the bottom panel of Figure 1. For a detailed discussion of the formation of the lunar wake, the interested reader is referred to the review by Spreiter et al. [1970]. Just exterior to the wake region are often observed increases of the field with decreases in the field strength at the edges of the wake. The decreases are thought to be due to the expansion of flow into the wake, but the sources of the increases in field strength were at one time very controversial. These increases are also very important in understanding the interaction of the solar wind with small obstacles. It is because of the existence of these field compressions above the lunar limbs that we include the moon in this tour of planetary bow shocks.

Fig. 2. Magnetic field measurements at about 100 km above the lunar surface by the Apollo 15 subsatellites in the solar wind (top panel), magnetosheath (middle panel), and magnetotail (bottom panel). In the center of each of the top two panels the weak enhancement associated with passage through the lunar wake is seen. In the top panel on the right-hand side of the wake is a lunar limb compression associated with the deflection of a small portion of the solar wind by the lunar magnetic field near the solar wind terminator. The field enhancements above background in the bottom panel are due to this lunar field reaching the orbit of the subsatellite in the near-vacuum conditions of the geomagnetic tail lobes [Schubert and Lichtenstein, 1974].

Figure 2 shows observations of the magnetic field much closer to the moon as obtained by the Apollo 15 subsatellite in near-circular orbit at about 120 km altitude. The top panel shows a region II magnetic enhancement similar to that seen in the Explorer 35 data. The bottom panel shows magnetic field measurements in the tail lobes of the earth, where the moon is shielded from the solar wind flow. The wiggles in the total field are caused by localized lunar magnetic fields. It is the presence of these small magnetic features, only a few hundred kilometers across, at the lunar limbs which deflects the solar wind enough to cause the observed compression. The absence of these features in the middle panel is due to the lack of magnetized regions at the limbs at this particular time rather than any special property of the magnetosheath. The importance of these observations is that very small magnetized regions, only a few hundred kilometers across, can deflect the solar wind. This distance is smaller than an ion gyroradius but larger than a Debye length or an ion inertial length. While these features have been called limb shocks [cf. Schwartz et al., 1969], they appear rather to be just compressional waves propagating at their usual velocity [Russell and Lichtenstein, 1975].

 

Mercury

Outwardly, Mercury looks very much like the moon. It has no atmosphere, its surface is pockmarked with craters, and its radius of 2434 km is only 40% larger than that of the moon. Its average density, 5.5 g cm-3, however, is much different from that of the moon, 3.3 g cm-3, and belies the apparent similarity of the two planets. Mercury, in fact, has its own global intrinsic magnetic field. This fact was well demonstrated by the two Mariner 10 passes past the nightside of Mercury in 1974 and 1975 [Ness et al., 1974, 1975].

Fig. 3. The magnetic field measurements of Mariner 10 on its passage past the nightside of Mercury in March 1974. From top to bottom are the magnetic field strength, the rms deviation of the field, and the solar ecliptic longitude and latitude of the magnetic field. The magnetic field shows a relatively clean multiple quasi-perpendicular bow shock inbound and a rather diffuse, irregular quasi-parallel bow shock outbound, associated with the different orientation of the shock orientation inbound and outbound [Ness et al., 1974).

Figure 3 shows the magnetic field observed on the first flyby. There are bow shock crossings inbound and outbound labeled BS, as well as magnetopause crossings labeled MP. Between the two magnetopause crossings the magnetic field increases and then decreases as the spacecraft approaches and then recedes from the planet. At the first crossing of the bow shock the field change is sharp, and the shock is crossed three times. Multiple crossings occur when the shock moves back and forth faster than the satellite moves along the shock normal. This can occur for a relatively incompressible obstacle, like Venus, when the spacecraft is moving nearly parallel to the shock surface. For compressible obstacles like a planetary magnetosphere, such multiple crossings occur even for nearly normal crossings of the shock surface, as occurs here. The sharpness of the crossing is consistent with the fact that the upstream field was nearly perpendicular to the shock normal [Fairfield and Behannon, 1976]. In contrast the outbound crossing is very diffuse with large amplitude waves. The angle between the upstream magnetic field and the model shock normal here is only 15o. The fact that the orientation of the interplanetary magnetic field controls the structure of the bow shock was in fact first pointed out by using planetary bow shock data from Venus and Mars [Greenstadt, 1970].

Fig. 4. The magnetic field across the multiple bow shock encounters of Mariner 10 inbound on March 29, 1974. From top to bottom are the magnetic field magnitude, the solar ecliptic longitude and latitude of the field, and the X, Y, and Z solar ecliptic components of the field [Ness et al., 1974].

Figure 4 shows the magnetic field measurements across the first set of inbound shock crossings at high resolution. These data show the presence of high frequency waves in the neighborhood of all three crossings. Analysis of these waves by Fairfield and Behannon [1976] shows that they are right-hand polarized with a very broad spectrum extending beyond their Nyquist frequency of 12.5 Hz. They are propagating along neither the solar wind direction nor the magnetic field direction, making large angles, 40o-7o, to each. The authors apparently did not check the angle of the wave normals to the shock normals. Although we do not know the plasma conditions at the time of the Mariner 10 flyby, the expected Mach number and beta, based on the heliocentric radial variation of the solar wind, should be much lower than at earth, and hence these shocks should be compared with what have been termed laminar shocks at earth. Here two types of precursor waves have been observed [Mellott and Greenstadt, 1984], a many-secondperiod standing wave propagating nearly along the shock normal and a nonstanding wave with a frequency of about 1 Hz propagating along the direction of the upstream field. From the published reports it is not clear that these waves are in fact related to those seen at Mercury.

 

Venus

Venus is much larger than Mercury, with a radius of 6050 kin, but it has at most an insignificant intrinsic magnetic field [Russell et al., 1980]. Thus it has a quite different interaction with the solar wind from that of Mercury and of the earth. This difference together with the fact that Venus is the next most studied planet, after the earth, means that Venus plays a critical role in our study of planetary bow shocks. The bow shock at Venus is weaker than that of the earth for several reasons. First, the Mach number of the solar wind flow relative to Venus is less than that of the earth because of the radial variation of the solar wind. Second, the bow shock does not flare as much at Venus, because the shape of the planetary obstacle is different, being more spherical over its forward hemisphere than the earth's magnetosphere. Finally, momentum can be removed from the solar wind flow via charge exchange, lessening the strength of shock needed to divert the flow around Venus. In the limit of complete absorption of the solar wind by the planet there would be no shock, as in the case of the moon, but of course that is not the case.

Because the interaction of the solar wind with Venus is different from that with the earth, and because this difference might be reflected in the location of the bow shock, it has been popular to study the location of the Venus shock. We will not concern ourselves with this topic now but defer this topic to a later section. Suffice it to say that the location of the Venus bow shock seems to be affected by these differences. Currently, observation leads theory here, and we do not presently have all the theoretical tools to interpret these differences unambiguously.

Fig. 5. Pioneer Venus magnetic field measurements across the Venus shock inbound and outbound on orbit 96, March 9, 1979, illustrating the difference between a quasi-parallel ( = 28o) and a quasi-perpendicular ( = 62o) shock for a moderately weak shock. The coordinate system used is the shock normal system with N along the normal and M perpendicular to the upstream magnetic field.

The dependence of the microstructure of bow shocks on the direction of the interplanetary magnetic field was discovered using Venus (and Mars) data [Greenstadt, 1970]. Specifically, the Mariner 5 outbound shock was pulsating and diffuse, whereas the inbound shock was quite sharp. Greenstadt [1970] postulated that this was due to the orientation of the magnetic field relative to the shock normal, and this observation has been confirmed in many studies since that time. Figure 5 shows this behavior with an inbound and outbound shock crossing on March 9, 1979, orbit 95. The angle between the interplanetary field and the (model) shock normal is 62o inbound and 26o outbound. The local (along the shock normal) fast magnetosonic Mach number was about 2.7 for each shock, and the beta about 0.6. The data here are displayed in local shock normal coordinates in which the N coordinate is along the shock normal and the L direction contains the shock jump. The M direction is perpendicular to both L and N so that LMN form a right-hand orthogonal triad and M is perpendicular to the upstream magnetic field. Choice of such a coordinate system allows us to two dimensionalize some of the variation across the shock and more easily compare one crossing to another. The top panel clearly illustrates the rotation of the magnetic field out of the coplanarity plane (L-N) required to explain the observed gain of electron energy at the shock [Goodrich and Scudder, 1984].

One important topic associated with the bow shock for which there has been much terrestrial activity, but little planetary work, is the nature of bow shock-associated waves well upstream of the shock. At Venus these waves have been shown to fall into the same categories as observed at the earth [Russell and Hoppe, 1983], and one category of wave has been shown to occur at Mercury, Venus, the earth, and Jupiter, suggesting that the mechanism for the formation of these waves is the same at each of these bow shocks [Hoppe and Russell, 1982]. For a detailed examination of the solar wind interaction with Venus, see the review by Russell and Vaisberg [1983].

 

The Earth

The earth, like Mercury, presents a magnetospheric obstacle to the solar wind. The terrestrial magnetosphere differs from the Mercury magnetosphere in scale, being about 2 x 105 km across at the terminators, and in its lower boundary condition, having an ionosphere. These differences, as far as we know today, have little effect on the physics of the shock, although of course the size of the shock is much greater at the earth than at Mercury.

Most of the study of planetary bow shocks is performed using terrestrial data. The complement of particles and field instruments on a terrestrial mission is far more complete than on a planetary mission. The telemetry bandwidth is greater, allowing better spatial and temporal resolution. Furthermore, two spacecraft were placed into the same orbit at the earth (ISEE 1 and 2) with controlled separation, allowing separation of spatial and temporal effects. The advent of the ISEE measurements, with their ability to determine spatial dimensions and with their new and improved instrument often with higher resolution than ever before and often with near-4-sr coverage, opened up a new era in bow shock studies.

Fig. 6. ISEE 1 and 2 magnetic field measurements across the terrestrial bow shock illustrating the transition between low Mach number low beta quasi-perpendicular shocks and high Mach number high beta quasi- perpendicular shocks [Russell et al., 1982].

Since this book will be filled with such observations, we need not linger long at 1 AU in our tour of planetary shocks. Figure 6 illustrates the behavior of the terrestrial bow shock over a range of parameter space that is difficult to attain elsewhere in the solar system. This figure is an attempt to illustrate the dependence of shock structure on the ratio of thermal to magnetic energy, i.e., This ratio maximizes in the solar wind near Mars, but since there are few high resolution data at the Martian bow shock and since beta at 1 AU is similar to that at 1.5 AU, the data from the earth best illustrates this. At low beta, as in the top of Figure 6, wave activity is low. However, as beta increases, the amplitude of waves at and downstream from the shock becomes very large. We note that it is difficult to separate Mach number from beta effects, because high Mach numbers and high beta values tend to occur together in the solar wind. The reason for this is that high solar wind densities cause both high thermal energy densities and low Alfven velocities. One other feature of Figure 6 to note is the overshoot directly behind the initial shock rise. The properties of this overshoot will be discussed in greater detail in the section on Jupiter and Saturn.

Much terrestrial bow shock work is also directed to determining the location and strength of the terrestrial shock and the jump across the terrestrial shock. Some of this we will discuss below.

 

Mars

The only fact we know for certain about the Martian obstacle to the solar wind is that it is small. It could be a weak magnetosphere, an ionosphere, or some combination. Basically, there has been very little work done on the solar wind interaction with Mars despite the intensity of the American and Soviet Mars programs. The only U.S. spacecraft to Mars with solar wind instrumentation was Mariner 4 in 1965. The Soviet program has been more comprehensive in this area, but limitations on bandwidth, orbital coverage, and spacecraft and subsystem lifetimes have, in turn, limited the scientific return. Specifically, there are no Martian data on the microstructure of the bow shock.

Fig. 7. Mariner 4 magnetic measurements obtained near Mars in July 1965. From top to bottom are shown the azimuthal angle a along the solar equator and the latitude angle P from the solar equatorial plane, the magnetic field strength, and the trajectory in a solar wind-aligned system assuming cylindrical symmetry of the solar wind interaction [Smith, 1969].

Figure 7 shows the only U.S. magnetometer data at Mars, obtained by Mariner 4 in July 1965 [Smith, 1969]. The bottom panel shows the trajectory of the spacecraft in a cylindrical coordinate system aligned with the solar wind. Mariner 4 just nicked the bow shock and magnetosheath well behind Mars. This distance was too far behind Mars for us to make unambiguous statements about the nature of the interaction. Later Soviet measurements have been more constraining. However, even these are controversial, as will be discussed later in this review. Nevertheless, we can already state that the magnetic moment of Mars must be so small that the size of the obstacle to the flow is not much larger than the size of the planet itself.

 

Jupiter and Saturn

Both Pioneer and Voyager spacecraft have probed the giant outer planets Jupiter and Saturn and have found them to have vast magnetospheres, shielding the planetary atmosphere quite effectively from the solar wind. Thus the solar wind interaction with these planets is expected to be much more earthlike than Venuslike. The major difference between the terrestrial magnetosphere and the Jovian and Saturnian magnetospheres is that the latter magnetospheres are rapid rotators. Since Jupiter's magnetosphere contains a strong source of plasma deep in its interior, this rapid rotation produces a more disked-shaped obstacle to the solar wind than the terrestrial magnetosphere [cf. Acuna et al., 1983].

Fig. 8. Voyager 1 and 2 magnetic field profiles of the Jovian bow shock illustrating the behavior of the quasi-perpendicular shock at high Mach numbers [Russell et al., 1982].

There were some good high-resolution data obtained on these missions, a sample of which is shown in Figure 8. Comparison with Figure 6 illustrates the effect of the increased Mach number at 5.2 AU. The wave amplitudes are much greater at Jupiter even when the beta is low. Further, one sees the size of the overshoot behind the shock. It is much larger at Jupiter than at the earth [Russell et al., 1982]. The overshoot becomes very large behind high Mach number shocks. We note that the shock shown in the second panel from the bottom has the highest fast Mach number reported to date for any planetary shock, 12, and the highest Alfven Mach number, 22, for moderate This is comparable to the Mach numbers used in recent high Mach number simulations which found such shocks to be pulsating [Quest, 1985]. We note that the record Alfven Mach numbers, up to 70, have been seen by Formisano et al. [1975], during a time of very high . The corresponding fast Mach number, however, was much closer to normal. Thus these outer planet bow shocks deserve some detailed study to see if there is a change in shock behavior at very high Mach number, for they are in many ways unique. Such critical data may already be in the Voyager and Pioneer archives simply unexamined or may be obtained during Voyager 2's flyby of Uranus in 1986.

 

Comets and Asteroids

Comets interact with the solar wind in a manner fundamentally different from that of the planets. Comets can be thought of principally as sources of neutral gas which expands away from the nucleus at supersonic speed in the absence of gravity. Thus a comet is surrounded by a large cloud of neutral gas, the size of which dwarfs the visible comet. For example, the Lyman halo surrounding comet Bennett on April 1, 1970 [Biermann, 1974], extended to 4 x 106 km in front of the nucleus and 20 x 106 km behind. The outgassing rate from a comet of this intensity is estimated to be about 3 x 1031 proton masses per second [Feldman and Brune, 1976; Opal and Carruthers, 1977]. If picked up by the solar wind, this flux of gas would decrease the solar wind flow velocity by half in a cylinder of radius 1 x 106 km. In fact, since the region of mass loading is much greater than this, the deceleration in the solar wind velocity must be small except in the neighborhood of the comet. We know the interaction strongly modifies the solar wind flow near the comet because of the magnetotaillike nature of the visible cometary ion tail.

Fig. 9. Schematic representation of the solar wind interaction with a comet. The solar wind encounters the hydrogen corona surrounding the comet and is slowed by mass addition. This distorts the magnetic field into a draping pattern about the obstacle. Closer to the comet the mass addition is strong enough to cause a bow shock across which the velocity drops further, and the plasma and magnetic field are further compressed. If the outgassing rate and production of ions are large enough, the interior region will be field-free, and an ionopause will form which diverts the shocked flow around the comet (modified from Mendis et al. [1985]).

This line of reasoning leads us to the picture of the cometary interaction shown in Figure 9, which is modified from a diagram by Mendis et al. [1985]. When the solar wind enters the region of the Lyman a halo, it begins to pick up mass through photoionization of the neutral hydrogen and charge exchange with any heavier ions. Charge exchange with neutral hydrogen creates fast neutral hydrogen and removes momentum from the flowing solar wind but does not add mass to the solar wind. The decelerated flow causes the magnetic field to be distorted as indicated. Eventually, the point is reached at which the solar wind must be deflected around the obstacle because the rate of mass addition has become too high. This is accomplished through the formation of a bow shock. If there is sufficient ionization found close to the comet, a cometary ionosphere may be formed with a tangential discontinuity forming an ionopause. If this ionosphere is expanding supersonically, it would have to be deflected with another shock, which has been termed the inner shock. This line of reasoning is, in part, mere speculation, for there exist few data and not much more theory.

Fig. 10. Plasma parameters along the axis of symmetry in a one- dimensional mass-accreting cometary interaction. Heavy lines show solution of Wallis [1973a, b]. Light lines show solution of Biermann et al. [1967]. The plasma velocity u is given in kilometers per second; the proton and new ion densities are np and ni, respectively, in cm-3. The pressure is given by p in terms of the dynamic pressure in the free stream, and is taken to be 2.

Wallis [1973a, b] has studied purely mass-accreting one-dimensional flows and finds that the maximum mass flux picked up is related to the mass flux at infinity by the ratio 2/(2 - 1) where is the ratio of specific heats, a number between 5/3 and 2. Thus when the solar wind has picked up 1/3 to 1/2 of its mass, a shock must form. As is illustrated in Figure 10, for a comet like Bennett this occurs at about 2-3 x 105 km from the nucleus in the one-dimensional solution. However, for an old, periodic comet, like Encke, the scale size may be 100 times smaller. We note that such a shock would be smaller, in dimension, than our presently smallest known planetary shock, that of Mercury. An important point raised by Wallis and illustrated by Figure 10 is that the cometary shock, unlike a planetary bow shock, occurs not at the leading edge of the disturbance but in the middle of the disturbed region.

It is appropriate at this point to note that there is a continuum between asteroids and comets and that the earth-crossing, Apollo asteroids are thought to be at least in part "dead" cometary nuclei because of the difficulty of supplying sufficient material from the asteroid belt to maintain the population at its present levels [Shoemaker et al., 1979]. Encke is thought to be well on its way to becoming an asteroid [Sekanina, 1972].

Fig. 11. Magnetic field strength and plasma parameters observed by Pioneer Venus on February 11, 1982, and interpreted as caused by the passage of a comet [Russell et al., 1983a]. The rapid increases just before and the rapid decrease just after the peak field strength have been interpreted as cometary shocks [Russell et al., 1984a].

Although there has yet to be a flyby of a visually sighted comet, there has been the report of a signature of a possible previously unknown comet passing by Pioneer Venus in February 1982 [Russell et al., 1983a]. Figure 11 shows the signature of this event in the magnetic field strength and the ion and electron densities and temperatures [Russell et al., 1984a]. The sudden jump in magnetic field strength near the peak in the gradual rise in field strength and the sudden drop after the passage of the peak have been interpreted as due to a very weak shock surrounding the comet. The ion temperature, which has dropped to near ionospheric temperature, rises rapidly at the shock. The solar wind velocity decreases across the shock as would be expected for a planetary shock. (The solar wind velocity always increases after the passage of a fast forward or reverse interplanetary shock.) Further, precursor waves are seen ahead of these shocks, similar to the precursors seen in front of weak interplanetary shocks [cf. Russell et al., 1983b].

Of 32 events examined by Russell et al. [1984b], only this one was large enough to be associated with a shocklike disturbance. Of these 32 events, eight appear to be associated with the outgassing of debris behind the asteroid 2201 Olijato [Russell et al., 1984c]. This asteroid, in fact, had already been postulated to be a dead comet [Drummond, 1982]. These results suggest that there are a lot of cometlike interactions in the solar system and that old data sets in the solar wind should be examined for such features, not just the new ones targeted for known comets.

 

The Shock Jump

One of the tests of our understanding of a physical process is whether we can use our theories to make a prediction. Thus our ability to predict the change in various plasma parameters across a planetary bow shock is a test that our equations include all the relevant physical processes.

The magnetohydrodynamic solution for the jump in plasma parameters across a collisionless MHD shock has been known for many years [cf. Spreiter et al., 1966; Tidman and Krall, 1971]. Given the upstream plasma conditions and the strength of the shock, we can predict the downstream conditions almost independently of the physical processes occurring in the shock. We do need to know whether the plasma becomes isotropized downstream. In a collisional gas, heating in one direction will lead to random thermal motions in all three directions through the collisions of the particles in the gas. In a monotomic gas there are three degrees of freedom, and the ratio of specific heats, , equals 5/3. In a plasma there may or may not be processes which isotropize the thermal motions of the plasma. Furthermore, there is the possibility of heat flow along magnetic field lines which could lead to more isothermal rather than adiabatic conditions. Thus the appropriate ratio of specific heats for a plasma may not be and may vary with plasma conditions. In practice, there is another complication in that the solar wind consists of several components, not a single fluid. The Rankine-Hugoniot MHD solution does not determine how these various components are heated, for example.

Another difficulty is that because of the limitations of current modeling capabilities it may not be possible to use the MHD formalism of the Rankine-Hugoniot, or shock jump equations. Although MHD models of the global interaction of the solar wind with a planetary obstacle now exist, they are in a preliminary state of development and lack adequate spatial resolution for many purposes. Currently, the only way to achieve the spatial resolution needed for a useful comparison with data obtained on a pass through a planetary magnetosheath is to employ the gas dynamic convected-field model [e.g., Spreiter and Stahara, 1980a, b]. This is tantamount to ignoring the magnetic pressure and magnetic tension terms and is accurate only when these terms are weak. Further, the Mach number in the gas dynamic solution is derived from the isotropic sound velocity. In the MHD fluid the velocity of compressional waves is the fast magnetosonic velocity, which is anisotropic, i.e., depends on the direction of propagation. Thus there has been some confusion as to which velocity to use in the gas dynamic solution when attempting to simulate an MHD situation. In view of the current importance of the gas dynamic convected-field model for obtaining the theoretical global solution needed for comparative studies with observations, we will examine in this section several key issues of the gas dynamic approximation. We first examine the question of the proper Mach number to use for both the local and global solutions. Then, we examine whether the observed shock jumps have the expected functional relationships expected from theory. Next we use observations to determine when the gas dynamic solution adequately simulates the observed jumps. Finally, we examine the question of the proper ratio of specific heats to use in the Rankine-Hugoniot equations.

 

The Proper Mach Number for Modeling the Bow Shock

The gas dynamic model requires a single Mach number to describe the solar wind flow (at infinity) relative to the planet. In the case of the real solar wind, the plasma is both highly electrically conducting and magnetized. The compressional wave in such a plasma is the fast magnetosonic wave, and the bow shock formed in front of the planet is a fast magnetosonic shock wave. It is also called a reverse shock because in the solar wind frame it propagates back toward the sun. We would expect that the magnetosonic Mach number should produce the best approximation to the MHD shock jumps when used as input to the gas dynamic code. We can demonstrate this without resorting to observations from theoretical considerations alone for the "local" shock jump problem. Here, the magnetosonic Mach number is well defined, because the shock normal is at a fixed angle with respect to the upstream magnetic field. To make the comparison, we calculate the jumps across the shock both with and without the magnetic terms [Tatrallyay et al., 1984]. Then we can compare the jumps versus Mach number as is done in Figure 12 for the number density across the shock when the angle between the upstream magnetic field and the shock normal, BN, is 45o. The gas dynamic solution is shown by a solid line. The MHD solution versus magnetosonic Mach number MMS is shown by broken lines for three different ratios of the Alfvenic to sonic Mach numbers, MA/MS. It can easily be shown that this ratio equals ( /2)1/2. These ratios bracket conditions usually seen in the inner solar system. Also shown with symbols in Figure 12 are the same MHD solutions plotted versus the sonic Mach number MS. Clearly, the best correspondence occurs between the gas dynamic solution and the MHD solution when the magnetosonic velocity is used.

Fig. 12. Predicted jump in the number density across a shock with its upstream magnetic field at a 45o angle to the shock normal as a function of Mach number. The solid line gives the gas dynamic calculation; the other curves give the MHD solution as a function of the fast magnetosonic Mach number. The symbols give the same MHD solution plotted versus the sonic Mach number. This plot demonstrates that at least for local solutions, use of the observed magnetosonic Mach number as the Mach number in the gas dynamic code gives a good approximation to the correct MHD solution [Tatrallyay et al., 1984].

The situation is not so clear for the global solution in which the angle between the upstream magnetic field and the shock normal varies with position on the shock. The magnetosonic velocity is given by

VMS2 = 1/2 (VA2 + CS2) x {1 + [1 - (2VACS cos BN)2/ (VA2 + CS2)2]1/2}

where VA is the Alfven velocity, CS is the sound velocity, and BN is the angle between the shock normal and the upstream magnetic field. When the interplanetary magnetic field is perpendicular to the flow, there is one plane in which the propagation is perpendicular to the magnetic field. In this situation the fast magnetosonic Mach number becomes

MMS = VSW/VMS = VSW/(VA2 + CS2)1/2 = (MA-2 + MS-2)-1/2

In the orthogonal situation when the magnetic field is aligned with the flow, well behind the obstacle where the shock surface has aligned with the "Mach cone," the angle between the shock normal and the solar wind and magnetic field is equal to the complement of the Mach cone angle. It is easy to show that the fast magnetosonic Mach number here becomes

MMS|| = MAMS(MS2 + MA2 - 1)-1/2

While this Mach number is appropriate for all clock angles around the planet-sun line, it is an accurate measure of the wave velocity only far behind the obstacle. Closer to the nose of the shock the shock normal will be more closely aligned with the flow, the magnetosonic velocity will be lower, and the local Mach number will be higher. Despite the theoretical difficulty introduced by the anisotropy of the velocity of propagation of magnetosonic waves, there is little difficulty in practice, because for the range of Mach numbers encountered in planetary bow shocks the difference in Mach numbers with direction of propagation is small. For example,

MMS/MMS|| = [1 - (MS2 + MA2)-1]1/2

For typical solar wind conditions at 1 AU when MS = MA = 6, this ratio is 0.99.

Fig. 13. Location of the bow shock as found in the "exact" gas dynamic simulation of the magnetic-field-aligned flow interaction by Spreiter and Rizzi[1974]. Different shock shapes are shown for constant sonic Mach number and varying Alfvenic Mach number. As the magnetosonic Mach number MMS|| approaches that used in the usual, or pure, gas dynamic calculation, the shock surface of the field-aligned flow solutions approaches that of the gas dynamic calculation. We note that at low Alfven Mach numbers the shock moves toward the earth at the nose and away from the earth at the flanks. The pure gas dynamic solution always expands with decreasing Mach number. This illustrates that while the usual gas dynamic solution is a good approximation, there may still be important differences.

There is one global MHD solution for which a high resolution solution has been determined. The field aligned flow case can be converted to a gas dynamic problem by a suitable change in variables [Spreiter and Rizzi, 1974]. The location of the bow shock in this solution is shown in Figure 13, for fixed MS and varying MA. The magnetosonic Mach number MMS|| is also given. As this Mach number approaches the gas dynamic Mach number 10, the MHD solution approaches the gas dynamic solution. It would have been interesting to compare the shock shape obtained from the MHD solution and the gas dynamic solutions for a variety of combinations of Alfvenic Mach numbers and sonic Mach numbers yielding the same magnetosonic Mach number. However, this comparison was not made explicitly. One can use the last figure of Spreiter and Rizzi's [1974] paper to calculate the distance to the nose and to the terminator shock for a few combinations of MA and MS yielding the same MMS. One finds that the terminator shock location is determined mainly by MMS. However, at the subsolar point where the shock normal is parallel to the field and the magnetosonic velocity becomes the sonic velocity, the sonic Mach number strongly influences the shock position.

Also shown in Figure 13 are the asymptotic Mach angles corresponding to the magnetosonic Mach numbers appropriate to each curve. As can be seen, the shock surfaces are tending to their asymptotic angles but are not yet there even 4 obstacle radii downstream. The observed shock shapes for Venus, the earth, and Mars far behind each planet have been compared with the expected asymptotic Mach angles and have been found to agree with the predictions of the magnetosonic Mach number [Slavin et al., 1984].

 

Functional Dependences

Fig. 14. The ratio of the downstream magnetic field strength to the upstream field strength for quasi-perpendicular shocks observed by Pioneer Venus as a function of Mach number. The solid lines show the predicted variation at 60o and 90o. Diamonds show median values [Tatrallyay et al., 1984].

As Figure 12 shows, the jump in number density across the bow shock is a function of the Mach number and a function of the beta of the plasma. As implied by Figure 12, it is also a function of BN. The magnetic field strength also has similar dependences. It is often more convenient to use the magnetic field in an examination of shock jumps because the magnetic field is generally measured more frequently than the density, and more accurately. An MHD shock jump also depends on the angle of the magnetic field to the shock normal. Since there are many factors controlling the size of the shock jump, there have been few examinations of whether planetary shocks actually obeyed the expected dependences on any one. Only one study of which this author is aware was large enough to determine separately the dependence of shock jump on Mach number and BN. This was the study of 386 Venus bow shock crossings by Tatrallyay et al. [1984]. Figure 14 shows the ratio of upstream to downstream magnetic field strength as a function of local Mach number for shocks whose normals lay within 30o of being perpendicular to the magnetic field. The two solid lines show the expected variation versus Mach number for = 1.85. There is much scatter in the data because of imperfections in the measurements and time variations. However, the medians shown by diamonds follow within experimental error the expected trends. Figure 15 repeats this exercise for Mach numbers from 3 to 4 as a function of BN. Again there is much scatter, but the medians follow the trend.

Fig. 15. The ratio of downstream magnetic field strength to upstream field strength for moderate strength Venus bow shocks, 3 MMS 4, as a function of the angle between the shock normal and the upstream magnetic field direction. The diamonds show median values [Tatrallyay et al., 1984].

Although there are a few measurements at low BN angles, it is important to caution potential users of such data on the shock jump here. If the average magnetic field were along the shock normal, the BN angle would be zero, and there would be zero jump in parameters across the shock. However, if the magnetic field oscillated about this direction, even though it remained along the shock normal on average, there would be a finite average shock jump, because the jumps at times of nonzero BN would not average out. Thus care must be used in interpreting shock jumps at low BN.

 

The Applicability of the Gas Dynamic Solution

Fig. 16. The ratio of the expected downstream magnetic field strength to the observed downstream magnetic bow shock for quasi-perpendicular Venus bow shock crossings using gas dynamic calculations (on the left) and magnetohydrodynamic calculations (on the right). Diamonds show median values. These curves show that the gas dynamic calculation reproduces the MHD calculation when the Mach number ratio MA/MS exceeds about 1.5 [Tatrallyay et al., 1984].

The gas dynamic Rankine-Hugoniot equations neglect magnetic pressure terms. Thus we would expect the gas dynamic solution to be inappropriate when the magnetic pressure was strong with respect to the thermal pressure and to be appropriate for high beta situations. Figure 16 demonstrates that the shock jumps at Venus support this conjecture. Here are the jumps across 207 quasiperpendicular shocks with 60o BN 90o. The expected shock jumps have been calculated using gas dynamic theory on the left and magnetohydrodynamic theory on the right and normalized by the observed jump in the magnetic field strength. The resulting ratios have been plotted versus the Mach number ratio MA/MS. This ratio is equivalent to the beta of the plasma upon change of scale. The MHD calculation agrees with observations except at the highest ratios. The gas dynamic calculation agrees with observations for 1.5 MA/MS 2 and with the MHD calculation for MA/MS 1.5. The reason for the deviation of theory from observations at very high beta cannot be due to any difference between gas dynamics and MHD, since both curves differ. It is possibly due to poor statistics, but also possibly due to a change in the appropriate value of at high beta, as discussed below.

 

The Appropriate Value for

Fig. 17. The ratio of calculated to observed downstream magnetic field strength for quasi-perpendicular Venus bow shocks as a function of Alfvenic Mach number for two ratios of specific heat, = 1.60 and = 1.85. The latter ratio gives the best predictions up to a Mach number of 7.0, and the former above this value. The absolute values of here may depend on peculiarities of the Venus interaction, but the same tendencies should occur at other planets [Tatrallyay et al., 1984].

Thus far we considered the value of as a known constant. However, the value of y depends on the processes acting at the shock. Is there isotropization? Is there significant heat flux? The MHD equations do not address the processes which may affect the appropriate value of . Furthermore, might change as one moves through parameter space. Figure 17, again taken from the study of Tatrallyay et al. [1984], suggests that does indeed change. At low MA a value of 1.85 gives good agreement between the observed shock jump and the calculated one, but above an Alfven Mach number of 7, = 1.60 is better.

Fig. 18. The ratio of calculated to observed downstream magnetic field strength for Venus bow shocks as a function of BN the angle between the upstream magnetic field and the shock normal, for two ratios of specific heat, = 1.60 and = 1.85. The former value seems to be slightly better at low BN but these data may be biased because of fluctuations [Tatrallyay et al., 1984].

Similarly in Figure 18, where the predicted over observed jumps are plotted versus BN there is a suggestion that = 1.85 is good for quasi-perpendicular shocks and not for quasi-parallel shocks. However, the possibility of rectification effects associated with fluctuations of the field at low BN angles, as noted above, leads us to be somewhat hesitant to conclude that there is necessarily a change in at low BN.

We also hesitate to conclude that = 1.85 would give the best agreement between theory and observation for other planetary shocks. The downstream observations at Venus were made, perforce, close to the shock. Had the measurements been available further downstream from the shock, as they are at earth, the plasma might have had more time to isotropize, and the most appropriate value of y might have been less. In fact, a recent study of the terrestrial shock jump finds a best fit gamma of Winterhalter et al., 1985].

 

The Location of the Shock

While the asymptotic shock location is determined by the properties of the solar wind flow, the location and the shape of planetary bow shocks are determined principally by the size and shape of the obstacle to the flow. In the case of no absorption or mass addition to the flow, the shock stands off from the obstacle at a distance that allows all the shocked solar wind to flow around the obstacle. This distance depends on the compressibility of the flow, which depends on . While seems to range from 1.6 to 1.85 for the local MHD jump across the Venus shock, it is not clear whether, when using the global gas dynamic simulation, one should use a value similar to that appropriate to the local MHD solution or pick some other value e.g., 2, which would help simulate the effect of the magnetic field on the flow. If the global solution requires a value of 2 for while the local solution requires a value of 5/3, one should not expect to be able to simulate both the shock jump and the shock position with the gas dynamic model. This seems to be the situation at Venus [Spreiter and Stahara, 1980b], but as we will discuss below, there are additional reasons for disparity at Venus. This uncertainty concerning the appropriate value of y to use in the gas dynamic model limits our ability to deduce effective obstacle size from the observed shock position. For a specific bow shock location we would infer a 6% smaller obstacle for = 2 than 5/3.

The location of the bow shock will also be affected by such non- MHD processes as charge exchange and photoionization. Charge exchange of protons and hydrogen will remove momentum from the flow with no change of mass. Charge exchange with heavier ions will add mass to the flow, as will photoionization of the neutral atmosphere. Any mass added to the magnetosheath will have to flow around the planet and may cause the shock to stand off farther from the planet at the terminator. With these considerations in mind, let us now examine where each of the planetary bow shocks is found.

 

Mercury

Fig. 19. Location of the observed bow shock and magnetopause encounters in the solar wind-planet-spacecraft plane. Eight degrees of solar wind aberration has been assumed [Russell, 1977].

The locations of the Mercury bow shock and magnetopause were probed both inbound and outbound on two encounters of Mariner 10 with Mercury [Ness et al., 1974, 1975]. These are shown in Figure 19 with an 8o correction for aberration of the solar wind flow by Mercury's orbital motion [Russell, 1977]. The extrapolation of these measurements to the nose of the bow shock and magnetopause is very uncertain. The subsolar shock radius is 1.9 + 0.2 Mercury radii (RM), and the subsolar magnetopause radius is 1.3 + 0.2 RM. The ratio of these two measurements, 1.46 + 0.4, is not significantly different from the terrestrial value of 1.33. Further, the observed magnetopause size is not inconsistent with the best estimate of the Mercury dipole moment of 2.4 x 1022 G cm3 [Jackson and Beard, 1977; Whang, 1977] for expected solar wind conditions at Mercury.

 

Venus

The location of the Venus shock has generated much controversy despite the relative simplicity of determining the location of a shock crossing. Russell [1977] noted that the location of the subsolar point of the Venus shock was closer to the planet than we would have expected on the basis of scaling the terrestrial shock. However, in order to determine the location of the subsolar shock he had to extrapolate some distance in solar zenith angle. Subsequent measurements on Venera 9 and 10 provided many new data but still not at the lowest solar zenith angles. However, they did constrain the location of the terminator crossing of the bow shock quite well. Since the measurement of the location of the bow shock as it crosses the terminator is quite easy and that of the location of the subsolar point quite difficult, we will proceed with the former first. Table 1 shows four measurements of the terminator crossing distance. The first entry used Mariner 5 and Mariner 10 shock observations as well as Venera 4 and 6 and one Venera 9 shock. There were several estimates made using the same data by testing the sensitivity of the solution to discarding extreme values. We have chosen to quote the median value. The second entry is the location of the terminator shock according to the Venera 9 and 10 orbiter data at solar minimum. Smirnov et al. [1980] also chose to calculate the terminator position using mixtures of Pioneer Venus and Venera data, but as we will see, there may be a real change in shock location from solar minimum to solar maximum. The next two entries in the table use Pioneer Venus magnetometer data and do correspond to solar maximum conditions. The first used 172 crossings, and the second 269 crossings forward of X = -1 RV. There seems to be a significant increase in the distance to the shock at the terminator from 1976 to 1979. The shock has moved out by 14%. One possible cause for this difference is an increase in the solar EUV flux at solar maximum, increasing both the scale height of the neutral atmosphere and the photoionizing flux, so that the amount of mass loading was greater. The additional mass might be expected to displace the shock outward. The most recent Pioneer Venus data, obtained in late 1984, show the shock location is returning to its size in 1976 [Alexander and Russell, 1985].

 

As mentioned above, it is more difficult to determine the location of the nose of the Venus bow shock because we do not have measurements there. Table 2 lists various attempts to determine the shock standoff distance. The first attempt, by Russell [1977], used the fewest data and is the closest to the planet. The second one used Venera 9 and 10 data at solar minimum. It appears to confirm the earlier estimates, but the next two Pioneer Venus estimates are in clear disagreement with the earlier two entries, being 10% farther from the planet. Since these earlier measurements of the Venus shock were obtained, the periapsis of the Pioneer Venus spacecraft has been allowed to rise and at this writing is at about 2200 km in altitude. As the spacecraft passes the subsolar bow shock, it is now spending some fraction of its time in the solar wind rather than the magnetosheath.

If the appropriate for the global gas dynamic model is 2, then all these nose positions are unexpectedly close to the planet. This closeness could be accomplished through some mechanism such as charge exchange which created fast neutrals which were lost to the atmosphere. Russell [1977] estimated that perhaps 29% of the incident solar wind was absorbed by Venus. As Table 2 indicates, the shock location used by Russell [1977] seems to be too close to Venus. However, the Mach number used by Russell [1977] in making this estimate was too high. The correct average Mach number at Venus is 4.5 rather than 8 [Tatrallyay et al., 1984]. A revised absorption estimate is still close to 29%. We believe that more work needs to be done on this problem. The precise location of the subsolar shock needs to be determined, but this is perhaps now the least source of error. We need accurate three-dimensional MHD models of the interaction of the solar wind with Venus, and we need to understand the effect of mass pickup and momentum loss on these models.

Fig. 20. The distant bow shock and magnetotail of Venus [Russell and Vaisberg, 1983].

Figure 20 shows the distant bow shock and tail of Venus [Russell and Vaisberg, 1983]. Two extrapolations of the tail are given. The dashed line was drawn supposedly because it is less biased by data selection because of the limited region accessible on some orbits. However, the asymptotic behavior of the solid curve best approximates the expected Mach cone angle of 12.5o. This is also quite comparable to the asymptotic Mach cone derived by Slavin et al. [1984] of 13.9o + 2o using Venera 9 and 10 data. It appears as if at least the distant Venus shock behaves as expected.

Fig. 21. The dependence of the terminator radius of the Venus bow shock on Mach number. The solid and dashed lines give the dependence as determined from the gas dynamic code [Tatrallyay et al., 1984].

Returning to the terminator region, we show in Figure 21 the location of the shock crossing at the terminator as a function of free stream Mach number [Tatrallyay et al., 1984]. It behaves qualitatively as expected but is farther from the planet than expected, even though the subsolar shock is closer than expected. This is consistent with an MHD effect [cf. Spreiter and Rizzi, 1974] but could also be due to a mass-loading effect. Again we are in need of models including these effects to help us quantitatively interpret these phenomena.

Fig. 22. The location of the bow shock in the terminator plane for both Venus and the earth as a function of angle from the projection of the interplanetary magnetic field on the terminator plane. Neither the Pioneer Venus nor the terrestrial data support the earlier suggestion of Romanov et al. [1978] that there is a clock angle asymmetry [Slavin and Holzer, 1981).

Venus is also a good place to look for clock angle asymmetries in the Venus shock cross section. These were predicted by Cloutier [1976] on the basis of variations in with clock angle and mass loading with clock angle. Romanov et al. [1978] have reported observing such an asymmetry. Figure 22 shows the asymmetry reported by Romanov et al. [1978] together with Pioneer Venus data and terrestrial data all rotated about the solar direction so that the projected magnetic field vector in the solar wind lay along Y||. No asymmetry is found in the other data sets [Slavin and Holzer, 1981]. This work was confirmed by Tatrallyay et al. [1983], who also found no effect of BN on the shock location.

 

The Earth

The location of the terrestrial bow shock has been studied for many years. The shock stands off far in front of the earth, about 13.8 RE on the average, and crosses the terminator plane at about 27 RE [Cf. Slavin and Holzer, 1981]. The location of the terrestrial bow shock is highly variable and very sensitive to the solar wind dynamic pressure explains the sensitivity of the bow shock to the solar wind dynamic pressure. The large obstacle that is responsible for this distant deflection of the solar wind is, of course, the terrestrial magnetopause. The dependence of the size of the magnetopause on the solar wind dynamic pressure. The difference in the shape of the terrestrial magnetopause from that of the Venus ionosphere leads to a difference in the shape of the shock.

To zeroth order the standoff distance of the bow shock depends on . To show this, we recall that Spreiter et al. [1966] used the empirical formula for the location of the nose of the shock:

l/D = 1.1( 0/)

where l is the thickness of the magnetosheath, D is the radius of the magnetopause, 0 is the upstream density, and is the downstream density. The density ratio can be expressed analytically as

0/ = ( + 1)/ ( - 1) - 2( + 1)/ [M0( _ 1)]2 + O(1/M04)

where M0 is the upstream Mach number [Zhuang and Russell, 1981]. Thus the location of the nose of the bow shock relative to the nose of the magnetopause should be a good indicator of what is appropriate to use in global models of the shock. This could be quite different from the value most appropriate for the jump in parameters across the shock because thermalization processes and heat flux could alter the state of the plasma well downstream of the shock whereas they might not have had a chance to play much of a role just downstream of the shock. When we compare with the predictions of the gas dynamic convected-field model, we find that the most appropriate value of is close to 2 [Fairfield, 1971; Zhuang and Russell, 1981]. It is not clear that the most appropriate value for use in an MHD model is also 2; we await the development of MHD models with sufficient resolution to define a precise location of the shock so that this can be tested. The interested reader is referred to Fairfield [1971] and Slavin and Holzer [1981] for further details of terrestrial shock modeling. It is important to emphasize that the empirical factor 1.1 in the equation for l/D depends on the shape of the obstacle.

 

Mars

Since the solar wind interaction with Mars has been ignored by the U.S. space program, which has flown the most missions to Mars, even the most indirect data have been used to infer the nature of this interaction. The question is whether Mars has a sufficiently large intrinsic magnetic field to deflect the solar wind flow or whether the ionosphere and atmosphere of Mars stand off the flow. It is clear that the flow is deflected, because all properly instrumented missions to Mars have detected a bow shock. The location of this bow shock, in turn, has been used to infer the presence or absence of an intrinsic field according to the inferred size of the obstacle to the solar wind. The gravitational field of Mars is weaker than that of Venus, and hence we could expect a greater atmospheric scale height. Furthermore, the solar wind is weaker at Mars than at Venus. Thus we might expect a relatively larger obstacle to the flow at Mars than at Venus. Counterbalancing this, the oxygen exosphere is expected to be smaller at Mars, so the mass loading of the solar wind should be less than at Venus. In short, it is difficult to use our Venus experience directly to determine whether or not Mars has a magnetic field without low altitude magnetic measurements inside the planetary ionosphere.

Fig. 23. Bow shock locations of Mars calculated by various authors [Slavin and Holzer, 1981].

Part of the problem has been controversy on exactly where the shock was. Figure 23 shows a variety of determinations of the shock location [Slavin and Holzer, 1981]. The early studies generally agreed on the terminator crossing of the bow shock but disagreed widely on the location of the nose. Gringauz et al. [1975] had the most distant nose positions and favored the existence of a planetary magnetic field. Bogdanov and Vaisberg [1975] extrapolated the shock to a close-in location and favored a Venuslike interaction. Part of the disagreement was due to misidentifications of shock crossings and a few "outliers" being included in the fitting procedures. Some of the disagreement was due to the method of extrapolation. Slavin and Holzer [1981] have sorted carefully through these data and have avoided the sampling bias introduced by the Mars 2 and 3 orbits. This bias occurs because of the restricted range in which Mars 2 and 3 sampled the space around Mars together with the fact that bow shock crossings will only be detected at points along the orbit. The technique of using the percent occurrence of magnetosheath and solar wind plasma in the region sampled would solve this problem but apparently was not used. A 1.50-Mars radii (Rm) nose distance to the shock implies an effective obstacle radius of 1.10 Rm or an altitude of 340 km at the subsolar point.

Fig. 24. The solar wind pressure dependence of the subsolar distance to the Martian bow shock. Including all the data available for Mars results in a dependence similar to that for Venus (dash-dot and dotted curves, respectively). Discarding the lowest point as an erosion event produces a curve more similar to the dipole model [Slavin and Holzer, 1981].

Another method of inferring the nature of the Martian obstacle is to examine the dependence of the location of the bow shock on the solar wind dynamic pressure. Figure 24 shows this dependence for Venus, a simple dipole field, and Mars for all the available data and with the farthest outlier discarded [Slavin et al., 1983a]. The distance to the nose of the bow shock is slightly greater at Mars than at Venus in terms of planetary radii, but the curves appear to be parallel. Even with the outlier removed the pressure dependence seems to be more similar to the Venus case than to the dipole case. Thus this author would claim that this study argues against the Martian obstacle being an intrinsic field. However, Slavin et al. believed otherwise.

 

Jupiter and Saturn

Because Jupiter and Saturn have been probed only with spacecraft on flyby trajectories, there are only a few scattered observations of their shock locations [Smith et al., 1976, 1980; Lepping et al., 1981; Ness et al., 1981, 1982; Acuna et al., 1983]. Thus our modeling of the locations of the Jovian and Saturnian shocks is more akin to our modeling of the Mercury shock than those of Venus and Mars. One of the basic problems with the solar wind interaction with Jupiter is that the rapid rotation distorts the magnetic field in the outer magnetosphere into a more disklike shape. Thus the Jovian magnetosphere is far from being axisymmetric about the incident flow direction. The gas dynamic model of Spreiter and Stahara [1980a], from which we derive much of our understanding, however, assumes axisymmetry. Thus even the gas dynamic requires extension to handle Jupiter, and this extension has not yet been made.

Fig. 25. Location of bow shocks of Saturn, earth, and Jupiter when their respective magnetopause locations are normalized at the subsolar point (J. A. Slavin, personal communication, 1984). The smaller standoff distance of the Jovian shock is probably due to the disklike nature of the Jovian magnetosphere. While it has a blunt equatorial cross section, it must have a rather sharp medional cross section. The greater Rare of the Saturn shock may be associated with a greater flare of the Saturn magnetopause.

Figure 25 summarizes our current understanding of the location of the shocks and magnetopause boundaries of Jupiter and Saturn [Slavin et al., 1983b; J. A. Slavin, personal communication, 1984]. The Jovian shock lies inside its scaled terrestrial counterpart. One reason for this thinner magnetosheath could be the higher Mach number at Jupiter than at earth, but this would explain only part of the difference. A more important reason could be the slimness of the object in its noon-midnight meridian cross section. The Saturn shock is close to the scaled terrestrial shock in the nose region. This behavior is consistent with the fact that rotation has not caused a disklike magnetosphere at Saturn because of the lack of a massloading source of the magnitude of Jupiter's Io. Saturn has Titan, but it adds cold ions and only to the distant fringes of the magnetosphere. At the terminators the Saturn shock is much farther from the planet than the terrestrial shock. This observation is quite surprising, especially since it is not seen at Jupiter. Slavin et al. [1983b] attribute this to the Zwan and Wolf [1976] effect. extension has not yet been made.

Fig. 26. The relative shapes of the planetary bow shocks (top) and planetary magnetopause surfaces (bottom) when normalized at their subsolar points (J. A. Slavin, personal communication, 1984). Saturn's shock flares noticeably more than the others. Earth has more flare than Jupiter, which in turn flares more than Venus. Venus, which definitely does not have an intrinsic magnetosphere, may have a magnetopauselike obstacle shape because of the effects of absorption in the subsolar region and mass addition in the flanks. Mars has the least amount of flare and most resembles the shape expected for a noninteracting ionospheric obstacle.

If we add the terrestrial planets to this plot and normalize at the subsolar point, we get the scaled positions shown in Figure 26 (J. A. Slavin, personal communication, 1984). The Saturn shock is most flared, then that of the earth, and next that of Jupiter. Venus and Mars both have a lesser flare angle than the planets with well-developed magnetospheres. The shock shape for Venus is surprisingly shaped for a planet without a magnetosphere. We attribute this as possibly due to some absorption of the solar wind by charge exchange with the neutral atmosphere on the front side of the planet and mass addition due to both charge exchange and photoionization. Mars has the least flared shock and a shape that most resembles that of the gas dynamic solution of the interaction of the solar wind with a planetary ionosphere.

 

Summary and Future Directions

The earth remains the best place to study the microstructure of the shock. It is only at the earth where multipoint measurements are available to enable us to deduce the motion of the shock, calculate the shock thickness accurately, infer current densities, etc. Further, it is only at the earth, thus far, that we have been able to fly the sophisticated instrumentation with large telemetry bandwidth requirements. Fortunately, the parameters of the solar wind are very changeable, and if we are willing to wait long enough, much of the parameter space is covered. However, not all of it is covered. Planetary bow-shocks are generally quite strong, high Mach number shocks, especially those at and beyond 1 AU.

If we wish to study strong shocks, then planetary shocks are the places to do it, and the farther one goes out in the solar system, the stronger these shocks should become. Finally, we should note the difficulty of separating high effects from high Mach number effects. These conditions often occur simultaneously at present at 1 AU. A possible solution to this separation is to examine the Jovian and the Saturnian shock for high Mach number effects, at which time should (usually) be small, and to examine the Venus shock at times of high , since the Mach number at Venus is usually less than that at 1 AU.

In the area of shock jumps and the MHD Rankine-Hugoniot relations, not much work has been done especially at the terrestrial bow shock. It is clear that the Rankine-Hugoniot relationships are being followed on the grossest scales, but microphysics changes with location in parameter space, and the parameter does not seem to be constant. More work needs to be done in this area on the terrestrial shock, where our diagnostics seem to be best.

The global problem seems to be amenable to much further work. Preliminary numerical models are now under development that can treat full MHD effects and mass loading. At earth they have been used mainly in understanding the dynamics of the magnetosphere. They can also be and should be used to study the magnetosheath and shock location as well. They should also be applied to the other planets. In particular, Mars and Venus may be affected by direct plasma gas interactions. These codes should be able to simulate these interactions and tell us how the global interaction is modified by these processes. Then we may be able to better determine how to deduce, for example, whether the Martian bow shock location implies a magnetospheric or an ionospheric obstacle to the solar wind. Further, the gas dynamic model should be extended so that it can handle a nonrotationally symmetric obstacle like that of Jupiter. The gas dynamic solution should be quite appropriate here because of the high Mach number at Jupiter.

In summary then, while we have learned much about planetary shocks over the last two decades, there is much left to do. These suggested studies will aid in our understanding of both the physics of collisionless shocks themselves and the nature of the interaction with the planets they surround.

 

Acknowledgments

I have been very fortunate over my career to work with a large number of individuals on the planetary shock problem, and these individuals have helped me greatly. I am particularly indebted to J. T. Gosling, E. W. Greenstadt, R. E. Holzer, C. F. Kennel, W. A. Livesey, J. G. Luhmann, M. Mellott, M. Neugebauer, J. V. Olson, G. Paschmann, F. L. Scarf, J. A. Slavin, J. R. Spreiter, S. S. Stahara, M. Tatrallyay and 0. L. Vaisberg. This work was supported by the National Aeronautics and Space Administration under contracts NAS2-9491 and NAS5- 25772. This is Institute of Geophysics and Planetary Physics publication 2546.

 

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