Advances in Space Research 33 (2004) 2113–2120 www.elsevier.com/locate/asr

Comparative : lessons for Earth

V.M. Vasyliunas *

Max-Planck-lnstitut fu€r Aeronomie, Max-Planck-Str. 2, 37191 Katlenburg-Lindau, Germany

Received 3 March 2003; received in revised form 3 April 2003; accepted 3 April 2003

Abstract

The comparative study of various magnetospheres is not only interesting in itself but also useful for understanding better many aspects of the of Earth. Scaling relations can be tested over a much wider parameter range than that provided by Earth alone. Comparison of Earth with other magnetospheres tells us about the relative importance of the ionosphere, the sig- nificance of kinetic effects, the dependence on the geometrical configuration of rotation axis, magnetic dipole, and solar wind flow direction, and the role of the external magnetic field. Processes such as magnetic field line reconnection and auroral particle ac- celeration are common to many different magneto-spheres and can be better understood when observed in different contexts. Diffusive transport across closed magnetic field lines plays a special role in the magnetospheres both of Jupiter and of Earth. Finally, some properties and limitations of numerical simulation work are illuminated by application under distinct conditions provided by different magnetospheres, in particular Jupiter and Earth. 2004 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Comparative magnetospheres; Lessons for Earth; Scaling relations; Planetary magnetospheres

1. Introduction significance; the first step in trying to understand a magnetosphere that is being observed for the first time Lessons for Earth, or lessons from Earth? Both are has always been to invoke analogies from the terrestrial objectives of comparative magnetosphere studies as magnetosphere and see how far they can be pushed. But traditionally understood (e.g. Vasyliunas, 1983): ‘‘The also the first objective – lessons for Earth – is now as- study of comparative magnetospheres, which aims at a suming greater and greater importance as the field of unified general description of magnetospheric phenom- comparative magnetosphere studies becomes more ma- ena and applicable to many different objects, is ture, the result both of increased number and variety of important for a twofold reason. First, it provides a test observed magnetospheres and of increasingly detailed for the correctness and general applicability of our observations within some; indeeed, magnetospheric concepts and theories of magnetospheric physics, often physics now includes concepts and theories developed to developed in the first instance to fit specific phenomena fit specific phenomena of magnetospheres other than of the terrestrial magnetosphere. Second, it provides a Earth. The purpose of this paper is to highlight some of tool by which our detailed knowledge, based on exten- the ways by which our understanding of the terrestrial sive observations, of the EarthÕs magnetosphere may be magnetosphere may profit from results of comparative used to gain insights into the properties of other, less magnetosphere studies. accessible, magnetospheres where direct observations may be quite limited or even non-existent.’’ The second of these objectives – lessons from Earth – is of obvious 2. Scaling relations

A magnetosphere is characterized by a set of pa- * Tel.: +49-5556-979-435; fax: +49-5556-979-169. rameters which can be divided into three groups (see E-mail address: [email protected] (V.M. Va- e.g. Vasyliunas, 1989a): solar wind (or, more generally, syliunas). external medium), planetary (or, more generally, central

0273-1177/$30 2004 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2003.04.051 2114 V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120 object) and magnetospheric parameters. One of the first 1983 it is the distance traveled by light in vacuum during tasks of comparative magnetosphere studies is to search a time interval of 1/299,792,458 of a second (Mohr and for scaling laws that establish relations among the Taylor, 2000). With the second defined in terms of an various parameters. atomic frequency standard, the meter can be shown to be, in essence, proportional to the classical electron ra- 2.1. Dependence of size on pressure of external medium dius divided by the cube of the fine structure constant. It is obvious that neither under the old nor under the A basic question is how the size of a magnetosphere, current definition does the meter have any relevance to conveniently described by the distance RMP from the magnetospheres. center of the planet to the subsolar point of the mag- Actually, most descriptions of a magnetosphere as netopause, depends on the parameters of the solar wind large or small in absolute terms are really meant in re- and of the planet. It is well known that RMP is deter- lation to the size of the terrestrial magnetosphere – a mined primarily by the requirement that the total pres- geocentric view somewhat at variance with the universal sure just inside the magnetosphere balance the total outlook we like to attribute to modern science. pressure just outside (for a more detailed discussion in the context of comparative magnetospheres, see e.g. 2.2.2. Relative to kinetic length scales Russell, 2004, and references therein). Equating the A physically more meaningful description of magne- pressure of the dipole magnetic field to the dynamic tosphere size is to relate it to some length scale defined pressure of the solar wind gives the scaling relation by plasma physics. One fundamental scale is the ion 1=3 1=6 inertial length (or ion collisionless skin depth) given by R ¼ðnlÞ ð8pqV 2Þ ; ð1Þ MP (Gaussian units) where l is the dipole moment, q and V the solar wind 2 2 1=2 density and velocity, and n a numerical factor correcting ki ¼ Mic =47pne pffiffiffi for the field of magnetopause currents (n ¼ 2 to first 3 1=2 ¼ 227 km A n=1cm ; ð2Þ approximation). The validity of Eq. (1) has been checked at Earth over and also equal to the gyroradius of an ion moving at the a range Alfven speed. In (2) Mi is the ion mass, A the atomic mass number, and n the concentration (number density). R 5 104 to 8 104 km ð8–12R Þ; MP E Kinetic effects, to be discussed in the later section, by using the normal variability of the solar wind, or depend on the relation of ki to other length scales. 4 4 The sizes of various magnetospheres in units of ki are RMP 3 10 to 11 10 km ð5–17REÞ; tabulated and discussed by Russell (2004). The ratio by including the rare extreme cases, for a total variation RMP=ki is large for all magnetospheres observed to date, of nearly a factor 4. With the use of data from all ob- ranging from 85 for Mercury to 5800 for Jupiter. For served magnetospheres, however, Eq. (1) can be checked objects (possibly to be found among the asteroids) over a range whose magnetic dipoles are weak enough to give RMP 4 6 RMP 3 10 to 8 10 km: comparable to or smaller than Ai; interesting structures are anticipated on theoretical grounds (Omidi et al., or a total variation of about a factor 2600. 2004), but no magnetospheres of such objects have yet been detected. 2.2. When is a magnetosphere large or small? 2.2.3. Relative to planetary radius It is common to hear a particular magnetosphere A third, in fact the most common way of expressing described as ‘‘large’’ or ‘‘small.’’ Large or small com- the size of a magnetosphere is as the ratio of RMP to the pared to what? One is reminded of the remark by radius of the planet Rplanet. The observed magneto- Chesterton (1959): ‘‘It is quite futile to argue that man is spheres fall into three groups, with typical RMP=Rplanet small compared to the cosmos; for man was always equal to: (1) 1.5 to 2 for Mercury and Ganymede, (2) small compared to the nearest tree.’’ There are at least 10 for Earth and 20 for Saturn, , Neptune, three ways of describing how big a magnetosphere is. and (3) 100 for Jupiter.

2.2.1. Relative to standard unit of length 2.3. Does size matter? When a magnetosphere is characterized as large or small simply on the basis of its size in kilometers, it is The size of a magnetosphere has, as we have seen, no being compared in effect to whatever defines the stan- particular significance if expressed in kilometers or dard meter. Until 1960 that was the distance between multiples thereof, and it is very large in relation to ki- two scratches on a particular metal bar in Paris; since netic length scales (at least for all the magnetospheres V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120 2115 observed to date). Does the size in units of planetary 3. Multifactor analysis radius make any difference, as far as magnetospheric physics is concerned? For most purposes, the answer is Magnetospheres are influenced by the various pa- no: as long as the dipole moment rameters not only through simple scaling relations but also in more complicated ways. To disentangle and l ¼ðR Þ3B ; planet surface understand these, a study of how they affect different is held fixed, changing the radius of the planet does not magnetospheres can be very useful. affect the magnetosphere. (This is largely true even for magnetosphere/ionosphere coupling, as noted below.) 3.1. Ionosphere There are, however, a few aspects for which size does matter: To understand the role of the ionosphere in magne- 1. The volume occupied by the planet is not part of the tospheric structure and dynamics, a comparison of magnetosphere. When the magnetosphere is not large Earth and Mercury is instructive. Earth has a fully de- compared to the planet (e.g. for Mercury, Gany- veloped ionosphere, electrodynamically coupled to the mede), regions typical of the inner magnetosphere magnetosphere, whereas Mercury has none. Neverthe- (e.g. plasmasphere, symmetric ring current) will be less, as summarized by Ogilvie et al. (1977), ‘‘as far as absent. plasma electron and magnetic field observations are 2. The high energies of particles in the radiation belts concerned, the magnetosphere of Mercury appears to are generally ascribed to acceleration by adiabatic be, to a remarkable extent, simply a miniature of the compression when inward transport carries plasma magnetosphere of the earth.’’ A quantitative estimate of through the decreasing volume of flux tubes in nearly the expected ionospheric influence on the magneto- dipolar magnetic fields. The maximum energies sphere can be obtained in two different ways: reached will therefore scale as some power (typically (1) The total current flowing across the polar cap around 2–3) of the ratio RMP=Rplanet. ionosphere and then closing in the magnetosphere can 3. The rate of loss of trapped charged particles by pre- be estimated as cipitation down to the planet is proportional, other things being equal, to the size of the loss cone and I ¼ RpðVBRMP=cÞ; ð3Þ hence to the inverse of the mirror ratio (ionosphere/ where Rp is the Pedersen conductance and the quantity magnetosphere ratio of magnetic field strength). in parentheses is the electric potential in the solar wind Hence, loss processes are proportionally larger for across a distance RMP, a fraction of which is assumed smaller magnetospheres. applied across the magnetosphere. The magnetic field 4. In going along a magnetic field line from the equato- disturbance associated with this current in the outer rial region of the magnetosphere to the high-latitude magnetosphere is, in order of magnitude ionosphere, the Birkeland (magnetic-field-aligned) current density increases in proportion to the mag- DB ð4p=cÞI=RMP; ð4Þ netic field strength. The (or at least the type and a measure of the importance of the ionosphere is the known as the discrete aurora) is believed to be pro- ratio of the field given by Eq. (4) to that which balances duced by parallel-electric-field acceleration that oc- the external pressure curs when the Birkeland current density exceeds pffiffiffi some particular threshold (see e.g. Hill, 2004, and ref- 2 1=2 2 DB= 8pqV 4pRpVA=c = 2; ð5Þ erences therein). The required large current densities,

however, can reasonably be expected only as the result where VA is the Alfven speed in the solar wind. Nu- of a sufficiently large mirror ratio (Vasyliunas, 1989a). merically Hence, the size of the magnetosphere relative to the 4pR V =c2 ¼ R =1 f ðV =796 km s1Þ; ð6Þ planet does affect the occurrence of the aurora, dis- p A p A crete aurora being expected only for magnetospheres and the right-hand side of Eq. (5) is usually 1 for the with RMP=Rplanet 1 (see also Nishida, 2004). case of Earth. The above argument was first made in the On the other hand, while the Birkeland current den- context of comparative magnetospheres by Hill et al. sity increases from magnetosphere to ionosphere by the (1976), who concluded that the role of the ionosphere mirror ratio, the divergence of the perpendicular electric was dominant for Mars, marginally significant for field also increases, on the average by a similar amount, Earth, and totally insignificant for Mercury. leaving the ratio Jk=r? E essentially unchanged. (2) Another effect of a highly conductive ionosphere Magnetosphere/ionosphere coupling, therefore, depends is to allow continuous penetration of magnetospheric only on the ionospheric conductivity and is not affected convection to low latitudes, suppressing the shielding (except for some subtle field-inclination effects) by the that is imposed by the inner edge of the plasma sheet or size of the magnetosphere, as stated above. ring current. The condition for significant shielding 2116 V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120

(implying that any magnetospheric convection at low netosphere but may depend instead on ki or a similar latitudes can only be transient) is (Vasyliunas, 1972) parameter. Also, many kinetic effects become important Z first for ions but not for electrons, so that the MHD Rp R dsnec=B; ð7Þ approximation with the integral taken along a magnetic field line from cE þ V B ¼ 0; ð10Þ the equator (distance R) to the ionosphere. Eq. (7) can remains valid if V is the bulk flow of the electrons be recast in a form similar to (5) only, but some properties of the magnetosphere follow 2 4pRpVA=c ðki=RÞ1; ð8Þ simply from the existence of a constraint of the form (10). with VAnow the Alfven speed in the magnetosphere. An unresolved issue is the role of kinetic effects in Ionospheric effects on the magnetosphere at Earth are forming the plasma sheet of the magnetotail. At Earth, always small when measured by Eq. (8). When measured the mean thermal energy of plasma sheet ions is 10 by Eq. (5), they are small under usual conditions. During keV. This can be taken either as a multiple of the kinetic exceptional magnetic storms, however, the Alfven speed energy of solar wind bulk flow (1 keV) or as a fraction in the solar wind may become large enough to make the of the cross-tail electric potential (50 kV). The former right-hand side of Eq. (5) P 1, which leads to the phe- is expected if plasma sheet formation is primarily an nomenon of polar cap potential saturation, predicted by MHD process, the latter if kinetic effects of ion drift are Hill et al. (1976) and subsequently seen both in obser- dominant. At Mercury, the solar wind kinetic energy is vations and in MHD simulations (see Siscoe et al., 2002, still equal to 1 keV, but the cross-tail potential is es- and references therein). It is thus no surprise that Mer- timated as 7 kV, much smaller than at Earth (Ogilvie cury, with no ionosphere, and Earth, with one that et al., 1977; Slavin, 2004, and references therein). usually (aside from exceptional cases) is in effect poorly There are, unfortunately, as yet no ion temperature conducting, have very similar magnetospheres. measurements in the magnetosphere of Mercury; when available, they should thus contribute decisively to an- 3.2. Kinetic effects swering an outstanding question about the terrestrial magnetosphere. Kinetic effects is a general term for those plasma phenomena that cannot be described purely in terms of 3.3. Geometry: rotation – dipole – solar wind flow angles the bulk quantities of ideal MHD but require explicit reference to particle properties and distribution func- Three directions in space are essential in fixing the tions. Included are, among others, energy-dependent geometry of a magnetosphere: the magnetic dipole mo- magnetic drift effects which appear in the generalized ment of the central object, its rotation axis, and the flow OhmÕs law, processes that lead to E B 6¼ 0, and parti- of the external medium. The canonical simplified mag- cle-wave interactions. The contribution of magnetic netosphere has the dipole and the rotation aligned and drifts to the total current density J, however, is not a the external flow perpendicular, an approximation that kinetic effect: the sum of all the drifts yields J given by is adequate for many purposes in describing the mag- (Parker, 1957) netospheres of Mercury, Earth, Jupiter, Saturn, and Ganymede. It is therefore a useful check on our un- q oV=ot V V P J B=c; 9 ð þ r Þþr ¼ ð Þ derstanding of magnetospheric geometry that Uranus the momentum equation of MHD, independent of and Neptune both have magnetic dipole at nearly 60 to particle properties (hence the statement sometimes made rotation axis. In addition, Uranus during the epoch of that MHD cannot describe the ring current is not cor- the Voyager flyby had its (uniquely oblique) rotation rect, although it is of course true that MHD simulations axis nearly aligned with solar wind flow, and Voyager in general cannot accurately describe the ring current – studies led to the recognition that, in this unusual ge- its details may very well depend on kinetic effects, but ometry, magnetospheric convection is not impeded by not its existence). corotation (Vasyliunas, 1986). The importance of kinetic effects in structures of spatial scale L is measured, to lowest order, by the ratio 3.4. External magnetic field ki=L where ki is given by Eq. (2). If magnetospheric structures scale in proportion to the size of the magne- The magnetic field of the external medium can, tosphere, kinetic effects should be most important at through the process of magnetic field line reconnection, Mercury and least important at Jupiter. In fact, they influence the magnetosphere in complicated ways which seem to be of comparable importance – limited but non- depend strongly on the direction of the external field negligible – in all magnetospheres. This may mean that relative to the dipole. The dependence on field magni- many structures do not scale with the size of the mag- tude scales as the ratio of the external field to the field V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120 2117 just inside the magnetopause and hence, by pressure fields) and different in others (driving process related to balance, as corotation and outflow rather than to the solar wind). Understanding the explosive onset of the magneto- B=ð4pqV 2Þ1=2 M 1; ð11Þ A spheric substorm remains, however, one of the most the reciprocal of the Alfven Mach number of the solar intractable problems in the physics of the EarthÕs mag- wind. Since the transverse magnetic field in the solar netosphere. There is a twofold dichotomy of proposed wind varies with distance from the as 1=r and the explanations: theories differ on whether the initial cause 1 density as 1=r2, MA 0:1 has nearly the same small of the onset lies in the magnetotail or in the inner value for all the magnetospheres of planets in the solar magnetosphere (see e.g. Vasyliunas, 1998, and references wind. therein) and also on whether the phenomenon is to be An exceptional case is presented by Ganymede where, treated as primarily MHD or kinetic in nature (e.g. instead of the ordering found in the solar wind Parker, 2000; Lui, 2000; Yoon, 2002; Pritchett and Coroniti, 2002; Birn et al., 2002). Particularly concern- V V v ; A thermal ing the latter aspect, comparative studies of other we have magnetospheres with their quite different ratios of magnetospheric to kinetic length scales may provide VA P V vthermal; lessons for substorm theories at Earth. An important so that B=ð4pqV 2Þ1=2 1; also, there is no bow shock. test of models for substorm onset and related instabili- To first approximation, the magnetosphere of Gany- ties and developments is: are the models still viable when mede can be modeled by a simple superposition of in- applied to Mercury or Jupiter? For example, some the- ternal dipole and uniform external field (Kivelson et al., ories relate substorm onset to the thinning of the current 1998). Such a model (sometimes called the ‘‘Dungey sheet down to thickness comparable to the ion gyrora- sphere’’) has, however, long been used extensively to dius; the obvious question then is whether substorm investigate and illustrate some basic properties of the occurrence in another magnetosphere is associated with terrestrial magnetosphere (e.g. Stern, 1973). Ganymede current sheet thickness approaching the ion gyroradius thus provides one unexpected lesson for Earth: an ex- there. isting physical model of what had been viewed as just a theoretical pedagogical device. 4.2. Cross-field transport The absence of a bow shock (and consequently of an externally bounded magnetosheath) at Ganymede forces The process of plasma transport across magnetic field a serious consideration of the magnetopause as con- lines, in a region where the field is nearly dipolar (or sisting of intermediate and slow-mode discontinuities – otherwise strong and well defined so that deformation an approach that may be useful at Earth as well. and reconnection play no role), is common to nearly all magnetospheres. At Jupiter, the dominant source of plasma lies at the orbit of Io, deep within the magne- 4. Common processes tosphere, and plasma must be transported outward; the situation is similar at Saturn and at Neptune, although There are many phenomena and processes that occur the plasma sources are probably more diffuse (and in repeatedly in various magnetospheres, and understand- any case not as well known yet). At Earth, on the other ing them at Earth is obviously helped by comparative hand, a predominantly inward plasma transport is nee- studies in other systems. Several are dealt with in detail ded to account for the large enhancements of ring-cur- in other papers of this volume: particle acceleration and rent plasma associated with magnetic storms (see, e.g. aurora (Hill, 2004), magnetotail formation and dy- review by Gonzalez et al., 1994). namics (Nishida, 2004; Russell, 2004). The essential step in describing cross-field transport is to represent each quantity as a mean plus a fluctuation. 4.1. Magnetospheric substorms The plasma mass flux density is then given by

The magnetospheric substorm is one of the most hqVi¼hqihViþhdqdVi; ð12Þ striking dynamical manifestations, extensively studied in where q is the density, V the bulk flow velocity, and hi the magnetosphere of Earth. Substorms entirely analo- denotes mean quantity. The first term on the right-hand gous to the terrestrial ones, differing only in space and side, mean density times mean flow, is advection, the time scales, occur at Mercury (see Slavin, 2004, for a second term is diffusion. With no net transport of mag- critical review). At Jupiter, events have been observed netic flux, the mean flow must be zero, and then only (see Russell, 2004, and references therein) that are sim- diffusion remains. A quasi-linear treatment of the fluc- ilar to terrestrial substorms in some respects (reconfig- tuating quantities allows the second term in Eq. (12) to uration and reconnection of highly stretched magnetic be rewritten in standard diffusion form, with a diffusion 2118 V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120 coefficient proportional to the autocorrelation of the physics (chemistry, with biochemistry, being a fair slice velocity field hdqdVi. of it), the answer is, Nothing less than the whole Uni- The above description of transport by diffusion verse. It is not too much of a guess to say that that is just across field lines (adapted from work by G.I. Taylor in what the Universe is: the calculation of the effects of 1921 on fluid turbulence) was first proposed for EarthÕs physical laws.’’ To put it more succintly: a computer that magnetosphere by Cole (1964), who assumed randomly could model the Universe would have to be as large as fluctuating E B drifts of (then) unknown origin. (A the Universe – in fact, it is the Universe. seemingly different description of what is in fact the same process was later independently proposed in an 5.1. Role of resistivity (physical or numerical) astrophysical context by Jokipii and Parker (1968).) It has been most extensively applied, though, to the mag- We are very far from having to worry about the netosphere of Jupiter. Ioannidis and Brice (1971) first Universe as computer, but there are a number of serious proposed that randomly fluctuating flows driven by a problems. One is general: numerical effects equivalent to centrifugal interchange instability constitute the primary resistivity and other dissipative terms in the equations, mechanism of radial transport at Jupiter. From this introduced by the finite-difference approximations that idea, various theoretical models have been developed for must be used. Another is important particularly for Jupiter (e.g. Siscoe and Summers, 1981; Southwood and Jupiter: modeling the plasma input process at the Io Kivelson, 1989; Pontius and Hill, 1989; Vasyliunas, torus, a process which has proved to be so intractable 1989b; Hill, 1994, and others), as well as (assuming that most MHD simulations to date have avoided diffusion by interchange motions without specifying a dealing with it directly and instead have tried to include driving mechanism) for Saturn (Richardson, 1992) and its effects indirectly, by means such as inner boundary for Neptune (Richardson, 1993; Eviatar et al., 1995, conditions (e.g. Walker et al., 2001). One of the very few 1996). exceptions, a direct simulation with the BATS-R-US While the conceptual and the mathematical aspects of code (Gombosi et al., 2001, and references therein) of diffusion theory have been widely applied at Jupiter, plasma input and outflow in the Jovian magnetosphere analogous studies of the ring current at Earth have re- including the Io torus, led to a peculiar result: instead of lied instead mainly on the fortuitous ability to do global alternating outflow and inflow, expected in order to monitoring via the Dst index, made possible by the conserve magnetic flux, the simulated flow was radially Dessler–Parker–Sckopke theorem (Carovillano and outward everywhere (T. Gombosi, presentation at Siscoe, 1973, and references therein), accompanied by Conference on Jupiter, Boulder, Colorado 2001 and detailed time-series comparison with the driving solar private communication). This was soon recognized as wind (e.g. McPherron and OÕBrien, 2001, and references possibly a resistivity effect. therein). With increasing interest to go beyond global If we include a resistivity term gJ in the generalized monitoring when interpreting the spatial profiles, in- OhmÕs law, the radial outflow from the source region of cluding those now provided by energetic-neutral-atom the Io torus is described by imaging (e.g. Mitchell et al., 2001, and references cE V B gcJ : 13 therein), approaches and techniques learned from Jupi- / r z ¼ / ð Þ ter may prove useful. On the average E/ ¼ 0 because no net magnetic flux is transported. Instead of achieving this by having Vr in (13) both inward and outward, as in the radial diffusion 5. Methodology theory, it is possible to have unidirectional flow if the right-hand side of (13) is non-zero. Radial stress balance Recently, a particular lesson for Earth has emerged of corotating flow requires an azimuthal current given from studies of the magnetosphere of Jupiter, concerning by not the physics itself but a method of investigation. The qX2r ð1=cÞJ B ; ð14Þ method in question is the use of extensive numerical / z simulations of the global system. As is well known, nu- where X is the corotation frequency. From Eqs. (13) and merical simulation has now progressed from being sim- (14) the radial flow velocity due to resistivity alone is, ply an equation-solving tool to becoming an additional normalized to corotation speed basic branch of research: instead of just observation- V =Xr ðgc2=4pÞX=V 2; ð15Þ theory, we now have observation-theory-simulation. r A This raises a number of problems, including some ulti- and is positive, corresponding to outflow. This is to be mate questions. The following (a reaction to a proposal compared to the value Vr=Xr 0:01 inferred from for a supercomputer to work out all of chemistry) is a observations. view according to Hoyle (1994): ‘‘If you ask what is Consider first the possibility of a physical effective needed to work out the full consequences of the laws of resistivity (e.g. from plasma turbulence). Then g can be V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120 2119 parametrized by an effective electron–ion collision fre- Acknowledgements quency mei (me is electron mass) I am grateful to Tamas Gombosi for discussions of Io g ¼ m m =ne2; ð16Þ e ei torus simulations and to Tom Hill and George Siscoe which inserted into (15) gives for comments on an earlier version.

Vr=Xr ¼ðX=XiÞðmei=XeÞ; ð17Þ with Xi, Xe the ion and electron gyrofrequencies, re- spectively. For an ion of mass 16 in the 2000 nT field References 5 near the orbit of Io, the ratio Xi=Xe 1:5 10 . Clearly, the outflow due to any physical resistivity, even Birn, J., Schindler, K., Hesse, M. Relating thin current sheet formation and tail reconnection to substorm development, in: Winglee, R.M. with an unrealistic mei Xe, is negligible. (Ed.), Sixth International Conference on Substorms. University of There remains the numerical resistivity in the simu- Washington, Seattle, pp. 197–204, 2002. lation, which can be estimated, very roughly, as the Carovillano, R.L., Siscoe, G.L. Energy and momentum theorems in value that makes the magnetic Reynolds number magnetospheric processes. Rev. Geophys. Space Phys. 11, 289–353, (Lundqvist number) based on grid size Dx equal to unity 1973. Chesterton, G.K. Orthodoxy. Image Books, Garden City, NY, 1959, 2 p. 61 [original edition: Dodd, Mead & Company, 1908]. gc =4p VADx: ð18Þ Cole, K.D. On the depletion of ionization in the outer magnetosphere Inserted into (15) this gives during magnetic disturbances. J. Geophys. Res. 69, 3595–3601, 1964. Vr=Xr XDx=VA; ð19Þ Eviatar, A., Vasyliunas, V.M., Richardson, J.D. Plasma temperature which equals or exceeds the observed value if Dx > 0:2R . profiles in the magnetosphere of Neptune. J. Geophys. Res. 100, J 19,551–19,557, 1995. Since grid sizes used in simulations to date are not as fine Eviatar, A., Vasyliunas, V.M., Richardson, J.D. Correction to as that, the unidirectional radial outflow may be ac- ‘‘Plasma temperature profiles in the magnetosphere of Neptune. counted for entirely by numerical effects, at least in J. Geophys. Res. 101, 27463, 1996. principle – what happens in the actual simulation, which Gonzalez, W.D., Joselyn, J.A., Kamide, Y., Kroehl, H.W., Rostoker, is still under development, is not yet conclusively estab- G., Tsurutani, B.T., Vasyliunas, V.M. What is a geomagnetic storm? J. Geophys. Res. 99, 5771–5792, 1994. lished (T. Gombosi, private communication). Gombosi, T.I., DeZeeuw, D.L., Groth, C.P.T., Powell, K.G., Clauer, Such an effect of the numerical resistivity may im- C.R., Song, P. From Sun to Earth: multiscale MHD simulation of mediately be seen at Jupiter because the actual physical , in: Song, P., Singer, H.J., Siscoe, G.L. (Eds.), Space flow is very slow. The lesson for Earth is that numerical Weather. AGU Geophysical Monograph 125, Washington, DC, resistivity effects are real and must be watched out for, pp. 169–176, 2001. Hill, T.W. The shape and size of convection cells in the Jovian even though – or, perhaps, especially because – at Earth magnetosphere, in: Burch, J.L., Waite Jr., J.H. (Eds.), Solar more than at Jupiter they may be masked by real System Plasmas in Space and Time. AGU Geophysical Monograph physical effects. 84, Washington, DC, pp. 199–205, 1994. Hill, T.W. Auroral structures at Jupiter and Earth. Adv. Space Res., this issue, 2004 (doi:10.1016/j.asr.2003.05.037). Hill, T.W., Dessler, A.J., Wolf, R.A. Mercury and Mars: The role of 6. Conclusion ionospheric conductivity in the acceleration of magnetospheric particles. Geophys. Res. Lett. 3, 429–432, 1976. Hoyle, F. Home Is Where the Wind Blows. University Science Books, Some lessons for Earth from comparative study of Mill Valley, CA, p. 417, 1994. magnetospheres: Ioannidis, G.A., Brice, N.M. Plasma densities in the Jovian magne- • Parameter range to test understanding and applica- tosphere: plasma slingshot or Maxwell demon? Icarus 14, 360–373, bility of basic scaling properties has been greatly ex- 1971. Jokipii, J.R., Parker, E.N. Random walk of magnetic lines of force in tended. astrophysics. Phys. Rev. Lett. 21, 44–47, 1968. • Kinetic effects found to be of limited but universal Kivelson, M.G., Warnecke, J., Bennett, L., Joy, S., Khurana, K.K., importance, regardless of scale. Mercury may provide Linker, J.A., Russell, C.T., Walker, R.J., Polanskey, C. Gany- a critical test of some concepts. medeÕs magnetosphere: magnetometer overview. J. Geophys. Res. • Theories of reconnection and substorm onset may 103, 19,963–19,972, 1998. Lui, A.T.Y. Electric current approach to magnetospheric physics profit from considering their applicability to Mercury and the distinction between current disruption and magnetic and Jupiter as well as Earth. reconnection, in: Ohtani, S.-I., Fujii, R., Hesse, M., Lysak, • There are many commonalities, especially mathemat- R.L. (Eds.), Magnetospheric Current Systems. AGU Geo- ical, between transport of plasma outward in Io torus physical Monograph 118, Washington, DC, pp. 31–40, and inward in EarthÕs ring current. 2000. McPherron, R.L., OÕBrien, P. Predicting geomagnetic activity: the Dst • Numerical diffusion effects in simulations may mask index, in: Song, P., Singer, H.J., Siscoe, G.L. (Eds.), Space physics; this is more apparent in some runs at Jupiter Weather. AGU Geophysical Monograph 125, Washington, DC, because of special conditions there. pp. 339–1345, 2001. 2120 V.M. Vasyliunas / Advances in Space Research 33 (2004) 2113–2120

Mitchell, D.G., Hsieh, K.C., Curtis, C.C., Hamilton, D.C., Voss, Siscoe, G.L., Crooker, N.U., Siebert, K.D. Transpolar potential H.D., Roelof, E.C., Brandt, P.C. Imaging two geomagnetic storms saturation: roles of region 1 current system and solar wind ram in energetic neutral atoms. Geophys. Res. Lett. 28, 1151–1154, pressure. J. Geophys. Res. 107 (A10), 1321, 2002, doi:10.1029/ 2001. 2001JA009176. Mohr, P.J., Taylor, B.N. CODATA recommended values of the Slavin, J.A. MercuryÕs magnetosphere. Adv. Space Res., this issue, fundamental constants: 1998. Rev. Mod. Phys. 72, 351–495, 2000. 2004 (doi:10.1016/j.asr.2003.02.019). Nishida, A. Driving mechanisms of magnetospheric dynamics of Southwood, D.J., Kivelson, M.G. Magnetospheric interchange mo- planets and satellites. Adv. Space Res., this issue, 2004 tions. J. Geophys. Res. 94, 299–308, 1989. (doi:10.1016/j.asr.2003.04.046). Stern, D.P. A study of the electric field in an open magnetospheric Ogilvie, K.W., Scudder, J.D., Vasyliunas, V.M., Hartle, R.E., Siscoe, model. J. Geophys. Res. 78, 7292–7305, 1973. G.L. Observations at the planet Mercury by the plasma electron Vasyliunas, V.M. The interrelationship of magnetospheric processes, experiment: Mariner 10. J. Geophys. Res. 82, 1807–1824, 1977. in: McCormac, B.M. (Ed.), EarthÕs Magnetospheric Processes. D. Omidi, N., Blanco-Cano, X., Russell, C.T., Karimabadi, H. Dipolar Reidel Publishing Company, Dordrecht, Holland, pp. 27–36, magnetospheres and their characterization as a function of 1972. magnetic moment. Adv. Space Res., this issue, 2004 (doi:10.1016/ Vasyliunas, V.M. Comparative magnetospheres, in: Carovillano, j.asr.2003.08.041). R.L., Forbes, J.M. (Eds.), Solar-Terrestrial Physics. D. Reidel Parker, E.N. Newtonian development of the dynamic properties of Publishing Company, Dordrecht, Holland, pp. 479–492, ionized gases of low density. Phys. Rev. 107, 924–933, 1957. 1983. Parker, E.N. Newton, Maxwell, and magnetospheric physics, in: Vasyliunas, V.M. The convection-dominated magnetosphere of Ura- Ohtani, S.-I., Fujii, R., Hesse, M., Lysak, R.L. (Eds.), Magneto- nus. Geophys. Res. Lett. 13, 621–623, 1986. spheric Current Systems. AGU Geophysical Monograph 118, Vasyliunas, V.M. Dimensionless parameters for classifying solar wind Washington, DC, pp. 1–10, 2000. interactions, in: Plasma AstrophysicsGuyenne, T.D., Hunt, J.J. Pontius Jr., D.H., Hill, T.W. Rotation driven plasma transport: the (Eds.), ESA SP-285, vol. I. Noordwijk, The Netherlands, pp. 31– coupling of macroscopic motion and micro-diffusion. J. Geophys. 35, 1989a. Res. 94, 15,041–15,053, 1989. Vasyliunas, V.M. Maximum scales for preserving flux tube content in Pritchett, P.L., Coroniti, F.V. The challenge for kinetic simulations of radial diffusion driven by interchange motions. Geophys. Res. Lett. substorm growth and onset, in: Winglee, R.M. (Ed.), Sixth 16, 1465–1468, 1989b. International Conference on Substorms. University of Washington, Vasyliunas, V.M. Theoretical considerations on where a substorm Seattle, pp. 189–196, 2002. begins, in: Kokubun, S., Kamide, Y (Eds.), Substorms-4. Terra Richardson, J.D. A new model for plasma chemistry and transport at Scientific Publishing Company/Kluwer Academic Publishers, Saturn. J. Geophys. Res. 97, 13,705–13,713, 1992. Dordrecht, The Netherlands, pp. 9–14, 1998. Richardson, J.D. A quantitative model of plasma in NeptuneÕs Walker, R.J., Ogino, T., Kivelson, M.G. Magnetohydrodynamic magnetosphere. Geophys. Res. Lett. 20, 1467–1470, 1993. simulations of the effects of the solar wind on the Jovian Russell, C.T. Outer planet magnetospheres: a tutorial. Adv. Space magnetosphere. Planet. Space Sci. 49, 237–245, 2001. Res., this issue, 2004 (doi:10.1016/j.asr.2003.04.049). Yoon, P.H. Drift instabilities in current sheet, in: Winglee, R.M. (Ed.), Siscoe, G.L., Summers, D. Centrifugally driven diffusion of Iogenic Sixth International Conference on Substorms. University of plasma. J. Geophys. Res. 86, 8471–8479, 1981. Washington, Seattle, pp. 181–188, 2002.