- Email: [email protected]
Bimodal nature of solar wind–magnetosphere–ionosphere–thermosphere coupling
ARTICLE IN PRESS
Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920 www.elsevier.com/locate/jastp
Bimodal nature of solar wind–magnetosphere–ionosphere–thermosphere coupling G.L. Siscoea,, K.D. Siebertb a
Center for Space Physics, Boston University, Boston, MA 02215, USA b ATK Mission Research, Nashua, NH 03062, USA
Received 21 June 2005; received in revised form 14 September 2005; accepted 18 November 2005 Available online 20 January 2006
Abstract The solar wind–magnetosphere–ionosphere–thermosphere system has two ways to transfer the force that the solar wind exerts at the magnetopause to the Earth: (1) a dipole interaction mode and (2) a thermospheric drag mode. This paper uses MHD simulations to discuss both modes comparatively. The dipole interaction mode is relatively well known and so is used as a model against which to contrast the less well known thermospheric drag mode. The thermospheric drag mode itself consists of two distinct mechanisms, a direct mechanism in which the solar wind pulls on the thermosphere and (here discussed for the first time) an indirect mechanism involving an interaction between the region 1 current system and the geomagnetic dipole which increases the drag on the thermosphere nearly an order of magnitude over the direct drag mechanism. This additional force appears to be necessary to account for observed high-latitude thermospheric winds that correlate with IMF Bz. r 2005 Elsevier Ltd. All rights reserved. Keywords: Solar wind–magnetosphere–ionosphere–thermosphere coupling; High-latitude thermosphere; Winds
1. Two modes of momentum coupling Aerodynamic theory and practice divide the drag that a blunt body experiences when standing in high Reynolds number flow into two kinds. One kind results from forces acting perpendicular to the surface of the body and the other from forces acting tangential to the surface. In the case of interest here, the blunt body is the magnetosphere; the high Reynolds number flow, the solar wind; and the body’s surface, the magnetopause. Aerodynamicists call forces acting perpendicular to the Corresponding author.
E-mail address: [email protected] (G.L. Siscoe). 1364-6826/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2005.11.012
surface normal stresses, and forces acting tangential to the surface tangential stresses. Drag resulting from normal stresses is exemplified by a higher pressure on the upwind side of the body than in the wake on the downwind side. (For detailed discussions of the normal stress as applied to the magnetosphere see Spreiter et al., 1966, Spreiter and Alksne, 1969.) Tangential stresses are exemplified by a viscous stress and a tangential Maxwell stress. Although the viscous form of tangential stress indeed operates at the magnetopause, we shall nonetheless ignore it in this paper because the drag from the tangential Maxwell stress can be much stronger, and we shall here be concerned with very strong drags.
ARTICLE IN PRESS 912
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
Usually, both normal stresses and tangential stresses operate simultaneously. The point of this paper is first to show that for the magnetosphere the strength of the drag from tangential stresses relative to the drag from normal stresses is highly variable, depending on solar wind conditions (although the drag from normal stresses usually dominates), and when one increases the other in general decreases. A second objective of the paper is to show that the consequences for solar wind–magnetosphere–ionosphere–thermosphere coupling in the two cases are radically different. Quantitatively, the strength of the drag on the magnetosphere falls in the range 2 107 to 108 N. The first number, 2 107 N, corresponds to a typical, everyday value in which normal stress dominates, and the solar wind ram pressure is about 1.7 nPa (Siscoe, 1966). The 2 107 N value for the drag was determined using results from an analytical solution to the solar wind–magnetosphere interaction problem with a pure normal stress (Midgley and Davis, 1963). The value was verified empirically using ATS 5 magnetic field data (Schieldge and Siscoe, 1971). The effective crosssectional area of the magnetosphere—that is, the area against which the ram pressure pushing would give the stated drag—turns out to be about the actual magnetospheric cross section (a circle of radius about 10 Re, Earth radii). The second number, 108 N, at the high end of the drag range is reported here for the first time. It represents a case of strong southward IMF in which the tangential Maxwell stress dominates. The value was obtained using MHD modeling, as described below. The drag that the solar wind exerts on the magnetosphere must, of course, act on some mass, but it is not at first obvious whether it is the mass that belongs to the magnetosphere, that is, the ring current and plasma sheet, or the mass that by gravitational attachment belongs to the Earth, including the ionosphere/thermosphere. A straightforward consideration, however, reveals that the drag force must act principally on the Earth’s mass. This conclusion follows from noting that the magnetically bound plasma residing within the magnetosphere (i.e., the ring current and plasma sheet) is almost always less dense than the solar wind and that it remains in residence for a time much longer than the time it takes the solar wind to flow around the magnetosphere. This observation makes apparent that most of the force that the solar wind exerts against the magnetopause cannot act on the
resident magnetospheric plasma for if it did it would quickly blow the plasma tailward, out of the magnetosphere, contrary to experience. To illustrate the point quantitatively, we apply the typical solar wind force on the magnetopause (2 107 N) to a sphere of radius 10 Re (Earth radii) filled with a uniform density of 1 proton/cm3 representing the magnetosphere’s magnetically bound plasma (ring current and plasma sheet). Then starting from rest the sphere would move its own diameter in about 2 min at which time it would be moving at about 2000 km/s. Thus, to repeat, the Earth and its gravitationally bound ionosphere/thermosphere are the only things within the magnetosphere massive enough to withstand the majority of the drag that the solar wind exerts on the magnetopause. The solar wind’s force can be transferred from the magnetopause to the Earth in two fundamentally different ways corresponding to the two kinds of stresses: (1) indirectly through a magnetic interaction with the geomagnetic dipole (the normal stress case) and (2) directly through a J B force dragging on the thermosphere (the tangential stress case). Most of the time both mechanisms act simultaneously, although there are also times when one or the other mechanism is essentially absent. For example, the thermospheric drag mechanism may be assumed to be negligible compared to the dipole interaction mechanism when the IMF points northward, whereas it can dominate when the IMF is strong and points southward. For clarity we shall discuss the two mechanisms separately. As reviewed below, the transfer of the solar wind drag to the Earth, especially via dipole coupling, is an old subject. The work presented here extends prior studies by showing that (1) the two dragtransferring mechanisms (dipole interaction and thermosphere drag) are not independent but rather compete in a game of strength to stop and deflect the solar wind around the magnetosphere, and (2) the total J B drag at the ionospheric end of the region 1 current loop is actually considerably greater than the total J B drag at the solar wind end of the loop owing to an interaction between the region 1 current system and the geomagnetic dipole. 2. Force transfer via dipole interaction This is the standard textbook mechanism by which the solar wind transfers its force to the Earth. It was first discussed by Chapman and Ferraro in their classical treatment of the interaction between a
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
field-free plasma stream from the sun and a vacuum geomagnetic dipole (Chapman and Ferraro, 1931). They noted that currents induced on the surface of the solar stream generate a magnetic field that to the Earth looks like an image dipole, thus one has an interaction in which one dipole repels another. Chapman and Ferraro considered a stream with a flat surface. The general problem of determining the shape of the surface of current that separates the stream from the dipole and that confines the total magnetic field within it (B-normal ¼ 0 everywhere) while balancing the pressure everywhere across it (local ram pressure outside ¼ local magnetic pressure inside) was solved analytically in the early 1960s. (For a recent review of this subject, see Siscoe, 2001.) In the Chapman–Ferraro problem the force on the boundary is purely normal. It is transferred from the magnetopause to the Earth by a gradient in the magnetic field that the Chapman–Ferraro current generates. The magnitude of the force is m jrBCFjEarth where m and BCF are, respectively, the geomagnetic dipole moment and the magnetic field generated by the Chapman– Ferraro current, the gradient of which is to be evaluated at Earth. Thus, one can obtain the solar wind force on the Earth from the gradient in the magnetic field that the solution to the Chapman– Ferraro problem gives. Fig. 1 uses an illustration from Midgley and Davis (1963) to explain force transfer by dipole interaction. The numbers given in the figure for the total Chapman–Ferraro current (3.5 MA),
913
compression of the magnetic field (2.3 times the dipole field strength at the nose), gradient of the Chapman–Ferraro field along the x-axis (1.5 nT/Re), and force on the Earth (2 107 N tailward) correspond to representative conditions in which the nose lies about 10 Re from Earth-center (Siscoe, 1966). Fig. 2 shows the Chapman–Ferraro current system obtained with an MHD simulation in which the interplanetary magnetic field was set to zero. The resemblance to the analytical solution shown in Fig. 1 is apparent. Solutions to the classical Chapman–Ferraro problem as exemplified in Fig. 1 are unique among solar wind–magnetosphere models in that features such as the magnetotail or the region 1 current system resulting from magnetic reconnection at the magnetopause seem to preclude finding a fully selfconsistent analytical solution that determines the size and shape of the magnetosphere and the distribution of magnetospheric currents and fields (Siscoe, 2001). One therefore also loses the ability to determine by means of a fully self-consistently analytical calculation the solar wind force on the magnetosphere. One can recover this ability, however, by using the output of an MHD simulation to numerically integrate the momentum stress tensor around a closed surface containing the Earth. The principle on which this procedure is based is the conservation form of the MHD momentum equation (e.g., Siscoe, 1983): qðrVÞ=qt ¼ r S;
(1)
Fig. 1. Chapman–Ferraro current lines and associated parameters for IMF ¼ 0 calculated analytically (Midgley and Davis, 1963).
ARTICLE IN PRESS 914
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
Fig. 2. Chapman–Ferraro current lines for IMF ¼ 0 shown relative to magnetopause current contours on various crosssections. Other parameters are solar wind proton speed ¼ 400 km/s, density ¼ 5 cm3, and temperature ¼ 20 eV. Ionospheric conductance was uniform with SH ¼ 0 and SP ¼ 6 S. The magnetosphere was dawn-dusk symmetric in this run. The simulation was done with the ISM global MHD code (White et al., 2001).
where S is momentum stress tensor which in this case has the form S ¼ rVV þ ðp þ B2 =2m0 ÞI¯ BB=m0
(2)
with r, V, p, and B, respectively, the mass density, velocity vector, pressure, and magnetic field vector, and I¯ is the identity matrix. Integrating (1) over a volume containing the magnetosphere and converting the volume integral over the divergence into a surface integral gives Z F ¼ S n ds, (3) where n is the unit outward pointing normal to the surface, s. The left-hand side is the total acceleration of the mass inside the magnetosphere, and so the force on the magnetosphere, F. The right-hand side is the closed surface integral over the momentum stress tensor. This technique is widely used in aerodynamics to compute the drag and lift on objects standing in an airflow. To test whether integrating S over a surface containing the Earth indeed gives valid results for the magnetosphere, we apply the technique to a situation that approximates the classical Chapman–Ferraro problem for which we have an analytical solution.
Fig. 3. Integration surface for calculating the force on the earth from the momentum stress tensor (1) using values from MHD simulations. The color contours represent number density which show that most of the magnetosphere lies within the integration surface.
Fig. 3 shows the surface over which we integrate the stress tensor S. It is a cylinder coaxial with the xaxis, of radius 50 Re extending from 25 Re sunward to 70 Re tailward of Earth. The magnetosphere that the MHD simulation creates has a tail current system even in the case of zero IMF, so we do not expect precise agreement with Midgley–Davis’s 2 107 N. Nonetheless, the integration gives 2.4 107 N, which is close to the analytically obtained result. Thus, the technique appears to work, and we shall use it for the case of dominant tangential drag, where there are no self-consistent analytical models for comparison.
3. Competing current systems As previously mentioned, the Chapman–Ferraro current system competes with the region 1 current system in providing the J B force to stop the solar wind and deflect it around the magnetosphere. For a given solar wind ram pressure, the relative contributions to the wind-stopping force of the two competing current systems is set by the y-component in the GSM coordinate system of the interplanetary electric field, IEFy. This is the component associated with the southward component of the interplanetary magnetic field.
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
To illustrate the way in which the Chapman– Ferraro current system and the region 1 current system depend on IEFy, we let ICF and IR1 stand for the total current flowing in the two systems and IT denote their sum, I T ¼ I CF þ I R1 . Note that from the solar wind’s viewpoint, IT is the appropriate quantity to consider since the total J B force, (JCF+JR1) B, stops and deflects the wind. As IEFy increases from zero, IR1 grows owing to magnetic reconnection at the magnetopause ramping up the transpolar potential. Then as IR1 grows, it increasingly usurps ICF’s contribution to IT causing ICF to decrease. But at the same time, as IR1 grows, IT also increases because the nose of the magnetopause becomes blunter (Merkin et al., 2005; Siscoe et al., 2004) which strengthens the
Fig. 4. Schematic illustration of the dependences on IEFy of the total current in the Chapman–Ferraro current system (ICF), the region 1 current system (IR1), and their sum (IT).
915
normal stress. In addition, a tangential stress arises which also demands a bigger IT. As a result IT can double as IEFy increases from zero to something exceeding about 10 mV/m, as the next section demonstrates. Fig. 4 illustrates qualitatively relation between of ICF, IR1, and IT and their dependences on IEFy. The plot is a schematic based on assuming that when IEFy is small (or negative) the region 1 current is small (represented here by zero), and it is large when IEFy is large. The values at the high ends of the axes are based on an MHD simulation described in the next section. Obviously, the linear dependences depicted here merely indicate general trends. The relation between ICF and IR1 illustrated in Fig. 4 is similar to the one that Atkinson (1978) proposed in the first published attempt to understand their relation. Atkinson added the current systems together on that part of the magnetopause (tailward of the cusp) where they flow in the same direction. To Atkinson’s picture, MHD simulation adds the aspect of a change in the shape of the magnetopause such that the area of CF current shrinks as the area of R1 current expands. Fig. 5 illustrates the relation between the Chapman–Ferraro and region 1 current systems for the typical case in which there is a mixture of the two systems but the Chapman–Ferraro current dominates. Color contours in the figure depict the sunward-directed (i.e., the x-component) of the J B force, tan being positive and blue negative. Thus, the tan portions represent the J B force at the magnetopause pushing outward against the solar wind and the blue portions represent the solar wind pushing in against the magnetopause. In the
Fig. 5. Chapman–Ferraro and region 1 current lines for the case of a southward 5 nT IMF. Other parameters are V ¼ 350 km=s, n ¼ 5/cm3, and T ¼ 20 eV. Color contours in the left panel depict the sunward component of the J B force with tan positive and blue negative.
ARTICLE IN PRESS 916
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
funnel of the cusp color contours represent diamagnetic current that weakens the field. The figure portrays a situation in which the IMF is 5 nT straight south, corresponding to IEFy ¼ 1.75 mV/m. This situation represents a relatively disturbed magnetospheric state, but nonetheless, the Chapman–Ferraro current still occupies most of the magnetopause where the J B force is strongest. Although there are more region 1 current lines traced in the figure, they lie in the weak part of the J B color contour. Earlier we used Figs. 1 and 2 to illustrate the case of pure Chapman–Ferraro currents with IEF ¼ 0.0, hence force transfer by dipole interaction alone. Next, we examine a case with IEF ¼ 15 mV/m which gives dominant region 1 currents, hence force transfer dominantly by thermospheric drag. 4. Force transfer via thermospheric drag Fig. 6 gives a region 1 counterpart to the Chapman–Ferraro situation depicted in Fig. 2. The figure is constructed from an MHD simulation
since, as earlier noted, no analytic solution exists to the problem of the interaction between the solar wind and the magnetosphere when magnetic reconnection occurs. To see that Fig. 6 represents the case of dominant region 1 current system note that all current lines initiated in the magnetopause descend to the ionosphere. None closes on the magnetopause, which is the defining signature of Chapman–Ferraro current lines. A second noticeable difference between Figs. 2 and 6 is that in Fig. 6 most of the region 1 current lines close on the bow shock at their high altitude ends, not on the magnetopause as in Fig. 2. Bow shock closure of a significant portion of the current in the region 1 system has been noted previously by Fedder et al. (1997), but it remains a not well-known aspect of the system. The reason that current in the R1 system closes on the bow shock is easy to understand. When, as here, the IMF is strong and southward, draping of the magnetic field in the magnetosheath around the magnetosphere causes the direction and strength of the field to change little between the lobes of the tail and the adjacent magnetosheath.
Fig. 6. Region 1 system current lines for IMF ¼ 20 shown relative to magnetopause and bow shock current contours on various planes. Other parameters are solar wind proton speed ¼ 500 km/s, density ¼ 5 cm3, and temperature ¼ 20 eV. Ionospheric conductance was uniform with SH ¼ 0 and SP ¼ 10 S. The magnetosphere was dawn-dusk symmetric in this run.
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
Consequently, the current that defines the magnetopause and which separates the lobe from the magnetosheath can be less than the total current flowing in the region 1 current system. MHD simulations show this clearly. Hence, in this situation region 1 currents close mostly on the bow shock instead of around the magnetopause. Although bow shock closure of region 1 currents is an interesting aspect of their geometry, it has no direct bearing on the mechanism of force transfer. Thus, its fuller discussion belongs elsewhere. Directly relevant to the present discussion, however, is the project of ascertaining the drag on the magnetosphere in this strong IEFy situation. Here we invoke the technique discussed in connection with Fig. 3 of integrating the momentum stress tensor (Eq. (2)) around a surface containing the earth. Recall that when applied to the MHD simulation of the Chapman–Ferraro situation, the force was found to be 2.4 107 N, in essential agreement with the analytically determined value. The high IEFy run for which we performed the integration of the momentum stress tensor around the surface has the following input parameters: V ¼ 500 km/s, n ¼ 5/cm3, T ¼ 20 eV, B ¼ (0, 0, 30) nT, and Sp ¼ 18 S. The force in this case turns out to be 1.2 108 N, or about five times the value for the zero IMF run corresponding to the Chapman–Ferraro case depicted in Fig. 2. Half of this factor of five can be accounted for by the difference in the solar wind ram pressures in the two runs (2.1 nPa here versus 1.0 nPa there). The other half arises from the increased bluntness of the shape of the magnetopause and the addition of tangential stress. Thus as indicated previously, IT here is about twice the value it would have for the same solar wind ram pressure but with zero IEFy. Most of this force must be communicated to the thermosphere via the region 1 current system since the Chapman–Ferraro current system, which communicates via the dipole coupling mechanism, is essentially gone. To have a mental image of the force transfer mechanism between the solar wind and the thermosphere involving the region 1 current system think of a horse dragging a barge along a canal by means of a rope tied to its harness. The straining horse in this analogy is the solar wind exerting a force through the total region 1 J B force at the magnetopause and above. The rope is the magnetic field connecting the magnetosheath to the ionosphere and exerting magnetic tension to communicate the force. The barge is the ionosphere,
917
which balances magnetic tension from above against thermospheric drag from the surrounding medium. The net result of all of this is to accelerate the thermosphere in the open polar cap in the tailward direction and set up a circulation pattern of neutral wind that copies the two-cell convection pattern of the ions in the ionosphere. The magnitude of the acceleration and the speed that the resulting neutral wind thus attains is a quantity that we now wish to estimate. Comparing the estimated acceleration with observed examples reveals that a force in addition to and stronger than the solar wind drag appears to operate to accelerate the thermosphere. 5. Tailward force on thermosphere can exceed solar wind drag on magnetosphere To illustrate the difference between the drag on the magnetosphere and the force on the thermosphere we use the case under discussion (IMF Bz ¼ 30 nT) as an example and compare it with the intense storm of 15 July 2000 (the ‘‘Bastille Day’’ storm) for which there are published observations of thermospheric winds (Goncharenko et al., 2004). These authors reported that about two hours after the strong southward IMF interval began, thermospheric wind corresponding to the afternoon convection cell had reached between 300 and 500 m/s above 115 km over the Millstone Hill radar facility at invariant latitude 541. To compare the MHD model results with the Millstone Hill observations we estimate the acceleration of the thermosphere above 115 km using half—the northern hemisphere half, say—of the MHD-calculated force (i.e., 6 107 N). We apply this value to the mass of neutral air in a two cell circulation pattern of 361 radius, corresponding to the magnetic latitude of Millstone Hill. (The large, 361 size of the convection pattern implied by the Millstone Hill observation is consistent with the MHD simulation, which has a correspondingly large open polar cap of 251 radius.) Taking values for thermospheric density from the MSIS model gives a total mass above 115 km over the stated area of about 1010 kg. (Another way to calculate the mass is to double the mass above 115 km over the area of the open polar cap since this corresponds to including the, so-called, virtual mass of a 2-dimensional disk—the polar cap—accelerating in a fluid of equal density, e.g., Le Me´haute´, 1976. The answer is the same, 1010 kg.) The resulting
ARTICLE IN PRESS 918
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
acceleration is then about 6 103 m/s/s or 22 m/s/ h. This acceleration acting for 2 h as in the Bastille Day storm would produce a wind of about 44 m/s, which is nearly an order of magnitude less than what was observed. Moreover, 44 m/s is an overestimate since some of the region 1 current would close in the E region below 115 km. At lower levels of activity, solar wind drag also appears to be too weak to account for observed high latitude thermospheric winds. In a statistical analysis of data from the URAS satellite. Richmond et al. (2003) found that high-latitudes winds above about 120 km correlate with IMF Bz (IEFy) if averaged over the previous 1–4.5 h and that the resulting wind speed ‘‘often’’ exceeds 300 m/s. If we assume that the IMF Bz-association means that these apparently relative common winds are driven by the force associated with the region 1 current system, then we should adjust the parameters in the comparison between solar wind force and thermospheric acceleration to more standard values: 107 N for the hemispheric force from solar wind drag and 5 109 kg for twice the mass above 120 km over a standard-size polar cap of 151 radius. The resulting acceleration in this case would be 5 103 m/s/s or 18 m/s/h, which again is an overestimate since much of the region 1 current would close below 120 km. It would take about 17 h for such an acceleration to produce a wind of 300 m/s. Even if the solar wind
could sustain a tangential stress of 107 N for 17 h (which seems highly unlikely), the rotation of the Earth would prevent the force from acting unidirectionally on the thermosphere. The estimate made here of acceleration and the previous one are admittedly crude, but they nonetheless suggest that some force associated with the region 1 current in addition to solar wind drag accelerates the thermosphere. Such an additional force is in fact a necessary consequence of the interaction between the region 1 current system and the geomagnetic dipole. The additional force is revealed in the MHD simulation with IMF Bz ¼ 30 nT by integrating the total tailward-directed J B force in the ionosphere over the open polar cap. The result is 4.6 108 N, nearly an order of magnitude bigger than the 6 107 N that the solar wind exerts. This force, 4.6 108 N, gives an acceleration of the stated mass, 1010 kg, above 115 km of about 170 m/s/h, which operating for 2 h gives a speed of 340 m/s. The estimate is in reasonable agreement with the observed speed over Millstone Hill during the Bastille Day storm. Fig. 7 shows in a direct way that the force associated with the region 1 current system is greater in the ionosphere than in the solar wind. The two text lines in the figure give approximate comparisons of the total J B forces per mega-amp of region 1 current operating at the high-altitude
Fig. 7. Region 1 system current lines used to illustrate the geometry on which estimates are based of the total region1 J B force at the high-altitude and low-altitude ‘‘ends’’ of the current loop.
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
and low-altitude ‘‘ends’’ of the region 1 current loop. The high-altitude estimate is based on a 10 Re east–west stretch of the region 1 loop and a solar wind-stopping field strength of 100 nT. The lowaltitude estimate uses an east–west stretch of 2000 km and half the total region 1 current assuming that the other half chooses the alternative path of closing at lower latitudes. Anyone else making these estimates might choose numbers that differ from ours by factors of 2 or 3 in either direction, but it would be hard to justify a set of numbers that avoids the high-altitude force being significantly less than the low-altitude force. In the case illustrated, there is an order of magnitude difference in the forces. The reason for the difference in the forces at the two ‘‘ends’’ of the region 1 current loop is easy to see. The total force at either end is the length of the segment at that end times the field strength there times the total current flowing in the loop. Now as one moves from the low-altitude segment to the high-altitude segment the field strength drops roughly as 1/r3 (as for a dipole field) and the length goes up roughly as r3/2 (also as for a dipole field), so the product of the two, and hence the force on the segment, drops roughly as 1/r3/2. An explanation at a more physical level goes as follows. The region 1 current generates a magnetic field that is southward on the dayside of the magnetosphere and northward on the nightside. Thus, there is a force-producing gradient from day to night across the dipole, which is in the sense opposite to that generated by the Chapman–Ferraro current. That is, the region 1 current exerts a sunward force on the dipole, and the dipole must exert an equal and opposite force on the region 1 current loop. This turns out to be a big force, typically comparable to or bigger than the Chapman–Ferraro force; thus, it must act on the ionospheric end of the region 1 current loop where there is sufficient mass to withstand it. The dipole interaction thus adds to the drag exerted by the solar wind. Thus, the mode of force transfer between the solar wind and the Earth by thermospheric drag involves two drag-producing mechanisms in the thermosphere. There is the direct and easy to comprehend horse-pulling-a-barge mechanism and the somewhat surprising, not previously recognized dipole interaction mechanism. Is there a horsepulling-a-barge-like metaphor for the region-1current-dipole-interaction mechanism? One can think of it as a DC motor in which the geomagnetic
919
field is the motor’s permanent magnet and the neutral wind flywheel is its armature. To appreciate the analogy, think of a common terrestrial example. A hydroelectric power plant takes energy out of flowing water and delivers it as energy (not momentum) in the form of a DC (to fit the analogy) Poynting’s flux over power lines a long way to where a DC electric motor plugged into an electrical outlet receives it. The motor consists of a permanent magnet and an armature through which the current from the remote generator flows. The current interacts with the permanent magnetic to create a torque that turns the armature. The only issue involving momentum is one of bolting the motor down so that the torque exerted on the armature can be absorbed by something with a huge moment of inertia, like the Earth. The generator back at the power plant does not supply the torque, nor does the stream of water that turns the generator. They just supply the energy and leave torque balance to the motor and its fastening. The analogy to our case is more or less perfect. The balance of force between the thermospheric flywheel as armature and the geomagnetic field as permanent magnet is a local affair in which the tailward force in the thermosphere is balanced by an equal and opposite force on the interior of the Earth; the solar wind just supplies the energy to turn the flywheel via Poynting’s flux down the region 1 current loop. 6. Summary Thought of as a blunt body standing in the solar wind, the magnetosphere experiences an aerodynamic drag. This drag must be transferred to the body of the Earth since it is too big for the resident magnetospheric mass to withstand. The solar wind–magnetosphere–ionosphere–thermosphere system has two distinct ways to transfer the drag from the magnetopause, where the solar wind exerts it, to the Earth which absorbs it: (1) a dipole interaction mode, and (2) an thermospheric drag mode. Both modes operate to some degree most of the time. The dipole interaction mode is conveyed primarily by the Chapman–Ferraro current and is usually the dominant force transferring mechanism. The thermospheric drag mode of force transfer is conveyed by the region 1 current system and dominates at times of major magnetic storms. In it two distinct mechanisms operate to accelerate the thermosphere: a direct horse-pulling-a-barge mechanism and an indirect DC motor mechanism.
ARTICLE IN PRESS 920
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
The DC motor mechanism is typically an order of magnitude stronger than the other. Thus, the direct drag that the solar wind experiences in this mode at the high-altitude end of the region 1 current loop is considerably bigger in the ionosphere at the lowaltitude end. The amplified drag appears to be needed to account for observed high-latitude thermospheric winds associated with IMF Bz. Acknowledgments GLS was supported in part by the National Science Foundation under grant ATM-0220396 and by the CISM project which is funded by the STC Program of the National Science Foundation under Agreement Number ATM-0120950. The Integrated Space Weather Prediction Model (ISM) was developed by Mission Research Corporation under contract from the Defense Threat Reduction Agency, Keith Siebert principal investigator. References Atkinson, G., 1978. Energy flow and closure of current systems in the magnetosphere. Journal of Geophysical Research 83, 1089–1103. Chapman, S., Ferraro, V.C.A., 1931. A new theory of magnetic storms. Terrestrial Magnetism and Atmospheric Electricity 36, 77–97 and 171–186. Fedder, J.A., Slinker, S.P., Lyon, J.G., Russell, C.T., Fenrich, F.R., Luhmann, J.G.A., 1997. A first comparison of POLAR magnetic field measurements and magnetohydrodynamic simulation results for field aligned currents. Geophysical Research Letters 24, 2491–2494. Goncharenko, L.P., Salah, J.E., Foster, J.C., Huang, C., 2004. Variations in lower thermosphere dynamics at midlatitudes during intense geomagnetic storms. Journal of Geophysical Research 109, A04304.
Le Me´haute´, B., 1976. An Introduction to Hydrodynamics and Water Waves. Springer, New York. Merkine, V.G., Milikh, G.M., Sharma, A.S., Papadopoulos, K., Lyon, J., Goodrich, C., 2005. Effect of anomalous electron heating on the transpolar potential in the LFM global MHD model. Geophysical Research Letters 32, L22101. Midgley, J.E., Davis, L., 1963. Calculation by a moment technique of the perturbation of the geomagnetic field by the solar wind. Journal of Geophysical Research 68, 5111–5123. Richmond, A.D., Lathuille`re, C., Vennerstroem, S., 2003. Winds in the high-latitude lower thermosphere: dependence on the interplanetary magnetic field. Journal of Geophysical Research 108 (A2), 1066. Schieldge, J.P., Siscoe, G.L., 1971. An empirical determination of aerodynamic factors for the magnetosphere. Cosmic Electrodynamics 2, 141. Siscoe, G.L., 1966. A unified treatment of magnetospheric dynamics. Planetary and Space Science 14, 947–967. Siscoe, G.L., 1983. Solar system magnetohydrodynamics. In: Carovillano, R.L., Forbes, J.M. (Eds.), Solar-Terrestrial Physics. D. Reidel Publishing Co., Dordrecht, Holland, pp. 11–100. Siscoe, G., 2001. 70 years of magnetospheric modeling. In: Song, P., Singer, H.J., Siscoe, G.L. (Eds.), Space Weather, Geophysical Monograph 125. American Geophysical Union, Washington, DC, pp. 211–227. Siscoe, G., Raeder, J., Ridley, A.J., 2004. Transpolar potential saturation models compared. Journal of Geophysical Research 109 (A9), A09203. Spreiter, J.R., Alksne, A.Y., 1969. Effect of neutral sheet currents on the shape and the magnetic field of the magnetotail. Planetary and Space Science 17, 233–246. Spreiter, J.R., Summers, A.L., Alksne, A.Y., 1966. Hydromagnetic flow around the magnetosphere. Planetary and Space Science 14, 223–253. White, W.W., Schoendorf, J.A., Siebert, K.D., Maynard, N.C., Weimer, D.R., Wilson, G.L., Sonnerup, B.U.O¨., Siscoe, G.L., Erickson, G.M., 2001. MHD simulation of magnetospheric transport at the mesoscale. In: Song, P., Singer, H.J., Siscoe, G.L. (Eds.), Space Weather, Geophysical Monograph 125. American Geophysical Union, Washington, DC, pp. 229–240.
Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920 www.elsevier.com/locate/jastp
Bimodal nature of solar wind–magnetosphere–ionosphere–thermosphere coupling G.L. Siscoea,, K.D. Siebertb a
Center for Space Physics, Boston University, Boston, MA 02215, USA b ATK Mission Research, Nashua, NH 03062, USA
Received 21 June 2005; received in revised form 14 September 2005; accepted 18 November 2005 Available online 20 January 2006
Abstract The solar wind–magnetosphere–ionosphere–thermosphere system has two ways to transfer the force that the solar wind exerts at the magnetopause to the Earth: (1) a dipole interaction mode and (2) a thermospheric drag mode. This paper uses MHD simulations to discuss both modes comparatively. The dipole interaction mode is relatively well known and so is used as a model against which to contrast the less well known thermospheric drag mode. The thermospheric drag mode itself consists of two distinct mechanisms, a direct mechanism in which the solar wind pulls on the thermosphere and (here discussed for the first time) an indirect mechanism involving an interaction between the region 1 current system and the geomagnetic dipole which increases the drag on the thermosphere nearly an order of magnitude over the direct drag mechanism. This additional force appears to be necessary to account for observed high-latitude thermospheric winds that correlate with IMF Bz. r 2005 Elsevier Ltd. All rights reserved. Keywords: Solar wind–magnetosphere–ionosphere–thermosphere coupling; High-latitude thermosphere; Winds
1. Two modes of momentum coupling Aerodynamic theory and practice divide the drag that a blunt body experiences when standing in high Reynolds number flow into two kinds. One kind results from forces acting perpendicular to the surface of the body and the other from forces acting tangential to the surface. In the case of interest here, the blunt body is the magnetosphere; the high Reynolds number flow, the solar wind; and the body’s surface, the magnetopause. Aerodynamicists call forces acting perpendicular to the Corresponding author.
E-mail address: [email protected] (G.L. Siscoe). 1364-6826/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jastp.2005.11.012
surface normal stresses, and forces acting tangential to the surface tangential stresses. Drag resulting from normal stresses is exemplified by a higher pressure on the upwind side of the body than in the wake on the downwind side. (For detailed discussions of the normal stress as applied to the magnetosphere see Spreiter et al., 1966, Spreiter and Alksne, 1969.) Tangential stresses are exemplified by a viscous stress and a tangential Maxwell stress. Although the viscous form of tangential stress indeed operates at the magnetopause, we shall nonetheless ignore it in this paper because the drag from the tangential Maxwell stress can be much stronger, and we shall here be concerned with very strong drags.
ARTICLE IN PRESS 912
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
Usually, both normal stresses and tangential stresses operate simultaneously. The point of this paper is first to show that for the magnetosphere the strength of the drag from tangential stresses relative to the drag from normal stresses is highly variable, depending on solar wind conditions (although the drag from normal stresses usually dominates), and when one increases the other in general decreases. A second objective of the paper is to show that the consequences for solar wind–magnetosphere–ionosphere–thermosphere coupling in the two cases are radically different. Quantitatively, the strength of the drag on the magnetosphere falls in the range 2 107 to 108 N. The first number, 2 107 N, corresponds to a typical, everyday value in which normal stress dominates, and the solar wind ram pressure is about 1.7 nPa (Siscoe, 1966). The 2 107 N value for the drag was determined using results from an analytical solution to the solar wind–magnetosphere interaction problem with a pure normal stress (Midgley and Davis, 1963). The value was verified empirically using ATS 5 magnetic field data (Schieldge and Siscoe, 1971). The effective crosssectional area of the magnetosphere—that is, the area against which the ram pressure pushing would give the stated drag—turns out to be about the actual magnetospheric cross section (a circle of radius about 10 Re, Earth radii). The second number, 108 N, at the high end of the drag range is reported here for the first time. It represents a case of strong southward IMF in which the tangential Maxwell stress dominates. The value was obtained using MHD modeling, as described below. The drag that the solar wind exerts on the magnetosphere must, of course, act on some mass, but it is not at first obvious whether it is the mass that belongs to the magnetosphere, that is, the ring current and plasma sheet, or the mass that by gravitational attachment belongs to the Earth, including the ionosphere/thermosphere. A straightforward consideration, however, reveals that the drag force must act principally on the Earth’s mass. This conclusion follows from noting that the magnetically bound plasma residing within the magnetosphere (i.e., the ring current and plasma sheet) is almost always less dense than the solar wind and that it remains in residence for a time much longer than the time it takes the solar wind to flow around the magnetosphere. This observation makes apparent that most of the force that the solar wind exerts against the magnetopause cannot act on the
resident magnetospheric plasma for if it did it would quickly blow the plasma tailward, out of the magnetosphere, contrary to experience. To illustrate the point quantitatively, we apply the typical solar wind force on the magnetopause (2 107 N) to a sphere of radius 10 Re (Earth radii) filled with a uniform density of 1 proton/cm3 representing the magnetosphere’s magnetically bound plasma (ring current and plasma sheet). Then starting from rest the sphere would move its own diameter in about 2 min at which time it would be moving at about 2000 km/s. Thus, to repeat, the Earth and its gravitationally bound ionosphere/thermosphere are the only things within the magnetosphere massive enough to withstand the majority of the drag that the solar wind exerts on the magnetopause. The solar wind’s force can be transferred from the magnetopause to the Earth in two fundamentally different ways corresponding to the two kinds of stresses: (1) indirectly through a magnetic interaction with the geomagnetic dipole (the normal stress case) and (2) directly through a J B force dragging on the thermosphere (the tangential stress case). Most of the time both mechanisms act simultaneously, although there are also times when one or the other mechanism is essentially absent. For example, the thermospheric drag mechanism may be assumed to be negligible compared to the dipole interaction mechanism when the IMF points northward, whereas it can dominate when the IMF is strong and points southward. For clarity we shall discuss the two mechanisms separately. As reviewed below, the transfer of the solar wind drag to the Earth, especially via dipole coupling, is an old subject. The work presented here extends prior studies by showing that (1) the two dragtransferring mechanisms (dipole interaction and thermosphere drag) are not independent but rather compete in a game of strength to stop and deflect the solar wind around the magnetosphere, and (2) the total J B drag at the ionospheric end of the region 1 current loop is actually considerably greater than the total J B drag at the solar wind end of the loop owing to an interaction between the region 1 current system and the geomagnetic dipole. 2. Force transfer via dipole interaction This is the standard textbook mechanism by which the solar wind transfers its force to the Earth. It was first discussed by Chapman and Ferraro in their classical treatment of the interaction between a
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
field-free plasma stream from the sun and a vacuum geomagnetic dipole (Chapman and Ferraro, 1931). They noted that currents induced on the surface of the solar stream generate a magnetic field that to the Earth looks like an image dipole, thus one has an interaction in which one dipole repels another. Chapman and Ferraro considered a stream with a flat surface. The general problem of determining the shape of the surface of current that separates the stream from the dipole and that confines the total magnetic field within it (B-normal ¼ 0 everywhere) while balancing the pressure everywhere across it (local ram pressure outside ¼ local magnetic pressure inside) was solved analytically in the early 1960s. (For a recent review of this subject, see Siscoe, 2001.) In the Chapman–Ferraro problem the force on the boundary is purely normal. It is transferred from the magnetopause to the Earth by a gradient in the magnetic field that the Chapman–Ferraro current generates. The magnitude of the force is m jrBCFjEarth where m and BCF are, respectively, the geomagnetic dipole moment and the magnetic field generated by the Chapman– Ferraro current, the gradient of which is to be evaluated at Earth. Thus, one can obtain the solar wind force on the Earth from the gradient in the magnetic field that the solution to the Chapman– Ferraro problem gives. Fig. 1 uses an illustration from Midgley and Davis (1963) to explain force transfer by dipole interaction. The numbers given in the figure for the total Chapman–Ferraro current (3.5 MA),
913
compression of the magnetic field (2.3 times the dipole field strength at the nose), gradient of the Chapman–Ferraro field along the x-axis (1.5 nT/Re), and force on the Earth (2 107 N tailward) correspond to representative conditions in which the nose lies about 10 Re from Earth-center (Siscoe, 1966). Fig. 2 shows the Chapman–Ferraro current system obtained with an MHD simulation in which the interplanetary magnetic field was set to zero. The resemblance to the analytical solution shown in Fig. 1 is apparent. Solutions to the classical Chapman–Ferraro problem as exemplified in Fig. 1 are unique among solar wind–magnetosphere models in that features such as the magnetotail or the region 1 current system resulting from magnetic reconnection at the magnetopause seem to preclude finding a fully selfconsistent analytical solution that determines the size and shape of the magnetosphere and the distribution of magnetospheric currents and fields (Siscoe, 2001). One therefore also loses the ability to determine by means of a fully self-consistently analytical calculation the solar wind force on the magnetosphere. One can recover this ability, however, by using the output of an MHD simulation to numerically integrate the momentum stress tensor around a closed surface containing the Earth. The principle on which this procedure is based is the conservation form of the MHD momentum equation (e.g., Siscoe, 1983): qðrVÞ=qt ¼ r S;
(1)
Fig. 1. Chapman–Ferraro current lines and associated parameters for IMF ¼ 0 calculated analytically (Midgley and Davis, 1963).
ARTICLE IN PRESS 914
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
Fig. 2. Chapman–Ferraro current lines for IMF ¼ 0 shown relative to magnetopause current contours on various crosssections. Other parameters are solar wind proton speed ¼ 400 km/s, density ¼ 5 cm3, and temperature ¼ 20 eV. Ionospheric conductance was uniform with SH ¼ 0 and SP ¼ 6 S. The magnetosphere was dawn-dusk symmetric in this run. The simulation was done with the ISM global MHD code (White et al., 2001).
where S is momentum stress tensor which in this case has the form S ¼ rVV þ ðp þ B2 =2m0 ÞI¯ BB=m0
(2)
with r, V, p, and B, respectively, the mass density, velocity vector, pressure, and magnetic field vector, and I¯ is the identity matrix. Integrating (1) over a volume containing the magnetosphere and converting the volume integral over the divergence into a surface integral gives Z F ¼ S n ds, (3) where n is the unit outward pointing normal to the surface, s. The left-hand side is the total acceleration of the mass inside the magnetosphere, and so the force on the magnetosphere, F. The right-hand side is the closed surface integral over the momentum stress tensor. This technique is widely used in aerodynamics to compute the drag and lift on objects standing in an airflow. To test whether integrating S over a surface containing the Earth indeed gives valid results for the magnetosphere, we apply the technique to a situation that approximates the classical Chapman–Ferraro problem for which we have an analytical solution.
Fig. 3. Integration surface for calculating the force on the earth from the momentum stress tensor (1) using values from MHD simulations. The color contours represent number density which show that most of the magnetosphere lies within the integration surface.
Fig. 3 shows the surface over which we integrate the stress tensor S. It is a cylinder coaxial with the xaxis, of radius 50 Re extending from 25 Re sunward to 70 Re tailward of Earth. The magnetosphere that the MHD simulation creates has a tail current system even in the case of zero IMF, so we do not expect precise agreement with Midgley–Davis’s 2 107 N. Nonetheless, the integration gives 2.4 107 N, which is close to the analytically obtained result. Thus, the technique appears to work, and we shall use it for the case of dominant tangential drag, where there are no self-consistent analytical models for comparison.
3. Competing current systems As previously mentioned, the Chapman–Ferraro current system competes with the region 1 current system in providing the J B force to stop the solar wind and deflect it around the magnetosphere. For a given solar wind ram pressure, the relative contributions to the wind-stopping force of the two competing current systems is set by the y-component in the GSM coordinate system of the interplanetary electric field, IEFy. This is the component associated with the southward component of the interplanetary magnetic field.
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
To illustrate the way in which the Chapman– Ferraro current system and the region 1 current system depend on IEFy, we let ICF and IR1 stand for the total current flowing in the two systems and IT denote their sum, I T ¼ I CF þ I R1 . Note that from the solar wind’s viewpoint, IT is the appropriate quantity to consider since the total J B force, (JCF+JR1) B, stops and deflects the wind. As IEFy increases from zero, IR1 grows owing to magnetic reconnection at the magnetopause ramping up the transpolar potential. Then as IR1 grows, it increasingly usurps ICF’s contribution to IT causing ICF to decrease. But at the same time, as IR1 grows, IT also increases because the nose of the magnetopause becomes blunter (Merkin et al., 2005; Siscoe et al., 2004) which strengthens the
Fig. 4. Schematic illustration of the dependences on IEFy of the total current in the Chapman–Ferraro current system (ICF), the region 1 current system (IR1), and their sum (IT).
915
normal stress. In addition, a tangential stress arises which also demands a bigger IT. As a result IT can double as IEFy increases from zero to something exceeding about 10 mV/m, as the next section demonstrates. Fig. 4 illustrates qualitatively relation between of ICF, IR1, and IT and their dependences on IEFy. The plot is a schematic based on assuming that when IEFy is small (or negative) the region 1 current is small (represented here by zero), and it is large when IEFy is large. The values at the high ends of the axes are based on an MHD simulation described in the next section. Obviously, the linear dependences depicted here merely indicate general trends. The relation between ICF and IR1 illustrated in Fig. 4 is similar to the one that Atkinson (1978) proposed in the first published attempt to understand their relation. Atkinson added the current systems together on that part of the magnetopause (tailward of the cusp) where they flow in the same direction. To Atkinson’s picture, MHD simulation adds the aspect of a change in the shape of the magnetopause such that the area of CF current shrinks as the area of R1 current expands. Fig. 5 illustrates the relation between the Chapman–Ferraro and region 1 current systems for the typical case in which there is a mixture of the two systems but the Chapman–Ferraro current dominates. Color contours in the figure depict the sunward-directed (i.e., the x-component) of the J B force, tan being positive and blue negative. Thus, the tan portions represent the J B force at the magnetopause pushing outward against the solar wind and the blue portions represent the solar wind pushing in against the magnetopause. In the
Fig. 5. Chapman–Ferraro and region 1 current lines for the case of a southward 5 nT IMF. Other parameters are V ¼ 350 km=s, n ¼ 5/cm3, and T ¼ 20 eV. Color contours in the left panel depict the sunward component of the J B force with tan positive and blue negative.
ARTICLE IN PRESS 916
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
funnel of the cusp color contours represent diamagnetic current that weakens the field. The figure portrays a situation in which the IMF is 5 nT straight south, corresponding to IEFy ¼ 1.75 mV/m. This situation represents a relatively disturbed magnetospheric state, but nonetheless, the Chapman–Ferraro current still occupies most of the magnetopause where the J B force is strongest. Although there are more region 1 current lines traced in the figure, they lie in the weak part of the J B color contour. Earlier we used Figs. 1 and 2 to illustrate the case of pure Chapman–Ferraro currents with IEF ¼ 0.0, hence force transfer by dipole interaction alone. Next, we examine a case with IEF ¼ 15 mV/m which gives dominant region 1 currents, hence force transfer dominantly by thermospheric drag. 4. Force transfer via thermospheric drag Fig. 6 gives a region 1 counterpart to the Chapman–Ferraro situation depicted in Fig. 2. The figure is constructed from an MHD simulation
since, as earlier noted, no analytic solution exists to the problem of the interaction between the solar wind and the magnetosphere when magnetic reconnection occurs. To see that Fig. 6 represents the case of dominant region 1 current system note that all current lines initiated in the magnetopause descend to the ionosphere. None closes on the magnetopause, which is the defining signature of Chapman–Ferraro current lines. A second noticeable difference between Figs. 2 and 6 is that in Fig. 6 most of the region 1 current lines close on the bow shock at their high altitude ends, not on the magnetopause as in Fig. 2. Bow shock closure of a significant portion of the current in the region 1 system has been noted previously by Fedder et al. (1997), but it remains a not well-known aspect of the system. The reason that current in the R1 system closes on the bow shock is easy to understand. When, as here, the IMF is strong and southward, draping of the magnetic field in the magnetosheath around the magnetosphere causes the direction and strength of the field to change little between the lobes of the tail and the adjacent magnetosheath.
Fig. 6. Region 1 system current lines for IMF ¼ 20 shown relative to magnetopause and bow shock current contours on various planes. Other parameters are solar wind proton speed ¼ 500 km/s, density ¼ 5 cm3, and temperature ¼ 20 eV. Ionospheric conductance was uniform with SH ¼ 0 and SP ¼ 10 S. The magnetosphere was dawn-dusk symmetric in this run.
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
Consequently, the current that defines the magnetopause and which separates the lobe from the magnetosheath can be less than the total current flowing in the region 1 current system. MHD simulations show this clearly. Hence, in this situation region 1 currents close mostly on the bow shock instead of around the magnetopause. Although bow shock closure of region 1 currents is an interesting aspect of their geometry, it has no direct bearing on the mechanism of force transfer. Thus, its fuller discussion belongs elsewhere. Directly relevant to the present discussion, however, is the project of ascertaining the drag on the magnetosphere in this strong IEFy situation. Here we invoke the technique discussed in connection with Fig. 3 of integrating the momentum stress tensor (Eq. (2)) around a surface containing the earth. Recall that when applied to the MHD simulation of the Chapman–Ferraro situation, the force was found to be 2.4 107 N, in essential agreement with the analytically determined value. The high IEFy run for which we performed the integration of the momentum stress tensor around the surface has the following input parameters: V ¼ 500 km/s, n ¼ 5/cm3, T ¼ 20 eV, B ¼ (0, 0, 30) nT, and Sp ¼ 18 S. The force in this case turns out to be 1.2 108 N, or about five times the value for the zero IMF run corresponding to the Chapman–Ferraro case depicted in Fig. 2. Half of this factor of five can be accounted for by the difference in the solar wind ram pressures in the two runs (2.1 nPa here versus 1.0 nPa there). The other half arises from the increased bluntness of the shape of the magnetopause and the addition of tangential stress. Thus as indicated previously, IT here is about twice the value it would have for the same solar wind ram pressure but with zero IEFy. Most of this force must be communicated to the thermosphere via the region 1 current system since the Chapman–Ferraro current system, which communicates via the dipole coupling mechanism, is essentially gone. To have a mental image of the force transfer mechanism between the solar wind and the thermosphere involving the region 1 current system think of a horse dragging a barge along a canal by means of a rope tied to its harness. The straining horse in this analogy is the solar wind exerting a force through the total region 1 J B force at the magnetopause and above. The rope is the magnetic field connecting the magnetosheath to the ionosphere and exerting magnetic tension to communicate the force. The barge is the ionosphere,
917
which balances magnetic tension from above against thermospheric drag from the surrounding medium. The net result of all of this is to accelerate the thermosphere in the open polar cap in the tailward direction and set up a circulation pattern of neutral wind that copies the two-cell convection pattern of the ions in the ionosphere. The magnitude of the acceleration and the speed that the resulting neutral wind thus attains is a quantity that we now wish to estimate. Comparing the estimated acceleration with observed examples reveals that a force in addition to and stronger than the solar wind drag appears to operate to accelerate the thermosphere. 5. Tailward force on thermosphere can exceed solar wind drag on magnetosphere To illustrate the difference between the drag on the magnetosphere and the force on the thermosphere we use the case under discussion (IMF Bz ¼ 30 nT) as an example and compare it with the intense storm of 15 July 2000 (the ‘‘Bastille Day’’ storm) for which there are published observations of thermospheric winds (Goncharenko et al., 2004). These authors reported that about two hours after the strong southward IMF interval began, thermospheric wind corresponding to the afternoon convection cell had reached between 300 and 500 m/s above 115 km over the Millstone Hill radar facility at invariant latitude 541. To compare the MHD model results with the Millstone Hill observations we estimate the acceleration of the thermosphere above 115 km using half—the northern hemisphere half, say—of the MHD-calculated force (i.e., 6 107 N). We apply this value to the mass of neutral air in a two cell circulation pattern of 361 radius, corresponding to the magnetic latitude of Millstone Hill. (The large, 361 size of the convection pattern implied by the Millstone Hill observation is consistent with the MHD simulation, which has a correspondingly large open polar cap of 251 radius.) Taking values for thermospheric density from the MSIS model gives a total mass above 115 km over the stated area of about 1010 kg. (Another way to calculate the mass is to double the mass above 115 km over the area of the open polar cap since this corresponds to including the, so-called, virtual mass of a 2-dimensional disk—the polar cap—accelerating in a fluid of equal density, e.g., Le Me´haute´, 1976. The answer is the same, 1010 kg.) The resulting
ARTICLE IN PRESS 918
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
acceleration is then about 6 103 m/s/s or 22 m/s/ h. This acceleration acting for 2 h as in the Bastille Day storm would produce a wind of about 44 m/s, which is nearly an order of magnitude less than what was observed. Moreover, 44 m/s is an overestimate since some of the region 1 current would close in the E region below 115 km. At lower levels of activity, solar wind drag also appears to be too weak to account for observed high latitude thermospheric winds. In a statistical analysis of data from the URAS satellite. Richmond et al. (2003) found that high-latitudes winds above about 120 km correlate with IMF Bz (IEFy) if averaged over the previous 1–4.5 h and that the resulting wind speed ‘‘often’’ exceeds 300 m/s. If we assume that the IMF Bz-association means that these apparently relative common winds are driven by the force associated with the region 1 current system, then we should adjust the parameters in the comparison between solar wind force and thermospheric acceleration to more standard values: 107 N for the hemispheric force from solar wind drag and 5 109 kg for twice the mass above 120 km over a standard-size polar cap of 151 radius. The resulting acceleration in this case would be 5 103 m/s/s or 18 m/s/h, which again is an overestimate since much of the region 1 current would close below 120 km. It would take about 17 h for such an acceleration to produce a wind of 300 m/s. Even if the solar wind
could sustain a tangential stress of 107 N for 17 h (which seems highly unlikely), the rotation of the Earth would prevent the force from acting unidirectionally on the thermosphere. The estimate made here of acceleration and the previous one are admittedly crude, but they nonetheless suggest that some force associated with the region 1 current in addition to solar wind drag accelerates the thermosphere. Such an additional force is in fact a necessary consequence of the interaction between the region 1 current system and the geomagnetic dipole. The additional force is revealed in the MHD simulation with IMF Bz ¼ 30 nT by integrating the total tailward-directed J B force in the ionosphere over the open polar cap. The result is 4.6 108 N, nearly an order of magnitude bigger than the 6 107 N that the solar wind exerts. This force, 4.6 108 N, gives an acceleration of the stated mass, 1010 kg, above 115 km of about 170 m/s/h, which operating for 2 h gives a speed of 340 m/s. The estimate is in reasonable agreement with the observed speed over Millstone Hill during the Bastille Day storm. Fig. 7 shows in a direct way that the force associated with the region 1 current system is greater in the ionosphere than in the solar wind. The two text lines in the figure give approximate comparisons of the total J B forces per mega-amp of region 1 current operating at the high-altitude
Fig. 7. Region 1 system current lines used to illustrate the geometry on which estimates are based of the total region1 J B force at the high-altitude and low-altitude ‘‘ends’’ of the current loop.
ARTICLE IN PRESS G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
and low-altitude ‘‘ends’’ of the region 1 current loop. The high-altitude estimate is based on a 10 Re east–west stretch of the region 1 loop and a solar wind-stopping field strength of 100 nT. The lowaltitude estimate uses an east–west stretch of 2000 km and half the total region 1 current assuming that the other half chooses the alternative path of closing at lower latitudes. Anyone else making these estimates might choose numbers that differ from ours by factors of 2 or 3 in either direction, but it would be hard to justify a set of numbers that avoids the high-altitude force being significantly less than the low-altitude force. In the case illustrated, there is an order of magnitude difference in the forces. The reason for the difference in the forces at the two ‘‘ends’’ of the region 1 current loop is easy to see. The total force at either end is the length of the segment at that end times the field strength there times the total current flowing in the loop. Now as one moves from the low-altitude segment to the high-altitude segment the field strength drops roughly as 1/r3 (as for a dipole field) and the length goes up roughly as r3/2 (also as for a dipole field), so the product of the two, and hence the force on the segment, drops roughly as 1/r3/2. An explanation at a more physical level goes as follows. The region 1 current generates a magnetic field that is southward on the dayside of the magnetosphere and northward on the nightside. Thus, there is a force-producing gradient from day to night across the dipole, which is in the sense opposite to that generated by the Chapman–Ferraro current. That is, the region 1 current exerts a sunward force on the dipole, and the dipole must exert an equal and opposite force on the region 1 current loop. This turns out to be a big force, typically comparable to or bigger than the Chapman–Ferraro force; thus, it must act on the ionospheric end of the region 1 current loop where there is sufficient mass to withstand it. The dipole interaction thus adds to the drag exerted by the solar wind. Thus, the mode of force transfer between the solar wind and the Earth by thermospheric drag involves two drag-producing mechanisms in the thermosphere. There is the direct and easy to comprehend horse-pulling-a-barge mechanism and the somewhat surprising, not previously recognized dipole interaction mechanism. Is there a horsepulling-a-barge-like metaphor for the region-1current-dipole-interaction mechanism? One can think of it as a DC motor in which the geomagnetic
919
field is the motor’s permanent magnet and the neutral wind flywheel is its armature. To appreciate the analogy, think of a common terrestrial example. A hydroelectric power plant takes energy out of flowing water and delivers it as energy (not momentum) in the form of a DC (to fit the analogy) Poynting’s flux over power lines a long way to where a DC electric motor plugged into an electrical outlet receives it. The motor consists of a permanent magnet and an armature through which the current from the remote generator flows. The current interacts with the permanent magnetic to create a torque that turns the armature. The only issue involving momentum is one of bolting the motor down so that the torque exerted on the armature can be absorbed by something with a huge moment of inertia, like the Earth. The generator back at the power plant does not supply the torque, nor does the stream of water that turns the generator. They just supply the energy and leave torque balance to the motor and its fastening. The analogy to our case is more or less perfect. The balance of force between the thermospheric flywheel as armature and the geomagnetic field as permanent magnet is a local affair in which the tailward force in the thermosphere is balanced by an equal and opposite force on the interior of the Earth; the solar wind just supplies the energy to turn the flywheel via Poynting’s flux down the region 1 current loop. 6. Summary Thought of as a blunt body standing in the solar wind, the magnetosphere experiences an aerodynamic drag. This drag must be transferred to the body of the Earth since it is too big for the resident magnetospheric mass to withstand. The solar wind–magnetosphere–ionosphere–thermosphere system has two distinct ways to transfer the drag from the magnetopause, where the solar wind exerts it, to the Earth which absorbs it: (1) a dipole interaction mode, and (2) an thermospheric drag mode. Both modes operate to some degree most of the time. The dipole interaction mode is conveyed primarily by the Chapman–Ferraro current and is usually the dominant force transferring mechanism. The thermospheric drag mode of force transfer is conveyed by the region 1 current system and dominates at times of major magnetic storms. In it two distinct mechanisms operate to accelerate the thermosphere: a direct horse-pulling-a-barge mechanism and an indirect DC motor mechanism.
ARTICLE IN PRESS 920
G.L. Siscoe, K.D. Siebert / Journal of Atmospheric and Solar-Terrestrial Physics 68 (2006) 911–920
The DC motor mechanism is typically an order of magnitude stronger than the other. Thus, the direct drag that the solar wind experiences in this mode at the high-altitude end of the region 1 current loop is considerably bigger in the ionosphere at the lowaltitude end. The amplified drag appears to be needed to account for observed high-latitude thermospheric winds associated with IMF Bz. Acknowledgments GLS was supported in part by the National Science Foundation under grant ATM-0220396 and by the CISM project which is funded by the STC Program of the National Science Foundation under Agreement Number ATM-0120950. The Integrated Space Weather Prediction Model (ISM) was developed by Mission Research Corporation under contract from the Defense Threat Reduction Agency, Keith Siebert principal investigator. References Atkinson, G., 1978. Energy flow and closure of current systems in the magnetosphere. Journal of Geophysical Research 83, 1089–1103. Chapman, S., Ferraro, V.C.A., 1931. A new theory of magnetic storms. Terrestrial Magnetism and Atmospheric Electricity 36, 77–97 and 171–186. Fedder, J.A., Slinker, S.P., Lyon, J.G., Russell, C.T., Fenrich, F.R., Luhmann, J.G.A., 1997. A first comparison of POLAR magnetic field measurements and magnetohydrodynamic simulation results for field aligned currents. Geophysical Research Letters 24, 2491–2494. Goncharenko, L.P., Salah, J.E., Foster, J.C., Huang, C., 2004. Variations in lower thermosphere dynamics at midlatitudes during intense geomagnetic storms. Journal of Geophysical Research 109, A04304.
Le Me´haute´, B., 1976. An Introduction to Hydrodynamics and Water Waves. Springer, New York. Merkine, V.G., Milikh, G.M., Sharma, A.S., Papadopoulos, K., Lyon, J., Goodrich, C., 2005. Effect of anomalous electron heating on the transpolar potential in the LFM global MHD model. Geophysical Research Letters 32, L22101. Midgley, J.E., Davis, L., 1963. Calculation by a moment technique of the perturbation of the geomagnetic field by the solar wind. Journal of Geophysical Research 68, 5111–5123. Richmond, A.D., Lathuille`re, C., Vennerstroem, S., 2003. Winds in the high-latitude lower thermosphere: dependence on the interplanetary magnetic field. Journal of Geophysical Research 108 (A2), 1066. Schieldge, J.P., Siscoe, G.L., 1971. An empirical determination of aerodynamic factors for the magnetosphere. Cosmic Electrodynamics 2, 141. Siscoe, G.L., 1966. A unified treatment of magnetospheric dynamics. Planetary and Space Science 14, 947–967. Siscoe, G.L., 1983. Solar system magnetohydrodynamics. In: Carovillano, R.L., Forbes, J.M. (Eds.), Solar-Terrestrial Physics. D. Reidel Publishing Co., Dordrecht, Holland, pp. 11–100. Siscoe, G., 2001. 70 years of magnetospheric modeling. In: Song, P., Singer, H.J., Siscoe, G.L. (Eds.), Space Weather, Geophysical Monograph 125. American Geophysical Union, Washington, DC, pp. 211–227. Siscoe, G., Raeder, J., Ridley, A.J., 2004. Transpolar potential saturation models compared. Journal of Geophysical Research 109 (A9), A09203. Spreiter, J.R., Alksne, A.Y., 1969. Effect of neutral sheet currents on the shape and the magnetic field of the magnetotail. Planetary and Space Science 17, 233–246. Spreiter, J.R., Summers, A.L., Alksne, A.Y., 1966. Hydromagnetic flow around the magnetosphere. Planetary and Space Science 14, 223–253. White, W.W., Schoendorf, J.A., Siebert, K.D., Maynard, N.C., Weimer, D.R., Wilson, G.L., Sonnerup, B.U.O¨., Siscoe, G.L., Erickson, G.M., 2001. MHD simulation of magnetospheric transport at the mesoscale. In: Song, P., Singer, H.J., Siscoe, G.L. (Eds.), Space Weather, Geophysical Monograph 125. American Geophysical Union, Washington, DC, pp. 229–240.