The Physics of Planetary Magnetospheres

Transcription

1 The Physics of Planetary Magnetospheres M. G. Kivelson UCLA With thanks to colleagues and especially Xianzhe Jia and David Southwood

2 40 minutes...a luxury... but still... Must pick and choose. What to do? A bit of background: The ideas we use are OLD. The applications are relatively new. Do not assume we have achieved the goal of understanding magnetospheres. Some idiosyncratic ways of thinking about aspects of planetary (and other) magnetospheres and the physics they reveal. ( Discussion of dirty linen.) I assume that the audience knows much about the basics of magnetospheres, but may not have thought about their properties quite as I have. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008

3 v t Some important foundations Euler (1755) v ( v+ ( v)v = )v = p + [ pg ] t ρ ρ Continuum mechanics e.g., Euler s equation (L. Euler, 1755) 1755 Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 3

4 Some important foundations Maxwell (1861) Maxwell (1861) equations grouped by Heaviside (1884) Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 4

5 Some important foundations Birkeland ~1900 Birkeland and field-aligned currents Critical to understanding magnetosphereionosphere coupling 1861 ~ Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 5

6 Some important foundations Alfvén (1950) MHD equations - Alfvén (1950) Most magnetospheric processes can be understood to lowest order using the continuum model that underlies MHD Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 6

7 Some important foundations Space is not empty - radiation belts Discovery of radiation belts Van Allen (1958) space is not empty Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 7

8 Some important foundations Reconnection Magnetic reconnection J. W. Dungey (1961) Breakdown of ideal MHD is required for this process but only in a highly localized region. The boundary conditions are still set by 1861 MHD! Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 8

9 Some important foundations Exploration of Earth s magnetosphere Exploration of Earth s (1961) and other (1973) magnetospheres Data are fundamental. Without data, 1950 theory becomes what Dessler once named astro-geo-poetry Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 9

10 Some important foundations Exploration of planetary magnetospheres Computer simulations A valuable tool but sometimes a false friend! ~ Kivelson 9/8/008 Exploration of the Solar System, UCL,

11 Magnetospheres can differ in many ways Jupiter s magnetosphere is ~100 times the scale of Earth s. Saturn, Uranus and Neptune have magnetic fields and are embedded within magnetospheres of dimensions roughly 10 times larger than Earth s. Ganymede s is close to Mercury in scale. JUPITER EARTH But what does small mean? GANYMEDE Kivelson 9/8/008 Exploration of the Solar System, UCL,

12 Big vs. small: Spatial dimensions must be related to something of physical significance Critical for a magnetosphere are: an external plasma, generally flowing and with kinetic scale lengths such as Larmor radius ρ L << radius a magnetized body with p mag at surface comparable to or greater than p total of the external plasma. Both internal and external parameters control structure. Differences and similarities should be framed in terms of dimensionless quantities... i.e., ratios. E.g., one can characterize SIZE in a physical sense by asking whether the magnetic pressure can stand off the external plasma pressure above the surface? B / μ [ ρu p + B / μ ] o of o central body and its external Kivelson 9/8/008 Exploration of the Solar System, UCL, o magnetosphere

13 Kivelson 9/8/008 Exploration of the Solar System, UCL, ] [ ] / [ / ext ext o o o u B p u B ρ μ ρ μ ] [ ] / [ / ext ext o o o u B p u B ρ μ ρ μ + + >>.. ] [ ] / [ / ext ext o o o u B p u B ρ μ ρ μ + + >> Earth Jupiter Ganymede Mercury Small and big in terms of standoff.. ] / [ ] / [ / ext o ext o o o B B p u B μ μ ρ μ + + > SMALL! very BIG rather SMALL BIG Ganymede s magnetopause lies at ~ R G, but Mercury barely stands off the external plasma above its surface.

14 What is the Mach number? (again dimensionless!) Is there a bow shock? For Mercury, Earth, Jupiter and the other gas giants [ ρ u ] ext. >> [ p + B / μoext. ] implies Mach numbers >>1. Bow shocks form and slow the flow to below the fast magnetosonic speed. In the magnetosheath: near the nose, the flow slows further around the flanks, the flow reaccelerates. For Ganymede: [ ρu ] << [ B / μ ] ext. ext. [ p] ext. << [ B / μo ] ext. implies Mach numbers <1. No upstream shock. o Spreiter et al. [1966]

15 Mercury/Ganymede: topology is the same despite greatly different forms Closed field lines (here at low latitudes both for Ganymede and Mercury). Open field lines linked to polar cap again found in both cases but the geometry differs bent back into bullet shape at Mercury and other planetary magnetospheres rising in a cylindrical shape for Ganymede We will return to a way of thinking about this difference. Kivelson 9/8/008 Exploration of the Solar System, UCL,

16 Many aspects of magnetospheric structure and dynamics can be understood using concepts of MHD Useful tools include: pressure balance, MHD waves. No E but field-aligned currents. Kinetic processes contribute (reconnection, diffusion, interchange, E ), but the boundary conditions that control those processes are established by MHD conditions. MHD discontinuity (tangential, rotational) and wave analysis give insight into the physics of the system. The basic wave excitations are illustrated to the left. Only the shear Alfvén wave carries a field-aligned component of the current! Kivelson 9/8/008 Exploration of the Solar System, UCL,

17 Bow shock: a steepened fast mode wave. Magnetopause: partly a tangential discontinuity and elsewhere, largely a rotational discontinuity. Across the discontinuity, rotational: field lines connect the solar wind to the polar cap ionosphere with no sharp change of field or density magnitudes. tangential: pressure balances but both B and thermal pressure can change across boundary. External boundaries as MHD waves/discont. Kaymaz et al., 1994 Kivelson 9/8/008 Exploration of the Solar System, UCL,

18 Some internal boundaries Plasma sheet boundary: Slow mode front: ~ pressure balance with increase of thermal pressure balancing decrease of magnetic pressure. Polar cap boundary separates anti-solar (sunward) flows on open (closed) field lines. Mixed. Plasmapause: A different sort of boundary - a separatix bounding flow streamlines that encircle the planet (Brice, 1967). HOW IS COROTATIONAL FLOW IMPOSED? Kivelson 9/8/008 Exploration of the Solar System, UCL,

19 Why does plasmaspheric plasma ~corotate with the planet? (Earth, Jupiter, Saturn) Source of plasma in the plasmasphere is at or close to the planet, i.e., the ionosphere at Earth or a close-in moon at the outer planets. At Earth the plasma diffuses out from ionosphere along a flux tube. In the absence of forces, outward moving plasma near the equator loses angular velocity (L = ρω r = const.) When plasma diffuses upward along flux tube, its ω decreases as r increases. The plasma is frozen to the field - the field bends back (considerably at Jupiter, negligibly at Earth)! j generated: when the plasma slows, the field curls. 1 (sinϑ B ϕ ) = μ o j r rsinϑ ϑ Near the equator, j r (<0) exerts force to accelerate the slowed plasma), but j must be divergenceless, so FACs couple to ionosphere. projection of field lines radial current

20 Current closes in ionosphere There it exerts a force to decelerate ionospheric rotation. Normally the atmosphere can provide the momentum needed to keep the ionosphere corotating with the surface, but it is also possible for the two ends to compromise so that rotation ends up being a bit slower than corotation along the entire flux tube. Please note that this argument does not invoke an E-field. In ideal MHD, E = -vxb, and E is a consequence of the flows. May be convenient to think in terms of E but not necessary. FOR EARTH. Reverse arrows for Jupiter/Saturn! Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 0

21 Planetary rotation: Is it important? Body Mercury Earth Jupiter Ganymede Flow time 0.5 to 1.5 min 10 to 30 min 16 to 40 hours -5 minutes Rotation period 59 days 1 day 10 hours No rotation The time to impose changes of external conditions on the magnetosphere is of order the time required to flow from the nose of the magnetosphere to the distant neutral line, or, let s say roughly 4 to 10 times the distance to the nose of the magnetosphere. This time may be usefully compared with the rotation periods. Evidently rotational effects matter most at Jupiter. Rotation is absent at Ganymede Insignificant at Mercury. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 1

22 MHD and dynamics A magnetosphere is a highly coupled system. When one end of a flux tube moves, the motion of the other end must correspond. Can discuss in terms of current circuits such as the substorm current wedge. similar to the previous argument. The concept is useful but flawed. Plasma currents not confined to wires! Currents are defined by curl of B. (From j get B through integrodifferential equations such as Biot-Savart law.) More appropriately: distant parts of the system coupled by WAVES. How does that work?

23 What happens, for example, when reconnection starts in the tail? Some equatorial plasma moves earthward. The field near the equator bends, partly out of the plane of the drawing. Bend out of the plane Alfvénic perturbation. It drives j along the background field. At the ionosphere, the signal is partially transmitted/reflected (impedance mismatch). When the perturbation reaches the opposite ionosphere, it is partially transmitted and partially reflected. Transmitted signals produce j that sets ionosphere into equatorward motion. Signals stop when both ends move together. On the ground, this is recorded as a high latitude Pi with decreasing period. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 3

24 Analogous arguments apply to the perturbations induced by a conducting moon (e.g., Io) Interaction with the moon slows the flow near the equator. We usually show the perturbations (the Alfvén wing picture) projected into the prime meridian plane of the moon. Here the slowed flow makes the perturbation look compressional. But the field also bends outward from the prime meridian so that B does not change. ALFVÉNIC prtrbtn. The signal goes to the ionosphere, possibly partially reflected at the boundary of the Io torus. Mismatch of impedance leads to partial transmission and partial reflection. Multiple bounces produce nested decametric arcs. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 4

25 Why does the front bounding the Alfvén wing tilt? Information is carried by Alfvén waves only along the background field in the plasma rest frame. But the plasma is in motion relative to the moon. In the moon s rest frame, the propagating wave is found at an angle to the field given by tan α = v/v A This angle defines the Alfvén characteristics B I shall show you that these characteristics also determine the loci of planetary magnetopauses! V A α v Front Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 5

26 In the solar wind, the Alfvén speed is << u. (Take B sw southward and M A ~6 then α = tan -1 M A ~ 80º. ) The bullet-shaped magnetospheres of the planets in the segments with flux tubes connected to the solar wind arises because of the large Alfvén angle implied by high M A. Does that really work? Yes. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 6

27 For Earth, Jupiter, etc., an open magnetopause is the locus of the kink propagating away from the reconnection point into the solar wind, i.e., the Alfvén wing front previously introduced [see (a)]. (c) shows that the flux tubes bulge. Those bulges or bends are imposed by the j carried by Alfvén waves. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 7

28 u x and field lines in the XZ plane In Jupiter s magnetosphere, u is small compared with the Alfvén speed. With M A ~ 0.7 near the center of the plasma torus, Ganymede s Alfvén wing bends by ~35º. Simulation of X. Z. Jia, UCLA, 008 Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 8

29 Simulation: a valuable tool with pitfalls. We start with Ganymede! Ganymede s magnetosphere provides a useful model for investigating simulations. Upstream conditions are steady. One cannot argue that discrepancies between observations and simulations arise from changes in upstream conditions. Small scale and constrained Alfvén speeds enables us to use small grid scales over large parts of the system. Reasonably good coverage in multiple Galileo flybys enables us to test success of predictions in different parts of the magnetosphere. The us referred to above is Xianzhe Jia, UCLA graduate student. I thank him for his contributions. Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 9

30 Jia s MHD model of Ganymede s magnetosphere has enabled us to establish how sensitive results are to: effects of changing grid sizes varied inner boundary conditions at Ganymede s ionosphere. different ways of modeling the resistivity of the plasma and the moon. Grid sizes were critical to getting the magnetopause location and spatial scale correctly. Current density and current paths can be seriously misrepresented if spatial grids are too large. Kivelson 9/8/008 Exploration of the Solar System, UCL,

31 Ganymede s magnetosphere Intrinsic magnetic field that creates a minimagnetosphere. As at Io, interaction with magnetospheric plasma drives current towards and away from Jupiter.. From Jia s simulation, 007 Ganymede field lines and parallel current Kivelson 9/8/008 Exploration of the Solar System, UCL,

32 Ganymede HST STIS image nm 10/30/1998 M. McGrath MOP 007 Simulations are tested by comparison with in situ measurements from GLL passes and from aurora, etc. Here good agreement with HST images. Facing +X direction, flow into the page +Y this is a composite image that includes By >0 and By = 0 orientations Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 X. Jia (UCLA) 3

33 Ganymede intrinsic field magnetosphere aurora, latitudinal dependence of surface weathering McGrath et al. Jupiter, 004. Khurana et al., 007 Kivelson 9/8/008 Exploration of the Solar System, UCL,

34 Inner boundary condition The simulation evolved from the version developed by J. Linker to simulate Io. Linker assumed v=0 at 1.05 R G For Ganymede, this assumption led to very odd behavior near the ionosphere (neither source nor sink) that propagated through the entire simulation. So Jia dropped that assumption and tried others to get solutions that I shall show you in the next slide. First Jia tried constraining the tangential flow at the ionosphere. You will see that this gives a totally nonphysical solution. A more valid assumption is to require continuous v perp (to B). This means that the ionospheric part of the flux tube moves with the rest of it. Flow along B is allowed. Kivelson 9/8/008 Exploration of the Solar System, UCL,

35 V θ and V φ continuous V perp continuous Very different flows over the polar cap and very different Vpc, but magnetic signatures change little on 6 GLL passes.

36 V θ and V φ continuous V perp continuous Magnetic signatures on GLL flybys for different inner b.c., little difference. Fit not fully satisfactory for either. What other simulation parameters matter? Resistivity, both inside Ganymede and elsewhere matters. Kivelson 9/8/008 Exploration of the Solar System, UCL,

37 V perp continuous η Resistivity r (R G ) diffeta13 diffeta17 Using bc giving v perp continuous, change the resistivity of the interior of the moon.(small outside) The reconnection rate changes markedly, as do the flow out of polar cap and the form and location of the magnetopause. lower interior resistivity higher interior resistivity Kivelson 9/8/008 Exploration of the Solar System, UCL,

38 V perp continuous η r (R G ) diffeta13 diffeta17 Resistivity This fit to B is almost too good to be true, but results from use of physically sensible b.c. Fits to other passes are as good. Kivelson 9/8/008 Exploration of the Solar System, UCL,

39 What about simulations of Earth s magnetosphere? Two runs for close to same conditions of sw, one from BATSRUS and one from GGCM. When the IMF turns southward, the dayside magnetosphere is eroded far more in the OpenGGCM (in which the resisitivity depends on the local current density) than in the BATSRUS code (which assumes ideal MHD wherein only numerical resistivity leads to reconnection). Also, the V x component of flow in the ionosphere differs for the two simulations. Correspondingly, the cross polar cap potential in the OpenGGCM is much higher than the BATSRUS result. Kivelson 9/8/008 Exploration of the Solar System, UCL,

40 Solar wind input (5 nt north, then 5 nt south) BATSRUS OpenGGCM Kivelson 9/8/008 Exploration of the Solar System, UCL,

41 Northward B z BATSRUS: Ideal MHD OpenGGCM: Current-dependent resistive MHD Kivelson 9/8/008 Exploration of the Solar System, UCL,

42 Southward B z BATSRUS: Ideal MHD OpenGGCM: Current-dependent resistive MHD Kivelson 9/8/008 Exploration of the Solar System, UCL, 008 4

43 BATSRUS: Ideal MHD OpenGGCM: Current-dependent resistive MHD Kivelson 9/8/008 Exploration of the Solar System, UCL,

44 Lesson Put the physics into your simulations. See how the simulated magnetosphere works. But be very cautious about inferring magnetospheric structure and/or dynamics from the results of computer simulations. Anything you think you have learned must be tested by comparison with real data. Kivelson 9/8/008 Exploration of the Solar System, UCL,

45 Turning to kinetic processes Rotation modifies familiar processes. Assume rigid corotation. then the momentum equation becomes nˆ nmσu = ( p + B b / μo ) Bb / μo R + δρ[ g Ω ( Ω r)] c In a rotating magnetosphere, gravitational acceleration may dominate at the ionospheric end of a flux tube and rotational acceleration at the other end. Can t simplify! Spatial dimensions need to be considered. A 10 kev heavy ion (m =0 AMU) moving outward from Jupiter covers 1 R J in 3 min. In the outer part of the magnetosphere, flux tube lengths are of order 100 R J. A round trip bounce may require a full Jovian rotation period (10 hours). The nd adiabatic invariant is not conserved. Kivelson 9/8/008 Exploration of the Solar System, UCL,

46 Centrifugal acceleration and its effects on magnetospheres of rapidly rotating planets Interchange can become important. Jupiter and Saturn have important sources of heavy ions deep within the magnetosphere. System energy is minimized by interchange of full and depleted flux tubes. Leads to a fundamental instability that is an important transport mechanism. Kivelson 9/8/008 Exploration of the Solar System, UCL,

47 Interchange conditions: The condition for instability is determined by relative flux tube content...but the rate of transport is limited by the resistance of the ionosphere because in interchange the entire flux tube must move as a unit. Kivelson 9/8/008 Exploration of the Solar System, UCL,

48 Interchange event at Jupiter Kivelson 9/8/008 Exploration of the Solar System, UCL,

49 Take away messages Magnetospheres are complex systems with properties resulting from interactions at scales from local to global, all highly coupled by field-aligned currents (carried by MHD waves). Thinking in terms of waves is useful. Spatial scales matter because coupling is not instantaneous, because the relevant forces may differ in regions near and far from the planet, because it takes finite times for particles to move from one end of a field line to another. Simulations are invaluable tools but we should use them to identify what to look for in our data. We should not think that extracting results from simulations has proved anything. Kivelson 9/8/008 Exploration of the Solar System, UCL,

50 I look forward to hearing other talks Please come share your interests with me during the next few days. I look forward to hearing about your work. Kivelson 9/8/008 Exploration of the Solar System, UCL,