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Keywords:

  • Saturn;
  • magnetosphere;
  • MHD simulation

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[1] We have carried out a global magnetohydrodynamic simulation study of the dynamic response of Saturn's magnetosphere to northward IMF. The response can be separated into three states. Early in the simulation (state 1) vortices form on the dayside magnetopause and propagate tailward. They form first in the morning and then in the afternoon. The flows around the dawn vortices are clockwise while double vortices form at dusk with both clockwise and counterclockwise flow. The magnetopause vortices are like those associated with the Kelvin-Helmholtz instability. Shortly after the northward IMF reaches the subsolar magnetopause reconnection begins at the equator. Later the reconnection occurs above and below the equator creating magnetic O-regions at the magnetopause (state 2). Finally late in the simulations a series of neutral lines forms in the tail (state 3).

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[2] Saturn's magnetosphere was originally thought to have aspects similar to both Jupiter and the Earth with both internally-driven and solar wind-driven dynamics. However, both Cassini observations and recent simulations have shown Saturn's magnetosphere to be unique. For example, we used three-dimensional magnetohydrodynamic (MHD) simulations to investigate the influence of the interplanetary magnetic field (IMF) on Saturn's magnetosphere [Fukazawa et al., 2007, and references therein] and found that the subsolar magnetopause and bow shock positions are relatively sensitive to changes in the solar wind dynamic pressure (more like Jupiter than the Earth) but insensitive to changes in the IMF (unlike either Jupiter or Earth).

[3] Most surprisingly we found that the plasma sheet was dominated by vortices for all IMF orientations (unlike either Jupiter or the Earth). For a simulation without an IMF we found that the vorticity was generated near the dawn magnetopause where the rotating flows and solar wind flow are opposite. For southward IMF the vorticity was generated by the interaction of flows associated with weak cusp reconnection and rotation while for northward IMF vortices formed on both the dawn and dusk sides. These phenomena are related to a region like the “cushion” identified at Jupiter as a transition region between the magnetopause and the rotation dominated flows of the middle magnetosphere. Under the average solar wind condition, the ratio of cushion region thickness to the magnetopause distance at Saturn is smaller than that of Jupiter [see Fukazawa et al., 2006].

[4] The earlier flybys of Pioneer 11 and Voyager 1 and 2 provided us with a picture of the overall configuration of Saturn's magnetosphere while now the Cassini orbiter is providing us with a view of magnetospheric dynamics. In this paper we use our MHD simulations to examine the dynamics of Saturn's magnetosphere. In particular we will present results for the response of the magnetosphere to a northward IMF. The emphasis of this paper is on the sources of the tail vorticity and the nature of dayside reconnection. In section 2 we briefly describe the simulation model. In section 3 we present the results showing the formation of vortices on both the dawn and dusk magnetopauses while in section 4 we examine reconnection at the dayside magnetopause. Our interpretation is in section 5.

2. Simulation Model

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[5] Our Kronian simulation model is based on the code developed for Jupiter's magnetosphere [Ogino et al., 1998] and described by Fukazawa et al. [2007]. In this section we briefly review the simulation model. We launched an unmagnetized solar wind with a dynamic pressure of ρvsw2 = 0.0083 nPa (vsw = 300 km s−1) and a temperature of 2 × 105 K from the upstream boundary of the simulation box and solved the normalized resistive MHD equations as an initial value problem.

[6] The Kronian magnetosphere was modeled on a 602 × 402 × 202 point Cartesian grid with grid spacing of 0.3 RS (1 RS = 60,040 km) thus the simulation domain covers the region, −120 < X < 60 RS, −60 < Y < 60 RS, 0 < Z < 60 RS. In the simulation the magnetic field (B), velocity (v), mass density (ρ) and thermal pressure (p) are maintained at solar wind values at the upstream boundary. Symmetry boundary conditions are used at the equator (Z = 0) while free boundary conditions (plasmas freely leave the boundary) are used at the top, sides and downstream boundaries. Our simulation started from a static equilibrium that included corotating flows, pressure gradients, the J × B force and gravity. At the inner boundary the parameters are fixed to those from the equilibrium evaluated at r = 5 RS. The simulation quantities are connected with the inner boundary through a smooth transition region (5 < r < 6.5 RS). The magnetic field is directed oppositely to that at Earth. The normalization factors for B, v, ρ, and p are given by the dipole magnetic field, the Alfvén velocity at the planetary surface VA = 4,359 km/s, the plasma mass density of the ionosphere ρs = 1.67 × 10−17 kg m−3 and the magnetic pressure at the planetary surface PS = 3.19 × 10−4 Pa. For simplicity we used 20,000 nT for the main dipole (g10) rather than the Cassini value of 21,084 nT [Dougherty et al., 2005]. This makes an 8 nT difference at the inner boundary of the simulation.

[7] Cassini observations indicate that the plasma is mostly H2O+ around the moon Enceladus at r = 3.96 RS and the source rate for Enceladus has been estimated to be between 3.0 × 1027 and 1.0 × 1028 H2O s−1 [Tokar et al., 2006; Pontius and Hill, 2006; Burger et al., 2007; Khurana et al., 2007]. The inner boundary condition allows plasma sources at all azimuths not just at Enceladus location. The source rate through a surface at 7 RS in our simulation is 1.1 × 1028 H2O s−1 or 2 × 1029 AMU s−1 which is at the top of the inferred range.

3. Formation of Flow Vortices

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[8] We have examined two simulations for northward IMF in detail. For the first (1) we started the simulation with a northward IMF while in the second (2) we first ran a simulation with a southward IMF and then turned the IMF northward. In general the simulations gave very similar results. Some results from simulation (2) were presented in Fukazawa et al. [2007]. We ran these simulations with an IMF of 0.4 nT [Ness et al., 1981]. The IMF was held constant for 60 hours. Our primary reason for keeping the IMF constant was to see if a quasi-steady magnetosphere resulted. The magnetosphere did become quasi-steady after about 40 hours. Note an examination of Cassini magnetic field data in the solar wind indicates that long intervals during which the IMF keeps one sign are common at Saturn.

[9] In Figure 1 we have plotted the vorticity perpendicular (Figure 1, top) and the magnitude of the vorticity parallel (Figure 1, bottom) to the magnetic field in the equatorial (Figure 1, left) and dawn-dusk meridian planes from simulation (1). A green line showing the open-closed field line boundary has been added to the equatorial perpendicular vorticity panel. A movie of the vorticity is in the auxiliary material of this paper. We have identified three characteristic states in the magnetospheric response to a northward IMF. They were found in both simulations. Early in the simulation (state 1) tailward propagating vortices formed on the pre-noon magnetopause. The vortices first appear at about 1000LT (local time) about 7 hours into both simulations (see Animation S1 of the auxiliary material). The state 1 snapshot in Figure 1 was taken 18 hours into the simulation just as similar vortices started on the afternoon magnetopause at about 1500LT. On the dayside the vortices are very well formed structures, however as they propagate tailward past dawn and dusk they become less well organized.

image

Figure 1. The magnitudes of the perpendicular vorticity to (top) the magnetic field and (bottom) the parallel vorticity in the equatorial plane. The results at (left) t = 18 hours, (middle) t = 29 hours, and (right) t = 40 hours from simulation (1). The green line in Figure 1 (top) shows the open-closed field line boundary. The isolated closed green lines in the tail are plasmoids.

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[10] In state 2 (29 hours) the amplitude of the boundary waves has decreased and a well defined cross-tail neutral line has formed in the tail. The location of this neutral line is indicated by the green line extending across the tail in Figure 1 (top). Note also that closed field lines extend down the tail at this time. The open-closed field line boundary looks like a U turned on its side. Although the neutral line remains relatively fixed in state 3 (40 hours) the closed field line region extends over 100RS down the tail on both the dawn and dusk flanks of the magnetosphere. Late in the simulation a series of magnetic O-regions were launched down the tail. They have a period of about 1 hour.

4. Reconnection at the Sub-Solar Magnetopause

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[11] Reconnection began at the subsolar magnetopause about 5 hours after the northward IMF entered the simulation box. A three dimensional (3D) view of magnetic field lines has been plotted in Figure 2 (right). Open field lines have been removed so that the magnetic structure near the equator is easier to see. The field lines have been superimposed on a color contour plot giving the magnetic field magnitude. Figure 2 (left) shows field lines projected into the noon-midnight meridian plane. The results for 22.5 hours into simulation (1) are plotted in Figure 2 (top). Up until this time the reconnection was very much like that seen in simulations of the Earth or Jupiter in that it occurred right at the sub-solar point. However, at about 22.5 hours (beginning of state 2) a small magnetic O-region formed. Note in the 3D plot that the O-regions initially are confined to a region very close to noon. By 39.75 hours (Figure 2, bottom) the magnetic O-region at noon has grown and the region containing O-regions extends along both the dawn and dusk sides of the magnetopause. The movie shows that the O-regions seem to propagate tailward along both flanks of the magnetosphere.

image

Figure 2. Magnetic field lines showing the formation of magnetic O-regions at the dayside magnetopause. (left) The magnetic field lines have been plotted in the noon-midnight meridian plane. (right) A three dimensional rendering of the field lines. The colored spectrogram gives the magnitude of the magnetic field. The results are from (top) t = 22.5 hours and (bottom) t = 39.75 hours from simulation (1).

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5. Discussion

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[12] Figure 3 is a cartoon showing the changes in the magnetospheric configuration in our simulations. In both of our simulations, the arrival of northward IMF leads to the formation of vortices propagating tailward along first the dawn side magnetopause and then along the dusk side magnetopause (state 1). The vortices grow and they propagate tailward until they reach approximately dawn and dusk after which they become disorganized. This breakup occurs where the shear in the flow velocity decreases. Since in the morning the solar wind flow is opposite to planetary driven rotational flows there is flow shear in the region where the vortices are found. We believe that a shear driven instability like the Kelvin-Helmholtz (KH) instability may be responsible for this wave-like behavior. Jupiter like Saturn has rotational flows but similar waves are not found in our Jupiter simulations [Fukazawa et al., 2006]. At Earth it is well known that the KH instability occurs along the flank of magnetopause for the northward IMF (recall the magnetic polarity of Saturn is opposite to that of the Earth), however for southward IMF the magnetic shear is thought to stabilize the boundary.

image

Figure 3. Schematic diagram showing the response of Kronian magnetosphere to northward IMF.

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[13] The vortices on the dusk side did not form until after those on the dawn side. Careful examination of the dusk side results indicates that the vortices did not form until flow toward Saturn from the magnetotail associated with reconnection reached the dusk magnetopause. The vortices on the dawn side have a single clockwise flow direction while those on the dusk side are double with counterclockwise flow nearest the magnetopause and clockwise flow nearer Saturn. This results because the flow from the neutral line is opposite to the solar wind flow near the boundary and opposite to the rotational flow nearer Saturn [Fukazawa et al., 2007].

[14] Dayside reconnection starts first near the subsolar point in our Saturn simulations much as it does in simulations of Jupiter or the Earth. However, later in the simulation the reconnection site moves off of the equatorial plane to two locations at higher latitudes. In Figure 4 we have plotted the thermal plus magnetic pressure at 22.5 hours minus that at 16.5 hours. The snapshot of the field at 22.5 hours in Figure 2 was taken just as the higher latitude reconnection began while the reconnection was at the subsolar point at 16.5 hours. In the 6 hours between these snapshots the pressure near the dayside magnetopause decreased by about 50%. When this happened the solar wind pushed the magnetopause toward Saturn changing the shape of the dayside magnetopause (see the sketch in state 2 of Figure 3). This caused the location of the reconnection to move away from midnight since anti-parallel reconnection is important in MHD simulations [Park et al., 2006].

image

Figure 4. The difference between the thermal and magnetic pressure at 22.5 hours and 16.5 hours from simulation (1) in the noon-midnight meridian and equatorial planes.

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[15] The vortices seem to influence the reconnection in two ways. We have plotted flow vectors and BZ in the equatorial plane in Figure 5 (top) and magnetic field lines and BZ in Figure 5 (bottom) at 16.5 hours in simulation (1). First the dayside vortices alter the flow of plasma to the magnetopause area (see Figure 5, top) from the dawn side magnetosphere leading to the reduction in pressure in Figure 4. In addition IMF and magnetospheric flux tubes become twisted by the vortices. By the time the vortices reach dawn the flow around the vortex brings IMF flux tubes (magenta) within the magnetosphere. These twisted flux tubes reconnect with magnetospheric flux tubes (white) forming the yellow loops. Recall that at this time the reconnection at noon was at the subsolar point and the dayside O-regions had not yet formed. La Bell-Hamer et al. [1988] have reported island formation similar to this in MHD simulations with the KH instability.

image

Figure 5. (top) Plasma flow vectors (white arrow) and BZ in the equatorial plane and (b) magnetic field lines across a flow vortex at 16.5 hours in simulation (1). The scale for BZ is from 2nT to −2nT. Closed magnetic field lines are white, IMF field lines are magenta and magnetic O-regions are yellow.

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[16] Finally late in the simulations (state 3 in Figure 3) a series of small magnetic O regions were launched down the tail at about 1 hour intervals. They were ejected from the neutral line and may be triggered by the extension of dawn and dusk side magnetic field lines. In another simulation, we found that the interval lengthened when the dynamic pressure increased. Thus the ejections are related to the solar wind conditions and tail dynamics are related to the interaction with the solar wind.

[17] In this paper we used our MHD simulation to examine the dynamics magnetospheric vorticity at Saturn for northward IMF. The vortices form due to a shear instability like the Kelvin Helmholtz instability along the magnetopause. Eventually dayside magnetic islands form. In the tail plasmoids are ejected tailward with a periodicity of about one hour. We plan a more detailed study of the one hour periodicity in reconnection including an examination of Cassini tail observations in a follow up study.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

[18] This work was supported by Grant-in-Aid for Scientific Research from Japan Society for the Promotion of Science (JSPS) and CREST, Japan Science and Technology Agency (JST). Computing support was provided by the Information Technology Center, Nagoya University and National Institute of Information and Communications Technology (NICT). NASA directly funded the work at UCLA through grant NASA NAG05GG85G. The IMF data near Saturn were courtesy of M. Dougherty and the Planetary Plasma Interactions Node of the Planetary Data System.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Simulation Model
  5. 3. Formation of Flow Vortices
  6. 4. Reconnection at the Sub-Solar Magnetopause
  7. 5. Discussion
  8. Acknowledgments
  9. References
  10. Supporting Information

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