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GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L12103, doi:10.1029/2007GL029315, 2007
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Measuring the stress state of the Saturnian magnetosphere J. S. Leisner,1 C. T. Russell,1 K. K. Khurana,1 and M. K. Dougherty2 Received 10 January 2007; revised 11 April 2007; accepted 15 May 2007; published 19 June 2007.
[1] The dynamics of a planetary magnetosphere can be quantified by subtracting the system’s ‘‘ground’’ state from the observed state and tracking their difference. When a magnetosphere is stressed, by external and internal forces, the magnetic field lines become stretched or compressed. In this paper, we construct an index of the stress state of the Saturnian magnetosphere using magnetometer measurements made in the equatorial inner magnetosphere. This index is analogous to the Dst index produced for Earth’s magnetosphere and a stress index created for Jupiter from the Galileo magnetometer data. This index identifies infrequent large perturbations of the magnetosphere from its ground state, and the smaller deviations that are consistent in duration and magnitude with those expected from pressure variations in the solar wind. Citation: Leisner, J. S., C. T. Russell, K. K. Khurana, and M. K. Dougherty (2007), Measuring the stress state of the Saturnian magnetosphere, Geophys. Res. Lett., 34, L12103, doi:10.1029/2007GL029315.
1. Introduction [2] A planet’s magnetosphere is shaped by the stresses acting on it, stresses both external and internal. Externally, the principal source of stress is the flowing solar wind. Internally, stresses on the magnetosphere are provided by the plasma, both hot and cold, in the rapidly rotating magnetosphere. When any of these sources of stress change, external or internal, the configuration of the magnetic field deep inside the magnetosphere is modified, as the pressure gradients change to affect a near force balance. [3] When the solar wind encounters a magnetosphere, it is deflected around the obstacle, compressing it. This increases the magnetic field strength over much of the equatorial region of the magnetosphere. If the solar wind magnetic field reconnects with the magnetosphere, or if an internal mass source is present in a rapidly rotating magnetosphere, the magnetic field may be stretched. Heating of the plasma will also stretch and weaken the magnetic field. While each of these last three stresses alter the overall configuration of the magnetosphere differently, they all result in a reduction in the equatorial field. [4] In order to study the dynamical states of the magnetosphere, it is useful to have a quantitative measure of its stress. Various indices have been developed to monitor the Earth’s magnetospheric stress. For example, the AE index monitors the auroral currents which respond to the tangential stress on the magnetopause and their effects on magne1 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA. 2 Space and Atmospheric Physics Group, Blackett Laboratory, Imperial College London, London, UK.
Copyright 2007 by the American Geophysical Union. 0094-8276/07/2007GL029315$05.00
tospheric convection. The Dst index monitors both the compression by the solar wind and the inflation associated with heating of the magnetospheric plasma. [5] The Dst index is calculated from Earth’s surface field by taking near-equatorial magnetic field measurements, removing an average ‘‘quiet day,’’ and averaging them longitudinally around the planet. While the solar wind pressure and plasma of solar origin do influence this index, Dst is principally affected by the energy contained in the magnetospheric plasma [Dessler and Parker, 1959; Sckopke, 1966]. The energization of the magnetosphere and the build up of Dst is principally controlled by changes in the southward magnetic flux convected by the solar wind to the magnetosphere. [6] At Saturn, however, the interplanetary magnetic field is weaker, and the magnetosheath hotter, so reconnection should be less significant than at Earth [Scurry and Russell, 1991], but solar wind dynamic pressure variations should continue to be important [Crary et al., 2005; Jackman et al., 2005]. Saturn also has significant dust and ice rings, icy satellites, and a water-group neutral cloud in the inner system, surrounding the E ring between 2 and 8 Saturn radii (Rs, 1 Rs = 60,268 km). This configuration is quite different than that of either the terrestrial or Jovian magnetospheres. Nevertheless, it may be equally as dynamic, albeit on different time scales and possibly for different reasons. While the mass loading of Saturn’s magnetosphere is expected to differ in detail from that at Jupiter, the end result is similar. The magnetic field lines will be stretched outward by the particles’ centrifugal force. [7] With Galileo magnetic measurements at Jupiter, Russell et al. [2001] created an index, similar to Dst for that magnetosphere, to monitor the compression and stretching of the magnetosphere on Galileo’s passages through perijove. Now that Cassini has returned over 2 years of data from the Saturnian magnetosphere, we can construct an index that does the same for Saturn as the Dst indices do for Earth and Jupiter. From the 27 orbits available to date, we find that the majority of the time the Saturnian magnetosphere is near its quiet, or ground, state, but occasionally is greatly perturbed from it.
2. Model [8] In order to represent the ground state of the magnetosphere we use the magnetic field model of Khurana et al. [2005] which is derived from one minute averaged observations from Voyager 1 and 2 and the first four orbits of the Cassini spacecraft. The model is developed using techniques and methods employed for Earth’s magnetosphere [Tsyganenko, 1998, 2002a, 2002b] to specify internal and external fields. The model consists of modules which specify the internal axially symmetric spherical harmonic model [Davis and Smith, 1986]; the ring current and the
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Figure 1. Magnetic perturbation from magnetospheric ground state of three Cassini orbits, plotted versus equatorial distance. A positive perturbation means the southward component of the magnetic field was enhanced and a negative perturbation means that it was diminished. magnetotail current system using models of disk-shaped current sheets by Tsyganenko and Peredo [1994]; the shielding fields for the dipole and the current sheet from an axially symmetric magnetopause using Cartesian and cylindrical harmonics; and the interconnection magnetic field between solar wind IMF and the magnetosphere. [9] Initially, a symmetric, non-tilted model of the magnetosphere is constructed which has its magnetotail parallel to the Sun-Saturn line. Next, the model introduces a general deformation in which the current sheet is close to the dipole magnetic equator in the inner magnetosphere and parallel to the solar wind at large distances. The fits to the observations are good with the root-mean-square difference between the model field and the observations being equal to 2.5 nT for the overall data set.
3. Constructing the Index [10] The total energy of the energetic particles stored in the magnetosphere is proportional to the change in the magnetic field at Earth’s center [Dessler and Parker, 1959; Sckopke, 1966]. Since we cannot measure the magnetic field there, we approximate this in the Dst index by finding the average deviation of the horizontal component over the low-latitude regions (avoiding the electrojet). At Jupiter and Saturn, we do not have surface measurements, so we find the average deviation of the theta component (parallel to the dipole axis) in the inner magnetosphere from a static model field. [11] As the complete satellite coverage of a planetary magnetosphere is rare, a model field may have small differences from the magnetosphere’s observed ground state [Russell et al., 2001]. We overcome this lacuna by adjusting our model using magnetometer observations from all of Cassini’s orbits. [12] For each orbital leg, we average the difference between the data and the model into 0.1 Rs annuli. We
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bin these annuli differences from all of the orbits into dayside and nightside measurements and subtract each bin’s median value. It is this subtraction of the bins’ median values that compensates for any deficiencies in the modeling of the current systems. We take the resulting residuals as the perturbation of the magnetic field from the nominal Saturnian field. [13] When we examine these residuals with respect to local time, we find that the region within 45 degrees of midnight shows a high level of variability that is not observed elsewhere on the orbit. During an orbit that is otherwise representative of the magnetosphere’s ground state, the tail residual can reach +/ 5 nT. This is perhaps due to dynamic tail processes not represented in our model whose effects are restricted to the midnight sector. We guard against this variable region from affecting our stress index by excluding those measurements from our calculations. [14] Lastly, we only include measurements made between 4.3 Rs, to avoid any variation due to proximity with Enceladus, and 6.3 Rs, to stay inside of the steady magnetic region described by Leisner et al. [2005]. We also examine only orbital legs where there are averages in at least at least five, out of a possible twenty, radial bins. These criteria together with the requirement of being within ten degrees of the equatorial plane exclude four of the twenty-seven orbits in our data set from consideration.
4. Results [15] At Earth, the Dst index generally ranges between 50 and 300 nT, with values outside of that range being rare. At Jupiter, the ring current strength index, averaged over each orbit, was within +/ 10 nT, with two orbits within +/ 15 nT. At Saturn, we find that the field was most often within +/ 2.5 nT of its quiet state, with a few orbits showing perturbations of up to +/ 8 nT. Figure 1 illustrates the different perturbations observed at Saturn by plotting the individual measurements that go into an index value on a compressed orbit (positive), a stretched orbit (negative), and one that does not vary much from the ground state. [16] These three orbits illustrate one of our study’s findings. For small perturbations from the ground state, the perturbation tends to be constant with radial distance, within a +/ 1 nT range. For large perturbations from the ground state, however, we find that the perturbation strongly varies with radial distance. The reason for this behavior is unclear at present. [17] The Saturnian stress index is constructed by averaging the perturbation over each orbital leg, excluding nearmidnight values. The orbital mean of these averages is the index. This index is plotted in Figure 2 for each orbit that fulfills the above criteria. A positive index indicates that the magnetosphere is compressed and a negative index indicates that it is stretched, both relative to the ground state. [18] With our stress index established, we reexamine the near-midnight perturbations, the measurements we exclude in our construction of the index. There, the local magnetic perturbation can differ from the orbit’s stress level by up to +/ 6 nT. We illustrate this behavior in Figure 3. [19] For each orbit where we have a stress level, we subtract that number from the magnetic perturbations within 45 degrees of midnight. Each point in Figure 3 is the mean
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of those differences plotted against the stress level calculated for the non-midnight portions of the orbit. The bars represent mark the range of the differences for each orbit. For comparison, we also mark the +/ 1 nT range that we find away from midnight at small stress levels. The variation in the near-midnight region is clearly not well correlated with the stress index. When the magnetosphere is near its ground state, a stress index of 0 nT, the nearmidnight region can be either compressed or extended. [20] Although we only show results using our magnetospheric model, we also performed this analysis using a simple dipole field. The results using that simple field were similar to the results found using the model field, but the variation of the magnetic perturbation within a single orbit was larger due to a dipole’s lack of local time effects. This gives us confidence that this index does not vary strongly with the model used and that use of our model is preferable to that of a dipole.
5. Discussion [21] As Cassini was approaching Saturn, the magnetometer observed regions of enhanced and reduced strength in the interplanetary magnetic field, associated with corotating interaction regions (CIRs) passing over the spacecraft, each of which were observed to last for about four days [Jackman et al., 2005]. As each of these regions reach the Saturnian magnetosphere, associated differences in the solar wind’s pressure would stress the system, either compressing it—raising the magnetic field strength near the planet—or allowing it to expand—lowering the near-planet field strength. [22] By scaling from observations made in the terrestrial magnetosphere, we can estimate the change in the magnetospheric field strength expected due to solar wind pressure changes. Russell et al. [1994] and Huang and Yumoto [2006] examined the response in the magnetic field at low-latitude ground station magnetometers due to sudden changes in the solar wind dynamic pressure when the
Figure 3. Difference in the magnetic field measurements from the stress index for each orbit, measured within 45 degrees of midnight. Each dot represents the mean difference between 4.3 and 6.3 Rs and within 45 degrees of midnight, and the associated bars mark the range of values within that region. interplanetary magnetic field was northward, removing the effects due to strong reconnection. The magnetic field strength increase was greatest at noon near the magnetic equator and could be estimated by 18.4 nT/(nPa)1/2 times the change in the square root of the dynamic pressure. For Earth, the pressure changes in that study ranged from 0.333 to 1.120 (nPa)1/2. [23] By drawing upon Earth as an example and scaling the pressure change down by a factor of 10, we expect that the magnetic field strength would then increase by around 0.5 to 2 nT, at noon, near Saturn. The majority of our calculated indices are in this predicted range and the steady nature of our observed magnetic perturbation is consistent with the observation that the solar wind magnetic field is steady for around four days at a time [Bunce et al., 2005; Jackman et al., 2005]. As suggested by the trend in Figure 2, there may also be long-term variation due to variable outgassing and mass loading at Enceladus. [24] We also note that our results show that the magnetosphere was expanded during the inbound portion of SOI, which is consistent with statements by Alexeev et al. [2006] and Jackman et al. [2005]. Later, when Cassini was outside of our method’s region of applicability, the magnetosphere became compressed.
6. Conclusions
Figure 2. Stress indices for each of orbit where Cassini made a near-equatorial pass through the inner magnetosphere.
[25] We use near-equatorial magnetometer measurements and a model of the Saturnian magnetosphere to examine the field perturbation near the planet. This perturbation is steady with both radial distance and local time, except for the nearmidnight region where field line stretching associated with dynamical processes in the tail may affect the observed difference from the nominal field. [26] By averaging the observed perturbation over each orbit, we have constructed an index of the stress state of the
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Saturnian magnetosphere. This index shows that the system spends the majority of time near its quiet state, although a few orbits show large perturbations from this level. The small stress levels are consistent with scaling the observed solar wind pressure-induced field enhancement at the Earth, and the time-steady nature of the observed perturbations is consistent with the likewise steady nature of the solar wind at Saturn. We also see what may be a long-term trend over the period of observations. More observations are needed to determine the reality of this apparent behavior.
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wind pressure enhancements, J. Geophys. Res., 111, A09316, doi:10.1029/2006JA011831. Khurana, K. K., C. S. Arridge, and M. K. Dougherty (2005), A versatile model of Saturn’s magnetospheric field, paper presented at General Assembly 2005, Eur. Geosci. Union, Vienna, Austria, 24 – 29 April. Leisner, J. S., C. T. Russell, K. K. Khurana, M. K. Dougherty, and N. Andre´ (2005), Warm flux tubes in the E-ring plasma torus: Initial Cassini magnetometer observations, Geophys. Res. Lett., 32, L14S08, doi:10.1029/ 2005GL022652. Russell, C. T., M. Ginskey, and S. M. Petrinec (1994), Sudden impulses at low-latitude stations: Steady state response for northward interplanetary magnetic field, J. Geophys. Res., 99(A1), 253 – 262. Russell, C. T., et al. (2001), Magnetic field changes in the inner magnetosphere of Jupiter, Adv. Space Res., 28, 897 – 902. Sckopke, N. (1966), A general relation between energy of trapped particles and disturbance field near Earth, J. Geophys. Res., 71(13), 3125 – 3130. Scurry, L., and C. T. Russell (1991), Proxy studies of energy transfer to the magnetosphere, J. Geophys. Res., 96(A6), 9541 – 9548. Tsyganenko, N. A. (1998), Modeling of twisted/warped magnetospheric configurations using the general deformation method, J. Geophys. Res., 103(A10), 23,551 – 23,563. Tsyganenko, N. A. (2002a), A model of the near magnetosphere with a dawn-dusk asymmetry: 1. Mathematical structure, J. Geophys. Res., 107(A8), 1179, doi:10.1029/2001JA000219. Tsyganenko, N. A. (2002b), A model of the near magnetosphere with a dawn-dusk asymmetry: 2. Parameterization and fitting to observations, J. Geophys. Res., 107(A8), 1176, doi:10.1029/2001JA000220. Tsyganenko, N. A., and M. Peredo (1994), Analytical models of the magnetic field of disk-shaped current sheets, J. Geophys. Res., 99(A1), 199 – 206. M. K. Dougherty, Space and Atmospheric Physics Group, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW, UK. K. K. Khurana, J. S. Leisner, and C. T. Russell, Institute of Geophysics and Planetary Physics, University of California, Box 951567, Los Angeles, CA 90095-1567, USA. (
[email protected])
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