Saturn's magnetospheric refresh rate

Authors


Abstract

[1] A 2–3 day periodicity observed in Jupiter's magnetosphere (superposed on the giant planet's 9.5 h rotation rate) has been associated with a characteristic mass-loading/unloading period at Jupiter. We follow a method derived by Kronberg et al. (2007) and find, consistent with their results, that this period is most likely to fall between 1.5 and 3.9 days. Assuming the same process operates at Saturn, we argue, based on equivalent scales at the two planets, that its period should be 4 to 6 times faster at Saturn and therefore display a period of 8 to 18 h. Applying the method of Kronberg et al. for the mass-loading source rates estimated by Smith et al. (2010) based on data from the third and fifth Cassini-Enceladus encounters, we estimate that the expected magnetospheric refresh rate varies from 8 to 31 h, a range that includes Saturn's rotation rate of ~10.8 h. The magnetospheric period we describe is proportional to the total mass-loading rate in the system. The period is, therefore, faster (1) for increased outgassing from Enceladus, (2) near Saturn solstice (when the highest proportion of the rings is illuminated), and (3) near solar maximum when ionization by solar photons maximizes. We do not claim to explain the few percent jitter in period derived from Saturn Kilometric Radiation with this model, nor do we address the observed difference in period observed in the north and south hemispheres.

1 Introduction

[2] Internal plasma sources load and inflate a magnetic cavity until the energy density of the trapped plasma exceeds the ability of the magnetic field to contain it. At this point, the magnetic field breaks apart, releasing plasma antiplanetward and returning plasma-depleted field lines planetward. In the absence of external perturbations, this process can display a strong clock-like repetition, like a dripping faucet, or the filling and unloading of a Japanese “Shishi Odoshi” (scare the deer) fountain.

[3] At Jupiter, quasi-periodic modulations have been observed with a period of about 2 to 3 days; the modulations have been identified in Galileo energetic particle data [Krupp et al., 1998; Woch et al., 1998, 2002; Kronberg et al., 2007], magnetic field data [Kronberg et al., 2005, 2007; Vogt et al., 2010] and Hubble Space Telescope images of the Jovian aurora [Radioti et al., 2008]. The period has been interpreted as an internal time constant of the Jovian magnetotail. Kronberg et al. [2007] (hereafter referred to as K07) described this quasi-periodic behavior in terms of a cycle of internally driven mass loading and unloading. This picture is similar to the terrestrial substorm process, which can exhibit periodicity on the order of 2–3 h [e.g., Borovsky et al., 1993], but is driven at Jupiter by internal plasma loading (mainly from the volcanic satellite Io) rather than by external plasma loading from the solar wind as at Earth. In the K07 model (illustrated for Saturn in Figure 1), forces associated with internal plasma loading stretch the planet's magnetic field causing field lines to become increasingly antiparallel. Eventually, this creates an x line that is unstable to reconnection, a portion of the magnetotail beyond the x line, a plasmoid, is torn off, and the magnetosphere returns toward the undisturbed initial state.

Figure 1.

Cartoon illustrating periodic magnetospheric reconfiguration at Saturn driven by internal mass loading. After Kronberg et al. [2007]. Panel (a) shows an approximately dipolar magnetospheric configuration with no mass loading, forces associated with internal plasma loading stretch the planet's magnetic field causing field lines to become increasingly anti-parallel, panel (b). Eventually this creates an x-line, pinch point on panel (c), that is unstable to reconnection, a portion of the magnetotail beyond the x-line, a plasmoid, is torn off, and the magnetosphere returns to the undisturbed initial state, panels (a) and (d).

[4] Jackman et al. [2009a] show evidence for occasional plasmoids, suggesting a repetition period on the order of 5–7 days and that plasmoid release occurs at a preferential longitude—which implies a mechanism linked to the planetary rotation. In a follow-up study, Jackman et al. [2011] estimate that the plasmoid release rate is actually more like one per 2.4 days and that we do not see that many because of limited spacecraft viewing opportunities (in particular, during Southern Hemisphere summer in 2006 when Cassini was executing its deep tail orbits, the spacecraft in the equatorial plane was situated below the hinged current sheet).

[5] Kronberg et al. [2007] argue that the timescale, τ, for magnetospheric loading/unloading depends on the current sheet configuration, the plasma-loading rate math formula, the downtail distance x at which tearing occurs, x, and the angular velocity Ω at that location, such that

display math(1)

where Br and Bθ are the radial and meridional magnetic field components and d is the current sheet thickness. Subscript “unstretched” corresponds to a roughly dipolar magnetic configuration (Figures 1a and 1d), and subscript “stretched” refers to values taken just before the tail collapses (Figure 1b).

[6] Equivalently, we can estimate the mass unloading timescale if we know the mass-loading rate math formula and the total mass M in the system, allowing for a much simpler expression for the refilling timescale, τ, albeit in terms of variables that are difficult to measure in practice. In order to maintain the total mass in the system, the refilling timescale, τ, must be at least M/math formula. For Jupiter, M ~ 109 kg and math formula ~ 103 kg/s [e.g., Hill et al., 1983] corresponding to τ ~ 12 days.

[7] For Saturn, estimates for M and math formula continue to vary quite widely. Arridge et al. [2007] estimated the total mass of Saturn's plasma sheet to be ~106 kg, Chen et al. [2010] estimate the total mass of the plasma sheet between 5 and 10 Rs to be ~5 × 107 kg, while Bagenal and Delamere [2011] estimate the cumulative ion mass between ~3 and 20 Rs to be 8.3 × 107 kg. Similarly, estimates for plasma production rate vary greatly: Tokar et al. [2006] estimate the Enceladus source rate to be ~100 kg/s, and Chen et al. [2010] estimate the total mass outflux at 10 Rs to be ~280 kg/s. Estimates for neutral outgassing by Smith et al. [2010] and Hansen et al. [2011] of ~200 kg/s along with ionization estimates of around 30% [e.g., Cassidy and Johnson, 2010] imply a lower ion production rate of 60 kg/s. Based on measurements derived from Cassini Plasma Spectrometer (CAPS) data Chen et al. [2010] estimate a plasma residence time of ~2 days inside 10 Rs.

[8] Although Saturn has a smaller plasma mass-loading rate than Jupiter, its magnetic field is also smaller by a factor of ~30. In fact, Vasyliünas [2008] showed that, when expressed in dimensionless form, as ratios of relevant planetary parameters (relative magnetospheric size, magnetic field strength, and the source location of the mass loading), the rate of plasma loading that Saturn can sustain before the energy density of the magnetic field is overcome is less than that of Jupiter by a factor of ~40 to 60. Vasyliünas showed that as a result of these fundamental differences Saturn's magnetosphere is intrinsically more mass loaded than the magnetosphere of Jupiter by a factor of ~4 to 6.

[9] Anticipating our results, if the 2–3 day period at Jupiter is indeed an internal time constant related to the amount of energy density Jupiter's magnetotail can contain as it is loaded and stretched by plasma loading from Io, then it follows that the equivalent timescale at Saturn is a factor of ~4 to 6 faster; we therefore expect the natural mass unloading timescale for Saturn to be between 8 and 18 h.

2 The Natural Mode of Mass Loading and Release at Jupiter and Saturn

[10] To investigate what range of periods is plausible for the magnetospheres of Jupiter and Saturn we apply equation (1) using relevant parameters as available in the literature or derived from Cassini data and listed in Table 1, using a Monte Carlo model. To compute the mass-loading rate per volume, math formula, K07 assume that the particles expand to fill a cylindrical volume of height d and radius x so that math formula = math formula/(π d x2) kg m−3 s−1, where math formula is the number of particles added per second. At Saturn, the volume that particles can expand to fill is limited on the dayside by the magnetopause with a noon local time standoff distance of ~20 Rs Kanani et al., [2010])—accordingly, we estimate the available volume to be an ellipse with Saturn at a focal distance from the origin f = x/2 − 10 (thus placing it 20 Rs in from the outer edge of the most oblate axis of the ellipse), and semimajor axis, A = (x + 20)/2 for a standard ellipse the semiminor axis, B = √(A2 − f2) = √(20x). So that in the Saturn case math formula = math formula/(πd (x/2 + 10)√(20x)) kg m−3 s−1.

Table 1. Characteristic Parameters Pretail and Posttail Collapse at Jupiter and Saturn
 JupiterSaturn
  1. aAssuming 26% ionization efficiency [Cassidy and Johnson, 2010].
Tear off distance, x, Rj70 to110Krupp et al. [2004]30 to 50Jackman et al. [2009b] Mitchell et al. [2005]
Cross tail velocity, v (Ω = v/x) (kms−1)50 to 300Krupp et al. [2001]100 to 200Thomsen et al. [2010]
Particle loading rate, math formula (kgs−1)100 to 1000 4 to 250Smith et al. [2010]a
Radial field magnitude at x line, Brrec (nT), where x = radial distance in Rj32,514.5 x−1.97Bunce and Cowley [2001a]350 x1.4Fit to Cassini [2006] data
Meridional field at x line, Bθrec (nT)0.193 x−0.87Bunce and Cowley [2001b]100 x1.5Fit to Cassini [2006] data
Post-tearing field configuration, Br0Bθ04.25(BrrecBthrec)Kronberg et al. [2007]Dipole 
Current sheet thickness post-tearing, d0, Rj−0.02ar + 5.9derived from Kronberg et al. [2007]1.5 to 3Giampieri and Dougherty [2004]
Current sheet thickness pre tearing, drec, Rjd0/17.0derived from Kronberg et al. [2007]d0/17.0Same ratio as Jupiter

[11] We use a Monte Carlo method to examine what periods are allowable given the parameters listed in Table 1. To do this, we created Gaussian distributions for x, v, d0, and math formula centered at the middle of the range of possible values and with a full width at half the maximum equal to the reported range of values. In Figure 2, we show our results for Jupiter. Given the parameters listed in Table 1, the most probable period is consistent with the 2 to 3 day period observed, as predicted based on the previous, similar, analysis by K07. A large range of periods is possible with the full width half maximum of the distribution ranging from approximately 1.5 days to 3.9 days, consistent with the longer range of possible periods suggested by Kronberg et al., [2009].

Figure 2.

Our reanalysis of the mass-loading/unloading period for Jupiter using the Monte-Carlo approach developed here, based on characteristic values given in Table 1. Dotted lines are at τ = 2 and 3 days. The curve is a best fit Gaussian to the data with properties as listed in the top right corner.

[12] Figure 3 shows our results on applying the same analysis at Saturn. Here we have treated the different source rates found by Smith et al. separately. We find a large range of possible periods varying from less than 4 to over 100 h depending (mostly) on the plasma-loading rate. Results from stellar occultation suggest that, while the neutral source rate is observed to be fairly volatile, the average neutral source rate is ~6.4 × 1027 molecules s−1 (based on measurements from 2005–2010 [Hansen et al., 2011]), and this is very close to the value of 6.3 × 1027 derived by Smith et al. [2010)] based on E3 flyby data, that is, ~193 kg s−1. Assuming an ionization rate of 30%, this corresponds to a plasma-loading rate ~57 kg s−1, which, as is shown in Figure 3b, corresponds to a most likely mass-loading/unloading period of 30.7 h.

Figure 3.

(a–c) Histograms showing the mass-loading/unloading period for Saturn based on values for neutral mass loading derived by Smith et al. [2010] for three different Cassini-Enceladus flybys (E2, E3, and E5), an assumed 30% ionization rate [cf. Jurac and Richardson, 2005; Cassidy and Johnson, 2010] and other parameters as listed in Table 1. Curves are best fit Gaussians with parameters as listed in the top right corner. (d) Reproduction of the three Gaussian fits on one (logarithmic) scale.

3 Discussion

[13] We suggest that Saturn has a natural global magnetospheric refresh rate that might be close to the planetary rotation rate. That it is faster than the equivalent period at Jupiter can be understood in the context of work by Vasyliünas [2008], who show that mass loading at Saturn from Enceladus is more significant than the (larger) mass-loading rate at Jupiter when expressed in the context of the relative planetary scale sizes. Our results may have implications in the context of the well-known mystery associated with the apparently variable period of planetary phenomena at Saturn.

[14] Periodic enhancements in Saturn Kilometric Radiation (SKR) and energetic plasma enhancements in the nightside sector of Saturn's near-tail region have both been linked to substorm-like activity at Saturn [Mitchell et al., 2005] and the idea of periodic substorms at Saturn postulated by Burch et al. [2008] (although refuted by Jackman et al., 2009b). The process we describe may provide a helping hand to models such as that described by Mitchell et al. [2009] in supplying a magnetospheric environment that is predisposed to refresh itself at something like the planetary rotation rate. However, the idea of periodic behavior at Saturn having a magnetospheric driver is not a popular one because the observed SKR period is very clock-like (for a given time period). (Although, by analogy with the Shishi Odoshi, a magnetospheric period can be very clock-like in the absence of internal or external changes or dynamics.) Most compelling though is that periodic mass release cannot explain the observation that there exist different north/south SKR periods [Gurnett et al., 2009]. So—while we do not suggest that the magnetospheric frequency described here can create the variable narrow band period observed at Saturn—we do suggest that Saturn has a natural magnetospheric frequency whose period (for modern-era Enceladus activity) is coincidentally close to Saturn's actual rotation rate. We note that, keeping other parameters fixed, a plasma mass-loading rate of 178 kg/s gives a most probable period of 10.8 h and 181 kg/s a most probable period of 10.6 h. Further, we show that the rate of mass loss varies with mass-loading rate; as such this model provides a simple mechanism to explain a slowly varying magnetospheric period.

Acknowledgments

[15] This work was supported by NASA-JPL contract NAS5-97271 between the NASA Goddard Space Flight Center and Johns Hopkins University for the MIMI investigation and by NASA-JPL contract 1243218 for the CAPS program at the Southwest Research Institute. AMR's work was also supported by NASA CDAP NNX09AE71G. CMJ's work at UCL was funded by a Leverhulme Trust Early Career Fellowship and a Royal Astronomical Society Fellowship. EAK and NK are supported by the German Space Agency DLR under contract number 50OH1101.

[16] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.