PERIODICITIES IN SATURN S MAGNETOSPHERE

Transcription

1 PERIODICITIES IN SATURN S MAGNETOSPHERE J. F. Carbary 1 and D. G. Mitchell 1 Received 31 August 2012; revised 2 February 2013; accepted 5 February 2013; published 27 March [1] Although the exact rotation period of Saturn is unknown, Saturn s magnetosphere displays an abundance of periodicities near ~10.7 h. Such modulations appear in charged particles, magnetic fields, energetic neutral atoms, radio emissions, motions of the plasma sheet and magnetopause, and even in Saturn s rings themselves. Known to an accuracy of four significant figures, these periodicities do not remain constant but vary by ~1% over time scales of a year or longer. Magnetospheric periodicities also display slightly different periods in the northern and southern hemispheres: ~10.6 h and ~10.8 h, respectively. The magnetic and spin axes of Saturn are aligned to within ~1, so that Saturn s magnetospheric periodicities cannot be explained as wobble caused by a geometric tilt, unlike those of the Earth and Jupiter. Furthermore, the variations in periodicity argue against a cause related to changes interior to an object as large as Saturn. Several models have been proposed for the periodicities, including rotating planetary vortices, periodicplasmareleases,andaflapping magnetodisk, but none can satisfactorily explain all of Saturn s periodicities. This review discusses the observations of these periodicities from their initial discovery during the Pioneer flyby to their long-term surveillance by Cassini and examines the various struggles to explain and model them. Understanding Saturn s periodicity may elucidate periodic phenomena in other magnetospheric environments. Citation: Carbary, J. F., and D. G. Mitchell (2013), Periodicities in Saturn s magnetosphere, Rev. Geophys., 51, 1 30, doi: /rog INTRODUCTION [2] The rotation period is a fundamental parameter of any physical object, from scales as small as molecules to that as large as galaxies. The rotation period of a planet is especially interesting and useful because it frames dynamic effects and organizes longitudes. Unlike other planets and astrophysical objects, the rotation period of Saturn is not known with any precision. Saturn s surface, if it has one, is hidden by impenetrable clouds and cannot be measured by radar. However, Saturn s magnetosphere and upper atmosphere do display periodicities, and all estimates of the planet s rotation derive indirectly from magnetospheric and atmospheric observations. The magnetosphere of Saturn does not exhibit a fixed period, though, and even this variable period often displays two branches that differ between the northern and southern hemispheres. Furthermore, no single model describes all the observed periodicities at all the locations they are observed in the magnetosphere. [3] This review recounts the history of periodicities observed in Saturn s magnetosphere, details all the observed 1 Applied Physics Laboratory, Johns Hopkins University, Laurel, Maryland, USA. Corresponding author: J. F. Carbary, Applied Physics Laboratory, Johns Hopkins University, Johns Hopkins Road, Laurel, MD 20723, USA. ( james.carbary@jhuapl.edu) periodicities, and presents the models (or combinations of models) most likely to explain them. The arrival of the Cassini spacecraft at Saturn in 2004 renewed interest in the variable periodicities of that planet, and the extensive measurements since then justify a timely review of observation and theory at the present time. [4] Before proceeding to the periodicities themselves, the reader should understand a few basic facts about Saturn [Williams, 2006]. The planet orbits the Sun at a mean distance of 9.58 AU with an orbital (sidereal) period of years. Saturn has an extremely high obliquity of and a very low mean density of 687 kg m 3. Its rapid rotation rate and low density combine to produce the most oblate shape of any planet in the solar system: its equatorial radius is 60,268 km (=1 R S ), while its polar radius is only 54,364 km (1 atmosphere pressure level). The planet s atmosphere is primarily hydrogen (96.3%) and helium (3.25%). Saturn has over 60 satellites, the major ones being Mimas (located at 3.08 R S ), Enceladus (3.95 R S ), Tethys (4.89 R S ), Dione (6.26 R S ), Rhea (8.74 R S ), and Titan (20.27 R S ). Titan has an extensive atmosphere with actual weather; Enceladus is cryo-volcanically active and ejects water and hydrocarbons into the magnetosphere and is, in fact, the major source of dust and neutral particles in the magnetosphere. Saturn has an extensive and well-known ring system in its equatorial plane. The most prominent rings are the A ring ( R S ) and the B ring ( R S ) American Geophysical Union. All Rights Reserved. Reviews of Geophysics, 51/ /13/ /rog Paper number 2012RG000416

2 The E-ring (~3 8 R S ) is more relevant to the magnetosphere; it is populated by ejecta from Enceladus. Of direct relevance to this review, the planet has magnetic field with a dipole moment of gauss-r S 3 ; the dipole axis has virtually no tilt relative to the spin axis. 2. PRE-CASSINI OBSERVATIONS OF SATURN S PERIODICITY [5] Magnetospheric periodicities at Saturn are primarily recognized in radio emissions in the kilometric band (~ khz). Analogous to auroral kilometric radiation (AKR) at Earth, the Saturn kilometric radiation (SKR) originates from the cyclotron maser instability (CMI) in regions above and magnetically connected to aurora [e.g., Lamy et al., 2008a, 2008b, and references therein]. SKR is beamed into a cone whose axis lies along the magnetic field, so its observation depends on the location of the observer. The radio emission is circularly polarized, with the handedness depending on the magnetic field orientation. Because of Saturn s magnetic field orientation, left-handed SKR originates from the southern hemisphere, while right-handed SKR originates from the northern hemisphere [e.g., Lamy et al., 2008a, 2008b]. Saturn s radio emissions cannot be detected at Earth primarily because of Earth s ionospheric cutoff and because of background from similar AKR. [6] The discovery of any periodicities at Saturn, therefore, required observations by spacecraft closer to the planet itself. The Pioneer 11 flyby of Saturn in September 1979 afforded the first such opportunity to observe Saturn s periodicities. That spacecraft carried a magnetometer, plasma detector, and several energetic particle instruments, but no radio emissions detector. Consequently, none of the Pioneer instruments initially reported any periodicities associated with Saturn s magnetosphere [e.g., Smith et al., 1980; Wolfe et al., 1980; Simpson et al., 1980]. Later re-examination of the magnetometer data did, however, confirm that a periodicity in the magnetic field was detected by Pioneer 11 [Espinosa and Dougherty, 2000]. [7] The Voyager 1 and Voyager 2 flybys of Saturn in November 1980 and August 1981 produced the first direct observation of periodicities in the magnetosphere. The Voyager Planetary Radio Astronomy (PRA) instrument first detected Saturn kilometric radiation, which was Fourier analyzed and found to have a period of h [Kaiser et al., 1980]. That period (Figure 1) was later revised to h [Desch and Kaiser, 1981a]. This period became the basis for a Saturn longitude system (SLS), which survives to the current era in various incarnations. The PRA instrument also discovered that the most intense SKR originates on the dawn side of the planet, where the most intense aurora are located [Kaiser and Desch, 1982; Kaiser et al., 1984]. Subsequent to finding the radio periodicity, a similar periodicity was discovered in the spectral ratios of energetic particles (>22 kev) [Carbary and Krimigis, 1982]. Voyager imagers reported mysterious spoke features appearing in Saturn s main rings [Smith et al., 1981], and these spokes were found to have a periodicity similar to that of the SKR and energetic particles Figure 1. Discovery of periodicity in Saturn s magnetosphere. The top panel shows the power spectrum of SKR radiation at 174 khz based on 267 days of observation, peaking at h. The bottom panel shows an expanded (low resolution) spectrum. The periodic signal is >10s above background [Desch and Kaiser, 1981a]. [Porco and Danielson, 1982]. Imagers also observed a hexagonal cloud pattern and an associated cloud spot circling the north pole with apparently the same period as the SKR radio emissions [Godfrey, 1988, 1990; Sanchez- Lavega et al., 1993; Caldwell et al., 1993]. Finally, the Voyager ultraviolet imagery strongly intimated that Saturn s auroral intensity depended on SLS longitude, having a peak near ~135 when the Sun was at ~100,which would imply some sort of periodicity in the aurora [Sandel and Broadfoot, 1981; Sandel et al., 1982]. [8] The radio periodicity observed by Voyager was interpreted as the true rotation period of the planet and was accepted for decades as the rotation period for Saturn [e.g., Davies et al., 1996; Seidelmann et al., 2002]. This interpretation of the SKR period was based on analogy with the periodic radio emissions observed from Jupiter in the decimetric and decametric bands [Seidelmann and Divine, 1977]. The Jovian periodicity, however, derived essentially from the 10 tilt of the planet s magnetic axis relative to its spin axis [e.g., Smith et al., 1976], while Saturn s magnetic axis is aligned with its spin axis [Ness et al., 1981, 1982; Davis and Smith, 1990]. Because of this alignment and also because the SKR emissions appeared strongest on the dawn side, the radio periodicities were interpreted as a pulsation ( clock-like ) phenomenon rather than a rotational phenomenon [Kaiser and Desch, 1982; Kaiser et al., 1980]. [9] Voyager radio observations also uncovered another type of periodicity in Saturn s kilometric radio emissions. This type of periodicity was not entirely unexpected, but its implications are not fully appreciated by the Saturn community even today. Further examination of the Voyager SKR signals over a sufficiently long interval revealed modulation at the solar wind rotation period (~25 days) and harmonics thereof (~13 days) [Desch, 1982; Desch and Rucker, 1983; Kaiser et al., 1984]. These investigations strongly suggested that the solar wind pressure controls this modulation, rather than other factors such as orientation of the interplanetary magnetic field (IMF) 2

3 or some combination of solar wind speed and IMF [Desch and Rucker, 1983]. [10] The Ulysses spacecraft did not reach Saturn, but its excursion to high solar latitudes did carry it to the distance of Jupiter where the spacecraft radio astronomy instrument could detect kilometric radiation from Saturn [Lecacheux et al., 1997]. In this case, SKR observations extended over several years from November 1994 to January As with the Voyager observations, the Ulysses power spectrum revealed peaks near the Saturn rotation period of ~10.7 h and at the Solar rotation period of ~25 days [Galopeau and Lecacheux, 2000]. Most surprisingly, however, the Saturn period clearly evidenced a change from h in April 1994 to h in March 1995 (Figure 2 shows this change). Furthermore, from April 1994 to the end of the observations in January 1997, the SKR period slowly declined at a rate of ~0.04 h/yr. Among the explanations offered for this was movement of the radio source, possibly caused by differential rotation of Saturn or reversal in Saturn s magnetic field [Galopeau and Lecacheux, 2000]. [11] In the years immediately preceding the Cassini orbit injection in 2004, a reanalysis of the Pioneer and Voyager magnetometer data revealed that those instruments had, in fact, observed a periodic signature in Saturn s magnetic field [Espinosa and Dougherty, 2000; Espinosa et al., 2003a, 2003b]. The reanalysis did not offer any measurement of the period but showed convincing evidence by over-plotting the time profiles of the ΔB r and B f field components with sine waves having periods of h. Furthermore, a hodogram analysis of these two components indicated that the periodicity could not have originated from the motions of a tilted dipole [Espinosa et al., 2003a]. The periodicities were interpreted in terms of a rotating anomaly (probably magnetic but not detected) that caused a spiral wave to propagate outward in Saturn s magnetosphere and thus generate the observed periodicities [Espinosa et al., 2003b]. Because of this mechanism s Figure 2. Ulysses observations of Saturn s SKR periodicity observed over a 3 year interval in the 1990s [from Galopeau and Lecacheux, 2000]. The solid dots indicate the observed period in units of the Voyager SLS period of h, and the horizontal line indicates that base line. A linear fit tothe periods after March 1995 indicates a drift in the period of h/yr. analogy to a rotating cam, the proposed mechanism was called the cam or camshaft model, a name that has persisted to the present era. 3. CASSINI-ERA OBSERVATIONS OF SATURN S PERIODICITY 3.1. The Cassini Instruments [12] The Cassini spacecraft entered Saturn s magnetosphere in July 2004 and revolutionized knowledge of the planet s periodicities. The spacecraft carried a host of instruments suitable for measuring the magnetosphere. The Radio and Plasma Wave Science (RPWS) instrument observed electric fields from 1 Hz to 16 MHz, magnetic fields up to 12 khz, and could perform direction-finding and polarization measurements [Gurnett et al., 2004]. RPWS also carried a Langmuir Probe (LP) that could measure the plasma temperature and density in the inner magnetosphere. The Cassini Magnetic Field Instrument (MAG) utilized a fluxgate magnetometer with an overall dynamic range between ~5 pt and nt with a time resolution of 32 vectors per second [Dougherty et al., 2004]. The Cassini Plasma Spectrometer (CAPS) instrument included the Electron Spectrometer (ELS) to observe low-energy (or thermal) electrons (0.6 ev to 28.2 kev) and the Ion Mass Spectrometer (IMS) to observe low-energy ions from 1 ev to 50 kev [Young et al., 2004]. CAPS employed a motorized actuator to sweep the ELS and IMS fields of view over approximately 2p steradians once every 3 min. To observe the non-thermal particles, the Magnetospheric Imaging Instrument (MIMI) employed three different detectors: the Low Energy Magnetospheric Measurement System (LEMMS), the Charge-Energy-Mass Spectrometer (CHEMS), and the Ion Neutral Camera (INCA) [Krimigis et al., 2004]. LEMMS observed energetic electrons (15 kev to 5 MeV) and energetic ions (30 kev to 160 MeV) and used a rotating platform to measure the angular distribution of such particles. CHEMS determined the chemical composition of energetic ions from 3 kev/nucleon to 220 kev/nucleon but had limited angular resolution. Saturn s magnetosphere was thought to have an extensive neutral cloud within it [e.g., Richardson, 1998], so an ENA detector was included in the Cassini payload; the INCA detector observes neutral atoms between 7 kev/nuc and 3 MeV/nuc with a two-dimensional angular resolution of ~5 and a time resolution of ~6 min per image. INCA could also be placed in an ion mode to detect ions with a similar energy and time resolution. [13] These magnetospheric and plasma science (MAPS) instruments are generally cited as those that measure periodicities at Saturn. Additional but much more limited measurements of magnetospheric periodicities could also be made by imaging instruments such as the Ultraviolet Imaging Spectrograph (UVIS) and the Visual and Infrared Mapping Spectrometer (VIMS) [Esposito et al., 2004; Brown et al., 2004]. These imagers could observe the aurora and certain atmospheric features at wavelengths from the extreme ultraviolet ( nm) to the far ultraviolet ( nm), to the visible and near infrared ( mm). The Hubble Space 3

4 Telescope (HST) also contributed a number of coordinated observations with Cassini during 2004, 2007, and 2008 [e.g., Clarke et al., 2009] and could observe auroral oscillations. [14] Most of these instruments continued to function from Saturn orbit insertion (SOI) in July 2004 to the present day. However, the LEMMS turntable jammed in March 2005 and could no longer supply angular information for energetic electrons and ions. The CAPS instrument suffered a short circuit in September 2011 and was turned off for several months. The instrument was turned back on in May 2012 but functioned for only a few weeks until a second, more serious short in early June 2012 resulted in an indefinite turn-off pending further review by the Cassini program Radio Observations [15] The RPWS instrument began observing Saturn s radio emissions well before the SOI event. SKR emissions were detected at ~2.5 AU from the planet [Gurnett et al., 2005] and were initially correlated with aurora observations made by HST and upstream plasma observed by CAPS [Kurth et al., 2005]. Using observations during the year prior to SOI, the Cassini radio astronomy instrument confirmed that the SKR period had changed significantly from those measured during the Voyager era, and a new period of h was established [Gurnett et al., 2005]. Figure 3 shows the first measurement of Saturn s period by RPWS. The new period amounted to a lengthening of over 6 min in Saturn s period from the official Voyager period, which led to considerable speculation about what, exactly, was the length of a Saturn day and how the radio period related to cloud motions [e.g., Sanchez-Lavega, 2005]. [16] Because the SKR is related to the aurora, and the aurora related to the magnetosphere, the variable radio period could still serve to organize magnetospheric phenomena as long as the variability could be characterized. Consequently, RPWS observations of kilometric radiation between day 1 of 2004 and day 240 of 2006 were employed to define a new variable longitude system [Kurth et al., 2007]. Christened SLS2, the new system involved fitting the period as a function of time to a third-order polynomial. Subsequent observations extended this system to day 222 of 2007 and resulted in the development of an SLS3 system based on a fifth-order polynomial [Kurth et al., 2008]. These data clearly demonstrated the slow drift in Saturn s radio period (Figure 4). An unexpected consequence of the SLS3 analysis was the recognition of a new, second period in the data. The older period of ~10.8 h served as the basis for the SLS3 longitude, while the new period of ~10.6 h was puzzling. [17] Further extension of the SKR analysis to day 139 of 2009 firmly established that two SKR periods existed at the same time and that the longer period of ~10.8 h was associated with radio sources in the southern hemisphere while the shorter period of ~10.6 h was associated with sources in the northern hemisphere [Gurnett et al., 2009a]. Figure 5 exhibits the radio spectrum showing the dual periodicities based on observations from late February 2008 to mid The separation of northern and southern sources was based on geometrical arguments related to the spacecraft location at the time of observation and the expected beaming properties of SKR radiation. Soon after dual SKR periodicities were seen, similar dual periodicities were discovered in Saturn s auroral hiss (f < 100 Hz) [Gurnett et al., 2009b] as well as in electrons with energies over Figure 3. The first measurement of Saturn s radio period by the Cassini RPWS instrument, compared to the older Voyager measurement [from Gurnett et al., 2005]. Figure 4. RPWS measurements of variations in Saturn s SKR period during the Cassini mission. The black dots and black trace show the data used to extend the SLS2 longitude system to make the SLS3 system. The red dots and red traces show the emergence of a new, second period [from Kurth et al., 2008]. 4

5 Figure 5. Dual periodicities in the SKR emissions. The spectrum exhibits the southern (red) and northern (blue) spectra in terms of rotation rates [from Gurnett et al., 2009a]. 100 kev [Carbary et al., 2009a] and in the magnetic field [Andrews et al., 2010b]. [18] The dual periodicities were ascribed to a seasonal effect having to do with differing conductivities in the summer versus the winter hemisphere. Higher (lower) conductivities in the summer (winter) hemisphere would allow higher field aligned currents (FACs), producing faster (slower) ionospheric responses (in terms of drag), and thus explain not only the dual periodicities but also their drift in time [Gurnett et al., 2009a, 2009b]. The seasonal hypothesis seemed particularly relevant as Saturn approached its vernal equinox on day 222 of Indeed, as the equinox was approached and eventually passed, the dual periodicities seemed to merge toward a common period near ~10.7 h. There was some indication that the northern period actually crossed the southern [Gurnett et al., 2010]. However, not all variations in the radio period can be ascribed to seasonal effects: short-term variations in the radio period (on the scale of weeks) can be attributed to variations in the solar wind speed [Zarka et al., 2007]. Furthermore, dual periodicity might also be a consequence of differential planetary rotation, thus being similar to the well-known differential rotation of the Sun and having a similar long-term cycle [Dessler, 1985]. [19] An absolute separation of northern and southern SKR signals, however, required an analysis of the polarized radio signals, since southern SKR must be left-handed and northern SKR must be right handed [Lamy et al., 2008a, 2008b]. Such an analysis of the polarized signals was eventually carried out using data from day 1 of 2004, through equinox in 2009, to day 292 of 2010 [Lamy, 2011]. Figure 6 shows this amazing history. The construction of this figure involved making Lomb-Scargle periodograms [Press et al., 1992] of the SKR signals in 200 day windows at the cadence of one day over the entire 6 years. The SKR signals were separated by north and south components (bottom panels in Figure 6) using the polarization of the signals, so no ambiguity of the source location exists. Slow time variations in the SKR period appeared in both north and south components, and the dual Figure 6. Spectrograms of total SKR signal (top), southern SKR signal (middle), and northern SKR signal (bottom) observed by the RPWS instrument over 6.6 years. One Lomb-Scargle spectrogram was generated each day within a 200 day sliding window; the northern and southern signals were separated by polarizations of the signal [from Lamy, 2011]. 5

6 signals clearly evidenced an anti-symmetry such that when one period increased, the other decreased. Note that the northern signal appeared at times to itself have two distinct periods, one of which corresponded to the southern period. By early 2010, about a year after equinox, all the periods seemed to have coalesced into a common period of ~10.7 h. These results, combined with the directionality of the SKR, were interpreted as evidence that the SKR periodicity derives from an intrinsically rotating source that brightens in the morning sector near 0800 h [Lamy et al., 2009; Lamy, 2011], as opposed to a pulsating, clock-like source. Having established the variations in the dual periods, a new variable longitude system, SLS4, was developed with a northern component and a southern component [Gurnett et al., 2011a]. The different north and south radio rotation periods were used to infer the existence and rotation of a plasmapause-like boundary at high latitudes [Gurnett et al., 2011b]. Observations of the SKR period continued into 2012, and so far, the north and south components are mixed and impure but close to ~10.6 h [Gurnett et al., 2012]. [20] Cassini observations of Saturn radio emissions have so far not been fully utilized to detect solar modulation at ~25 days, although the RPWS dataset could certainly serve that purpose. However, a very interesting investigation using the short-term power spectra of the SKR showed that the solar wind speed causes variations of ~1% in the SKR period on time scales of days [Zarka et al., 2007]. These small variations could have a critical impact on the derived periodicities, which are usually determined on time scales of hundreds of days. [21] Long-term observations of the radio emissions can also serve to establish effects by the satellites of Saturn, which have orbital periods ranging from ~1 to ~16 days. Voyager measurements suggested that Dione (period = 2.7 days) might control certain radio emissions [Desch and Kaiser, 1981b; Kurth et al., 1981]. Subsequent examination of RPWS data over a longer time span showed that Dione did not influence Saturn s radio emissions nor did any of the planet s other satellites, with the notable exception of Titan [Menietti et al., 2007, 2010]. SKR appears to have a higher occurrence probability when Titan is located in the midnight sector than that when it is in the midmorning sector [Menietti et al., 2010]. Insofar as substorms (or tail reconnection events) may be identified in Saturn s magnetosphere, they seem to occur at times when Titan lies in the midnight sector [Russell et al., 2008]. Thus, the orbital phase of Titan might be considered in some sense as a modulator of magnetospheric activity, and its period (~15.9 days) might appear somewhere in the magnetospheric spectrum of periodicity Plasma Observations [22] Charged particle observations of Saturn s periodicities may be divided into those observed in the low-energy particles or thermal plasma (E < ~50 kev) and those observed in the high-energy or non-thermal particles (E > ~50 kev). While periodicities similar to those of the SKR are evident at all energies, the strongest ones (or at least those most reported) seem to be best observed in the higher-energy particles. [23] The first evidence of periodicity in Saturn s lowenergy plasma is derived from measurements made by the RPWS in the inner magnetosphere (3 5 R S ). The plasma density in this region was deduced from the upper hybrid resonance frequency seen in the radio wave data [Persoon et al., 2005]. Shown in Figure 7, the plasma density showed a sinusoidal variation when plotted as a function of the new (variable) SLS2 longitude, convincing evidence that it had a period similar to that of the SKR [Gurnett et al., 2007]. Plotting the magnetic field data in SLS2 longitude also revealed a similar sinusoidal variation in the magnetic field. These longitudinal variations were interpreted in terms of a co-rotating convection pattern, first discussed for the planet Jupiter in the 1980 s [Hill et al., 1981]. [24] Observations from CAPS also confirmed the existence of periodicity in Saturn s plasma densities in the outer magnetosphere [Burch et al., 2008, 2009; Arridge et al., 2008b; Morooka et al., 2009; Jackman et al., 2009]. Figure 8 exhibits the strongly periodic signals in plasma density seen in the thermal electrons by the CAPS/ELS (red) and by the RPWS/LP (black) for one of Cassini s passes through the distant magnetotail [Morooka et al., 2009]. These periodicities engendered interpretations as a string of plasmoids periodically released along a spiral Figure 7. Plasma density derived from plasma wave measurements between 3 and 5 R S (top). Sinusoidal variations appear in the magnetic field (middle) and plasma density (bottom) when plotted in the SLS2 longitude system, which implies that the field and density have the same period as the SKR used to construct the longitude system [from Gurnett et al., 2007]. 6

7 Figure 8. Periodicities in plasma data (top), SLS2 longitude (middle), and periodicities in magnetic field components (bottom). In the top panel, the black trace shows plasma density variations in time from the RPWS Langmuir Probe and the red trace shows plasma densities derived from the CAPS/ELS sensor. The sample covers the time range from days 18 to 26 of 2006 when Cassini was in Saturn s magnetotail [from Morooka et al., 2009]. pattern [Burch et al., 2008], as the wobbling of a magnetodisk with a very small tilt (<1 )[Morooka et al., 2009, 2011], or as regular vertical oscillations of a magnetodisk [Arridge et al., 2008b, 2011; Jackman et al., 2009]. [25] Because of the rapid rotation of Saturn s magnetosphere, centrifugal forces acting on the plasma are expected to trigger a centrifugal interchange instability (CII) whereby magnetic flux tubes with high densities of cold plasma are thrust outward in radial distance and change locations with flux tubes having low densities of more energetic plasma [Hill, 1976; Hill et al., 1981; Siscoe and Summers, 1981]. The existence of this instability has been confirmed at both Jupiter and Saturn by analysis of signatures in both the plasma and energetic particles [Mauk et al., 1997; Burch et al., 2005; Hill et al., 2005; Mauk et al., 2005]. Any intrinsic periodicity of the CII injections seen in CAPS data was immediately addressed by examining the location of these events in SLS longitude, after correction for expected particle drift in Saturn s magnetic field. A small sample of 48 injection events, observed during the early orbits about Saturn, revealed no organization in the original SLS longitude [Hill et al., 2005]. A more extensive search of CAPS injection events from the first 26 orbits of Cassini revealed no organization in the newer (variable) SLS2 longitude system but a surprising organization in the old SLS longitudes based on Voyager data [Chen and Hill, 2008]. In the old constant-rotation longitude system, injections seemed to appear most often near 80 SLS longitude. Continued statistical studies of these injections continue as the longitudes and drift correction techniques are refined, but no periodicity (as revealed in longitudinal location) has yet been confirmed in the plasma injections [Chen et al., 2010]. [26] The intense interest in Titan has resulted in several investigations of its magnetospheric environment. Because Titan orbits at 20 R S, usually within the magnetopause, the moon experiences pronounced effects of magnetospheric periodicities. In particular, periodic oscillations of the magnetodisk at Titan s orbit generally cause the moon to encounter the plasma sheet once every ~5 h [e.g., Arridge et al., 2008b; Simon et al., 2010]. Plasma observations at Titan s orbit also exhibit periodicity close to that of the SLS3 longitude system, albeit heavy-rich plasma (O+, C +, etc) require a longer period than the SKR and exhibit a phase shift of ~0.35 /day relative to the SLS3 periodicity [Szego et al., 2011] Energetic Charged Particle Observations [27] Notably, no plasma measurements by CAPS or LP have ever been used to independently determine a period in the low-energy plasma but have established only that variations in the plasma density have a period similar to that of the radio emissions. On the other hand, a myriad of energetic charged particle observations made by the MIMI instrument have been used to determine actual periodicities and track them over time. [28] Strong periodicities in energetic particles were recognized immediately after Cassini entered Saturn s magnetosphere in 2004 [Krimigis et al., 2005]. As Cassini s initial orbits migrated into the tail of the magnetosphere, very strong periodic modulations appeared in the energetic 7

8 Figure 9. Periodicities in energetic electrons (top) and magnetic field magnitude (bottom). Vertical lines mark periods of 10.7 h. Note that peaks in the energetic particle flux occur at times of magnetic field peaks [from Krupp et al., 2005]. charged particles, especially the energetic electrons [Krupp et al., 2005]. Figure 9 shows a sample time profile of the kev electrons observed during one outbound pass through the magnetotail. The charged particle modulations proved so compelling they were translated into periodicities using wavelet and Lomb periodogram analyses [Carbary et al., 2007a, 2007b]. As expected, the resulting period agreed well with the ~10.8 h period observed in the SKR signal, although the energetic electrons and oxygen ions showed much better agreement than the energetic protons [Carbary et al., 2007b]. Figure 10 illustrates periodograms of energetic charged particles typically observed in Saturn s magnetotail. The close correspondence of the electron period with the SKR period encouraged organizing their fluxes in the new SLS2 longitude system. When binned in both longitude and radial distance, the electrons evidenced spiral patterns that persisted for over a month and resembled the cam-spiral of the magnetic field [Carbary et al., 2007c]. As the Cassini orbit evolved and more samples were collected at more locations, a dual periodicity at 10.6 and 10.8 h was recognized in the kev electrons from late 2007 to 2009, the same time interval of the dual SKR periodicity [Carbary et al., 2009a]. Even more interesting, a Lomb analysis of 5 years of energetic electron data revealed a solar wind periodicity at 13 and 26 days, the amplitude of which exceeded that of the 10.8 h modulations by several times [Carbary et al., 2009b]. Figure 11 demonstrates the spectral dominance of the solar wind on energetic electrons in Saturn s magnetosphere. [29] The energetic ions also evidence periodicities near the SKR periods, but the energetic oxygen ions (O + ) have strong periodicities while the energetic protons (H + ) often display weak or non-existent periodicities [Carbary et al., Figure 10. Energetic electron (top) and ion (middle and bottom) periodograms common in the magnetotail of Saturn. The strongest periodicities typically occur in the energetic electrons (top) and energetic oxygen ions (bottom), while the energetic protons often show little evidence of periodicity at all [from Carbary et al., 2007b]. Figure 11. An expanded periodogram of the energetic electrons ( kev) shows a solar wind periodicity (13 and 26 days) that is much stronger than the SKR period at 10.8 h [from Carbary et al., 2009b]. 2007b]. The energetic ions are well organized in the variable SLS3 longitude system, although their peak fluxes shift somewhat with increasing energy [Carbary et al., 2010]. Such a shift may be explained in terms of energy-dependent drift speeds in a non-rigidly rotating magnetosphere. Curiously, no dual periodicities have ever been reported in any of the ion observations. [30] The understanding of energetic electron periodicities seemed well in hand until about a year after Saturn s equinox in mid Periodogram analyses showed that like the SKR periodicity, the electron periods had merged 8

9 to a common period in 2010 [Carbary et al., 2011b]. The dual periodicity reappeared around the beginning of 2011, persisted for several months, and then all periodicity vanished by the middle of Figure 12 exhibits this curious phenomenon, which was interpreted as a possible effect of Cassini orbital precession toward noon, and the disappearance of charged particle periodicities in that sector. Very recent observations of energetic electrons ( kev) in 2012 indicate an unusually short period of 9.95 h in addition to the SKR period near h [Carbary et al., 2012b]. [31] Very short periodicities of ~1 h have been recognized occasionally in the energetic particle data and also detected in broadband electrostatic noise and the magnetic field [Mitchell et al., 2010a]. These phenomena are observed at high latitudes in ion conics and electron beams associated with auroral processes. The short period pulses may be linked to flux tube interchanges that are reported throughout the magnetosphere. with the low-energy neutrals, charge exchange, and produce energetic neutral atoms. The charge exchange produces fluxes of hydrogen and oxygen atoms with energies essentially those of the energetic ions that formed them [Gruntman,1997].The MIMI/INCA instrument images these energetic neutral atoms (ENA) and provides essentially a photograph of the energetic source ions that generated the neutrals, just as an image in the far ultraviolet produces, say, a photograph of the auroral emission caused by precipitating electrons. In particular, the ENA observations of Earth and Jupiter reveal the ring currents of those planets in surprising detail [e.g., Mitchell et al., 2003, 2004]. [33] Similarly, the INCA imager on Cassini has provided a revealing portrait of Saturn s ENA emissions. Figure 13 shows a composite map of energetic neutral hydrogen and 3.5. Energetic Neutral Particle Observations [32] Even before the arrival of Cassini, an extended neutral cloud collocated with the particulate E-Ring was known to exist in Saturn s middle magnetosphere between ~3 R S and ~8 R S [Richardson, 1998]. Cassini discovered geologic activity on Enceladus (~4 R S ), whose icy jets provide the source of this neutral cloud and of the E-ring itself [Porco et al., 2006]. The energetic ions in the magnetosphere collide Figure 12. Post-equinox periodicities in energetic electrons as revealed in a color periodogram (top), compared with the local time of the spacecraft (middle) and its periapsis distance (bottom) [from Carbary et al., 2011b]. Figure 13. Statistical maps of the energetic neutral hydrogen (top) and oxygen (bottom) made from combining ENA images and projecting them onto the equatorial plane of Saturn. In this representation, the Sun is to the right, dusk is up, etc. The circles identify the orbits of Saturn s principal moons, while the squares indicate (for example) regions over which intensities are integrated to produce time profiles that yield ENA periodicities [from Carbary et al., 2010]. 9

10 oxygen obtained by combining 120 days of observations from high latitude [Carbary et al., 2010]. The map shows ENA intensities projected onto the equatorial plane of Saturn, with the Sun at the right and dusk at the top, etc. Both the hydrogen and oxygen emissions peak on the nightside of the planet, about 90 away from where aurora intensities peak [Carbary et al., 2008c]. By integrating the ENA image fluxes, either over the entire image or over a selected region, and analyzing the time profiles of these integrations, one can arrive at the ENA periodicities. Figure 14 shows the first realization of the ENA periodicity from dawn-side observations made in 2004 [Paranicas et al., 2005]. Both the hydrogen and oxygen atoms exhibited strong periodicities near the 10.7 h SKR period [Krimigis et al., 2005; Paranicas et al., 2005]. Subjecting the ENA intensities to Lomb analyses revealed a very strong periodicity in the oxygen at 10.8 h, which was exactly the southern SKR period [Carbary et al., 2008a, 2008c, 2010] (Figure 15). However, the hydrogen atoms (like their proton precursors) displayed a much weaker and more chaotic periodicity [Carbary et al., 2008a, 2009c]. The strength of the oxygen periodic signal compared to the hydrogen signal may be understood on the dynamical basis of their different drift anisotropies in Saturn smagneticfield [e.g., Paranicas et al., 2005]. No evidence for dual periodicities in the ENA has yet been seen nor has any solar wind periodicity (at 13 or 26 days) been yet reported in the ENA. [34] Because of the similarity between the ENA and SKR periods, cross correlations between the two periodic signals sought to establish the definitive phase of the two signals (and thus, possible causal relation). The initial attempt at this cross-correlation, based on a limited dataset of high-latitude observations, showed that such a constant phase did not exist between the ENA and SKR and that even the phase between the hydrogen and oxygen ENA signals shifted [Carbary et al., 2010]. Another cross correlation study using somewhat more data (as obtained from dawn-side observations) revealed the hydrogen ENA signal led the SKR signal by ~1.5 h while the oxygen ENA signal led SKR by ~2.2 h [Carbary et al., 2011a]. Notably, this cross correlation used observations from 2004, while the other one used observations from 2007, so the possibility exists of some time variability of the relation between the ENA and SKR. [35] From low latitude, ENA imaging provided an edgeon view of the plasma sheet. On the dawn side, sequences of ENA images evidenced a periodic tilting of the plasma sheet as seen in the slope of its centerline [Carbary et al., 2008b]. With respect to the plane of Saturn s orbit, the tilt angle varied from ~17 to 24 with a period of h; the maximum tilt occurred in phase with the maximum intensity of SKR radiation. Figure 16 shows a sample of the tilt angle period and its Lomb spectrum. The periodicity in the plasma sheet tilt was observed in 2004 when Saturn was near its Figure 14. ENA periodicities observed from the dawn side in The top panel shows periodicities in energetic hydrogen atoms, and the bottom panel shows periodicities in energetic oxygen atoms. The wavy curve is a model assuming a rotating asymmetric source plus an axisymmetric source (gray line); the dotted curve shows a 1/r 2 dependence [from Paranicas et al., 2005]. Figure 15. Typical Lomb periodograms of energetic hydrogen atoms (top) and energetic oxygen atoms (bottom). The spectral peak periods are identified in each panel [from Carbary et al., 2008a]. 10

11 Figure 16. Tilt angle of the centerline of the plasma sheet as seen in INCA images (top) and the Lomb periodogram of the tilt angle oscillations [from Carbary et al., 2008b]. Solstice. Later in the seasonal cycle, however, the plasma sheet shows no periodic oscillations in ENA images Magnetic Field Observations [36] The initial Cassini report of Saturn s magnetic field did not mention periodicities but did note that Saturn smainfield had changed little since the flybys of Voyager [Dougherty et al., 2005]. As more data became available, the periodicities in the magnetic field became readily apparent. Inspired by the Voyager-era interpretations [Espinosa et al., 2003a, 2003b], these periodic oscillations were explained in terms of a spiral wave moving radially outward from Saturn at the Alfvén speedrelativetocassini[cowley et al., 2006; Giampieri et al., 2006]. The apparent period of this spiral wave should therefore be Doppler shifted on account of the relative motion between it and Cassini in orbit. Wave speeds of ~50 km/s (or ~3 R S /hr) were deduced and shown to be consistent with the observed period [Cowley et al., 2006]. Correcting for this Doppler shift implied a magnetic period of h, at least from MAG data taken in the first 2 years of the mission [Giampieri et al., 2006]. The effects of a Doppler shift on the periodicities have been discussed by various authors [e.g., Cowley et al., 2006; Carbary et al., 2007b, 2011c] and, of course, depend on the relative wave-spacecraft speed as well as the angle between the wave and spacecraft velocity. Close to the planet (within ~15 20 R S ) Doppler effects can be considered significant enough to warrant correction, while in the outer magnetosphere, they may be ignored. [37] To eliminate effects of the ring current and FAC, magnetic observations may be confined to the innermost part of the magnetosphere to find the true magnetic period of Saturn. Two attempts have been made at this. Based on an inversion of a magnetic field model for a range of rotation rates, a tentative rotation rate of h was obtained with a dipole tilt of less than 0.1 [Burton et al., 2010]. However, a similar analysis of the data based on the maximum power in the non-axisymmetric components of a model field revealed that no period at all could be determined [Sterenborg and Bloxham, 2010]. Both attempts cited the need for more field observations close to the planet. [38] Because of the putative Doppler effects, analysts of the magnetic field periodicities did not attack the oscillations by direct spectral analysis, the method favored by radio wave and charged particle workers. Rather, they approached the field periodicities by comparing them to an established periodicity, usually that of the SKR. This method fitted the oscillations of each magnetic field component in spherical coordinates (B r, B θ, B f ) to a time-variable phase function (usually, a cosine function) [e.g., Andrews et al., 2008, 2010a, 2010b, 2011; Provan et al., 2009a, 2009b]. This phase fit method had the advantages of tracking the known time variations of the magnetic field period as well as any Doppler shifts. The method also allowed extrapolation outside the measurement interval as well as tracking the phase of the signal over long time intervals. Before any analysis was performed, the main (dipolar) field of Saturn [Dougherty et al., 2005; Burton et al., 2010], which has no known periodicity, was carefully subtracted from the observations, and a smoothing filter was applied to remove high-frequency oscillations (periods <<10 h) [e.g., Andrews et al., 2008, 2010a, 2010b]. Figure 17 shows an example of the magnetic field periodicities seen in the Cassini MAG data and demonstrates the filtering and fitting, while Figure 18 compares the [fitted] magnetic field period with the variable SKR period [Andrews et al., 2008]. [39] Initial results of this analysis, applied to MAG data from October 2004 to July 2006 when Cassini was at low latitudes, indicated a magnetic field period within a few seconds of the SKR period, although a slow drift of the magnetic phase might exist within the scatter of the SKR phase [Andrews et al., 2008]. A later analysis showed that similar oscillations existed in the high-latitude magnetic field observations made between mid-2006 and mid-2007, which required an extension of the equatorial phase model [Provan et al., 2009a]. Phase modeling of the magnetic oscillations at the equator was then related to the displacements observed in the center of the auroral oval by the Hubble Space Telescope during its campaigns in 2007 and 2008 [Nichols et al., 2008]. Specifically, phase differences of ~180 were obtained between the auroral center oscillations and the magnetic field (phase) oscillations [Provan et al., 2009b]. The amplitudes and phases of the magnetic field oscillations change with radial distance, with the (phase) gradients being larger on the nightside (~3 /R S ) than the dayside (~1 /R S )[Andrews et al., 2010a]. The phase speeds of the oscillations vary from ~150 km/s (nightside) to 500 km/s (dayside) and are consistent with the Alfvén speeds in the equatorial regions [Andrews et al., 2010a]. 11

12 Figure 17. Example of observed magnetic field periodicities (panels 1, 3 and 5) and their filtered rectifications with the main field removed (panels 2, 4, and 6), with attendant spacecraft location (bottom 3 panels) [from Andrews et al., 2008]. Figure 18. Magnetic field period (solid line) compared to the SKR period (dashed line) as a function of time from 1 January The actual magnetometer data from which the fit was obtained came from days 301 to 936. The bottom panel shows the deviation of the magnetic period from the SKR period [from Andrews et al., 2008]. [40] The discovery of the dual periodicity in the SKR led to the discovery of a similar duality in the magnetic field oscillations. Using the phase-guide approach on ~5 years of magnetometer data, equatorial and high southern latitude magnetic fields were shown to have the southern SKR period, while high northern latitude fields were shown to have the northern SKR period [Andrews et al., 2010b]. The duality in the magnetic field period was elegantly verified by a non-phase technique that counted the magnetic oscillations over several orbits and divided by the number of cycles; this approach determined a northern magnetic period of h and a southern period of h, in exact agreement with the dual SKR periods [Southwood, 2011]. Dual periodicities in the magnetic field have also been detected in the magnetotail [Provan et al., 2012]. At distances ~3 R S or more north of the model current sheet [Arridge et al., 2008a], the magnetic field exhibited the northern SKR period, while at similar distances south of the current sheet, the field had the southern SKR period. Furthermore, when the north and south oscillations were in anti-phase, the current sheet thickness itself was modulated by a factor of ~2 [Provan et al., 2012]. The post-equinoctial magnetic observations showed a convergence of the dual magnetic periods, as with the SKR and electron dual periods, but no crossing of the periods [Andrews et al., 2012]. Figure 19 displays the latest measurements of the magnetic field periodicity as compared to the SKR periods. [41] Magnetic field as well as plasma observations have also demonstrated periodic oscillations in Saturn s magnetopause and bow shock [Clarke et al., 2006, 2010a, 2010b]. The magnetopause oscillates with an amplitude of ~2 R S along the Saturn-Sun line, amounting to a ~10% change in the boundary radius [Clarke et al., 2006]. Such magnetopause oscillations occurred ~60% of the time at all local times sampled by Cassini [Clarke et al., 2010b]. Saturn s bow shock displayed similar periodic oscillations with typical amplitudes of ~1 2 R S throughout the local time range sampled by Cassini [Clarke et al., 2010a]. The periodicities of the bow shock and magnetopause were confirmed using a simple oscillation model tied to the magnetic phases established previously [Provan et al., 2009a] Aurora Observations [42] During the Cassini era, Saturn s aurora has been extensively imaged from both the Hubble Space Telescope (HST) in Earth orbit [e.g., Gérard et al., 2004; Badman et al., 2006; Grodent et al., 2005; Clarke et al., 2009] and from Cassini imagers including VIMS and UVIS [Badman et al., 2010, 2011; Carbary et al., 2012]. Unfortunately, neither of these imager data sets is continuous, but both were bunched into campaigns of several weeks each. Therefore, continuous monitoring for periodicity, which is possible for most of the MAPS instruments, is not feasible using the imagers. Nevertheless, some important information concerning auroral periodicity can be obtained from the sporadic auroral observations. [43] All evidence for periodicity in Saturn s aurora derives, so far, from oscillations discovered by HST observations of the auroral boundaries [Nichols et al., 2008, 2010a, 2010b]. Figure 20 shows one HST image of Saturn s southern aurora with its boundaries marked with crosses. The crosses are fit to a circle, which has a radius and a center. (Note that HST could not observe the entire auroral oval.) Known as a function of time, the X and Y center positions (in local time 12

13 Figure 19. Magnetic field periodicities compared to the SKR periodicities. (a) The north and south magnetic field periods (blue and red, respectively) compared to those from the north and south SKR (dotted lines). (b) The difference on these periods (t S t N ) compared with the solid line from the magnetic field and the dotted line from the SKR. Panel c shows the beat period (=t N t S /(t S t N )), while the bottom panel indicates differences between the SKR and magnetic field phases (blue for north, red for south). The vertical dotted line shows Saturn s vernal equinox [from Andrews et al., 2012]. Finally, during the 2009 equinox campaign, the centers of the northern and southern aurora were shown to vary by ~1 2 in the dawn-dusk direction and to depend on SKR phase, with the duskward displacement lagging the SKR power by ~90 [Nichols et al., 2010b]. Figure 22 displays the organization of the dawn-to-dusk (Y) displacement of the northern and southern aurora in northern and southern SKR phase. [44] No direct measurement of auroral periodicity has yet emerged from the VIMS or UVIS data sets, although their complete coverage of the auroral oval would certainly complement the partial coverage so far rendered by HST. Figure 20. Sample HST image of the aurora, projected onto the southern polar region of Saturn. The image was obtained in January 2007 when Saturn was close to it southern solstice. Crosses represent the equatorward edge of the aurora; the solid line shows a circle fit to the crosses, while the white cross shows the center of the circle. The fit yields a radius and center location that can be analyzed as a function of time [from Nichols et al., 2008]. coordinates) were then subjected to a periodogram analysis and revealed periods of h from a campaign in 2007 and h for a 2008 campaign [Nichols et al., 2008]. Figure 21 displays the periodograms for the circle centers. When actually plotted as a function of time, the centers of the circles described eccentric ellipses whose centers were offset by ~1 2 from the spin axis. A later HST study showed that both northern and southern auroral power depended on SKR phase, varying diurnally by factors of ~3 [Nichols et al., 2010a] Other Observations [45] Saturn s atmosphere and shape can also yield important information about the planet s rotation rate. The strong zonal winds of Saturn have been observed both remotely and proximally [Sanchez-LaVega, 1982; Sanchez-LaVega et al., 2000; Vasavada et al., 2006; Choi et al., 2009]. Tracking features embedded in Saturn s clouds allows measurement of the wind speeds. A review of all previous cloud tracking resulted in a pre-voyager estimate of ~10.67 h for Saturn s period [Sanchez-LaVega, 1982]. Cloud features are generally tracked relative to some established coordinate system such as that of SLS or SLS2. In this respect, the northern hexagon is observed to rotate at the radio period [Godfrey,1990;Baines et al., 2009], although its actual rotation period has not been obtained. Notably, in the SLS systems, some of the zonal winds appear to be moving faster than might be expected [e.g., Choi et al., 2009; Read et al., 2009]. [46] Two very interesting measurements of Saturn s period are derive from observations of the planet s gravity field 13

14 Figure 21. Lomb periodograms (top) of X and Y locations of centers of southern aurora observed by HST during campaigns in 2007 (left) and 2008 (right). In the bottom panels, the phases of these X and Y locations appear in SLS3 longitude [from Nichols et al., 2008]. and atmospheric vorticity. A rotation period of h results from using Cassini gravitation observations in combination with Pioneer and Voyager observations of its winds [Anderson and Schubert, 2007]. Derived from cloud observations, analysis of the atmospheric-planetary wave configuration (i.e., potential vorticity) leads to a rotation period of h for Saturn [Read et al., 2009]. Both of these atmospheric periods are faster than even the fastest SKR period (~10.6 h) and help resolve the issue of excessive zonal wind speeds. The potential vorticity method has been validated using Jupiter, which has a stable, well-established period. [47] Determining Saturn s true rotation rate is the ultimate goal of all periodicity measurements. One expects that a magnetospheric periodicity would lag that of an ionospheric periodicity, which in turn would lag that of an atmospheric periodicity, which finally should lag that of the true core. The degree of lag would depend on the viscosities of the different media. Furthermore, one may expect, based on analogy with Jupiter and the Sun, that a latitude-dependent differential rotation of the atmosphere at least may also be occurring and should affect measurements of the various periodicities [Dessler, 1985]. Figure 22. The locations of the centers of the northern aurora in northern SKR phase (top) compared to the locations of the centers of the southern aurora in southern SKR phase (bottom) [from Nichols et al., 2010b]. 4. MODELS OF SATURN PERIODICITY 4.1. Types of Models [48] Two basic types of models have been proposed to explain Saturn s magnetospheric periodicities. First, analytical 14

15 models describe particular observational effects, such as the periodicities of particles or magnetic fields. These models may not be self-consistent in the sense that they do not attempt to satisfy the Maxwell equations or MHD equations and they may or may not supply actual numbers such as the period, flux, or current strength. Indeed, they may accept as given the observed frequency of an observable and proceed heuristically to its consequences. Examples of this type of model are the magnetic anomaly model [Dessler and Hill, 1985; Hill and Dessler, 1976], the corotating convection model [Vasyliunas, 1978; Hill et al., 1981; Gurnett et al., 2007], the camshaft model [Espinosa et al., 2003a, 2003b], the wavy magnetodisk model [Carbary, 1980;Arridge et al., 2011], the rotating transverse fields model [Southwood and Kivelson, 2007; Andrews et al., 2010b, 2012], and the partially corotating ring current model [Brandt et al., 2010, 2011]. [49] A second type of model, numerical simulation models, do attempt to solve a set of physical equations, usually in a closed, self-consistent form subject to imposed boundary conditions. This category includes several general MHD models used to examine the dynamics of Saturn s magnetosphere and possibly its periodicities. The principal models are derive from the theoretical groups at Rice University (the Rice Convection Model, RCM) [Liu et al., 2010], Nagoya University/ UCLA [Fukazawa et al., 2007a, 2007b], the University of Washington (multi-fluid model) [Kidder et al., 2009], and the University of Michigan (Block Adaptive Tree Solar wind Roe-type Upwind Scheme, BATSRUS) [Hansen et al., 2005; Zieger et al., 2010; Jia et al., 2012a, 2012b]. Originally developed for the Earth or Jupiter, these models have all been adapted to Saturn and the solar wind conditions at Saturn. All the models have in common an aligned dipole as the main field, a rapid planetary rotation rate at or near the 10.7 h SKR period, and a plasma source at the moon Enceladus (~4 R S ). The models are all global, threedimensional solutions to the usual MHD equations governing mass conservation, momentum and energy balance, and current continuity. They differ in assumptions about rotationalinterchange effects, plasma sources, current drivers, solar wind effects, and regions of validity. [50] Whether numerical or analytical, three general types of models have emerged to explain the periodicities at Saturn. These are the rotating anomaly models [e.g., Jia et al., 2012a], waving magnetodisk models [e.g., Arridge et al., 2011], and natural oscillation models [e.g., Liu et al., 2010]. Rotating anomaly models propose that there are some features, whether located in the atmosphere, ionosphere, or magnetosphere, that rotate at essentially the period of Saturn and trigger the periodicities. Wavy magnetodisk models suppose a latitudinal up-and-down movement of the plasma sheet (or magnetodisk) that generates periodicities, especially in the magnetotail. Natural oscillator models explain the periodicities as the natural oscillation of Saturn s magnetosphere. Combinations of these ideas have also been proposed. [51] There are six main obstacles to any model of Saturn s periodicity. First, periodicity must be imposed in the absence of any known tilt of the magnetic axis relative to the spin axis and in the absence of any significant higher order magnetic multi-poles [e.g., Dougherty et al., 2005; Burton et al., 2010]. Second, periodicity near T 10.7 h must be imposed in spite of a notably sub-corotating magnetosphere in which the angular speed o of the plasma is less than 2p/T throughout most of the magnetosphere [Kane et al., 2008; Wilson et al., 2008; Thomsen et al., 2010; see also Hill and Michel, 1976]. (Corotation does seem to prevail within L ~3[Wilson et al., 2009].) Third, the same periodicity must be imposed on particles of opposite charge (ions and electrons) and no charge (energetic neutrals) over an extremely wide energy range (10 ev 1 MeV) that encompasses vastly different drift periods [Brandt et al., 2010]. Fifth, the models should account for the dual (or more) periodicities evident in different phenomena. Finally, the models must address longterm variations observed in the periodicities, as well as any phase changes that are observed. Let us state at the outset: in spite of some extremely vociferous hand waving, none of the extant models can overcome all these difficulties Rotating Anomaly Models Driven From the Ionosphere [52] Before proceeding, consider the connection between a rapidly rotating planet and its magnetosphere. Because of centrifugal forces, plasma concentrates in a magnetodisk in the equatorial region of the magnetosphere. The magnetodisk is coupled, more or less, to the planet s upper atmosphere and ionosphere by field-aligned or Birkeland currents J. The Birkeland currents close radially in the magnetodisk, transferring angular momentum from the planet to the magnetodisk by a J B force that causes plasma in the disk to move in a corotation sense with the planet (Figure 23a]. If the ionosphere-magnetosphere coupling is perfect, this motion is purely corotational and the ionosphere and magnetosphere rotate in perfect synchronism. Imperfect ionospheremagnetosphere coupling, either in the ionosphere or in the magnetosphere, disrupts this synchrony and causes drag effects [Hill, 1979]. Longitudinal asymmetries, or anomalies, in the ionosphere or magnetosphere can affect the coupling and, hence, the corotation of the magnetodisk. [53] The original magnetic anomaly model was first proposed to explain periodicities in the Jovian magnetosphere [Hill et al., 1974; Hill and Dessler, 1976]. In this model, high-order magnetic multipoles near a planet s surface cause a magnetic anomaly that allows plasma to preferentially escape in one longitudinal sector. As the planet rotates, the pressure of the longitudinally loaded sector blows open the field on the nightside while the field remains closed because of solar wind pressure on the dayside. Such an idea explained not only the magnetospheric periodicities and associated periodic accelerations in Jupiter s magnetotail [Carbary et al., 1976] but also observations of periodicities in energetic particles that escaped into the solar wind [Chenette et al., 1974]. This model competed with and was eventually (partly) superseded at Jupiter by the wavy magnetodisk model [Eviatar and Ershkovich, 1976; Carbary, 1980], although some form of the anomaly model may be required to explain the non-primary modulations at Jupiter [e.g., Woch et al., 1998; Anagnostopoulos et al., 1998]. 15

16 Figure 23. A corotating convection system seen in three dimensions (a) and from the north pole looking down (b). Although the pattern rotates at the corotation period, plasma flows outwards at one longitude (marked F C (2)) [from Gurnett et al., 2007] [54] In the case of Saturn, the first uses of the term anomaly appeared in explanations of the energetic particle periodicities [Carbary and Krimigis, 1982] and SKR periodicities [Kaiser and Desch, 1982]. These preliminary anomaly models suggested there existed an ionospheric source, presumably at high latitudes, that rotated with the planet and triggered periodicities when it reached a certain local time [Desch and Kaiser, 1981a, 1981b; Galopeau et al., 1991]. Unlike Jupiter, Saturn s anomaly is probably not magnetic because its period changes too rapidly to be caused by motions internal to the planet s magnetic dynamo layer [see Stevenson, 2006]. However, the change might reflect a reversing of the magnetic field such as that occurs at Earth, which would imply that current observations are occurring at a special time in the evolution of Saturn s magnetic field [Galopeau and Lecacheux, 2000]. If the anomaly cannot be attributed to a magnetic field asymmetry, then it must lie in the ionosphere or upper atmosphere. [55] Several authors have suggested that some ionospheric or thermospheric anomaly exists. The anomaly might be one of ionospheric conductivity. A conductivity anomaly would also impose a seasonal dependence because north and south poles receive seasonally more or less sunlight for ionization [Gurnett et al., 2009a, 2009b]. Alternately, such an anomaly might arise from longitudinal asymmetries in Saturn s upper atmosphere and thermosphere [Smith, 2006, 2011]. These asymmetries would be driven by asymmetric heating of the thermosphere from below. An ionospheric/thermospheric anomaly would generate field-aligned currents that would connect to the magnetosphere, ultimately producing the observed magnetic field periodicities. An anomaly in the auroral region could be modulated by the solar wind, specifically its velocity, and this modulation might possibly explain the slow change of the SKR period from year to year [Cecconi and Zarka, 2005]. Unfortunately, such an ionospheric or auroral anomaly has yet to be discovered (only inferred) nor were the Cassini instruments intended to detect such a feature. [56] The BATSRUS adaptation specifically attempts to generate periodicities by imposing a localized vortical flow in the (southern) ionosphere of Saturn [Jia et al., 2012a]. This flow vortex rotates with the planet and generates field-aligned currents that connect to the magnetosphere, producing, not surprisingly, virtually all of the periodicities observed: plasma, energetic neutrals, radio emissions, magnetic fields, and boundary movements. Figure 24 indicates the geometry of this vortex, which is itself an m =1harmonic pattern. As shown in Figure 25, the vortex model easily reproduces periodic features observed in the inner magnetosphere in plasma density and magnetic field [e.g., Gurnett et al., 2007]. Similarly, the model describes many of the magnetic field variations observed in the outer magnetosphere, as shown in Figure 26. Dual periodicities can be readily accommodated in this model by imposing a second vortex, rotating at the SKR-northern period, in the northern polar regions [Kivelson et al., 2011, 2012; Jia and Kivelson, 2012]. The twin vortices would also generate a periodic flapping of the magnetotail [Kivelson et al., 2012; Jia and Kivelson, 2012] Rotating Anomaly Models Driven From the Magnetosphere (and Those Not Specifically Driven From the Ionosphere) [57] Several models explain Saturn s periodicity as a consequence of an anomaly that exists in the equatorial region of the magnetosphere. A centrifugally driven convective instability in the magnetodisk can cause plasma outflow in one (or more) longitudinal sector. This asymmetry slowly slips relative to Saturn s internal rotation, with the slippage rate determined by the J B coupling between the magnetodisk and Saturn and by the drag force caused by the Enceladus torus [Gurnett et al., 2007; Goldreich and Farmer, 2007; Burch et al., 2008]. Such a model would explain the plasma and magnetic field periodicities in the inner magnetosphere in the vicinity of the Enceladus torus and E-ring (4 8 R S ). This idea is attractive because the source of the asymmetry is the magnetodisk and does not require an asymmetry in Saturn sinternalfield or ionosphere, which have not been observed. Furthermore, a centrifugal asymmetry in the inner magnetosphere could also drive the cam mechanism that generates periodicities and spiral geometries in the outer magnetosphere. Figure 23b illustrates the corotating convection system envisioned for creating this magnetodisk asymmetry. However, this model does not explain how the centrifugal instability maintains a single longitudinal asymmetry (i.e., an m =1 wave ) rather than multiple asymmetries (m > 1 harmonics) nor does it explain how the dominant m = 1 wave can persist on decadal time scales. 16

17 Figure 24. Field-aligned currents driven by a rotating vortex presumed in the southern polar region of Saturn (left panels) and its effect on the northern polar region (right). The vortex is shown at 2 times separated by 54 h. The m = 1 azimuthal structure is assumed [from Jia et al., 2012a]. [58] Observations of the periodicities in the magnetic field components have led to the rotating transverse fields model [Southwood and Kivelson, 2007]. In the initial version of this model, FACs flow between hemispheres along the quasi-dipolar field lines on a quasi-dipolar shell at L ~ 15. This current configuration generates a perturbation dipole field perpendicular to the main field. If the FAC strength varies sinusoidally in longitude, then the perturbation fields, which rotate with the planet, will evidence periodicities at the planetary period. Figure 27 schematically illustrates the transverse field model and its FAC system. The transverse magnetic field represents the cam field originally postulated by Espinosa et al. [2003a, 2003b]. A later version of the field model includes azimuthal sweep-back effects and connections to the SKR radiation: as the cam currents rotate through the dawn sector, they naturally excite the radio emissions known to peak in that sector [Southwood and Kivelson, 2009]. [59] The transverse magnetic field model has been used extensively in the interpretation of magnetic field periodicities. With the discovery of dual periodicities, the model has been extended to two rotating perturbation field systems: one rooted in the southern hemisphere and rotating with the southern SKR period, and one in the northern hemisphere and rotating at the northern SKR period [Andrews et al., 2010b, 2012; Provan et al., 2011, 2012]. Figure 28 exhibits the dual-rotating systems. In this case, the FAC systems do not cross the equator the northern system closes entirely in the northern hemisphere, and the southern system closes entirely in the southern hemisphere. The two rotating systems, operating in the inner part of the magnetosphere, can generally produce the observed perturbation fields 17

18 and, just as important, the phase relations between them. The perturbation fields can be envisioned as planet-centered transverse dipoles that rotate at their respective north and south frequencies. The actual sources of the perturbation fields are not specified. [60] A partial ring current has also been proposed as the cause of ENA and energetic particle periodicities [Brandt et al., 2008, 2010, 2011]. In its initial form, this model demonstrated that a combination of plasma rotational velocities and gradient-curvature drifts of energetic particles could reproduce the spiral patterns and dispersions observed by the INCA and LEMMS detectors, assuming that large-scale radial injections occur near midnight [Brandt et al., 2008]. A more refined version of this model generated magnetic field periodicities from constructing a three-dimensional pressure-driven current system, which is a type of partial rotating ring current (PRC) [Brandt et al., 2010, 2011]. In this case, the low-energy plasma is azimuthally uniform, while the high-energy particles become azimuthally asymmetric owing to injections. The energetic particle asymmetries effectively drive the partial ring current. As shown in Figure 29, this PRC model reproduces not only magnetic field periodicities (if not the quasi-uniform perturbations of the inner magnetosphere) but also ENA and energetic charged particle Figure 25. Examples of the periodicities resulting from the vortex model. The top panel indicates periodic variations in the Bf component of the magnetic field in the inner magnetosphere, while the bottom panel indicates similar variations in the plasma density. Compare these to the observed variations reported by Gurnett et al. [2007] [from Jia et al., 2012a]. Figure 26. Comparison of the perturbation magnetic fields observed by the Cassini magnetometer (blue traces) with those predicted by the vortex model (red traces) [from Jia et al., 2012a]. 18

19 Figure 27. Transverse field model in which field-aligned currents (FACs) flow on a dipolar shell at L ~ 15 (left), which generates a transverse dipole field exterior to the shell and a uniform field interior to the shell (right). The strength of the FACs varies sinusoidally in longitude, and the entire system rotates with Saturn to produce periodicities observed in the magnetic fields [Southwood and Kivelson, 2007]. Figure 28. A model of rotating perturbation fields that produce the dual periodicities in the magnetic field, as well as the observed phase differences. Top panel shows the perturbation magnetic fields of the south (red) and north (green) of these systems, superposed on the main magnetic field (dashed lines), while the bottom panel indicates the field-aligned currents that generated these fields (blue). The northern and southern perturbed fields, and their respective currents, rotate at the northern and southern SKR periods [from Andrews et al., 2010b]. periodicities as well as spiral structures, at least in several case studies examined. A numerical model of the PRC system, based on MAG observations, is under development [Tsyganenko et al., 2010] Oscillating Magnetodisk Models [61] In the outer magnetosphere of Saturn, periodicities apparently arise from the flapping motion of a plasma sheet [Jackman et al., 2009]. Two models explaining this periodic flapping postulate a mass or blob that rotates at the outer edge of the cam region, variously placed at 10 to 25 R S. In one model, the rotating blob exerts centrifugal forces that alternately stretch and contract the field as the mass rotates, and this stretching-contracting cycle generates periodic waves in the magnetodisk that travel radially outwards 19

20 Figure 29. Partial rotating ring current (PRC) model reproduces the magnetic field periodicities (a) by assuming a rotating pressure blob (b) generated by quasi-periodic injections. (c) and (d) Simulated and observed ENA emissions [from Brandt et al., 2010]. from the inner cam region [Carbary et al., 2007d]. In Figure 30, this eccentric blob model can reproduce the periodicities observed in energetic particles in the outer magnetosphere. In a second model, the solar wind ram pressure acts at an angle to the magnetodisk, which is usually tilted at angles between 0 and 27,andessentially buffets the blob upward and downward to generate the periodicities in the outer magnetosphere [Khurana et al., 2009]. This heavy-lift model has been employed to explain periodicities in magnetic current sheet crossings in the outer magnetosphere (Figure 31). The eccentric blob model has the advantage of operating through the equinoctial conditions, while the heavy-lift model should not operate at equinox. [62] While no tilt has ever been measured between the spin and magnetic axes of Saturn, the wavy magnetodisk continues to have appeal for explaining periodicities in the outer magnetosphere. Measurements of Saturn s plasma and current sheets exhibit a northward curvature in a bowl shape, at least when the solar wind approaches from a southern declination [Arridge et al., 2008a; Carbary et al., 2012b]. The wavy magnetodisk model supposes that the plasma sheet is somehow hinged at the outer edge of a cam region, such that this edge is displaced up (north) or down (south). 20

21 One can apply the same equations as for Jupiter s wavy magnetodisk [Carbary, 1980], albeit superposed on the general bowl shape. Figure 32 shows the wavy magnetodisk Figure 30. Waves propagating downtail from an eccentric cam anomaly can generate periodicities in particles observed in Saturn s magnetotail without recourse to any tilt between the spin and magnetic axes [from Carbary et al., 2007d]. and its relation to the inner magnetospheric cam. The wavy magnetodisk model naturally produces a spiral shape described by the early observations [Espinosa et al., 2003a, 2003b]. The wavy magnetodisk model has been applied on an orbit-by-orbit basis to the plasma and magnetic field observations of Cassini [Arridge et al., 2011]. However, fits to the multi-parameter wavy magnetodisk lead to wildly and unsystematically varying parameters. Even a small tilt (<1 ) of the magnetodisk might be enough to cause the observed plasma modulations in both the inner and outer magnetospheres [Morooka et al., 2009] Natural Oscillation Models [63] The MHD models were initially employed to estimate stand-off locations of the bow shock and magnetopause and generally agreed that Saturn s magnetosphere, unlike that of the Earth s, is sensitive to solar wind pressure but not IMF direction [Hansen et al., 2005; Fukazawa et al., 2007a]. Of relevance to Saturn periodicities, the Nagoya model evidenced plasmoids ejected tailward in quasi-periodic bursts at ~1 h intervals [Fukazawa et al., 2007b]. The Michigan MHD model demonstrated a similar quasi-periodic release of plasmoids, with the release frequency dependent on the solar wind pressure, mass loading rate, or axial tilt of Saturn relative to the solar wind [Zieger et al., 2010]. Plasmoid releases occurred even when the solar wind was quiescent with low ram pressure. However, the plasmoid releases of this model never achieved release periods under ~20 h for reasonable parameters and could not match the SKR period. Figure 31. When rammed by the solar wind, a rotating plasma mass will cause the magnetodisk to alternately go up and down, thus generating the periodicities observed in the plasma sheet [from Khurana et al., 2009]. 21

22 Figure 32. The wavy magnetodisk model seen in latitudinal profile (top) and how it generates a spiral wave of up-and-down motions of the plasma sheet in the outer magnetosphere (bottom) [from Arridge et al., 2011]. [64] A variation of the vortex model (without a vortex) explores the effects of changing solar wind conditions [Jia et al., 2012b]. Here centrifugal acceleration leads to reconnection in the magnetotail and to the formation of plasmoids. This process can take place independently of solar wind conditions, although the solar wind conditions can affect the rate of formation of these plasmoids [as in Zieger et al., 2010]. The tail reconnection and plasmoid formation is quasiperiodic and becomes faster as the solar wind dynamic pressure increases. However, without the ionospheric vortex, this quasiperiodicity does not achieve the 10.7 h SKR periodicity. [65] The Rice and Washington MHD models do not impose an m = 1 vortex, and their results differ from those of the Michigan model. These models stress the effect of centrifugal force on magnetospheric plasma and demonstrate the importance of the interchange instability [Kidder et al., 2009; Liu et al., 2010]. Both models impose a rotation rate near the ~10.7 h period and consider a cold inner plasma meeting with a hot outer plasma. This population inversion resembles a Rayleigh-Taylor instability and dynamically leads to multiple fingers of alternating hot and cold plasma permeating the magnetosphere. As the magnetosphere rotates, the fingers spread and bend, as illustrated in Figure 33. Unless very unrealistic plasma parameters are assumed, no m =1 finger pattern appears, so no definitive 10.7 h period can be produced. Changes in the mass-loading rate of the cold plasma can influence, though, the number and shape of the fingers [Kidder et al., 2009; Liu et al., 2010]. The possibility does exist that one or two of these fingers dominate the others and could thus produce a significant rotational periodicity, shown for Jupiter [Yang et al., 1994] and for Saturn [Winglee et al., 2011]. The finger configurations appear in Figures 33 and 34. The lifetime of any m = 1 feature would not be expected to be very long, however, since the interchange processes would continually modify the fingers. A persistent finger asymmetry in the outer magnetosphere would require a similarly persistent asymmetry of the plasma source in the inner magnetosphere. These fingers do seem very similar to the observed ENA blobs, albeit the ENA blobs should represent energetic plasma while the fingers would be cold plasma [Carbary et al., 2008d; Mitchell et al., 2009]. [66] There are subtle differences between the RCM and Washington multi-fluid models. First, the RCM model extends to a larger radial distance (by a factor of ~2) than the Washington model. Second, the fingers of the Washington model (Figure 33) appear in solar local time, while those of the Rice model (Figure 34) appear in a corotating frame, which explains the different sense of the spiraling. Third, the fingers of the Washington model seem notably wider than those of the Rice model, although this may be an artifact of the code resolutions rather than an actual feature of the models. Note also that CNO density of Figure 33 differs somewhat from the EETA of the Rice figure, the latter representing flux tube plasma content. [67] These MHD models are in the early stages of development and do not completely address the effects of a time-varying solar wind or the (possibly) asymmetrical mass-loading rate of the Enceladus torus. In particular, the random variability seen in the fingers suggests that the models cannot maintain a periodicity that lasts for a long time (months 22

23 Figure 33. Production of plasma fingers in a magnetosphere subject to interchange instabilities The asterisk follows one of the larger fingers in its rotation. Should the cold plasma features be compared to the energetic particle blobs seen in ENA observations? [from Kidder et al., 2009]. Figure 34. Simulated ion content after 30 h of simulation by the Rice Convection model. The contour lines indicate equipotential lines at 15 kv intervals [from Liu et al., 2010]. or years), let alone the phase stability noticed between, say, the magnetic field and SKR emissions. [68] Two other natural periodicity models have arisen. Although neither has been published, their novelty and possible relevance deserve mention. As with the magnetodisk models, one of these has its genesis in explaining a Jovian periodicity [Woch et al., 1998; Kronberg et al., 2007]. The model may explain Saturn s ~10 h period in analogy with Jupiter s 2 3 day quasi-period as consequences of internally driven mass loading and unloading rate [Rymer et al., 2011]. Released by Enceladus, mass in the inner magnetosphere builds up until the magnetosphere can no longer restrain it, at which point it is released. The buildup-and-release cycle for Saturn has a time scale in the range of ~8 12 h, while for Jupiter, it is 2 3 days. Because of the model s similarityto a Japanese deer-scarer fountain, the mechanism is called shishi-odoshi. [69] A model similar to shishi odoshi addresses the puzzle of how a magnetosphere rotating at angular speeds less than 2p/T can nevertheless have a period near T [Mitchell et al., 2010b, 2011]. Even if the mass loading is only a dribble, it can build up to a point where the magnetosphere must unload mass in the form of plasmoid release on the nightside. The release then triggers an azimuthal asymmetry or wave that gives rise to the periodicities. This release must be linked to field-aligned currents, energetic neutral blobs, and particle injections. The plasmoid release need not be periodic in itself, nor does the periodic wave need to persist for many rotations, since it will eventually be regenerated by plasma buildup. Like the rotating anomaly models, this 23