Saturn’s spin periodicities caused by a rotating partial ring current Krishan Khurana Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA,

The correct clock mechanism must explain: The rotation rate of SKR source in the summer hemisphere and its variations over the season. Plasma density variations in the inner magnetosphere at the SKR period. “Cam” currents in the inner magnetosphere at the SKR period. A rotating uniform field in the equatorial plane with B r leading B . Nearly out of phase relationship between B  and B  in the inner magnetosphere. Rotating partial ring current ENA rotations at the SKR period. Current sheet tilt in a frame rotating at the SKR period. The SKR clock has characteristics of both a rotating beam and a strobe. 2

A successful model must explain … Gurnett et al Summer Clock Winter Clock

The correct clock mechanism must explain: The “Rotation rates” of SKR sources in the summer and winter hemispheres and their variations over the season. Plasma density variations in the inner magnetosphere at the SKR period. “Cam” currents in the inner magnetosphere at the SKR period. A rotating uniform field in the equatorial plane with B r leading B . Nearly out of phase relationship between B  and B  in the inner magnetosphere. Rotating partial ring current ENA rotations at the SKR period. Current sheet tilt in a frame rotating at the SKR period. The SKR clock has characteristics of both a rotating beam and a strobe. 4

5 Gurnett et al. (2007)

The correct clock mechanism must explain: The “Rotation rates” of SKR sources in the summer and winter hemispheres and their variations over the season. Plasma density variations in the inner magnetosphere at the SKR period. “Cam” currents in the inner magnetosphere at the SKR period. A rotating uniform field in the equatorial plane with B r leading B . Nearly out of phase relationship between B  and B  in the inner magnetosphere. Rotating partial ring current ENA rotations at the SKR period. Current sheet tilt in a frame rotating at the SKR period. The SKR clock has characteristics of both a rotating beam and a strobe. 6

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Field-aligned current system proposed by Southwood and Kivelson (2007) 8 Equatorial view

The correct clock mechanism must explain: The “Rotation rates” of SKR sources in the summer and winter hemispheres and their variations over the season. Plasma density variations in the inner magnetosphere at the SKR period. “Cam” currents in the inner magnetosphere at the SKR period. A rotating uniform field in the equatorial plane with B r leading B . Nearly out of phase relationship between B  and B  in the inner magnetosphere. Rotating partial ring current. ENA rotations at the SKR period (partial ring current). Current sheet tilt in a frame rotating at the SKR period. The SKR clock has characteristics of both a rotating beam and a strobe. 9

10 Paranicas et al. 2005, GRL Khurana et al. 2009, JGR

In the equatorial plane dB r  dB  > 0 11 Andrews et al. 2010

A closer look at the SKR periodicities Gurnett et al

A Comparison of SKR and atmospheric rotation periods 13 Faster Rotation

Saturn’s summer clock For the summer clock, the plasma containing the SKR sources must be subcorotational and the field-aligned currents should be distributed in a sinusoidal fashion to account for the SKR’s periodic modulation. A plasma convection system with these essential properties was mooted by Gurnett et al. (2007) and Goldreich and Farmer (2007) to explain the plasma density periodicities in the inner magnetosphere. I will now show that the summer clock is a manifestation of the inner magnetospheric two cell convection system proposed by these authors. 14

15 Two cell convection models Goldreich and Farmer 2007, JGR Gurnett et al 2007, Science The magnetic field from a radial current generated by plasma outflow is zero at the center of the current sheet, precisely where the oscillating B  is seen. Cannot change sign of B 

ENA and partial ring current periodicities 16 The partial ring current impounds the inner magnetospheric plasma and pushes it inward creating an inflow. At the mouth of the inflow region (8-12 Rs), the plasma is hot and tenuous. In the outflow region, the plasma is cold and dense forming a partial ring current. The plasma in the ring current region may not be corotational but the pressure peak would be.

Two-cell plasma convection system 17 After Gurnett et al 2007 Assume a mass outflow rate of 300 kg/s, the width of outflow sector =  /2, D= 2 Rs. At r = 6 R S where the local plasma density is 30 cm -3 (Persoon et al. 2006), we get an average V r  ~1.35 km/s. Convection cycle time = 28 days or 60 rotations. Long memory Inertial currents driving the system would be too weak to detect directly.

Current system associated with the convection system 18

19 Surface of B  reversal moves northward

For very low northern hemisphere conductivity 20

Why are the return flow SKR sources quiescent? SKR generation requires accelerated electrons created by strong field- aligned electric potentials (~ 10 keV and higher). Weaker currents in the inflow region because plasma densities are lower and the region in submerged in subcorotating plasma. Large field-aligned potentials develop in regions just above the ionosphere to facilitate the MI coupling when the ambient plasma population is unable to support the large currents required (Knight, 1973). In fast-rotating magnetospheres, the high atomic-mass ions are confined tightly to the magnetodisc by the centrifugal forces. Ambipolar potentials develop which also confine most of the lighter ionic species and electrons to the magnetodisc and only hotter electrons with temperatures ~ 100 eV and higher are able to overcome the ambipolar potential and participate in current closure at high latitudes (Ray et al. 2009). 21

22 Schippers et al. 2008

Why are the inflow middle magnetospheric SKR sources quiescent? Current density required in the ionosphere for corotation enforcement in the equatorial plane is given by: (Nichols and Cowley, 2004) Thus at L = 6, assuming an outflow rate of 300 kg/s average current density in each hemisphere is 2.5 nA/m 2. Because mainly the summer hemisphere is supplying most of the torque, the summer hemisphere current should be doubled or = 5 nA/m 2 Also, because the southern hemisphere exerts torque on the northern hemisphere. The average current density may be 10 nA/m 2. This should be compared to the electron thermal current density given by qnv e,thermal. At L =6, the hot electrons have a temperature of only 50 eV and a density of ~ cm -3 for an estimated J s = 2 nA/m 2. At L =12, the density of 1 keV electrons is 0.1 cm -3 for Js (L=12) = 300 nA/m 2. 23

For very low northern hemisphere conductivity 24

The effect of enhanced conductivity in southern ionosphere 25 “Cam” currents can be generated without a sinusoidal conductivity distribution in the magnetosphere.

Explains electron density modulation 26 Gurnett et al. (2007) Explains why n e and B  are in phase (The outflow region (max B   has maximum density.

Explains “cam” currents 27 Does not require sinusoidal variation of ionospheric conductivity

In the equatorial plane dB r  dB  > 0 28 Andrews et al. 2010

Field perturbations in a partial ring current 29

Explains current sheet tilt 30

Explains why the SKR is both a rotating beam and a strobe 31

Conclusions The summer clock is a manifestation of the rotating partial ring current/inner magnetospheric two cell convection system partially proposed by Gurnett et al. (2007) and Goldreich and Farmer (2007). It explains the plasma density variations in the inner magnetosphere at the SKR period. It explains the “cam” currents in the inner magnetosphere at the SKR period. A rotating uniform field in the equatorial plane with B r leading B . It explains a tilted current sheet in the SKR rotating frame. The magnetospheric vortex would imprint itself on the ionosphere and possibly the thermosphere (the flywheel) explaining its persistence and longevity. 32

Reserve slides follow 33

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Paranicas et al. 2005, GRL 35

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The conceptual model explains seasonal variations of the clock periods. 37

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39 Sittler et al. 2006

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For low northern hemisphere conductivity 41