Saturn’s Magnetospheric Period

1. Saturn’s Magnetospheric Period Abigail Rymer, D.G. Mitchell, T. W. Hill, E. A. Kronberg and N. Krupp MOP Boston University 11-15 July 2011

2. Saturn’s deer scarer Enceladus Pre-tail collapse mass density Post-tail collapse mass density A Japanese “shishi odoshi”

3. Introduction All loaded magnetospheres have a natural mass loading rhythym that - in the absence of external or internal variability - produce a natural clocklike “magnetospheric rhythym”. The ‘dripping fawcett’ analogy. At Jupiter a quasi-periodic modulations have been observed with a period of about 2 to 3 days [Krupp et al., 1998; Russell et al., 1998]. Kronberg et al. [2007] described this quasi-periodic behaviour in terms of a cycle of internally driven mass loading and unloading. We use the same technique as Kronberg et al. 2007, to explore what the equivalent period at Saturn is expected to be.

4. after Kronberg et al. 2007

5. Anticipating our results The Enceladus source is estimated to be almost an order of magnitude less than internal mass loading at Jupiter. However 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 amount 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. As a result Saturn is intrinsically more mass loaded than the magnetosphere of Jupiter by a factor of ~ 4 to 6. It follows from this that the equivalent timescale at Saturn of the 2 to 3 day rhythm of Jupiter’s magnetosphere is expected to be between 8 and 18 hours.

6. Kronberg et al. (JGR2007) show the time constant depends on the initial current sheet configuration, the angular velocity and mass-loading rate. Radial and azimuthal field before (rec) and after (0) tail tearing Distance downtail of tail tearing Current sheet thickness Mass loading rate, kg/(m3s1) Angular rotation rate at tearing site

7. Jupiter and Saturn magnetotail properties

8. Jupiter’s magnetospheric period 2 days 3 days FWHM 1.25 – 5 days

9. Saturn’s magnetospheric period 10.8 hours FWHM 5 – 25 hours

10. Period derived from TOTAL magnetospheric mass content: An alternative method to calculate the mass unloading rate is possible if we know the mass loading rate (M_dot) AND the total mass in the system (M). The refilling timescale, , is at least M/M_dot . For Jupiter: M ~ 109kg and M-dot ~103kg/s ~106 seconds = 12 days. For Saturn: M ~ 106kg and M-dot ~75 kg/s ~ 1.3x104 seconds = 3.7 hours. (Arridge et al., 2006; Cassidy and Johnson 2010) M ~ 5x107kg and M-dot ~280 kg/s ~ 1.8x105 seconds = 2 days. (Chen et al., 2010) “Perhaps Jupiter and Saturn both relieve themselves more often then they have to – I do, don’t you?” anonymous.

11. Summary and musings Given appropriate parameters the natural mass-loading/unloading period at Saturn, exactly analogous to the quasi-periodic 2-3 day period at Jupiter, could be around 10-12 hours. This period is inversely proportional to mass loading rate and therefore an increase with in the Enceladus source rate results in a shorter period. We note that Zeiger et al., 2010 actually show the opposite effect. A final note in support of this theory, if the natural period of Saturn, like that known to exist at Jupiter, is not 10/11 hours, what is it? and where in the data is it? So, while this does not address dual North South periods, it does speak to the existence of a natural magnetospheric rhythym that (given approprite parameters) is somewhat close to the planetary rotation rate and therefore should be considered as we explore the mystery of rotational modulation at Saturn.

12. Saturn’s deer scarer Enceladus Pre-tail collapse mass density Post-tail collapse mass density A Japanese “shishi odoshi”

13. after Kronberg et al. 2007

14. Saturn’s azimuthal Carnot cycle 4. Rotation into weaker B-field cools 90 more efficiently than field aligned particles. Adiabatic process. 5. Pitch angle scattering re-isotropises the PAD again. Isothermal process.     3. Pitch angle scattering re-isotropises the distribution storing energy gained. Isothermal process. 1. Isotropic distribution on the nightside  2. Rotation into stronger B-field heats 90 more efficiently than field aligned particles creating “pancake” PADs. Adiabatic process.

17. Plasma follows paths of constant potential, V, (bottom half). Goertz et al., 1978.

18. Affect of changing ion production rate. ~3.25x 10 27 ions/s  For fixed parameters: Location of break off point 50 Rs velocity at break off point 200 km/s

19. Affect of changing azimuthal velocity at the break off point distance:  ~210 km/s FOR fixed parameters: mass loading rate 3x1027 ions/s break off point in the tail at 50 Rs.

20. ~210 km/s

21. Affect of changing break off point distance:  ~ 50 Rs For fixed parameters: mass loading rate 3x1027 ions/s velocity at break off point 200 km/s

22. Affect of changing ion production rate. ~3.25x 10 27 ions/s  For fixed parameters: Location of break off point 50 Rs velocity at break off point 200 km/s

23. Allowed parameter space for period to be between 10.5 and 11.5 hours: v = 200 km/s v = 150 km/s v = 100 km/s

24. Kronberg et al. (JGR2007) also show the time constant depends on the initial mass density, mass loading rate, and the threshold mass density at which the tail collapse begins. Post-collapse density, kg/m3 Pre-collapse density, kg/m3 Mass loading rate, kg/(m3s1) These values are less easy to guesstimate, however this form of the equation allows for an intuitive grasp of the physics of this process.

25. The Japanese “shishi odoshi” Enceladus Pre-tail collapse mass density Post-tail collapse mass density