An Update on Saturn's Planetary Period Oscillations -Surprises From

An update on Saturn’s Planetary Period Oscillations -surprises from the F ring orbits

Gabby Provan, Stan Cowley, Greg Hunt, Emma Bunce and Michele Dougherty

The r and theta components are Rev17 in anti-phase RPWS - pulsing of Saturn kilometric radiation (SKR)

CAPS/ELS - magnetopause oscillations Near-planetary rotation period oscillations ubiquitous throughout Saturn’s magnetosphere ‣ Their source is by no means obvious MAG/FGM ‣ Saturn’s internally generated field is -field oscillations apparently axisymmetric - e.g. After Gérard et al., 2006 Dougherty et al. [2005] • Near planetary period oscillations are observed throughout Saturn’s magnetosphere. • Saturn kilometric radiation (SKR) • magnetic field • hot & cold plasma populations • narrowband radio emissions • auroral oval position, emitted power • magnetopause & bow shock location • Their source is by no means obvious as Saturn’s internally generated field is close to axisymmetric (Burton et al., 2010)

• There are two PPO perturbation systems, one in the Northern hemisphere and one in the Southern hemisphere.

• Both oscillations are presented within Saturn ‘core magnetosphere’, L< 12 Rs. Br

• The periods, amplitudes and relative Br filtered amplitudes of the oscillations change over time.

• The PPO magnetic oscillation can be Btheta modelled by the following ‘m=1’ rotating field: Btheta filtered Bi (ϕ, t) = B0 i (t)cos(Φg(t)−ϕ −ψ i ) is the phase of a guide oscillation with period Φg close to the period of the oscillations Bphi ϕ is the azimuthal location of the observer - is the ‘phase difference’ between the ψ i guide oscillations and the observed Bphi filtered oscillations. - determined by a cross-correlation analysis.

North polar – Rev 32

For the northern polar oscillations, the Br and Btheta components are in anti-phase and the Bphi component is in leading quadrature.

For the southern polar oscillations, the Br and Btheta components are in phase, and the 𝑟𝑟 𝑟𝑟 𝐵𝐵 𝐵𝐵 Bphi component is in leading quadrature. θ θ 𝐵𝐵 𝐵𝐵

φ φ 𝐵𝐵 ‘Core’ revs 𝐵𝐵

𝐵𝐵𝑟𝑟 𝐵𝐵𝑟𝑟 θ θ 𝐵𝐵 𝐵𝐵

𝐵𝐵φ 𝐵𝐵φ North polar – Rev 32 In the ‘core’ magnetosphere the two oscillations beat together, constructively and destructively interfering in a manner described by their beat period and their relative amplitudes .

Rev 24 – Southern summer - Southern oscillations dominate. 𝑟𝑟 𝐵𝐵𝑟𝑟 Revs 120 and 126 – around equinox the oscillations 𝐵𝐵 have equal amplitudes in the core. The phi θ component is in lagging quadrature with r. θ Rev 120, theta is in lagging quadrature with r and in 𝐵𝐵 phase with phi 𝐵𝐵 Rev 126 theta is in leading quadrature with r and in anti-phase with r. Rev 120 and 126 are at different parts of ‘beat cycle’. φ φ 𝐵𝐵 ‘Core’ revs 𝐵𝐵

𝐵𝐵𝑟𝑟 𝐵𝐵𝑟𝑟 θ θ 𝐵𝐵 𝐵𝐵

𝐵𝐵φ 𝐵𝐵φ

• Two magnetic perturbation loops. • Quasi-uniform field within the ‘core’ region, and quasi-dipolar over the polar region • Within the polar region only the northern or the southern oscillations are observed. • Within the ‘core’ magnetospheric region (L<12 Rs) both oscillations are observed.

Northern polar polarization phi in leading quadrature with r r and theta components in anti-phase Northern core polarization phi in lagging quadrature with r r and theta components in anti-phase

Southern core polarization phi in lagging quadrature with r r and theta components in phase

Southern polar polarization phi in leading quadrature with r r and theta components in phase

Black lines the axisymmetric planetary field, green lines and symbols the electric currents, blue lines and symbols the resulting perturbation magnetic field.

Northern polar region

BiN (ϕ, t) = B0 iN (t)cos(Φ g (t)−ϕ −ψ iN )= B0 iN (t)cos(Φ N (t)−ϕ) = B0 iN (t)cos(ΨN (ϕ,t))

Equatorial core region (L< 12 Rs)

Bi (ϕ, t) = B0 iN (t)cos(ΨN (ϕ, t))+ B0 iS (t)cos(ΨS (ϕ, t))

Southern polar region

Bis (ϕ, t) = B0 is (t)cos(Φ g (t)−ϕ −ψ is )= B0 is (t)cos(Φ s (t)−ϕ) = B0 is (t)cos(Ψs (ϕ, t))

Black lines the axisymmetric planetary field, green lines and symbols the electric currents, blue lines and symbols the resulting perturbation magnetic field.

• With increasing time these current system rotate about the vertical axis with slightly different rotational periods, producing beats in the equatorial magnetosphere where the two quasi- uniform field co-exist, but single periods in the equatorial magnetosphere where the two quasi-dipolar field are uniquely present.

Northern polar region

BiN (ϕ, t) = B0 iN (t)cos(Φ g (t)−ϕ −ψ iN )= B0 iN (t)cos(Φ N (t)−ϕ) = B0 iN (t)cos(ΨN (ϕ,t))

Equatorial core region (L< 12 Rs)

Bi (ϕ, t) = B0 iN (t)cos(ΨN (ϕ, t))+ B0 iS (t)cos(ΨS (ϕ, t))

Southern polar region

360 Bis (ϕ, t) = B0 is (t)cos(Φ g (t)−ϕ −ψ is )= B0 is (t)cos(Φ s (t)−ϕ) = B0 is (t)cos(Ψs (ϕ, t)) τ = N ,S  dΦ   N ,S   dt  Black lines the axisymmetric planetary field, green lines and symbols the electric currents, blue lines and symbols the resulting perturbation magnetic field.

• Two magnetic perturbation loops. • Consistent with two systems of rotating field aligned currents • Very important when comparing SKR and mag PPO observations.

Hunt et al., 2014, 2015 ΨS ,N (ϕ,t) = Φ g (t)− ϕ −ψ S ,N (t) = Φ S ,N (t) − ϕ

Φ S ,N (t) is the phase of the magnetic oscillation at local noon – analogues to universal time is the phase of the magnetic oscillation at a specific local time Ψ (ϕ,t) S ,N – analogues to longitude.

Ψ (ϕ,t) = 0 this defines when the quasi-uniform ‘core’ field points radially away from the S ,N planet – this is analogues to Greenwich!

North/South plane Equatorial plane

DAWN

The principal field-aligned currents flow into the ionosphere on the left and out on the right – producing a quasi-uniform perturbation field In the equatorial magnetosphere. DUSK DAWN PPO results presented @ ISSI 2015 Bis (ϕ, t) = B0 is (t)cos(Φ g (t)−ϕ −ψ is )= B0 is (t)cos(Φ s (t)−ϕ) BiN (ϕ, t) = B0 iN (t)cos(Φ g (t)−ϕ −ψ iN )= B0 iN (t)cos(Φ N (t)−ϕ)

Bθ

Bϕ

Psi_s and psi_n are determined for all 3 components of the magnetic field on a rev by rev basis. Plotted with respect to the S and N guide period, 10.7 h in the S and N format, where the expected phase difference between r and theta and r and phi are subtracted from theta and phi. If only N or S oscillations present - would result in all phases lying on the black line. Black line represents the changes in phases of the oscillations over time with respect to the guide phase, so this line is the phase of the southern and northern oscillations plotted with respect to the guide phase. This phase gradient then defines the period of the N and S oscillations, plotted in the top panel .

PPO results presented @ ISSI 2015

- used 5-Rev running fits to make piecewise linear fits for both N-format (top two panels) and S-format (bottom two panels) data τ τ = g ατ ψ ′(t) = α t + β  g  1−   360  1 N Calculate the variance for each fit using directional = ( − (ψ −ψ ′( ))) statistics, best fit gives the minimum variance. V ∑ 1 cos n tn N n=1

Coalesced periods suggest the presence of weak inter-hemispheric coupling of the two current systems that maintain commonality of the periods in antiphase during this interval

The total deviation in magnetic phase from antiphase over the one-year interval was no more than 45° -difference in the mean periods of the two systems of no more than 6 sec.

The associated perturbation field are such that the quasi-uniform (r, phi component) field in the equatorial region tend to cancel each other out, while the co-latitudinal fields add – connecting the perturbation fields of the two systems from pole to pole.

The resulting current system has upward and downward field-aligned currents located at the same local time in the two hemispheres, closing principally through the central region of the magnetosphere – thereby producing a common rotating force on the plasma. PPO current and perturbation field looking down at planet from the North.

Green circles dots and crosses indicate current flow out and into plane of diagram – Representing downward and upward FAC.

Blue line shows perturbation field lines and green lines show orthogonal current streamlines. PPO current and perturbation field looking down at planet from the North.

Green circles dots and crosses indicate current flow out and into plane of diagram – Representing downward and upward FAC.

Blue line shows perturbation field lines and green lines show orthogonal current streamlines.

Under these antiphase conditions, the thermospheric and ionospheric two-vortex flows which drive the current and perturbation fields flow in the same sense as each other in the two ionosphere – out of the plane of the diagram in the polar region and reversing into the plane of the diagram in the regions equatorward of the principal FAC in both hemispheres.

The flow driven from one ionosphere will generally exert a drag force on the other ionosphere, at least in the region of outer closed field lines where the principal PPO-related field-aligned currents flow (Hunt et al., 2014, 20.15) – thus tending in this relative phase condition to reinforce the two flows. These flows combine to drive associated rotating twin-vortex flows within the magnetosphere via the above force, thus tending in this relative phase condition to reinforce the two flows.

These flows also combine to drive associated rotating twin-cortex flows within the magnetosphere via the above force- thus giving rise to e.g. the ‘plasma-cam’ effect described by Burch et al., 2009.

The consequent in-phase condition of the field-aligned currents (with respect to the ionosphere) in the two hemispheres also results in approximately in-phase modulation of the northern and southern SKR emissions.

Grey-scaled SKR power plotted modulo 360 guide phase vertically – showing 2 cycles of phase.

Lighter grey corresponds to higher SKR power.

Northern (RH) SKR emission with N and S SKR periods (southern SKR – period determined over shorter intervals of continuous measurements)

Southern (LH) SKR emission with N and S SKR Periods.

Note in-phase SKR emission at least for earliest part of coalesced period

In-phase SKR emission = anti-phase magnetic PPO Perturbation system. k=northern amplitude/southern amplitude k > 1 = Northern dominance

Bθ

Bϕ Summary of new results

(1) From mind-2013 to mid-2014 the periods converged. (2) When the periods converged the mag PPO phases were phase-locked in anti- phase. (3) The period crossed in mid-2014 and currently the northern oscillation is dominating the southern.

Results from the F ring orbits (and the pre F-ring orbits)

F-ring ‘ White-knuckle’

periapsis apoapsis Southern Polar

Northern Polar

SUMMARY OF NEW RESULTS

Southern phases and periods

Southern phases and 5 rev fits

Plot shows variance between linear fits of varying periods and observed phases. Red line shows best-fit southern period.

Note the oscillations in the southern period starting around Rev 242 Northern phases and periods.

Northern phases and 5 rev fits

Plot shows variance between linear fits of varying periods and observed phases. Blue line shows best-fit northern period.

After Rev 242 the periods (observed in the polar region!) start to converge and diverge – at the beat period.

Northern and southern phase models plotted versus a gp of 10.7 h. When the periods cross they are in-phase.

Southern polar amplitude

Northern polar amplitude

When the oscillations are in anti-phase -the periods move together and their amplitude increases. Opposite effect when the oscillations are in phase

When the oscillations are in anti-phase -the periods move together and their amplitude increases. Opposite effect when the oscillations are in phase (purple line shows oscillations in anti-phase, orange line shows oscillations in phase)

We have observed PPO periods converging when the PPOs are in anti-phase before – But not studied the amplitude modulations.

The r and theta amplitude modulations are in-phase – this is not a straight forward interference of the two oscillations (we think). Andrews et al., 2012

The r and theta amplitude modulations are in-phase – this is not a straight forward superposition of the two oscillations (we think).

Probably not related to the changing solar activity.

When the oscillations are in anti-phase -the periods move together and their amplitude increases. Opposite effect when the oscillations are in phase (purple oscillations in anti-phase, orange oscillations in phase)

Similar behaviour seen in 2012/2013. Not related to solar activity.

SUMMARY OF NEW RESULTS

(1) From mind-2013 to mid-2014 the periods converged. (2) When the periods converged the mag PPO phases were phase-locked in anti-phase. (3) The period crossed in mid-2014 and the northern oscillation is dominating the southern. (4) We start to observe new and unusual PPO behaviour around Rev 242, when orbital cadence drops to below 10 days. (5) Periods move together when oscillations are in anti-phase – and amplitude of the oscillations increases. Periods move apart when oscillations are in phase – and the amplitude of the oscillations decreases. (6) Do not think that these changes are due to changes in external solar or solar wind conditions – though this is still a small possibility!

Plasma sheet modulations Error analysis.

Relative to guide phases corresponding to fixed period, , the total change in the period can be expressed as:

the “error” in Δψ might typically be ~45°, with the higher cadence SKR data in these intervals certainly confirming that no “whole cycles” are lost via period variations between Rev-to-Rev determinations of the magnetic phases. Then taking τ ≈10.67 h and T ≈ 200 days yields an uncertainty in the mean period of δ (τ )≈ 0.003 h (i.e., ~10 s), entirely compatible with the uncertainties in period previously quoted by Provan et al. (2013, 2014). Determining the northern and southern phase models

BiN (ϕ, t) = B0 iN (t)cos(Φ g (t)−ϕ −ψ iN )= B0 iN (t)cos(Φ N (t)−ϕ) = B0 iN (t)cos(ΨN (ϕ,t))

Bis (ϕ, t) = B0 is (t)cos(Φ g (t)−ϕ −ψ is )= B0 is (t)cos(Φ s (t)−ϕ) = B0 is (t)cos(Ψs (ϕ,t))

On a rev by rev basis we determine ψ iN and ψ is for all three components of the magnetic field with respect to a guide phase. Plot these in the ‘Northern’ and ‘Southern’ phase format – takes account of the expected polarization of the oscillations. We plot the ‘r’ component as is, and then add/subtract the expected phase different between the r and phi component and the r and theta component.

If only N or S oscillations present - would result in phases for all three component being equal.