Comparison of magnetic to SKR phases after Saturn equinox G. Fischer 1, D.A. Gurnett 2, W.S. Kurth 2, S.-Y. Ye 2, and J.B. Groene 2 (1)Univ. of Graz, Graz, Austria (2)Univ. of Iowa, Iowa City, USA 1st ISSI Team Meeting, Oct. 2015

Saturn‘s magnetic field is highly axisymmetric (only dipole, quadrupole and octupole needed to model the field), but despite of that SKR is modulated with the rotation of Saturn Magnetospheric period oscillations (MPO) Suggestion: MPO (Andrews et al., 2010) is better expression than PPO (planetary period oscillations) since the period of the planet should be constant (10h 32min 45s±46 s after Helled et al., 2015)

SKR generation mechanism: radiated at local electron cyclotron frequency f ce =eB/m e via CMI (Cyclotron Maser Instability) mechanism (unstable hot electron distribution converts its free energy to EM waves) in auroral regions with downgoing e - SKR 100% circularly polarized (elliptical above 30° magnetic latitude), radiated in R-X mode (right-hand extraordinary mode), i.e. RH SKR from northern hemisphere, LH from southern SKR flux density and polarization spectra for 3 days for equatorial observations in 2007 (from Lamy, 2011). SKR-north: observable above 20°S, SKR- south: below 20°N

SKR rotational modulation shows two periods before equinox, and mainly one period after equinox. Not only the periods are similar, but also the phases of northern and southern SKR. Icarus, July 2015

Separation of SKR flux by polarization/hemispheres to get N+S periods Real double periodicity before equinox: 10.8 h for S- SKR, 10.6 h for N-SKR Red arrow shows that N period makes jump right after equinox (11 Aug. 2009)

Similar SKR phases from March 2010 until February 2011 and August 2011 until June 2012 (afterwards it‘s hard to tell) Possible disruption of N-S phase lock by Great White Spot SKR phases are defined as phases of (broad) SKR maxima relative to guide phase with constant period of h Comparison of N to S phases requires same guide period for N+S and choice of  g,n =  g,s =0° at t=0 (Jan. 1, 2004)

Rotation rate  i (i for north or south) derived from slope d  d,i /dt (tracking SKR maxima) in phase plot Determination of SKR rotation rate from tracing the phase of SKR maximum Phase tracing follows SKR maxima from plot of integrated SKR intensities vs. time and guide phase (constant guide period)

Did north and south period cross or not? According to phase tracing they did cross right after equinox (not seen in tracking filter analysis), but it is not important Important is the phase and period matching in March 2010 When will we have two periods again?

Different interpretation of what happens to SKR north right after equinox compared to Lamy (2011) Southern period signal in north SKR due to amplitude modulation by orbit

Northern SKR of 2007 organized with guide periods of h and h (amplitude modulation by Cassini orbit)

Why are there such differences between SKR and magnetic field period after Saturn equinox? Smoothed SKR periods over 4 years compared to magnetic field periods derived by Provan et al. (2013, 2014) Merging of SKR periods after equinox sounds reasonable due to similar conditions in northern and southern hemisphere No merging of magnetic periods found by Provan et al. (2013) Understanding of method of Andrews et al. (2012) is difficult

Magnetic field model of Andrews et al. (2012) assumes uniform perturbation fields rotating with different periods close to equatorial plane in N+S hemisphere caused by rotating current systems

S-format (guide period 10.7 h) and N-format (10.64 h) magnetic phase plots plots versus time. Deviations from true phase (solid black line) depend on phase difference  MAG and amplitude ratio k (plots for k=0.5, 1, 2) between N & S (Provan et al., 2013)

Comparison of phases: SKR phase (magenta crosses or white background color) to magnetic field phases of B r (red), B  (green) and B  (blue) of north and south over 4 years Same guide periods/ phases are need for SKR & magnetic field!

All phases are brought to a common phase after model above: Phase of B r is unchanged:  rn (t)-  in =  rn (t),  rs (t)-  is =  rs (t) Phase of B  :   n (t)-   n =   n (t)-180°,   s (t)-   s =   s (t) Phase of B  :   n (t)-   n =   n (t)-90°,   s (t)-   s =   s (t)-90° Phase of SKR:  SKRn  SKRn -90°,  SKRs  SKRs +90° Upward current (downgoing e - where SKR is created) is 90° behind for north (comes later at larger SKR phase) and 90° ahead for south (comes first at smaller SKR phase) Phase difference  SKR =  SKRn -  SKRs =0° means  MAG =180°!

Northern hemisphere: partial agreement in E1, fair agreement in interval E2, very good agreement for E3 and E4 Early part of E1 (days ): right after equinox bad agreement between SKR and magnetic phases Later part of E1(days ): SKR phase is similar to green dots (B θ component), shift of blue/red dots (B  /r ) by ~120° (red arrows) can lead to good agreement

Southern hemisphere: good agreement in E1 after day 2300 (April 2010), excellent agreement in E2, agreement of green dots (B θ ) to SKR phase in E3, and fair agreement in E4 E2: southern dominance (k<<1) and most excellent agreement pointing to problematic nature of employing piecewise linear fits E3: 180° shift of B  /r (blue/red dots) would lead to excellent agreement between MAG and SKR phases. This points to  MAG =180° (k>1), and  SKR,N =  SKR,S =  MAG,S

Formulas for magnetic phase deviations for important special case of similar periods and phases (i.e.  SKR =0 implies  MAG =180°;  rs =   s =180° for k>1, E3 south;  rs =   s =-120° for k  1,  MAG =190° for E1, i.e. single B  -component shows true mag. phase!)

The case of interval E3, south Provan et al. (2013, 2014) determined magnetic period of E3 by simply connecting phase values from end of E2 to beginning of E4 (white line) which can be criticized: Real magnetic phase values at start of E4 are ignored Conditon of 0.2<k<5 of their method is violated with k  6 No physical reason for linear relation of phase with time (see E2) No S SKR signal corresponding to their derived period of h Ignorance of clear southern SKR signal at ~10.64 h, and claim that it is a N signal (DF and polarization point to South!) with S oscillation amplitude below detectability in E3 Do not take special case of same periods/phases of N+S into account (a priori exclude coalescing periods)

Calculated SKR phase deviation for after this model with orbit-averaged deviations determined by prolonged seeing of SKR around Cassini apoapsis. Constant SKR phase deviation  no change in period, i.e. clocklike behavior for rotating source! Is an SKR phase correction needed? Model of rotating SKR source after Andrews et al. (2011) and „seeing“ of SKR at ±4 LT from sub- s/c meridian

Interval E2 south (day ): Cassini apoapsis local time shifts from 18 LT to 15 LT. Predicted SKR phase deviations of 140° to 70° but agreement between SKR S and MAG phases (k  6) is so excellent  no SKR phase correction warranted Where are the SKR sources viewed from LT? Should be around LT, and phase of those sources is around  S =0° (i.e. clock-like!) according to Fig. 5 of Lamy (2011). Note that strongest SKR sources at 8 LT are ~270° and not at maximum  S =0°.

Clock-like source vs. rotating source For Cassini going around Saturn in eastward direction we would miss one rotation of a strictly rotating signal each time Cassini completes one orbit (e.g. 360°/20 day=18°/day) However, rotating SKR signal can appear as clocklike! Magenta line=Cassini LT, SKR sub-solar longitude stays constant despite LT change (right), predicted phase change for rotating SKR source in white dashed line (left figure)

Major SKR component behaves like a clock (no rotation rate correction!) – minor rotating SKR component can be seen besides main emissions at 120° (north) and 180° (south) Normalized N+S SKR intensities with respect to guide phase of variable period (clocklike SKR clusters around horizontal lines)

Summary Saturn kilometric radiation (SKR) period is varying with time and had 2 periods attributed to northern & southern hemisphere before equinox (which cross shortly after equinox) SKR of N+S have similar periods and phases from March 2010 until Feb and from Aug until June 2012 Tracking filter analysis technique and tracing of SKR phase with respect to a constant guide phase yield similar results Comparison of SKR periodicities after equinox to planetary period oscillations of magnetic field shows major differences Comparison of phases (SKR to MAG) shows that agreement can be obtained (for part of E1 and E3 south) when single B  - component is tracked (special case of  MAG =180°) No correction of SKR phases w.r.t. local time of spacecraft seems to be needed. Points to clock-like SKR behaviour (no rotation rate correction necessary!), as model of rotating SKR source cannot explain this.

SKR separation by polarization 1 st method: each time-frequency measurement with SNR>10 & 0.5<d c <1.1 is LH and SKR south (-1.1<d c <-0.5 is RH and SKR north). Method does not take superposition of RH & LH into account (Fischer et al., 2014; similar to Lamy, 2011). 2 nd method: for each time-frequency measurement northern and southern flux (S N, S S ) are calculated with the following equations: S N and S S are calculated from measured intensity S and circular polarization d c, only error of d c around 10% has to be taken into account (Fischer et al., 2015). S N /S S ratio 0.1 to 10 1 st and 2 nd method yielded almost identical results.

No real difference between Fischer et al. (2014, left) and (2015, right)

Contour plot of phase difference   -r vs. 1/k and  B between N and S (Cowley & Provan, 2015) Provan et al. (2013) One or two periods? Fischer et al. (2015)   -r is used as indicator of a beat phase  B between between north & south. For k  1   -r should oscillate between 270° (-90°) and 90° with time. Is this an unequivocal evidence for two periods in 2010? Not really, because the same signature of   -r can be produced by a small oscillation around  B =180°! Note that  SKR is not exactly 0° but varies around 0° over several tens of days.

Panel (c) of Fig 4 from Cowley & Provan (2015) show   -r for consecutive periapsis passes with predicted variation between -90° and +90° Note the points far from the predicted values e.g. 30° for Rev 131, -60° for Rev 133, 45° for Rev 134, 40° for Rev 137, 125° for Rev 139, -170° for Rev 142, 120° for Rev 143 Deviations of   -r from ±90° can be explained for Revs 131, 134, 143 when  B =0°,180° but not for the others! Errors in phase of ~10° cannot explain the large deviations

Deviations of -60° for Rev 133, 40° for Rev 137, 125° for Rev 139, - 170° for Rev 142 can only be explained by a value of  B  0° or 180° by slight variations of 1/k and  B  B around 180° as suggested by similar N+S SKR phases would mean just one magnetic period from spring 2010 until early 2011 (Fischer et al., 2015) Same plot as Cowley & Provan (2015) including smaller k

 B  180° implies following the green B  -component! B  value at Rev 131 is in bad agreement with beat phase model of Provan et al. (2013) A true N magnetic phase in E1 following the green arrows is in good agreement with the SKR north phase! Amplitude of B r is small and constant from days 2300 to No minimum close to 0 in B r or B  at Revs 134, 143 as beat phase model predicts it Unclear over which distance anti-parallel perturbation fields (  B =180°) superpose