Towards jointly-determined magnetospheric periods

Transcription

1 Towards jointly-determined magnetospheric periods Dave Andrews ISSI, October 2015

2 Outline Lots of independent work done on determining rotation periods of various magnetospheric phenomena at Saturn Evidence points towards a common underlying period (and phase) for each of the Northern and Southern systems Best measures of the properties of the underlying clocks will be obtained by using all available data to obtain a single time-varying rotation period More data - better temporal and frequency resolution More opportunities to detect transient phase skips / instantaneous period changes etc. Keeps everyone happy (maybe?) However, doing this presents several critical problems, as the nature of observations of the SKR, magnetic field, plasma densities are all unique Essentially, a need to combine both remote measurements and in-situ Single approach needed that is appropriate for all data sets 2

3 Observables Core Magnetic Field In-situ, purely rotational m=1 Superposition of N&S Polarization reveals N or S Well sampled Perturbed by fields due to ring current (low latitude), auroral field-aligned currents (high latitude) Lobe Fields Different polarization Pure N or Pure S? SKR Remote measurement Complex beaming LT dependent intensity Equatorial shadow zone Polarization reveals N or S (but incomplete?) Solar wind signal also present? Continuously measured ENA Remote and in-situ? Cannot separate N & S- driven emission Intermittently measured (high latitude orbits best for imaging) Plasma moments / fluxes Hot and cold plasma densities In-situ measurements - rotating m=1 No polarization - cannot resolve N or S independently Cold plasma density has very steep spatial gradients Others: remote Narrowband emissions (continuous) Auroral Hiss (continuous) UV emission (imaged) IR emission (imaged) Others: Boundary crossings (difficult to include) Others: ground based Probably not regular enough to be useful here? 3

4 Examples of previous analyses methods Magnetometer data: Remove internal field using (e.g.) Burton et al. model 5-20 h band-pass filter, to suppress ring current fields + higher-frequencies Select (e.g.) core-region data intervals on each orbit Sinusoidal fits to each component on each orbit - phase relative to arbitrary guide determined Results negated if amplitude is low compared to remaining noise Results also negated if RC fields of similar amplitude and effective period (r, θ components), or auroral currents (φ and r) SKR data: Separation by polarization, or spacecraft location Lomb-Scargle periodogram - trace maxima Or, Kurth et al. / Fischer et al. phase tracking methods 4

5 Description of the data sets For any modulated quantity A: Static, or slowly varying amplitude Position-dependent phase shift (visibility, clock vs. strobe etc.) A(r,t)=A 0 (r, t) cos ( (t) A (r) A ) Common phase function Constant offset Example - magnetic field: m=1 rotation {0º, 0º, 90º} B i (r,t)=b i0 (r, t) cos ( (t) ' i r i ) radial propagation SKR visibility function ξ(r) will be more complex In-situ particles can be written into this framework as well (probably?) A Lomb-Scargle approach (or something like it) is required Introducing -ξ(r) (variable in along-orbit time) effectively the same as un-even sampling of the data 5

6 Position dependent SKR phase SKR ξ(r) simply approximated in Andrews et al Took Laurent s measurements of SKR brightness vs. LT Assumed a restricted viewing of the SKR sources (beaming) Computed LT - dependent phase deviation Visualization of position-dependent phase Guide phase or pure strobe Rotating 6

7 Directional statistics 7 Statistics of angular quantities (modulo 2π, 360º etc.) Phase organization in a a set of measurements {Ai, Φi} can be computed. Angles Φi weighted according to amplitudes Ai Individual weights can be negative Positive contribution since: cos(x) = -cos(x+π), sin(x) = -sin(x+π) Calculate Degree of organization R: R = 0: no organization - values are evenly distributed throughout 360º R = 1: perfect organization R 0.78: equivalent to a pure sinusoidal variation Ai = A0 cos (Φi) Mean angle + variance (assuming a wrapped normal distribution) {A i, i} C = S = P i A i cos( i ) pp i A2 i P i A i sin( i ) pp i A2 i f(θ) σ = R = tan = q p θ / deg. R~0.94 S 2 + C 2 = S/C R~0.35 2lnR Figure A1

8 Lomb-Scargle Spectral power at a frequency w: P (!) (P A i cos(!(t i )) 2 P cos2 (2!t i ) + (P A i sin(!(t i )) 2 P sin 2 (2!t i ) Determine tau that makes P(w) invariant My approach: P (!) (P A i cos(!t i (r) i )) 2? + (P A i sin(!t i (r) i )) 2? Include a position dependent phase Implicitly makes temporal sampling uneven. Stochastic phase drifts always present due to orbital motion. Normalization scheme still causing trouble. 8

9 Revised approach Pre-process measured time-series as necessary Magnetic field: remove internal field, ring current, group into spatial regions SKR: separate polarizations, mask shadow zone, correct for r -2 Others: various Construct ξ(r) for each input data source For each test period: construct sliding windows compute degree of organization R, variance, constant phase offset, for each source linearly combine results to form a single confidence at this period and time How good is the overall result - how continuous is the signal? Rinse and repeat, varying free parameters in ξ(r), or other unknowns Look for change points, if any? Avoid mistaking slow drifts for step changes. 9

10 Initial test - Bφ and SKR 10

11 Optimising the SKR visibility function SKR ξ(r) simply approximated in Andrews et al Simple, but was it optimal or accurate? Parameterize the function, and vary free parameters Piecewise linear, constant near intensity maximum 11

12 Initial test - southern hemisphere Find a visibility function that gives the best organisation of the SKR data Confidence = mean [dτ/dt] -1 Higher value: lower number of period jumps - more continual variation Local maximum near expected location SKR data are intrinsically better organised in a quasi-rotating coordinate system More to do here Is this confidence parameter appropriate? What about the north? Andrews 2011 value Test points 12

13 In more detail - Southern SKR periodograms Top - with LT dependent phase function Bottom - without (assuming a pure strobe emission) 13

14 Conclusions / further work Very preliminary, but shows the technique is viable Single algorithm for all data sets, making it easy to compare results Mag data: better separation of core field Ring current still needs to be treated Radial phase delays not implemented yet Update SKR data Northern system period locatable by this method? Northern SKR visibility function determinable by this method? Fit particle data into this scheme Change-point analysis - set upper bounds on maximum period jumps? Compare driving factors at the same time (solar wind pressure, EUV flux) 14

15 Alternative normalisation scheme 15

16 Thermal ion densities from RPWS/LP Langmuir Probe measures current flow from the plasma to the probe at different biased voltages Linear fit at negative bias yields ion density (and relative velocity) Photoelectron current must be calibrated out (depends on E-UV flux to the probe; TIMED/SEE data used) 16 Example of an LP sweep showing the measured current (blue dots), the theoretical fit (red line), the photoelectron current I ph (black dashed line), the ion current I i (red dashed-dotted) and electron currents I e (green lines).

17 Density modulations in the inner plasma disc First investigated by Gurnett et al. [2007] Modulation in ne with SKR phase detected within 3-5 RS However, consider the static density profile derived by Persoon et al. [2009] ne ~ r -4 Small shifts in r will give large shifts in density LP ion densities, grouped into phase quadrants, with Z < 0.1 RS. 17 N.B: On-going comparisons between RPWS upper hybrid and LP measurements Person et al. 2015

18 Addendum, the other Scargle algorithm Bayesian Blocks - Scargle et al. [2012] addresses the problem of detecting and characterizing local variability in time series and other forms of sequential data. The goal is to identify and characterize statistically significant variations, at the same time suppressing the inevitable corrupting observational errors. Belongs to the nonparametric class of statistical models - just a description of variations Closely related to change-point analyses Can be used for adaptively selecting binedges in histograms optimal segmentation of data based on prior assumptions simple, efficient, elegant 18

19 Addendum, the other Scargle algorithm Parameterization of a varying time series 19

20 The loose connection to radio pulsars Aligned rotators do not pulse : received wisdom Clearly not true, for the case of our own nearby aligned rotator Saturn P~0.5 d, P ~ 10-6 : slow drift in period one seasonal timescales A consequence of seasonal variability in the neutral atmosphere? Examining individual hemispheres - apparent intervals when no modulations were present? Pulsars - a zoo of phenomena Rotation periods P ~seconds (or significantly less?), spin-down rates P ~10-15 General stable slow-down in rotation period, with interspersed glitches and nulling secular deviations from linear decrease in period are observed Question is what to do on this topic, if anything 20