Analysis of Density Waves in UVIS Ring Stellar Occultations

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Presentation transcript:

Analysis of Density Waves in UVIS Ring Stellar Occultations Josh Colwell January 2008 UVIS Team Meeting

UVIS Team Meeting. Colwell. Introduction Problem: Thousands of density wave profiles in occultation data contain information on ring mass density and viscosity. Data are of variable quality, and wave signals are on top of other features in the rings. Goal: Find a procedure with minimal decision-making to extract ring properties from thousands of wave profiles. January 8, 2008 UVIS Team Meeting. Colwell.

Derivation of Surface Mass Density Following Tiscareno et al. (2007): Density wave phase depends quadratically on distance from resonance far from resonance. (1) (2) (3) (4) L subscript refers to location of Lindblad resonance. RS is radius of Saturn,  is the mean motion,  is the surface mass density, and m is the azimuthal parameter of the resonance. January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Synthetic Wave Technique is based on the linear density wave theory of Shu (1984). Generate a synthetic wave data set with the parameters of the Prometheus 10:9 density wave: RL=13004 km, =40 g cm-2 D=6 January 8, 2008 UVIS Team Meeting. Colwell.

Synthetic Wave Profile January 8, 2008 UVIS Team Meeting. Colwell.

Wavelet Transform of Synthetic Data January 8, 2008 UVIS Team Meeting. Colwell.

Isolate the Wave by Filtering January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Fit Cumulative Phase January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Chi-Squared Values January 8, 2008 UVIS Team Meeting. Colwell.

Amplitude of Filtered Wave January 8, 2008 UVIS Team Meeting. Colwell.

Determine Damping Length January 8, 2008 UVIS Team Meeting. Colwell.

Compare Signal and Model January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Recovered Parameters Surface mass density: 39.96 g cm-2 (40 input) Damping Length: 5.87 (6 input) Resonance Location: fixed at 130004 km. Initial phase determined from satellite location. Derived phase required to fit initial phase. Get better fits with wrong resonance location. January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. With Search for RL… January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Wrong RL and  Found January 8, 2008 UVIS Team Meeting. Colwell.

Cumulative Phase Fits, but not Phase January 8, 2008 UVIS Team Meeting. Colwell.

Allow Initial Phase to be Unconstrained January 8, 2008 UVIS Team Meeting. Colwell.

This Locates Correct Resonance Location January 8, 2008 UVIS Team Meeting. Colwell.

Then Run with RL and 0 Fixed January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Still Get a Good Fit January 8, 2008 UVIS Team Meeting. Colwell.

Mass Density from Wave Dispersion  = 45 g cm-2 (40 input) (Data generated from model) January 8, 2008 UVIS Team Meeting. Colwell.

Mass Density from Wave Dispersion  = 42 g cm-2 (40 input) (Data generated from model) January 8, 2008 UVIS Team Meeting. Colwell.

Synthetic Wave Dispersion Analysis Gives  = 46 g cm-2 Calculate sigma at each point from wavelength at that point. January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo (9) Ingress: Pr10:9 January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo (9) Ingress: Pr10:9 January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo (9) Ingress: Pr10:9 Fit appears to be offset. January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo (9) Ingress: Pr10:9 So readjust RL to get January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo 9I Wave Dispersion Analysis =35 g cm-2 Significantly lower than model fitting or cumulative phase suggest. January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo 9I Wave Dispersion Analysis January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo 9I Phase Analysis Unconstrained initial phase January 8, 2008 UVIS Team Meeting. Colwell.

Alpha Leo 9I Phase Analysis Constrained initial phase (offset by 2PI) January 8, 2008 UVIS Team Meeting. Colwell.

Model Fit with Mean Dispersion Value January 8, 2008 UVIS Team Meeting. Colwell.

Model Fit with Phase Value January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Conclusion (1) Forget about removing human inspection of the wave and the fit when extracting ring properties from density wave. January 8, 2008 UVIS Team Meeting. Colwell.

Analysis of Actual Density Waves January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Pandora 9:7 January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Pandora 9:7 January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Pandora 9:7 January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  Pandora 5:4 January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  Pandora 5:4 January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  Janus 2:1 January 8, 2008 UVIS Team Meeting. Colwell.

Variation in Background  Janus 2:1 Hiccups probably due to J/E swap January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Status See variations in wave dispersion across wavetrain. Offset in dispersion from underlying optical depth. Change in surface mass density not proportional to change in optical depth in Pandora 5:4. Anti-correlated with optical depth in Janus 2:1. January 8, 2008 UVIS Team Meeting. Colwell.

UVIS Team Meeting. Colwell. Next Steps Finish a systematic extraction of surface mass density and viscosity from density waves using a combination of techniques, validated by visual inspection of fit of model to data. Determine mass of Cassini Division. Look for waves with variable surface mass density and links between mass and optical depth. January 8, 2008 UVIS Team Meeting. Colwell.