Micro-structural size properties of Saturn’s rings determined from ultraviolet measurements made by the Cassini Ultraviolet Imaging Spectrograph Todd Bradley UVIS Team Meeting Boulder, Colorado June, 2008

2 Investigation summary Analyzed multiple observations in FUV Observations were all of lit side Phase angles ranged from 0.8° to 27° Computed I/F Fit I/F with Hapke model for single scattering albedo Found variations in microstructure with radius UCF

3

4 Water ice absorption feature Imaginary index of refraction for water ice decreases with increasing wavelength Solar flux is mostly featureless from 150 to 175 nm I/F = Measured radiance/solar irradiance Absorption feature at ~ 165 nm characteristic of water ice UCF

5 Chandrasekar Classical Radiative Transfer Approach I/F is the bidirectional reflectance  w o is the single scattering albedo P(  ) is the phase function  and  o are the cosine of the incidence and emission angles, respectively  is the optical depth f water is the fraction of water ice R c is the reflectance of a “grey” contaminant UCF

6 S e = Fresnel reflection coefficient for externally incident light S i = Fresnel reflection coefficient for internally incident light Both S e and S i are computed from the complex index of refraction Hapke formulation of the scattering efficiency For short wavelengths (2pa/l >> 1), Hapke (1992) models the single scattering albedo in this way Q is the internal transmission factor and is modeled as: where is the mean path length UCF

7 Mean path length is a measure of the distance light travels after an encounter with a ring particle is affected by: – the microscopic size of water ice grains on the much larger ring particles – distance between cracks or other scattering surfaces –mean spacing between contaminants in a water-ice matrix UCF

8 Data processing and analysis Bin pixels azimuthally in 4000 km radial bins Using Hapke model along with bidirectional reflectance data, scale the magnitude of the model to the data Fit model to extract UCF Observation: UVIS_036RI_SUBML17LP001_CIRS Cassini division Outer A ring Inner B ring Inner C ring Saturn Rayleighs

9 Least squares extraction of Compute D =1/N l *∑(model – I/F) 2 over a range of path lengths Minimum D = Width of curve denotes uncertainty UCF

10 Retrieval technique is independent of I/F magnitude (7.125 microns) UCF 2X +.032X +.03

11 Use extracted in model Plot of model using from minimum squared difference (blue) Red curves are model results for additional path lengths in 1 micron increments For a single spectra, can only distinguish to within 2 – 3 microns from center Compare multiple observations UCF Center = microns

12 Multiple observations Decrease uncertainty by considering multiple observations Clearly observations are repeatable with some exceptions UCF Inner C ring Inner B ring Cassini Division Outer A ring Mean a ~ 0.85 to 0.84 Mean a ~ 7 to 27

13 Phase angle (a) dependence Observations within the B ring As a increases, the photon has to scatter more times within an ice grain in order to escape UCF

14 a dependence for different radial distances UCF

15 Heuristic model interpretation of interaction of photon with ice grain For low a observations, the photon has probably had few scatterings For high a, the photon probably had to scatter multiple times For high a, photon travels more within ice leading to more absorption (shifts absorption edge to longer wavelengths) Could be contaminants, cracks, etc. UCF Ice grains

16 I/F displacement Observations from the same location in the A ring Larger a shifts absorption edge to longer wavelengths UCF

17 Average of larger a observations as a function of radius for all 6 high a observations averaged Average I/F for same 6 observations does not seem correlated with UCF Inner C ring Inner B ring Cassini Division Outer A ring

18 Summary microns planet 135,400 km79,400 km UVIS offers unique ability to see microphysical variations Comparing multiple observations gives more confidence in the results Present model does not relate a to If simple heuristic model is correct, then low a deals more with single scattering UCF For a > 7

19 Future/ongoing work Need to incorporate more low a and high a (> 50 °) observations If the explanation for phase angle effects is multiple scattering from contaminants, then need to start thinking about fraction of contaminant Need to use a model that accounts for phase angle effects/multiple scattering in the path length in order to constrain ice grain size UCF