1. Ring Spectroscopy and Photometry Todd Bradley January 9, 2014

2. Overview Review of ring particle albedo modeling Compositional modeling of the rings using a Hapke approach Compositional modeling of the rings using the Shkuratov model

3. Model discretely averaged I/F with Chandrasekhar-granola bar model 3 I/F at 180 nm Also did I/F at 155 nm (not shown) Need to do this for more wavelengths and shorter wavelengths if possible

4. Compositional Modeling Cuzzi and Estrada (1998) used a Van de Hulst to relate A B to ϖ g = regolith grain anisotropy parameter n and k are the optical constants, d is the grain diameter, α = 4πk/λ and ς is the internal scattering coefficient 4

5. Two-component mixture (99.5% calcite; 0.5% nano-phase iron) 1Calcite crushed with a mortar and pestle 2nano-phase iron added and lightly crushed and the reflectance (black curve). 3Mixture was then crushed two more times (blue and red curves).

6. MaterialCompressive Strength (10 6 N/M 2 ) Ice at 77K40-100 Lake Ice10 Sea ice0.01-0.04 Basalt100-350 Coal20-100 Granite100-300 Compressive Strength of Materials

7. Try Two Different Two Component Mixtures 7 μ = bulk density, ρ = solid density, D = size Assume ρ is same for both ( Hapke, 1993 ) Linearly add optical constants and get one single scattering albedo; a single regolith grain is a well mixed combination of components (Cuzzi and Estrada, 1998) Water Ice and Triton Tholin (irradiation of 0.999:0.001 N2:CH4; bulk substance: C 3 H 5 N 4 Separate grains for each component. Calculate single scattering albedo for each. Add together.

8. Linear Mixing Approximation Free parameters in the model are the grain size, water ice abundance, and asymmetry parameters The model was compared to either the FUV data points or the FUV-NIR data points in the minimization routine.

9. Discrete Grain Mixture Free parameters are the water ice grain size, contaminant grain size, water ice abundance, and asymmetry parameter. The model was compared to either the FUV data points or the FUV-NIR data points in the minimization routine.

10. Hapke Central A Ring Discrete Grain Water Ice-Ammonia

12. Recent Work Retrieve ring particle albedo at 3 nm intervals for more regions of the rings (B2, B3, B4, CD, A1, A2, A4) Consider species other than Triton Tholin (gray contaminant and ammonia), for FUV Use Shkuratov model to compare with data

14. Ring Particle Bond Albedo

15. Absorption Values

16. B3; Hapke model fit

17. CD; Hapke model fit

18. Minimum Value of D

19. Fraction of Water Ice

20. Grain Size

21. Shkuratov Model Requires geometric (physical, A p ) albedo Ratio of brightness of a body at g = 0 to the brightness of a perfect Lambert disk of the same radius and at the same distance as the body but illuminated and observed perpendicularly Previously I derived ring particle bond (spherical, A s ) albedos and ring particle phase functions q = phase integral Φ(g) is integral phase function, i.e. the relative brightness of a body at phase angle g normalized to its brightness at 0° phase angle

22. Ring Particle Geometric Albedo

23. Shkuratov Discrete Grain Model (B3)

24. Shkuratov Discrete Grain Model (CD)

25. Fraction of Water Ice

26. Ratio of albedos Comparison of ratio of albedos to water ice fraction retrieved from water ice- tholin model

27. Porosity

28. Minimum Value of D

29. Water Ice Grain Size

30. Contaminant Grain Size

31. Summary Hapke linear mixture does not fit the data as well as Hapke discrete mixture Hapke water ice-tholin discrete mixture model fit FUV and long wavelength data very well for B3 Hapke water ice-ammonia discrete mixture model did not fit at long wavelengths For Hapke two-component discrete mixture all three contaminants fit the FUV data about the same

32. Summary For Shkuratov two-component discrete mixture all three contaminants fit the FUV data about the same Water ice fraction radial distribution appears more believable from using Shkuratov model but disagrees with albedo ratio at outer A ring Absolute values of water ice fraction from Shkuratov are less than 0.6 – This could a matter of proper model interpretation – Could be that model does completely reproduce the reflectance – Could be that UVIS is sensitive to small contaminant grains near surface, which decreases the retrieved water ice abundance

33. Conclusions and Future Plans May need to consider different mixing models for broad wavelength range May need variable size distribution for broad wavelength range Try Shkuratov model on long wavelength data provided phase function is available Investigate other rings regions at longer wavelengths where I now have the ring particle albedo Try lower spectral resolution sampling to improve SNR

34. Different Mixtures for Regolith Grains Water ice grains Contaminant grains Water ice and contaminant grains are separate with their own single scattering albedo but are thoroughly mixed within the regolith. Compute single scattering albedo for each component and then combine fractions of single scattering albedos to get overall single scattering albedo Water ice and contaminant are thoroughly mixed within each grain Combine fractions of optical constants then calculate overall single scatter albedo Contaminant grains Water ice grains Cuzzi mixture Hapke mixture 34

35. EXTRA

38. Shkuratov Discrete Grain Model (B3)

39. Shkuratov Discrete Grain Model (CD)

40. Shkuratov Linear Mixing Model (B3)

41. Shkuratov Linear Mixing Model (CD)