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Ring Spectroscopy and Photometry Todd Bradley January 9, 2014 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 Model discretely averaged I/F with Chandrasekhar-granola bar model I o AB * P * 1 exp n / exp n / o F 4 o 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 3 Compositional Modeling Cuzzi and Estrada (1998) used a Van de Hulst to relate AB to ϖ AB 1 S 1 0.139S 1 1.17S where S 1 SI Qs Se 1 SE 1 SI 1 r exp 1 1 g g = regolith grain anisotropy parameter n 12 k 2 4 SE 0.05 , S 1 I 2 n 12 k 2 nn 1 where r 1 1 2d /3 ri exp 2di /3 i i i / / n and k are the optical constants, d is the grain diameter, α = 4πk/λ and ς is the internal scattering coefficient 4 Two-component mixture (99.5% calcite; 0.5% nano-phase iron) 1 Calcite crushed with a mortar and pestle 2 nano-phase iron added and lightly crushed and the reflectance (black curve). 3 Mixture was then crushed two more times (blue and red curves). Compressive Strength of Materials Material Compressive Strength (106 N/M2) Ice at 77K 40-100 Lake Ice 10 Sea ice 0.01-0.04 Basalt 100-350 Coal 20-100 Granite 100-300 Try Two Different Two Component Mixtures Water Ice and Triton Tholin (irradiation of 0.999:0.001 N2:CH4; bulk substance: C3H5N4 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) ni 1 fe nio fenie nr 1 fe nro fenre Separate grains for each component. Calculate single scattering albedo for each. Add together. H O X , 1 2 x H o DH o = H o x Dx 2 2 2 μ = bulk density, ρ = solid density, D = size Assume ρ is same for both (Hapke, 1993) 7 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. 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. Hapke Central A Ring Discrete Grain Water Ice-Ammonia Hapke Central A Ring Discrete Grain Water Ice-Ammonia 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 Ring Particle Bond Albedo Absorption Values B3; Hapke model fit CD; Hapke model fit Minimum Value of D Fraction of Water Ice Grain Size Shkuratov Model • Requires geometric (physical, Ap) 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, As) albedos and ring particle phase functions As Ap q q 2 (g)sin gdg 0 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 q = phase integral Ring Particle Geometric Albedo Shkuratov Discrete Grain Model (B3) Shkuratov Discrete Grain Model (CD) Fraction of Water Ice Ratio of albedos Comparison of ratio of albedos to water ice fraction retrieved from water icetholin model Porosity Minimum Value of D Water Ice Grain Size Contaminant Grain Size 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 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 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 Different Mixtures for Regolith Grains Hapke mixture Cuzzi mixture Water ice grains Contaminant grains Water ice grains Contaminant grains Water ice and contaminant are thoroughly mixed within each grain Combine fractions of constants then calculate single scatter albedo optical overall 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 34 EXTRA Shkuratov Discrete Grain Model (B3) Shkuratov Discrete Grain Model (CD) Shkuratov Linear Mixing Model (B3) Shkuratov Linear Mixing Model (CD)