1. Photometric & Polarimetric Phase Effects Kuliah AS8140 & AS3141 (Fisika) Benda Kecil [dalam] Tata Surya Prodi Astronomi 2006/2007

2. Observing Plane The plane Sun-Object-Observer is the plane of light scattering of the radiating reaching us from the Sun via the object. It is a symmetry-breaking plane, and because of this, makes the light from the object polarized Karttunen et al. 1987

3. Photometry – Polarimetry vs Phase Angles Photometric & Polarimetric Phase Curves Kaasalainen 2002

4. Phase Effect Photometric: Opposition effect (spike): A nonlinear increase in disk-integrated brightness at small solar phase angles Polarimetric: Negative polarization surge (polarization opposition effect): A peculiar degree of linear polarization for unpolarized incident sunlight

5. Muinonen et al. 2002 Photometric & Polarimetric Phase Effects

6. Physical Phenomena behind the Effects (Classical) Shadowing Mechanism (SM) First-order multiple scattering Coherent Backscattering Mechanism (CBM) Higher-order (>2 nd, inclusive) multiple scattering Backscattering phenomena of atmosphereless solar system bodies (Muinonen 1994, Shkuratov et al. 1994)

7. Coherent Backscattering Mechanism Photometry Polarimetry Muinonen et al. 2002

8. Spacecraft Photometry Muinonen et al. 2002

9. Hapke’s Photometric Model Effect of shadowing (and surface roughness)   the single scattering albedo (efficiency of average particle to scatter and absorb light) h  The width of the opposition peak (soil structure) S(0)  the amplitude of the peak g  the asymmetry factor of the particle phase function (the Henyey- Greenstein approximation)  Is the average topographic slope angle of surface roughness

10. Degree of Linear Polarization I  and I  are proper intensities Lyot 1929

11. Laboratory Result Muinonen et al. 2002

12. Empirical Modelling (1) Photometric phase-effect: Shevchenko 1997, Belskaya & Shevchenko 2000:  Relation between parameter a and b  Relation between the parameters (a & b) and albedo p v b = 0.013(  0.002) – 0.024(  0.002) log p v  Relation between the parameters (a & b) and P min b = 0.016(  0.002) + 0.015(  0.002) P min

13. Empirical Modelling (2) Polarimetric phase-effect: Lumme & Muinonen 1993: Describe polarization throughout the phase angle range [0, 2  ] The values of the function are limited to the range [-1,1] when the parameter ranges are correctly defined Penttilä et al. 2006 Juno Halley

14. Empirical Modelling (3) Photometric & Polarimetric phase-effects: Muinonen et al. 2002, Kaasalainen 2002: Photometry: f(  )  the relative intensity a  the height of the brightest peak d  the width of the brightest peak b  the background intensity Polarimetry: f(  )  the degree of linear polarization a  an amplitude coefficient d  the angular scale b  the balancing amplitude coefficient k  the slope of linear part of the phase curve

15. Ceres Empirical Models of Photometric & Polarimetric Phase-effects Muinonen et al. 2002