1. Phase Effects: Photometry & Polarimetry AS3141 Benda Kecil dalam Tata Surya Prodi Astronomi 2007/2008 B. Dermawan

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

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 (Asteroids III) 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 (Asteroids III)

9. Hapke’s Photometric Model Effect of shadowing (and surface roughness) w  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 approx.)  the average topographic slope angle of surface roughness (does not directly obtained from the equation)

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

12. Laboratory Result Muinonen et al. 2002 (Asteroids III)

13. Empirical Modeling (1) Photometric phase-effect: Shevchenko 1997, Belskaya & Shevchenko 2000:  Relation between parameter a and b Shevchenko 1997 c is a parameter

14. Empirical Modeling (2)  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 Shevchenko 1997

15. Empirical Modeling (3) 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. 2005 Juno Halley

16. Empirical Modeling (4) Photometric & Polarimetric phase-effects: Muinonen et al. 2002 (Mem. S. A. It., 73, 716-721), Kaasalainen et al. 2002 (Asteroids III): 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

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