Phase Effects: Photometry & Polarimetry

AS3141 Benda Kecil dalam Tata SuryaProdi Astronomi 2007/2008

B. Dermawan

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

Photometry – Polarimetry vs Phase Angles

Photometric & Polarimetric Phase Curves

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

Muinonen et al. 2002 (Asteroids III)

Photometric & Polarimetric

Phase Effects

Physical Phenomena behind the Effects

(Classical) Shadowing Mechanism (SM)

First-order multiple scattering Coherent Backscattering Mechanism (CBM)

Higher-order (>2nd, inclusive) multiple scattering

Backscattering phenomena of atmosphereless solar system bodies (Muinonen 1994, Shkuratov et al. 1994)

Coherent Backscattering Mechanism

Photometry

Polarimetry

Muinonen et al. 2002

Spacecraft Photometry

Muinonen et al. 2002 (Asteroids III)

Hapke’s Photometric Model

Effect of shadowing

(and surface roughness)

)1(

)1)(0(

)tan(1))0(,,(

2

0

21

0

gw

gSB

BShB

h

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 peakg 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)

Degree of Linear Polarization

I and I are proper intensities

//

//

II

IIP

Lyot 1929

Laboratory Result

Muinonen et al. 2002 (Asteroids III)

Empirical Modeling (1)Photometric phase-effect:Shevchenko 1997, Belskaya & Shevchenko 2000:

ba

cV

1

1 ),(

Relation between parameter a and b

Shevchenko 1997

c is a parameter

Empirical Modeling (2)

Relation between the parameters (a & b) and albedo pv

b = 0.013(0.002) –

0.024(0.002) log pv

Relation between the parameters (a & b) and Pmin

b = 0.016(0.002) + 0.015(0.002) Pmin

Shevchenko 1997 Shevchenko 1997

Empirical Modeling (3)

Polarimetric phase-effect:Lumme & Muinonen 1993:

)sin(2

cos)(sin)( 021

ccbP

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

Empirical Modeling (4)

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

kbd

af

exp)(

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

Ceres

Empirical Models of Photometric & Polarimetric Phase-effects

Muinonen et al. 2002