SUJAN SENGUPTA

Indian Institute of Astrophysics, Bangalore

Chandrasekhar Centenary Conference

December 07-11, 2010

Multiple Scattering Polarization -

Application of Chandrasekhar’s Formalisms to the Atmosphere of

Brown Dwarfs and Extra-solar Planets

),(4

0

/ 0

pFe

1

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),,(),(2

),,(),,(

dIpI

d

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d = dr, = a + s

),,(),,(),,(), ,(1

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rIrrjrI

rr

rI

1

1

),,(),(2

),,(),,(

d

d

dIpI

I

V

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The state of polarized light is expressed by the Stokes parameters I, Q, U and V where I is the total intensity and Q, U, V are the polarized intensity. For linear polarization V=0.

jIds

dI

IVUQp /222

Scattering Polarization

Rayleigh Scattering : Scattering by atoms and molecules

Thomson Scattering : Scattering by free non-relativistic

electrons

Mie Scattering : Scattering by dust

)]'cos()'1()1('2

)'(cos)'1)(1('1[4

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p

Phase function/matrix for Thomson and Rayleigh scattering

1'

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3)',(

2

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Polarization is the measure of anisotropy in a radiation field

Mass – less than 0.084 M ,

greater than 0.011 M

SUB-STELLAR MASS OBJECTS

BROWN DWARFS

EXTRA-SOLAR PLANETS

Mass – less than 0.011 M

Credit : NASA (1995)

Credit : C. Chauvin et al (2004) Teff 1400 K

L dwarfs :

1300 K < Teff < 2400 K

Signature of primordial lithium

T dwarfs :

600 K < Teff < 1300 K

Signature of methane

Credit : B. Openheimer et al. (1995)Credit : D. Kirkpatrick et al. (2000)Credit : M. C. Cushing et al. (2009)

Sengupta and Krishan, 2001, ApJ Letts, 561, L123

Menard et al. 2002, A & A Letts. 396, L35

Sengupta, 2003, ApJ Letts, 585, L155

Sengupta and Kwok, 2005, ApJ, 625, 996

Polarization of Dusty Brown DwarfsSingle Scattering

Credit : S. Sengupta and S. Kwok (2006)

Rotation Induced Oblatenesse

pe

R

RR

Darwin (1899) – Radau (1885) Relationship :

12

2

32

2

31

2

5

5

2

MR

I

GM

Re

Chandrasekhar, S. 1933, MNRAS, “The quilibrium of distorted

polytropes IV. The rotational and the tidal distortions as functions

of the density distribution”, Vol. 93, p-553, Table 1.

GM

RC e

32

3

2

12

22

31

2

5

5

2

2

3

MR

IC

DARWIN-RADAU-CHANDRASEKHAR RELATIONSHIP

Credit : S. Sengupta and M. S. Marley (2010)

Polarization of Dusty Brown DwarfsMultiple Scattering : Application of Chandrasekhar’s equations

The World Is Not Enough

8 planets within the solar system

51 Pegasi : The first confirmed exoplanet reported in 1995

PSR 1257+12 : a system of planets discovered in 1992

Radial Velocity

Transit

Imaging

Microlensing

Timing

506 planets (http://exoplanet.eu :Dec. 09, 2010)

Credit : F. Allard (2008)Credit : S. Berdyugina (2008)

Credit : Chauvin et al (2004)

2MASS 1207 b

Credit : Marois et al. (2008)

HR 8799

Credit : Marois et al. (2010)Credit : Lagrange et al. (2010)

b Pictoris b

Credit : S. Sengupta and M. S. Marley (2010)

Credit : NASA

Polarization by a Partially Cloudy Atmosphere ??

Credit : JPL, NASA (Spitzer)