1. 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

3. d  =  dr,  =  a +  s 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.

4. Scattering Polarization Rayleigh Scattering : Scattering by atoms and molecules Thomson Scattering : Scattering by free non-relativistic electrons Mie Scattering : Scattering by dust Phase function/matrix for Thomson and Rayleigh scattering Polarization is the measure of anisotropy in a radiation field

5. 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) T eff  1400 K L dwarfs : 1300 K < T eff < 2400 K Signature of primordial lithium T dwarfs : 600 K < T eff < 1300 K Signature of methane

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

8. 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 Dwarfs Single Scattering Credit : S. Sengupta and S. Kwok (2006)

9. Rotation Induced Oblateness Darwin (1899) – Radau (1885) Relationship : 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. DARWIN-RADAU-CHANDRASEKHAR RELATIONSHIP

10. Credit : S. Sengupta and M. S. Marley (2010) Polarization of Dusty Brown Dwarfs Multiple Scattering : Application of Chandrasekhar’s equations

11. 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)

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

13. 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)   Pictoris b

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

15. Credit : NASA Polarization by a Partially Cloudy Atmosphere ??

16. Credit : JPL, NASA (Spitzer)