Multiple Scattering Polarization of Substellar-Mass Objects: T Dwarfs

Abstract

While there have been multiple observational programs aimed at detecting linear polarization of optical radiation emitted by ultracool dwarfs, there has been comparatively less rigorous theoretical analysis of the problem. The general expectation has been that the atmospheres of those substellar-mass objects with condensate clouds would give rise to linear polarization due to scattering. Because of rotation-induced non-sphericity, there is expected to be incomplete cancellation of disk-integrated net polarization and thus a finite polarization. For cloudless objects, however, only molecular Rayleigh scattering will contribute to any net polarization and this limit has not been well studied. Hence in this paper we present a detailed multiple scattering analysis of the polarization expected from those T-dwarfs whose spectra show absence of condensates. For this, we develop and solve the full radiative transfer equations for linearly polarized radiation. Only atomic and molecular Rayleigh scattering are considered to be the source of polarization. We compute the local polarization at different angular directions in a plane-parallel atmospheres calculated for the range of effective temperatures of T dwarfs and then average over the whole surface of the object. The effects of gravity and limb darkening as well as rotation induced non-sphericity are included. It is found that the amount of polarization decreases with the increase in effective temperature. It is also found that significant polarization at any local point in the atmosphere arises only in the optical (B-band). However, the disk integrated polarization-even in the B-band-is negligible. Hence we conclude that, unlike the case for cloudy L dwarfs, polarization of cloudless T-dwarfs by atomic and molecular scattering may not be detectable. In the future we will extend this work to cloudy L-and T-dwarf atmospheres.

Linear polarization of rapidly rotating ultracool dwarfs

“…In addition, J1254−0122 (T2) is the coolest target in our sample. Sengupta & Marley (2009) theoretically studied the possible detection of linear polarization in the oblate atmospheres of cloudless T-type sources, which are even cooler than the L-types. Their calculations showed that polarization may arise only for λ ≤ 0.6 μm (a range where T-dwarfs are extremely faint), and the net disk integrated polarization may be neglible.…”

Probing the physical properties of directly imaged gas giant exoplanets through polarization

“…As in Sengupta & Marley (2010) we employ the gas and dust opacity, the temperature–pressure profile and the dust scattering asymmetry function averaged over each atmospheric pressure level derived by the atmosphere code in a multiple scattering polarization code that solves the radiative transfer equations in vector form to calculate the two Stokes parameters I and Q in a locally plane‐parallel medium (Sengupta & Marley 2009). For each model layer we fit a Henyey–Greenstein phase function to the particle scattering phase curve predicted by a Mie scattering calculation.…”

“…Polarization of exoplanet radiation arises from scattering by either gas or dust in the atmosphere. Clear atmospheres lacking dust grains can be polarized, but only at blue optical wavelengths where gaseous Rayleigh scattering is important (Sengupta & Marley 2009). Even the hottest young exoplanets will not emit significantly in the blue.…”

Multiple scattering polarization – Application of Chandrasekhar’s formalisms to the atmosphere of brown dwarfs and extrasolar planets

“…We apply, for the first time [2][3][4], Chandrasekhar's formalism to estimate scattering polarization of the atmosphere of substellar mass objects. As the atmosphere of these objects is sufficiently cool, condensation of various molecular species takes place at the visible atmosphere and scattering by condensates yields detectable amount of polarization.…”

“…These quantities are then used as inputs in a multiple scattering polarization code that solves the radiative transfer equations in vector form as given by Chandrasekhar to calculate the linear polarization in a locally plane-parallel medium. Finally, the polarization is integrated over the rotation-induced oblate disk of the object using a spherical harmonic expansion method [2].…”