# Multiple Scattering Polarization of Substellar-mass Objects : T-dwarfs

## TL;DR

This paper provides a detailed theoretical analysis of the polarization caused by Rayleigh scattering in cloudless T-dwarfs, concluding that the polarization is negligible and unlikely to be observed.

## Contribution

It develops a full radiative transfer model for polarized light in cloudless T-dwarfs, focusing on atomic and molecular Rayleigh scattering effects.

## Key findings

- Polarization decreases with increasing effective temperature.
- Significant local polarization occurs only in the optical B-band.
- Disk integrated polarization is negligible even in the B-band.

## 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.