Evolution of spheroidal dust in electrically active sub-stellar atmospheres

Understanding the source of sub-stellar polarimetric observations in the optical and near-infrared is key to characterizing sub-stellar objects and developing potential diagnostics for determining properties of their atmospheres. Differential scattering from a population of aligned, non-spherical dust grains is a potential source of polarization that could be used to determine geometric properties of the dust clouds. This paper addresses the problem of the spheroidal growth of dust grains in electrically activated sub-stellar atmospheres. It presents the novel application of a mechanism whereby non-spherical, elongated dust grains can be grown via plasma deposition as a consequence of the surface electric field effects of charged dust grains. We numerically solve the differential equations governing the spheroidal growth of charged dust grains via plasma deposition as a result of surface electric field effects in order to determine how the dust eccentricity and the dust particle eccentricity distribution function evolve with time. From these results, we determine the effect of spheroidal dust on the observed linear polarization. Numerical solutions show that $e\approx 0.94$ defines a watershed eccentricity, where the eccentricity of grains with an initial eccentricity less than (greater than) this value decreases (increases) and spherical (spheroidal) growth occurs. This produces a characteristic bimodal eccentricity distribution function yielding a fractional change in the observed linear polarization of up to $\approx0.1$ corresponding to dust grains of maximal eccentricity at wavelengths of $\approx1 \mu$m, consistent with the near infrared observational window. The results presented here are relevant to the growth of non-spherical, irregularly shaped dust grains of general geometry where non-uniform surface electric field effects of charged dust grains are significant.