The degree of polarization in L dwarfs of spectral types L0 to L6 resulting from dust scattering in a rotation-induced oblate photosphere is calculated. Assuming that forsterite is the main condensate, the atmospheric dust distribution is derived for different spectral types based on a chemical equilibrium model. The degree of polarization at optical is then calculated using a single scattering model. The expected linear polarization at optical is found to peak at around spectral type L1. For a fixed rotational velocity, the degree of polarization decreases from hotter to cooler objects. However, with the increase in mean grain size, the degree of linear polarization reduces significantly. We fit the recently observed linear polarimetric data of L dwarfs and find that single dust scattering model coupled with the chemical equilibrium models of condensates is consistent with the observational results.

Latex (aastex sty), 23 pages including 7 postscript figures. Accepted for publication in the Astrophysical Journal (Part 1)