Circumstellar disc of beta Pictoris: constraints on grain properties from polarization

We model the positional dependence of the optical polarization (BVRI-bands) in the circumstellar disc of beta Pictoris as observed by Gledhill et al. (1991) and Wolstencroft et al. (1995). The particles are spherical, have a size distribution n(a) \sim a^{-q} and their number density decreases with distance from the star as r^{-s}. We consider both compact and porous grains. Varying the grain size and the exponent, s, of the density distribution as well as the refractive index of the grain material m, we find that the measured polarization, colours and brightness distribution in the disc are best reproduced by a model in which the grains are larger than interstellar grains (the minimum grain size a_min=0.15 mkm. The value of the maximum size is ill determined because it has little influence and was taken to be a_max=100 mkm. The best-fit exponents of the power laws are q=3.2 and s=3. The grains have in the R-band a refractive index m_R=1.152-0.005i. Such a value is roughly appropriate for porous grains where half of the volume is ice and the other half vacuum, or where 24% of the volume consists of silicate and the remaining 76% of vacuum.