Polarization in reflection nebulae. I - Scattering properties of interstellar grains

The scattering properties, including both intensity and polarization, of the dust mixture which Mathis, Rumpl, and Nordsieck found to provide the best fit to the observed interstellar extinction are calculated. Simple empirical parameters necessary to describe approximately all elements of the scattering matrix are derived; it is found that the required parameters are the extinction cross section, the albedo, three parameters describing the forward and backward scattering of the intensity phase function, two parameters describing the linear polarization (which is essentially Rayleigh-like), and three parameters describing the circular polarization properties. The same parameters should be useful in parametrizing the scattering properties of almost any dust mixture. The variation of those parameters with wavelength for Mathis, Rumpl, and Nordsieck's grain mixture is discussed.