Can Reflection from Grains Diagnose the Albedo?

Abstract

By radiation transfer models we show that the optical properties of grains are poorly constrained by observations of reflection nebulae. The interstellar medium is known to be hierarchically clumped, from a variety of observations (molecules, H I, far-infrared). We have performed radiative transfer through four-tiered, hierarchically clumped dust in a sphere surrounding a central star. Our models have realistic power spectra of the projected density distributions (index ~-3). The input parameters are the albedo (a) and phase parameter (g) of the dust, the radial optical depth of the sphere averaged over all directions (τ0), and the detailed random distribution of the dust clumps within the sphere. The outputs are the stellar extinction, optical depth, and flux of scattered light as seen from various viewing angles. Observations of a reflection nebula provide the extinction and scattered flux as viewed from one particular direction. Hierarchical geometry has a large effect on the flux of scattered light emerging from a nebula for a particular extinction of the exciting star. There is a very large spread in both scattered fluxes and stellar extinctions for any distribution of dust. Consequently, an observed (τext, τsca) can be fitted by a wide range of albedos. There are lower limits on a set by the scattered flux. As an example, in the best-observed reflection nebula, NGC 7023, a(1300 Å) must be higher than ~0.5 if the scattered flux from Witt et al. and a reasonable value for the optical depth within the nebula are adopted. However, the same observations can be fitted with a=0.8 and 0.6