Two-dimensional Radiative Transfer in Protostellar Envelopes. I. Effects of Geometry on Class I Sources

We present two-dimensional radiation transfer models of class I protostars and show the effect of including more realistic geometries on the resulting spectral energy distributions and images. We begin with a rotationally flattened infalling envelope as our comparison model and add a flared disk and bipolar cavity. The disk affects the spectral energy distribution most strongly at edge-on inclinations, causing a broad dip at about 10 μm (independent of the silicate feature) due to high extinction and low scattering albedo in this wavelength region. The bipolar cavities allow more direct stellar+disk radiation to emerge into polar directions and more scattering radiation to emerge into all directions. The wavelength-integrated flux, often interpreted as luminosity, varies with viewing angle, with pole-on viewing angles seeing 2-4 times as much flux as edge-on, depending on geometry. Thus, observational estimates of luminosity should take into account the inclination of a source. The envelopes with cavities are significantly bluer in near-IR and mid-IR color-color plots than those without cavities. Using one-dimensional models to interpret Class I sources with bipolar cavities would lead to an underestimate of envelope mass and an overestimate of the implied evolutionary state. We compute images at near-, mid-, and far-IR wavelengths. We find that the mid-IR colors and images are sensitive to scattering albedo and that the flared disk shadows the midplane on large size scales at all wavelengths plotted. Finally, our models produce polarization spectra that can be used to diagnose dust properties, such as albedo variations due to grain growth. Our results of polarization across the 3.1 μm ice feature agree well with observations for ice mantles covering 5% of the radius of the grains.