On the Effects of Self-obscuration in the (Sub)Millimeter Spectral Indices and the Appearance of Protostellar Disks

摘要

In this paper we explore the effects of self-obscuration in protostellar disks with a radially decreasing temperature gradient and a colder midplane. We are motivated by recent reports of resolved dark lanes ("hamburgers") and (sub)millimeter spectral indices systematically below the ISM value for optically thin dust, α ISM?=?3.7. We explore several model grids, scaling disk mass and varying inclination angle i and observing frequency ν from the VLA Ka band (~37 GHz) to ALMA Band 8 (~405 GHz). We also consider the effects of decreasing the index of the (sub-)millimeter dust opacity power-law β from 1.7 to 1. We find that a distribution of disk masses in the range M disk?=?0.01–2 M ⊙ is needed to reproduce the observed distribution of spectral indices, and that assuming a fixed β?=?1.7 gives better results than β?=?1. A wide distribution of disk masses is also needed to produce some cases with α??×10, and are consistent with recent hydrodynamical simulations. Although we do not rule out the possibility of some grain growth occurring within the short protostellar timescales, we conclude that self-obscuration needs to be taken into account.