Dust Envelope and Opacity

The gas raining down on the protostar originates much farther away, in the outer envelope. This is the infalling region where, as we noted in ยง 10.2, the gas temperature rises sluggishly with density as a result of efficient cooling by dust. Despite the nomenclature, we recall that the matter here does not fall until it is inside the rarefaction wave gradually spreading throughout the cloud. Most of this expanding volume is nearly transparent to the protostellar radiation. However, as the infalling gas continues to be compressed, the radiation eventually becomes trapped by the relatively high opacity from the grains. Inside the dust photosphere, located at Rphot ~ 1014 cm, the temperature rises more quickly. The sphere with radius Rphot is the effective radiating surface of the protostar, as seen by an external observer.

We define the dust envelope to be the region bounded by Rphot that is opaque to the protostar's radiation. Once the temperature here climbs past about 1500 K, all the hot grains vaporize. The precise temperature depends on the adopted grain model, but the qualitative effect is always the same. Inside this dust destruction front (Rd ~ 1013 cm), the opacity is greatly reduced. The infalling gas, which also collisionally dissociates above 2000 K, is nearly transparent to the radiation field. The region of vaporized grains is therefore known as the opacity gap. Even further inside, collisional ionization of the gas, and an attendant rise in the opacity, occur in the radiative precursor, immediately outside the accretion shock itself. We recall from Chapter 8 that such layers are ubiquitous features of high-velocity, J-type shocks.

Protostar Structure

Figure 11.2 Structure of a spherical protostar and its infalling envelope. The relative dimensions of the outer regions have been greatly reduced in this sketch. Note the convection induced by deuterium burning in the central, hydrostatic object. Note also the conversion of optical to infrared photons in the dust envelope.

Figure 11.2 Structure of a spherical protostar and its infalling envelope. The relative dimensions of the outer regions have been greatly reduced in this sketch. Note the convection induced by deuterium burning in the central, hydrostatic object. Note also the conversion of optical to infrared photons in the dust envelope.

Simple arguments suffice to demonstrate the vast difference in the character of the radiation field near the shock and at the dust photosphere. Gas approaches R* with speeds that are close to the surface free-fall value Vff. This is

280 km s"

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