Transfer of Radiation in Circumstellar Dust Envelopes. III. The Case of Distant Envelopes

In this paper we have studied not only the continuous conversion of optical to infrared radiation but also the continuous conversion of directional flow of stellar radiation to the diffused radiation fields. Such a case exists when the envelope is far away from the star, in contradistinction to the case discussed in a previous paper in which the envelope was assumed to be close to the star. In order to formulate the present problem in a mathematically manageable form, it has been assumed that the central star as seen by any point in the envelope appears as a point source. The two ways of approximating the problem-one discussed in the previous paper and the other presented here-do not give greatly different results as far as the infrared radiation field and the temperature distribution in the envelope are concerned if everything else remains the same. However, the nature of the optical radiation field is quite different in the two cases.