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A tensor formulation of the equation of transfer for spherically symmetric flowsA tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.
Document ID
19760050319
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Haisch, B. M. (Joint Institute for Laboratory Astrophysics Boulder, Colo., United States)
Date Acquired
August 8, 2013
Publication Date
April 15, 1976
Publication Information
Publication: Astrophysical Journal
Volume: 205
Subject Category
ASTROPHYSICS
Funding Number(s)
CONTRACT_GRANT: NGL-06-003-057
CONTRACT_GRANT: NSF MPS-74-01489
Distribution Limits
Public
Copyright
Other