Statistics – Computation
Scientific paper
Jul 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986a%26a...163..307l&link_type=abstract
Astronomy and Astrophysics (ISSN 0004-6361), vol. 163, no. 1-2, July 1986, p. 307-312. Research supported by the University of S
Statistics
Computation
Computational Astrophysics, Masers, Constraints, Inversions, Linear Equations, Size (Dimensions), Uniqueness Theorem
Scientific paper
The paper provides exact analytic solutions to the two-level, steady-state, maser problem in parametric form, with the emergent intensities expressed in terms of the incident intensities and with the maser length also given in terms of an integral over the intensities. It is shown that some assumption must be made on the emergent intensity on the nonobservable side of the astrophysical maser in order to obtain any inversion of the equations. The incident intensities can then be expressed in terms of the emergent, observable, flux. It is also shown that the inversion is nonunique unless a homogeneous linear integral equation has only a null solution. Constraints imposed by knowledge of the physical length of the maser are felt in a nonlinear manner by the parametric variable and do not appear to provide any substantive additional information to reduce the degree of nonuniqueness of the inverse solutions. It is concluded that the questions of precision, resolution and uniqueness for solutions to astrophysical maser problems will remain more of an emotional art than a logical science for some time to come.
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