G.D. Finn

Studies in spectral line formation: I. Formulation and simple applications

Abstract The integral equations for the source functions for lines formed in a multi-level atom are derived and a simple general method of solution is presented. To check the numerical stability and accuracy of the method, several special cases are solved in the two-level approximation for comparison with existing solutions. The physical significance of the net radiative bracket and the thermalization length are discussed.

Studies in spectral line formation: II. Linear coupling in multilevel atom problems

Abstract The transfer of line radiation through an atmosphere of three-level model sodium atoms and four-level model oxygen atoms is studied. The physical significance of the source functions and the net radiative brackets of the spectral lines is considered, with particular emphasis on the conditions for the multiplet line source functions to have a common depth dependence.

Probability distributions for photon exit

Abstract A linear integral equation is formulated for the probability that a photon in a spectral line formed at a specified depth in a scattering atmosphere eventually escapes at a particular frequency in the spectral line. Numerical solutions are obtained for an isothermal atmosphere and their physical meaning discussed under a variety of conditions.

Studies in spectral line formation. III - Non-linear multi-level atom problems.

Abstract Solutions are presented for some non-linear multi-level atom line transfer problems. These include the transfer of Lyα, Lyβ, and Hα radiation through plane parallel atmospheres of three-level model hydrogen atoms, and the transfer of magnesium b-line radiation using four-level model magnesium atoms. The physical meaning of some characteristics of the solutions is emphasized in the discussion.

Theoretical intensity ratios for some Fe XIII coronal lines

Theoretical values for the relative intensities of the Fe XIII lines λ110747, λ110798, and λ3388 are presented as functions of electron density using recent values of the cross-section for collisionl excitation by protons. Our results are compared with those of Chevalier and Lambert.

Statistical functions in radiative transfer

Abstract Integral relations are obtained for the mean and mean square number of scatterings undergone by a photon formed at a specified depth in an isothermal atmosphere and destined to escape from the atmosphere at a particular frequency in a spectral line, there being complete redistribution of frequency in the scattering process. Theoretical estimates of these functions are compared with numerical solutions for cases in which the frequency profile of the absorption coefficient has Doppler and Voigt forms.

Comments on multilevel atom radiation problems

Abstract The multilevel atom problems considered here give rise to linear, though often simultaneous integral equations. We discuss resonance line problems of a simple two-level atom, a three-level atom (the sodium D lines) and a four-level atom (the oxygen triplet 7774 A). A continuum of energy levels is also introduced, the computations being done for the hydrogen Lyman continuum with and without a second discrete level. In all cases, the integral equations are solved for the source functions of the radiative transitions involved. Purely for convenience, a semi-infinite, constant temperature (and, when required, constant electron pressure) atmosphere is assumed throughout. The integral equations resulting from the equations of statistical equilibrium and radiative transfer for the type of atom assumed are solved initially by dividing the optical depth axis into a number of intervals within each of which the source function is assumed constant. The integral equations are then evaluated at interior points of the intervals, producing systems of well-conditioned linear equations. Other procedures are considered in which the source functions are assumed to be linear within each interval and continuous between intervals. The source functions obtained from these procedures for various types of atoms and parameter values are compared and discussed at some length. Some criteria for equality of the source functions of a multiplet are treated, and the behaviour of the net radiative brackets is discussed.

Probabilistic radiative transfer: Mean number of scatterings

Abstract Integral relations are formulated for the mean numbers of scatterings for escaping and for non-escaping photons. Numerical solutions are obtained and discussed for cases of transfer through finite and semi-infinite atmospheres. The association between these functions and the source function is also discussed.

Studies in spectral line formation—IV. Singly ionized calcium

Abstract The integral equations for the source functions of the Ca II H and K lines, and the lines of the infrared triplet, are formulated and solved in the case of transfer through a homogeneous atmosphere. Methods for estimating the thermalization lengths of these lines are discussed and criteria for source function equality are investigated.

Probabilistic radiative transfer

Abstract A linear integral equation is formulated for the probability distribution with frequency and angle of the escape of photons from an atmosphere in which the radiation is generated internally and scattered noncoherently. This probability function is simply related to a similar distribution function when the radiation is generated externally. Numerical solutions are obtained for an isothermal atmosphere and their physical meaning is discussed.