The Emitting Atmosphere: Charles Lundquist
After completing my RZ-Cas paper I returned to the subject of radiative transfer to work on a theoretical problem that remained after Chandra left this subject to venture into another (turbulence). The problem concerned the multiple scattering of light by a plane-parallel "emitting atmosphere" that contains a given distribution of sources. It turned out possible to solve the case of the uniform distribution of sources by using the so-called "principles of invariance," and this warranted two papers in the Astrophysical Journal. The polynomial source distribution was more subtle, although I was able to write out the four equations that expressed the principles of invariance. However, to solve these required an additional relation, most likely a symmetry condition. It seemed reasonable first to attempt the linear case, but my immediate thoughts weren't clever enough to achieve success.
A few days later, while working at my desk in 500 Lindley Hall, a student came up the stairs and introduced himself. He was Charles Lundquist, a graduate student in physics, and he asked me if I could recommend an appropriate problem for his Ph.D. thesis. He hadn't yet been able to find a sufficiently promising problem, and since he was working part time for a professor in the Petroleum Engineering Department, he might as well come upstairs and see what would be suggested by an astrophysicist. It was easy enough for me to go to the blackboard and show him what I'd been doing with the emitting atmosphere problems. In particular I pointed out the symmetry difficulty, and expressed optimism. He immediately became interested, and asked if it would be possible to work on them. I suggested that he read through the parts of Chandra's book Radiative Transfer that dealt with the invariance principles, and not to worry about the polarization. A short time later we began working together and attacked the mathematics for the linear case; the symmetry aspects turned out to be relatively simple (but not trivial), and we were able to solve the problem exactly.
While I was at Yerkes that summer writing up our linear paper, I got a letter from Lundquist in which he outlined his solution of the polynomial case, and this would be the core of his thesis. The thesis title was The Application of the Invariance Principle Method to Layers Containing Sources (November 2, 1953). We published a total of six papers on this subject during the period (1952-1954) that included his Ph.D. thesis (in physics) and paper V which he wrote up while at Pennsylvania State University, his first position after leaving K.U.
Much later (1980!), while at Los Alamos, I derived the solutions from the point of view of the so-called doubling method, which is more easily programmed on the digital computer. Dr.R.W.Whitaker, also of Los Alamos, cooperated with me to calculate numerical results using a CDC-7600 machine, and we published paper VI some twenty-eight years after the original emitting atmosphere paper I !
Sometimes I'm asked why anybody would investigate such an abstract problem, indeed it would appear that we accomplished solutions without being given the problem. To answer this I have to tell a short story: I was attending a radiative transfer meeting in 1974 at the Jet Propulsion Laboratory in Pasadena, CA, and was approached by a Dr.Hudson, who introduced himself and then said "You know that you saved my life!". This of course intrigued me very much. He continued, "You published a paper in the Ap.J. at a crucial time for me, and it concerned the emitting atmosphere." I asked him to clarify this, and he just laughed and replied "Unfortunately I can't tell you, it's classified!"
Dr.Lundquist eventually became the Director of the Space-Science Laboratory, NASA-Marshall Space Flight Center, Huntsville, Alabama. For awhile he was the Associate Director of the Smithsonian Astrophysical Observatory, Cambridge, MA. He is presently (1998) the Vice President for Research at the University of Alabama. In 1979 Dr.Lundquist received the D.Sc.(honorary) from South Dakota State University, his undergraduate alma mater. He and his wife Pat (the former Patricia J.Richardson) live in Athens, GA., and they have five grown children.
I received a letter from Lundquist dated April 13, 1955; in part it reads: "I surely am pleased that the emitting atmosphere problem worked out as well as it did. I am greatly indebted to you for introducing me to radiative transfer, for teaching me much about the subject, and for a great deal of help and guidance while I was working on my thesis. My association with you will surely be one of the most pleasant memories of my life. You have my most sincere thanks." Receiving such a letter is more than compensation for being a member of the teaching profession, and it was a great boost to my morale.