By S. Chandrasekhar, Kameshwar C. Wali
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Extra info for A Quest for Perspectives: Selected Works of S. Chandrasekhar: With Commentary (Volume 1)
91, 456, 1931 (referred to as I). See also the earlier papers of the author in Phil. , II, 502, 1931, and Astrophysical Journal, 64, 92. t In I we denoted by M s what we have now denned as M3fl-*l%. " J In I this "singularity" was formally avoided by introducing a state of "maximum density" for matter, but now we shall not introduce an) such hypothetical states, mainly for the reason that it appears from general consid rations that when the central density is high enough for marked deviations from the known gas laws (degenerate or otherwise) to occur the configurations then would have such small radii that they would cease to have any practical importance in astrophysics.
228] . (i2) We are simply defining is soluble in *. If a solution for (12) exists, then for values of x much smaller than the root of (12) the pressure would be given by (9), and for values of x much larger than the root of (12) the pressure would be given by (10). The criterion for degeneracy then is the following : For a given p and T formally calculate on the perfect gas law the value for /J (as we have done in equation (3)), and with this value for /? seek a solution for (12); if a solution exists, and if the value of x at the specified density p is much greater than the root, then the system is degenerate; if a solution exists, and if the value of x at the density p is much smaller than the root, then the system is a perfect gas in the classical sense.
1 -ftt) •OI •02 •05 •I •2 •3 •4 •s •6 •8 1-0 RJl xio 0-9S733 0-92419 0-84709 0-7S243 0-61589 0-51218 0-42600 0-3S033 0-28137 0-15316 07446 0-6966 06596 0-5746 0-4732 o-3358 02414 0-1718 0-1187 0-0779 0-0236 0 0 1 o II 0 •07767 •10223 •14460 •18657 •24168 •28434 •32320 •36222 •40475 •52453 00 We have thus fixed the "end-points" for the curves of constant mass with M < M3 in the domain of degeneracy. The corresponding pairs of points on the (R0, 1 - ft) curve and the R axis are shown in figs. 1 and 3 (the points marked 5 to 15 on the R axis and also on the (R0, 1 - ft) curve).
A Quest for Perspectives: Selected Works of S. Chandrasekhar: With Commentary (Volume 1) by S. Chandrasekhar, Kameshwar C. Wali