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By S. Chandrasekhar, Kameshwar C. Wali

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Additional info for A Quest for Perspectives: Selected Works of S. Chandrasekhar: With Commentary (Volume 1)

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These are tabulated in Table I for the different values of y0. 12. From the figures of Table I it is easy to calculate the mass in units of M3, the radius in units of lt and the central density (=x 0 s ) m u m t s °f & * When yt -*• 00, q -*• 1 and the series (74) goes over into the expansion for Emden 6, near the origin (cf. British Association Tables, 2, Introduction, equation on top of page v). [215] (=08848 x io 6 /x grams cm. -3 ). These express the chief physical characteristics of these configurations in the "natural system" of units occurring in the theory of these configurations.

F l — = ^ = 0 - I O I 4 6 7 8 • • •' Pco 9 DO (is) or 1 - j S ^ =0-09212 . . ; jSto =0-90788. . (16) If for material at density p and temperature T the fraction (1 -/3) calculated by means of the equations (1), (2) and (3) is greater than 1 - /J^, then the system is definitely not degenerate. For values of /3 greater than fi^ (12) admits of a solution in finite x, and this value of x would define a convenient measure as to at what densities degeneracy would set in for a system with this prescribed j3.

1 5. —The mass of the material enclosed up to a point 7) is clearly rv rv M(TI)=^TT\ By ' pr2dr =^naa\ pr)2di). sJ^jK [210] < 2 '> Remembering that p 0 is given by (18) we have explicitly The mass of the whole configuration is therefore We notice that in (28) and (29) y0 does not explicitly occur. It is of course implicitly present inasmuch as in the differential equation defining , y0 occurs. 6. —Let j>(ij) be the mean density of the material inside 17. Then M(ij)=fcraVp(ij). (3°) Comparing (28) and (30), we have w ™--»w*irrf% (3I) or JO 3 Pjjj) = _ PO 3 £ (' denoting the derivative)—a relation analogous to the corresponding relation in the theory of polytropes.

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