By S. Chandrasekhar, Kameshwar C. Wali
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Extra resources for A Quest for Perspectives: Selected Works of S. Chandrasekhar: With Commentary (Volume 1)
Since D is fixed by the boundary condition, it follows that the value of | " at which & (£") becomes equal to 6>max (where cf. equation (17")) 6^ = Q^KIU> (21) is fixed as a function of A3. In other words the discontinuity in 0, AG" at the interface | " is a single-valued function of L, M, x and A or AG" = F(L,M,x;^) (21') or by (21) AQ" = f(L,M,x; A3) (22) where A q" is the discontinuity of density at the interface. But it has been suggested by LANDAU1) (among others) that the maximum density of matter will arise after some kind of overcompressibility, the incompressibiiity setting in later (see Fig.
The integration has been numerically effected for the following ten different values of the parameter :— i/V=0-8. o6 > °-5> o-4. ** 6 40 g W + »4)„ , g8(339g2 + 280) 7! 3x9! g7(i425g«+ 11436^ + 4256) ? Sxii! a = i - - 2 . (75)* The important quantities of interest are the boundary quantities occurring in equations (66), (67), (69). 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.
These completely collapsed configurations correspond to j3x = 1. Hence we know from (43) the point at which the curves of constant mass for M < M3 must intersect the R axis. Also for any mass we can calculate the value /3j has in the wholly gaseous state. x for a wholly gaseous configuration, which in its completely collapsed state has a central density corresponding to y =y0. 1-0 r- F I G . —The upper curve illustrates the (M, xa)-relation for configurations in which degeneracy is just developing at the centre.
A Quest for Perspectives: Selected Works of S. Chandrasekhar: With Commentary (Volume 1) by S. Chandrasekhar, Kameshwar C. Wali