SSC/Stability/GammaVariation

How Does Stability Change with γ_g?

Isolated Uniform-Density Configuration

From the general solution derived by 📚 T. E. Sterne (1937, MNRAS, Vol. 97, pp. 582 - 593), we have …

Sterne (1937)

Sterne (1937)

The first few solutions are displayed in the following boxed-in image that has been extracted directly from §2 (p. 587) of 📚 Sterne (1937); to the right of his table, we have added a column that expressly records the value of the square of the normalized eigenfrequency that corresponds to each of the solutions presented by Sterne37.

Table of exact eigenvector expressions extracted from §2 (p. 587) of … T. E. Sterne (1937) Models of Radial Oscillation Monthly Notices of the Royal Astronomical Society, Vol. 97, pp. 582 - 593	$\frac{n^2}{4\pi G\overline{\rho }}$
$j=0;$      $\mathfrak{𝔉}=0;$       ${\xi }_1=1$	$\gamma -4/3$
$j=1;$      $\mathfrak{𝔉}=14;$      ${\xi }_1=1-(7/5)x^2$	$2(5\gamma -2)/3$
$j=2;$      $\mathfrak{𝔉}=36;$      ${\xi }_1=1-(18/5)x^2+(99/35)x^4$	$7\gamma -4/3$
$j=3;$      $\mathfrak{𝔉}=66;$      ${\xi }_1=1-(33/5)x^2+(429/35)x^4-(143/21)x^6$	$12\gamma -4/3$