Lane-Emden mass formula
= Lane-Emden mass formula
{c}
If $\rho=\rho_c\theta^n$, $r=\alpha\xi$, and $\xi_1$ is the first zero of the Lane-Emden function, then a spherical polytrope has
$$
M=4\pi\alpha^3\rho_c\left[-\xi_1^2\theta'(\xi_1)\right].
$$
= Lane-Emden mass formula
{c}
If $\rho=\rho_c\theta^n$, $r=\alpha\xi$, and $\xi_1$ is the first zero of the Lane-Emden function, then a spherical polytrope has
$$
M=4\pi\alpha^3\rho_c\left[-\xi_1^2\theta'(\xi_1)\right].
$$