An Introduction to Modern Astrophysics · Problem 12.11

Main-Sequence and Post-Main-Sequence Stellar Evolution — Carroll & Ostlie

Physics — Astrophysics · jeans-mass-alternate-form

Problem

Show that the Jeans mass (Eq. 12.14) can also be written in the form

M_J = \frac{c_J v_T^4}{P_0^{1/2} G^{3/2}} \tag{12.33}

where the isothermal sound speed,

v_T

, is given by Eq. (12.18),

P_0

is the pressure associated with the density

\rho_0

and temperature

T

, and

c_J \simeq 5.46

is a dimensionless constant.