An Introduction to Modern Astrophysics · Problem 14.8

The Fate of Massive Stars — Carroll & Ostlie

Physics — Astrophysics · linearization-stefan-boltzmann

Problem

(a) Linearize the Stefan--Boltzmann equation in the form of Eq. (3.17) to show that

\frac{\delta L}{L_0} = 2\frac{\delta R}{R_0} + 4\frac{\delta T}{T_0}.

(b) Linearize the adiabatic relation

TV^{\gamma-1} = \text{constant}

, and so find a relation between

\delta L/L_0

and

\delta R/R_0

for a spherical blackbody model star composed of an ideal monatomic gas.