An Introduction to Modern Astrophysics · Problem 9.21

The Interiors of Stars — Carroll & Ostlie

Physics — Astrophysics · slab-transfer-equation-blackbody-emission

Problem

Consider a horizontal plane-parallel slab of gas of thickness LL that is maintained at a constant temperature TT. Assume that the gas has optical depth τλ,0\tau_{\lambda,0}, with τλ=0\tau_\lambda = 0 at the top surface of the slab. Assume further that no radiation enters the gas from outside. Use the general solution of the transfer equation (9.54) to show that when looking at the slab from above, you see blackbody radiation if τλ,0≫1\tau_{\lambda,0} \gg 1 and emission lines (where jλj_\lambda is large) if τλ,0≪1\tau_{\lambda,0} \ll 1. You may assume that the source function, SλS_\lambda, does not vary with position inside the gas. You may also assume thermodynamic equilibrium when τλ,0≫1\tau_{\lambda,0} \gg 1.

Browse the problem library