University:
Massachusetts Institute of Technology
Course:
8.282J | Astrophysics
Academic year:

2023
Views:

397

Pages:

1
Author:

Coigobell464

Stellar Structure Equations As given in lecture: 1. [\frac{dm}{dr} = 4\pi r^2 \rho] 2. [\frac{dp}{dr} = -g\rho] 3. [\frac{dL}{dr} = (\mathcal{E} - T\frac{ds}{dt})\rho + 4\pi r^2] 4. [\left{\begin{matrix} \frac{dT}{dr} = -\frac{3\kappa \rho L}{4\pi r^4 T^3} & \text{radiative} \ \frac{dT}{dr} = (1-\frac{1}{\Gamma})\frac{T}{P}\frac{dp}{dr} & \text{convective} \end{matrix}\right.] As used in a stellar evolution code: [Lagrangian (mass) coordinates] 1. [\frac{dr}{dm} = \frac{1}{4\pi r^2 \rho}] 2. [\frac{dp}{dm} = -\frac{GM}{4\pi r^4}] 3. [\frac{dL}{dm} = \mathcal{E} - T\frac{ds}{dt}] 4. [\left{\begin{matrix} \frac{dT}{dm} = -\frac{3\kappa L}{256\pi^2 \sigma r^4 T^3} & \text{radiative} \ \frac{dT}{dm} = (1-\frac{1}{\Gamma})\frac{T}{P} & \text{convective} \end{matrix}\right.] Enclosed mass is the independent variable