7th Week: Stellar Structure and Evolution

Stellar structure

Stars of different mass and age have varying internal structures. Stellar structure models describe the internal structure of a star in detail and make detailed predictions about the luminosity, the color and the future evolution of the star.

Equations of stellar structure

Pressure equilibrium: Pressure and gravity must balance or the star will expand or contract. The balance of the gravity force and the pressure gradient is known as the hydrostatic balance.

${\frac {dP_{r}}{dr}}=-\rho _{r}{\frac {GM_{r}}{r^{2}}}$

Conservation of mass

${\frac {dM_{r}}{dr}}=4\pi r^{2}\rho _{r}$

Energy generation: To keep the temperature constant everywhere luminosity $L$ must be generated.Considering the energy leaving the spherical shell yields the energy equation

${\frac {dL_{r}}{dr}}=4\pi r^{2}\rho _{r}\epsilon$

where $\epsilon$ is the energy generation rate (sum of all energy sources and losses) per g and s

Energy transport:The temperature inside a star must increase progressively towards its center to make energy flow from the center to the surface.

${\frac {dT_{r}}{dr}}=\left(1-{\frac {1}{\gamma }}\right){\frac {T_{r}}{P_{r}}}{\frac {dP_{r}}{dr}}$

where $\gamma =c_{p}/c_{v}$ is the adiabatic index, the ratio of specific heats in the gas