Template:ASTR508/Assignment6

Following the derivation in class, calculate the pressure at the surface of an isothermal core as a function of the radius of the core including the effects of electron degeneracy. Use units of the envelope pressure times $(M_c/M{)}^2$. That is on the vertical axis you will have

${\left(\frac{M_c}{M}\right)}^2\frac{P_c}{P_e}$

where

$P_e=\frac{81}{4\pi }\frac{1}{G^3{M}^2}{\left(\frac{k{T}_c}{{\mu }_e{m}_H}\right)}^4$

and on the horizontal axis you will have $R_c$. Try several values of $M$.

Hints: First choose $M_c$, $T_c$ (say $5\times 10^7\mathrm{K}$) and plot as a function of $R_c$. What is $P_c/P_e$ in equilibrium? How can you figure out $M$? How can you fix $M$?