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

$P_{e}={\frac {81}{4\pi }}{\frac {1}{G^{3}M^{2}}}\left({\frac {kT_{c}}{\mu _{e}m_{H}}}\right)^{4}$

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 $M$?