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A white dwarf is essentially a degenerate electron gas, in which pressure of degenerate electrons supports gravitational pressure. As a simplified model of such an object, consider a spherical star of ideal gas consisting of electrons and completely ionized hydrogen atoms, and of constant density. Radius of star is $R$, Mass of star is $M$, $N$ = number of electrons.

Consider the electrons to be ultra-relativistic. Density of star is given to be ${10}^{12}\, \mathrm{kg \cdot m}^{-3}$ . What is the critical mass for which the dwarf can be in equilibrium?

I am trying to find the gravitational pressure and the Fermi pressure due to the electrons, and then I will equate them. I have successfully calculated the gravitational pressure, but to calculate Fermi pressure, I need total energy to Pauli Exclusion principle applied to electrons. The total energy is coming to be a function of $N$, and due to some mistake (which I do not know, where am I making), the radius term is not cancelling on both sides (which should). How to calculate total energy due to Pauli exclusion principle?

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closed as off-topic by John Rennie, JamalS, DavePhD, Kyle Oman, user10851 Jun 27 '14 at 14:55

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  • $\begingroup$ As this is a good legitimate theoretical astrophysics question, you may have more luck when asking it here on Astronomy. $\endgroup$ – Dilaton Jun 28 '14 at 15:30
  • $\begingroup$ Possibly related: physics.stackexchange.com/q/92489/44126 $\endgroup$ – rob Jun 28 '14 at 16:02
  • $\begingroup$ Take a look at the Wikipedia article on Fermi-Dirac statistics. Then follow that up with the article on the Fermi gas. These two should get you pointed in the right direction. $\endgroup$ – Kyle Kanos Jul 4 '14 at 0:40
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    $\begingroup$ It is clearly not a homework. $\endgroup$ – peterh Mar 27 '17 at 18:37