# Can there be Electron and/or Proton Stars?

1. What happens to all of the electrons and protons in the material of a neutron star?

2. Could there ever be an electron star or a proton star?

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btw, there is "Electron stars for holographic metallic criticality": arxiv.org/abs/1008.2828; maybe some experts in the field can comment about this? –  Idear Jun 5 at 2:46
I figure an electron star would probably better be referred to as a "Coulomb bomb"... –  Johannes Jun 5 at 2:48

If a dense, spherical star were made of uniformly charged matter, there'd be an attractive gravitational force and a repulsive electrical force. These would balance for a very small net charge: $$dF = \frac1{r^2}\left( - GM_\text{inside} dm + \frac1{4\pi\epsilon_0}Q_\text{inside} dq \right)$$ which balances if $$\frac{dq}{dm} = \frac{Q_\text{inside}}{M_\text{inside}} = \sqrt{G\cdot 4\pi\epsilon_0} \approx 10^{-18} \frac{e}{\mathrm{GeV}/c^2}.$$ This is approximately one extra fundamental charge per $10^{18}$ nucleons, or a million extra charges per mole — not much. Any more charge than this and the star would be unbound and fly apart.

What actually happens is that the protons and electrons undergo electron capture to produce neutrons and electron-type neutrinos.

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Dear rod, would you care to say a bit about yourself on your user page, you've got a very broad knowledge. You're a bit of dark horse coming onto the scene and getting 5000 rep in 2 mnths - well done BTW - and we don't know anything about you! –  WetSavannaAnimal aka Rod Vance Jun 7 at 15:18
@WetSavannaAnimalakaRodVance, Rob's mystery is actually pretty cool :D. –  Nick Jun 8 at 14:16
@WetSavannaAnimalakaRodVance I don't really like online profiles. Maybe I should add this? –  rob Jun 8 at 14:49
@rob Fair enough - I understand. I just like to know a little about the wonderfully impressive people with excellent technical writing as well as physics skills I meet here. I guess I'm 50, so the NSA probably has less time to catch up with me than you :). I also liked your link :) –  WetSavannaAnimal aka Rod Vance Jun 9 at 2:07

The inner force of gravitation is so strong than outward pressure that the electron is forced inside the nucleus and fuses with the proton so become a neutral particle similar to neutron. In a sense , we can tell that the nuclues contains only neutron and thus called neutron star.

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+1, although I think it would be correcter to say (I'm not a particle physicist) that the electron capture or "inverse beta decay" reaction, exactly the same as that undergone by a proton in certain unstable isotopes, EXACTLY yields a neutron. Also, I'm not sure that we can directly "tell" the neutron star is neutrons: my guess is that this is a theoretically inferred and we haven't confirmed it directly (since we haven't probed a neutron star with instruments), but I'd be interested to hear differently. –  WetSavannaAnimal aka Rod Vance Jun 5 at 3:36
Actually Johannes makes a good point in his comment above: "I figure an electron star would probably better be referred to as a "Coulomb bomb"" - this is another way we know that there can only be neutrons: the other kind would be unstable. –  WetSavannaAnimal aka Rod Vance Jun 5 at 3:41

Addon to the present answers. They so far neglect the strong interaction, which keeps the known atom cores together, working "against" the mutual electric repulsion of the protons. But even $^2$He is not stable. Since the gravitational force is significantly weaker as the electromagnetic, proton stars are (as far as I know) not possible.

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The strong force is a "contact force": the form of the potential is $V = \alpha_s r^{-1} \exp-m_\pi r$, where $m_\pi c^2 = \hbar c/\mathrm{1.2\,fm}$ is the mass of the pion. Nucleons separated by more than eight or ten femtometers don't feel the strong force, which is why there aren't any stable nuclei with masses greater than about 250 grams per mole. –  rob Jun 5 at 6:48
@rob I'd like to understand the relation of nucleon distance and mass per mol you're using - could you give me a hint where to look? (ie a related concept or so) –  Volker Siegel Jun 5 at 7:15
@rob I know, therefore it's just an addon to the prevoius answers –  Lord_Gestalter Jun 5 at 7:36
@VolkerSiegel Molar mass in grams per mole is approximately the number of nucleons in a nucleus (4 for helium, 27 for aluminum, 230-240 for uranium, usually written $A$). Nuclear matter has roughly constant density, so the radius of a nucleus is roughly $1.2\mathrm{fm}\,A^{1/3}$; even uranium only has radius $^3\sqrt{240}\approx6$. The Yukawa potential is important enough to find in any book on nuclear physics. –  rob Jun 5 at 12:46