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Does gravitational collapse limit Neutron Star size?

  1. Oct 17, 2017 #1
    Is there a theoretical limit to the size of neutron stars? It seems likely neutron stars are not simply electrons orbiting a proton so what is their life cycle? Can they just evaporate slowly by neutron decay?
  2. jcsd
  3. Oct 17, 2017 #2


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    The neutrons are not free neutrons, so they don't decay. The neutrons are crushed together like a big atomic nucleus. They won't evaporate because they are very tightly gravitationally bound so no matter can really escape. In answer to your question about the maximum size, there is a maximum mass beyond which the neutron star will collapse to a black hole, but we don't know exactly what it is because the exact properties of matter at these densities are only known approximately. The maximum mass is probably somewhere between 2 and 3 solar masses.
  4. Oct 17, 2017 #3
    OK, phyzguy. So I'll imagine them as protons in a fixed 3D lattice surrounded by an electron "cloud". For stability all the proton-proton links will be the same at a given star radius, with the links maybe getting shorter at smaller radii due to increasing pressure. Perhaps the protons shrink together until they all touch!
    2.5 solar masses are about 5 x 10^30kg, and 3 x 10^57 protons, giving a sphere radius of 9 x 10^18 protons. So a proton radius of 0.86fm would give a star radius of about 7.7km. Does that make any sense?
    Do we know if neutron stars rotate?
  5. Oct 17, 2017 #4


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    The size makes rough sense. Neutron stars are about 10km in diameter. The nucleons are basically touching, like they are in an atomic nucleus. But I don't think you should imagine it as protons and an electron cloud. Most (all?) of the nucleons in the neutron star are neutrons - hence the name.

    Yes, most of them are rotating rapidly. Pulsars are rotating neutron stars, and some of them are rotating as fast as 1000 revolutions per second (60,000 RPM). Imagine something the mass of the sun, 10 km in diameter rotating at 60,000 RPM!
  6. Oct 17, 2017 #5
  7. Oct 18, 2017 #6
    Protons touching? This begs the question, why does the matter in neutron stars stop shrinking at the proton radius? If, as in the Standard Model, protons consist of quarks with space between them, why can’t they be compressed further? One possible answer is … there is no space to compress and the proton radius indicates the quark size. But a radius of 0.865fm, a circumference of 5.44fm, corresponds to a quantum loop of one 36.3MeV wavelength. The proton radius is uncertain by at least ± 5%, so the the energy is in the range 34.6MeV to 38.1 MeV.

    The electron is frequently considered a photon in a toroidal orbit and relativistic by the inverse fine structure constant, 1/α, (= 137), so the EM energy in a frame rotating close to velocity c is 137 x 0.511MeV, (the electron rest mass energy), at about 70MeV. It's perhaps a coincidence that half the spin-1 electron EM energy is 35MeV, within the uncertainty of the 36.3MeV noted above.

    In regard to my previous “electron cloud” comment, my main point was the rigid crystal like proton lattice. I don’t think a neutron is an electron orbiting a proton. But the neutron charge is zero so it seems likely the neutron is an EM wave orbiting a proton with its E field oriented to cancel the proton charge. So perhaps the EM waves in a neutron star bind the protons together in a similar manner to which shared electrons bind atoms in a crystal.

    Are there any theories about neutron stars along this line of thought?
  8. Oct 19, 2017 #7


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    Neutrons packed close together repel each other strongly due to the Pauli exclusion principle.
    "Touching" is not really a meaningful concept for these particles.
    None of this makes any sense at all.
    There is no such thing.
    That doesn't make any sense.

    You can't randomly put words together and expect the result to be meaningful.
  9. Oct 19, 2017 #8
    The theoretical limit to the mass of neutron stars is called the Tolman-Oppenheimer-Volkoff Limit, and is approximately 3.0 solar masses. Their paper was published in February 1939. A relatively recent paper (originally published in 2002 and revised in 2013) suggests that the maximum mass limit of a neutron star could be as much as 3.8 solar masses.

    Tolman-Oppenheimer-Volkoff Limit - Wikipedia
    On Massive Neutron Cores - American Physical Society, Phys. Rev. 55, 374, February 15, 1939
    The Maximum Mass of a Neutron Star - Astronomy & Astrophysics, Volume 305, pp. 871-877, January 1996 [PDF]
    On the Minimum and Maximum Mass of Neutron Stars and the Delayed Collapse - Astronomy & Astrophysics, Volume 367, Number 2, pp. 582-587, February 2001 (free article)
    A New Look to Massive Neutron Cores - arXiv : gr-qc/0210057v1
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