Degeneracy pressure fails to self-adjust to resist gravitational collapse beyond certain limits
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Astrophysical reference literature indicates that when mass exceeds specific thresholds such as the Chandrasekhar limit, relativistic effects and core pressures render degeneracy pressure insufficient to prevent further gravitational collapse.
Some of the electrons are now gone, so the core can no longer resist the crushing mass of the star’s overlying layers. The core begins to shrink rapidly. More and more electrons are now pushed into the atomic nuclei, which ultimately become so saturated with neutrons that they cannot hold onto them. At this point, the neutrons are squeezed out of the nuclei and can exert a new force. As is true for electrons, it turns out that the neutrons strongly resist being in the same place and moving in the same way. The force that can be exerted by such degenerate neutrons is much greater than that produced by degenerate electrons, so unless the core is too massive, they can ultimately stop the collapse. This means the collapsing core can reach a stable state as a crushed ball made mainly of neutrons, which astronomers call a neutron star. We don’t have an exact number (a “Chandrasekhar limit”) for the maximum mass of a neutron star, but calculations tell us that the upper mass limit of a body made of neutrons might only be about 3 MSun. So if the mass of the core were greater than this, then even neutron degeneracy would not be able to stop the core from collapsing further.
# Why can't the degeneracy pressure self-adjust itself to resist gravitational collapse?
Tags: quantum-mechanics, black-holes, astrophysics, gravitational-collapse
- Score: 23
- Views: 1797
- Answers: 2
- Answered: yes
- Asked by: Soumita (585 rep)
- Asked: 2021-05-24
- Site: physics
## Question
After a star becomes a White dwarf, it resists gravitational collapse mainly due to the electron degeneracy pressure. If the mass of the white dwarf is greater than the Chandrasekhar limit, the degeneracy pressure cannot resist the collapse any longer and is doomed to become a neutron star or a black hole. Why can't the degeneracy pressure keep on self-adjusting itself to resist collapse forever?
## Answers
### Answer by Michael Seifert (score: 39 [ACCEPTED])
The basic problem is that for a sufficiently massive star, the electrons become relativistic. The fine details of this calculation are rather complicated, but you can get a qualitative sense of the argument as follows:
For non-relativistic fermions at zero temperature, it is possible to show that the total energy of $N$ particles in a box of volume $V$ is proportional to $N^{5/3}/V^{2/3}$. This can be done via counting the densi
Chandrasekhar limit
The Chandrasekhar limit (/ˌtʃəndrəˈʃeɪkər/) is the maximum mass of a stable white dwarf star. These stars resist gravitational collapse primarily through electron degeneracy pressure, compared to main sequence stars, which resist collapse through thermal pressure. The Chandrasekhar limit is the mass above which electron degeneracy pressure in the star's core is insufficient to balance the star's own gravitational self-attraction. The value of the Chandrasekhar limit depends upon the ratio of the number of electrons to nucleons (neutrons plus protons) in the star. For small stars this ratio is around 1/2 and the limit is about 1.44 M☉. The limit was named after Subrahmanyan Chandrasekhar who won the 1983 Nobel prize together with William Alfred Fowler for work on stellar models.
## Physics
Radius–mass relations for a model white dwarf.
Using the general pressure law for an ideal Fermi gas
Non-relativistic ideal Fermi gas
Ultrarelativistic limit
Normal stars fuse gravitationally compressed hydrogen into helium, generating vast amounts of heat. As the hydrogen is consumed, the stars' core compresses further allowing the helium and heavier nuclei to fuse ulti
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