Degeneracy Pressure and Its Role in Formation of Compact Stars

Prosad Bhattacharya

Abstract: Under the influence of excessively high gravitational pressure, identical electrons, i.e., electrons with same set of quantum numbers, in the core of an hugely compressed red giant star are forced to occupy the same energy states at the same time violating the Pauli?s Exclusion Principle. Such degenerated electrons create and exert Electron Degeneracy Pressure in the star?s core that acts against the gravity and halts the core collapse of a cold star. When inwardly acting gravitational pressure becomes equal to the newly created outwardly acting electron degeneracy pressure, core-collapse of the cold star stops and the star becomes a stable White Dwarf star. Stars having mass maximum up to the Chandrasekhar limit (1.44 times the solar mass) can only become white dwarfs. Electron degeneracy pressure, however, is unable to restrict the core collapse of cold giant / super giant stars of mass heavier than the Chandrasekhar limit. As its radius reduces, the gravitational pressure of the star increases exponentially. Incredibly high gravity forces the electrons of a star?s core to combine with the protons in their nuclei and form neutrons. The cold star becomes a sphere made of neutrons. Core collapse continues, gravitational pressure increases and in due course gravitational pressure compels the identical neutrons occupy the same energy states at the same time defying the Pauli?s Exclusion Principle. These degenerated neutrons, like the degenerate electrons, create another type of quantum pressure inside the core of a cold star called neutron degeneracy pressure. Neutron degeneracy pressure restricts the core collapse of the red giant / supergiant stars and finally helps to create Neutron Stars when it becomes equal to the gravitational pressure of the stars. Stars having masses in between the Chandrasekhar limit (1.44 M?) and the TOV limit (2.928M?) will become only neutron stars. At and beyond the TOV limit, a star, upon core collapse, will become a Black Hole first as its escape velocity will become equal to the velocity of light. But newly formed black holes are not pressure balanced and up to a certain mass limit, the black holes eventually will become neutron stars also. Above that mass limit, a black hole will explode as a supernova before becoming a neutron star.

Keywords: Electron Degeneracy Pressure, Neutron Degeneracy Pressure, Pauli's Exclusion Principle, Gravitational Energy, Quantum Chromo-dynamics Binding Energy

How to Cite?: Prosad Bhattacharya, "Degeneracy Pressure and Its Role in Formation of Compact Stars", Volume 14 Issue 10, October 2025, International Journal of Science and Research (IJSR), Pages: 898-904, https://www.ijsr.net/getabstract.php?paperid=SR251016190731, DOI: https://dx.doi.org/10.21275/SR251016190731