White Dwarfs, Neutron Stars & Black Holes Part II : Electron Degeneracy Pressure✳️

In part I of the subject topic, we studied that a star in its Red Giant phase with an inert helium core shrinks & heats up. Eventually, the core becomes degenerate with the free electrons detached from the helium atoms, keeping the core stable. This force or pressure exerted by the free electrons, avoiding the core from further collapse, is called “The Electron Degeneracy Pressure”.
 
Now to elaborate on this “Electron Degeneracy Pressure”, it is based on “Pauli’s Exclusion Principle” which states that “2 or more identical fermions cannot occupy the same quantum state at the same time & in the same volume” (note: Fermions are sub-atomic particles which follow Fermi-Dirac statistics. Fermions can be “Elementary or Composite”. Electrons are part of Elementary type Fermions while protons & neutrons are classified as Composite Fermions”). Now since an electron can have 2 types of spin namely “spin-up” (spin vector pointing in the +ve z-axis) & “spin-down” (spin vector pointing in the -ve x-axis) so following “Pauli’s Exclusion Principle” 2 electrons in the same orbital has to be non-identical ie 2 electrons in the same orbital cannot share the same quantum number including spin. In general, atoms with their sub-atomic particles have a lot of space to move around, but in a collapsing star the inward gravitational push brings all the atoms to their maximally compacted space & state. In other words, in this state, electrons in the outermost shell of atoms come a lot closer to electrons in the outermost shell of other neighbouring atoms, but a physical barrier gets created between these outermost shells of atoms, preventing them from compressing any further. Now one may think that this physical barrier formed between the outer shell electrons of neighbouring atoms is due to the electrostatic repulsion of electrons as like charges repel each other, but in the year 1967 physicist Freeman Dyson gave the observation that the physical barrier existing between densely compacted atoms in a star core is a result of the “Pauli’s Exclusion Principle” & not due to the natural tendency of repulsion of likely charged electrons.

Now, as stated above, for a star in its Red Giant phase, this “Electron Degeneracy Pressure” helps stabilize the inert helium core during the pre-helium fusion phase till the helium flash phase. But it’s not the main primary force supporting the star & avoiding core collapse. In fact, for the majority of the period, a star in its Red Giant phase, where its core shrinks & expands periodically, the primary force balancing the inward gravitational push is the outward pressure exerted due to nuclear fusion in the core & the resulting thermal energy released as heat. This also determines the overall structure & size of the red giant along with its luminosity.
 
But when a small to intermediate mass star turns into a white dwarf with carbon & oxygen core, then this same “Electron Degeneracy Pressure” acts as the main dominant force preventing any further collapse of this white dwarf star due to gravity acting inward. Here the white dwarf core is also degenerate, meaning the core elements “Carbon & Oxygen” exists not as atoms but as ions & the free electrons stuffed together closely exists in a state of electron degeneracy, generating the necessary outward pressure required to counteract the inward gravitational push, thus preventing any further collapse & stabilizing the white dwarf core. This state of degeneracy that a white dwarf experiences is due to the immense density of it’s core which results in the ionization of the Carbon-Oxygen core & the free electrons in confined space are forced into higher energy levels where they gain a greater kinetic energy that translates into an outerward pressure called “The Electron Degeneracy Pressure” & this becomes the dominant force acting outward, keeping the core stable without any nuclear fusion. The working mechanism of “Electron Degeneracy Pressure” remains the same even in Red Giant stars, but it is not the dominant force acting outward keeping a Red Giant core stable against gravity, as nuclear fusion in the core still works. To elaborate more, a white dwarf star is extremely dense & small, having the size roughly that of Earth but a mass of approximately the Sun, with no nuclear fusion in the core (like a stellar ember) but still very hot, having initial temperatures of exceeding 100000 Kelvin. Though a white dwarf will eventually cool down & become a black dwarf emitting no more energy or light, but this shall take a very long time ie in billions of years & so far no any black dwarf has been discovered yet & it is assumed that no any black dwarf could have been formed yet as the universe is not old enough.

Now considering our Sun as a medium mass star in the solar system which will become a White Dwarf with Carbon-Oxygen core in about 5 billion years from now of its stellar evolution lifecycle, after having lost much of its mass as planetary nebula then as stated above it’s size will be that of our planet Earth but around 200000 times more dense or massive. To imagine this, the planet Jupiter is about 320 times more massive than Earth & our Sun, about 300,000 times more massive than Earth & also about 110 times wider. But there exists a limit in regards to the amount of mass a white dwarf star can have or in other words a limit concerning the massivity or density of the core of a white dwarf, meaning the limit beyond which the core’s “Electron Degeneracy Pressure” acting outward fails & inward gravitational push overcomes resulting in further collapse of the white dwarf star & this limit was discovered by Indian American physicist “Dr.Subrahmanyam Chandrashekhar” in the year 1930 when he calculated that a white dwarf star has a maximum mass limit, beyond which it would collapse into a more compact object, such as a neutron star or black hole. This limit is approximately “1.44 solar masses” & it was given the name the “Chandrashekhar Limit”. Chandrasekhar’s work revolutionised our understanding of stellar evolution and compact objects!