Neutron Star and it’s uncertain Mass Limiting Formula

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In this wicked world, when nothing is certain for sure. Then how can the mass limiting formula for the formation of a neutron star be? Pardon me !!! Sometimes I can’t control my feelings.

Coming back to the topic of discussion. Well, soon after the discovery of neutrons, the hypothesis for the existence of neutron stars started to surface.

In 1967, all the speculation regarding the fact that whether the neutron star exists or not came to the end with the discovery of neutron stars by Irish Astrophysicist Jocelyn Bell Burnell. In fact, the discovery of neutron stars also paved the way for the future discovery of black holes.

To put it differently, neutron stars and black holes are formed by the same astronomical phenomena i.e gravitational collapse of a giant star or death of a star. Not to mention, the formation of a white dwarf and even the formation of a star too.

Well, I could have explained here about black holes too. But I don’t wanna go there. You can check this article where I have explained each and everything about black holes in detail. I am sure, you will love it.

Even after a half-century later, we are still not able to precisely determine the upper mass limit of a neutron star. In this article, I will try to shed some light on the undetermined Tolman Oppenheimer Volkoff Limit of a neutron star. Stick me with till the end. Let’s start.


Thermodynamics And Cosmology Goes Hand In Hand

Everything in this universe (of course the observable universe) is Thermodynamics dependent. In fact, thanks to the cosmologist Stephen Hawking, our so-called black holes too have thermodynamics named Black Hole Thermodynamics.

Well, according to the laws of thermodynamics, it’s the pressure of the stellar object (or giant star) that protects its core from gravitationally collapsing under its own weight.

In other words, when the stellar core of a star runs out of its nuclear fuel. It becomes impotent to produce enough heat and pressure to protect itself from gravitational collapse. Hence, a neutron star is born.

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We Are Brothers Forever

In fact, just like a neutron star; black holes or White dwarfs are also formed by the same principle. Duh, I know, now I made you confused here. Bear with me. Soon enough, you will get a clear picture.

In order to generalize things here. Let us assume that whether black holes, neutron stars, or, even white dwarf comes from the same family. In other words, they are like brothers to each other. The only difference comes from the fact that how much stellar mass they have….!!!!


Relation b/w Stellar Mass And Equation Of State

Suppose an old gigantic star runs out of its nuclear fuel. For this reason, an old star collapses under its own gravity. The outer layer of the stellar object burst out into a supernova. What left behind is maybe a white dwarf or neutron star or simply a black hole.

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The whole characterization process that whether the remnant of an old giant star would become a white dwarf or neutron star, or black hole depends on the thermodynamic equation known as the equation of state where mass plays a very important role.

Formation Of A White Dwarf

As you know, when the stellar core of a star runs out of its nuclear fuel, it collapses under its own gravity. Here comes the role of mass. If the newly formed compact star has a mass up to 1.4 solar masses, what we get is a white dwarf.

This mass limit formula for white dwarf stars was calculated by an Indian astrophysicist Subramaniam Chandrasekhar, hence called Chandrasekhar limit. You would be thinking that why don’t white dwarf further collapses under its own gravity to form a neutron star.

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Well, it’s the electron degeneracy pressure of white dwarfs that counters the effect of gravity. Thus, protects itself from further collapsing. The Chandrasekhar limit is the maximum mass that a stable white dwarf can have. However, above that; the pressure of the electrons becomes impotent.

Formation Of A Neutron Star

Now, suppose that the newly formed compact star has a mass above the Chandrasekhar limit. Things here are about to go fuzzy. So stay sharp.

When the newly formed stellar core has a mass above the Chandrashekar limit, the electron degeneracy pressure becomes impotent to counterbalance the effect of gravity. Therefore, instead of having a white dwarf, what we get is a neutron star.

Above the Chandrasekhar limit, the electrons get mingled with protons to form neutrons. In that case, instead of electron pressure, now neutron degeneracy pressure will come into force to counterbalance the gravitational force.

Hence, protects itself from further collapsing – forming a black hole. Finally, I have reached the point where I can talk about the neutron star and its uncertain mass limiting formula.


Neutron Star And TOV Limit

On one hand, Subramaniam Chandrasekhar derived a precise maximum mass limiting formula for white dwarfs. A formula that is both theoretically as well as practically correct.

On the other hand, well we do have a mass limiting formula for neutron stars too. A formula that goes by the name Tolman Oppenheimer Volkoff limit. Currently, we don’t have a precise value of the TOM (Tolman Oppenheimer Volkoff limit) limit.

This limit was jointly derived by Richard chase Tolman, J. Robert Oppenheimer, and, George Volkoff. In fact, you will be baffled to know that when this formula was derived, they jointly proposed the TOM limit to be approximately 0.7 solar masses which was almost half of the Chandrasekhar limit.

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But later with further research, Tolman Oppenheimer Volkoff’s limit was revised to be approximated between 1.5 and 3.0 solar masses. Although our universe has trillions of neutron stars. Yet, we don’t have an exact or precise value of it. And that’s sad….!!!!

As per the current astronomical data available, the largest neutron star ever discovered is of 2.14 solar masses. PSR JO740+6620 was observed in 2019, located approximately 4,600 light-years away from earth.



Should we accept that 2.14 solar mass to be the exact TOM limit for the formation of a neutron star? Or should we be waiting for the next discovery of much massive neutron star?

I mean, on one hand; neutron stars are the densest stellar object of the universe. On the other hand, our universe has trillions of neutron stars available to be discovered.

Well, who knows; maybe in the near coming future, we could discover a neutron star exceeding the 2.14 solar mass limit. What do you think? Feel free to leave a comment. I mean maybe you could enlighten me with something new……!!!!!

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I am a mechanical engineer by profession. Just because of my love for fundamental physics, I switched my career, and therefore I did my postgraduate degree in physics. Right now I am a loner (as ever) and a Physics blogger too. My sole future goal is to do a Ph.D. in theoretical physics, especially in the field of cosmology. Because in my view, every aspect of physics comes within the range of cosmology. And I love traveling, especially the Sole one.

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