# Why There Are Maximum Mass Limits for Compact Objects

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• PeterDonis
In summary, white dwarfs and neutron stars are the only two known cases where an object's mass is limited by its own gravity instead of by the pressure of other matter.
PeterDonis
Mentor
In this article, we will look at why there are maximum mass limits for objects that are supported against gravity by degeneracy pressure instead of kinetic pressure. We will look at the two known cases of this, white dwarfs and neutron stars; but it should be noted that similar arguments will apply to any postulated object that meets the general definition given above. For example, the same arguments would apply to “quark stars” or “quark-gluon plasma objects”, etc.

1The Chandrasekhar LimitThe Tolman-Oppenheimer-Volkoff LimitA Final Note
The Chandrasekhar Limit
First, we’ll...

Ken G, curious_mind, vanhees71 and 1 other person
Perhaps one should add the interesting fact that the upper limit of the so observed neutron-star masses (around 2 solar masses) is an important constraint to figure out the equation of state of "strongly interacting matter". Of course this also has to do with the question, whether there are neutron stars with "quark cores" or other more exotic states of matter and socalled "twin stars", i.e., stars with the same mass but different radii due to being composed of different kinds/states of matter. For a recent review, see

https://arxiv.org/abs/2105.03747

PeterDonis
OK, so my understanding about the final fate of stars is:

M < 1.4 -> white dwarf

1.4 < M < 3 -> neutron star

M > 3 -> black hole

Is this accurate?

swampwiz said:
OK, so my understanding about the final fate of stars is:

M < 1.4 -> white dwarf

1.4 < M < 3 -> neutron star

M > 3 -> black hole

Is this accurate?
The "3" number is not known for sure, but it's a reasonable estimate given our best current knowledge.

Also, all of these "M" values are for the mass after the collapse process is complete. That process involves things like novas, supernovas, and other catastrophic processes that can throw off large amounts of matter and significantly reduce the mass of the remaining object. So you can't, for example, look at a main sequence star with M > 3 solar masses and say it must end up as a black hole; during the process of collapsing to its end state after it leaves the main sequence it might well throw off enough mass to end up as a neutron star or even a white dwarf.

In fact, as I understand it, most astronomers believe that most main sequence stars with a mass less than about eight solar masses will end up throwing off enough mass to put them below the 1.4 solar mass limit so that their final state is a white dwarf; and most main sequence stars with a mass from about eight to about twenty solar masses will end up throwing off enough mass to put them below the 3 solar mass limit so that their final state is a neutron star. Only main sequence stars of more than about 20 solar masses would be likely to end up as black holes.

mattt, Ken G, vanhees71 and 3 others

## 1. Why do compact objects have maximum mass limits?

Compact objects have maximum mass limits because of the fundamental laws of physics, specifically the Pauli exclusion principle and the general theory of relativity. These laws dictate that as a compact object, such as a neutron star, becomes more massive, the gravitational force becomes stronger and the object becomes more compact. At a certain point, the object becomes so compact that the electrons and protons within it are forced to merge together, creating a black hole.

## 2. What happens when a compact object reaches its maximum mass limit?

When a compact object reaches its maximum mass limit, it collapses under its own gravity and becomes a black hole. This means that the object becomes infinitely dense and has a gravitational pull so strong that not even light can escape from it.

## 3. Are there different maximum mass limits for different types of compact objects?

Yes, there are different maximum mass limits for different types of compact objects. For example, neutron stars have a maximum mass limit of about 2-3 times the mass of our sun, while black holes have a maximum mass limit of about 20-30 times the mass of our sun. This is due to the different properties and behaviors of these objects.

## 4. Can a compact object exceed its maximum mass limit?

No, a compact object cannot exceed its maximum mass limit. The laws of physics prevent this from happening, as the object would collapse into a black hole before reaching a mass greater than its limit.

## 5. How do we know that compact objects have maximum mass limits?

We know that compact objects have maximum mass limits through observations and theoretical calculations. Scientists have observed the behavior of compact objects and have found that they cannot exceed a certain mass without collapsing into a black hole. Additionally, theoretical models based on the laws of physics support the existence of maximum mass limits for compact objects.

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