Why There Are Maximum Mass Limits for Compact Objects

[PeterDonis]

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.

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

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[vanhees71]

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

 

[swampwiz]

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?

 

[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?

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.