# How massive can a cold solid object be?

I understand that a neutron star is dense enough that adding more matter will increase the amount of degenerate matter directly, and the limit to its size is about 1.4 solar masses.

But if an object were formed not by an explosion that crushes it down to neutron matter, is it necessarily so?

Given normal atoms of any desired species, and it is piled up carefully so it does not get hot. When it gets around one solar mass, will it necessarily collapse into a neutron star, or can it get more massive? Will such an object eventually collapse catastrophically or can it have a degenerate matter core and a substantial thickness of less-compressed matter on top and normal matter on top of that?

What is the largest possible mass of a cold solid object? Can it be several solar masses?

By cold I mean that it’s not a star, puffed up by ongoing consumption of energy. Whatever it's made out of is not being “used up”.

• How cold does it have to be? Brown dwarfs might have a solid core, but they would have deuterium fusion. – called2voyage Jul 7 '16 at 21:13
• @called2voyageAs I understand it, after deuterium fusion ends, lithium burning begins. After that ends, the brown dwarf begins contracting again until it is supported by electron degeneracy pressure in its core. At that point, it reaches about its final radius, but will continue cooling and radiating away thermal energy. – HDE 226868 Jul 7 '16 at 22:08
• The 1.4$M_\odot$ TOV limit for neutron stars might be regarded as the limit because it accounts for neutron degeneracy pressure, not electron degeneracy pressure. As I understand it, quark stars or other exotic stars might be more massive and supported by other types of degeneracy pressure, but that's an enormous "might". – HDE 226868 Jul 7 '16 at 22:15
• Just a small point, the $1.4\:M_\odot$ appears to be a reference to the Chandrasekhar Limit for white dwarfs supported by electron degeneracy pressure. Neutron stars are of course supported by neutron degeneracy pressure and they have an upper mass limit described by the TOV Limit which ranges from $1.5\:M_\odot$ to $3.0\:M_\odot$, depending on the equation of state you choose (which EOS is correct is not currently known). – zephyr Jul 8 '16 at 13:54
• I think there also needs to be a good definition of what is meant by "cold" and more specifically, how you're defining "temperature". There are many ways to consider the concept of temperature in large planets and stars and they're not all equivalent. – zephyr Jul 8 '16 at 13:56

The limit to the neutron star mass is at least $2M_{\odot}$, since at least two have measured masses as large as this (e.g. Demorest et al. 2010).
The answer to this question is also unknown and depends on the uncertain equation of state (the relationship between pressure, density and composition) at ultra-high densities, but must be somewhere between the $2M_{\odot}$ I mentioned above and an upper limit of around $3.5M_{\odot}$, which is imposed by General Relativity and an equation of state where the speed of sound equals the speed of light (the hardest possible equation of state).
To answer a comment by @zephyr - cold in this context means that the Fermi energies of degenerate fermion species are very much higher than $kT$. White dwarfs and neutron stars (older than a few seconds) are "cold", despite having interior temperatures, in the case of the latter, of a billion degrees. Making them even colder does not change the size/density of the object but does enable the interior of a white dwarf to crystallise.