A quark star is a hypothetical type of compact exotic star composed of quark matter. These are ultra-dense phases of degenerate matter theorized to form inside particularly massive[citation needed] neutron stars. -Wikipedia
If you add enough mass to a neutron star it forms a black hole but how much mass is needed to form a quark star? When do neutrons and protons start to break down into a mush of quarks and gluons?
Answer
A quark star may or may not be possible - as the wikipedia page you refer to says - they are "hypothetical".
As the mass of a neutron star increases, generally speaking, it become smaller and the central density increases.
Quarks are ``confined'' within nucleons by a strong force that increases with quark separation. However, at very small separations it may be that quarks attain an asymptotic freedom where they can to first order be treated as non-interacting fermions.
At densities of $\sim 5-10\rho_{0}$ (where $\rho_0 = 2.7\times 10^{17}$ kg/m$^3$ is the density of normal nuclear matter) it is possible that the nucleons dissolve into a quark-gluon plasma, containing the lightest three quarks, u,d,s. There will then be a weak-force equilibrium between the species, which results in equal populations of each. Since the rest mass energies of the quarks are thought to be $2-150$ MeV/, they will be extremely relativistic at these densities, with a pressure that approaches $\rho c^{2}/3$. This is a soft equation of state that could not support the overlying neutron star (or indeed a star made entirely of quark matter). However, it is inconceivable that there are no strong-force interactions between the quarks (or why would nuclei have the size they do?) and these may harden the equation of state sufficiently to form a stable object with a quark matter core.
As there equal amounts of u,d,s quarks these are sometimes called Strange stars or described as being made of Strange Matter. However, these terms are more usually reserved for stars that are entirely made of such material, which is something more exotic entirely.
It is unknown whether such objects exist and therefore it is very difficult to answer your question. It may be that quark matter is just an ephemeral state on the way to the collapse to a black hole and that no quark stars in equilibrium exist. A possible avenue of exploration is that neutron stars with a quark matter core should cool more rapidly than "normal" neutron matter, because the direct URCA neutrino cooling process is feasible. It would be interesting to see whether neutron stars of different masses follow radically different cooling tracks, but those measurements are not available yet.
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