Ordinary matter consists of atoms, and atoms are made of nuclei and electrons. But in a neutron star, gravity compresses matter so strongly that electrons are squeezed into protons, and almost everything turns into a dense packing of neutrons. It's like one giant atomic nucleus the size of a city. What if you squeeze even harder? Then neutrons start to break apart into their constituent parts — quarks. You get something like a hot 'soup' of free quarks that exists only in the deepest interiors.
The authors of the study tried to model this transition from neutron 'porridge' to quark soup. They based their approach on a theory similar to the description of superconductivity: quarks can pair up into diquarks. But pairs alone are not enough. To keep the star from collapsing under its own weight, additional stiffness is needed. This comes from the particles that carry the interaction — vector mesons. It's like adding not only flour and water to the dough, but also hard nuts that prevent it from spreading. As a result, the equation of state, the law linking pressure and density, becomes steep enough to support a mass of more than two Suns.
The calculations showed that if a neutron star is heavier than about two Suns, its central density exceeds four nuclear densities. That's like each grain-of-sand-sized cube weighing a billion tons. The radius of such a star is about twelve kilometers, and inside hides a quark core. These numbers agree well with actual observations: the most massive known neutron stars fit this description perfectly.
The density at the center of such a star is so high that a teaspoon of its matter would weigh more than all the mountains on Earth combined.
In Robert Forward's novel 'Dragon's Egg', life on a neutron star is described, where creatures made of nuclear matter live a million times faster than humans.