A neutron star is a city squeezed to the size of a metropolis, where matter is packed to the limit. At the very center of such a city, a redevelopment may begin: familiar neutrons and protons give way to quark plasma — free quarks, the building blocks of almost everything around us. Usually, this process was considered instantaneous: as if an old neighborhood were demolished in a second and a skyscraper erected in its place. But construction can also proceed slowly, block by block.

The authors of the study considered exactly this scenario: the phase transition (the transformation of one type of matter into another) lasts longer than a single radial oscillation of the star. In this case, the star develops a "slow stable branch"—a whole set of configurations where a hybrid star with a quark core remains stable. Depending on the transition pressure and the density jump, this branch takes different shapes. A waterfall: the mass gradually decreases from the maximum of a purely neutron star. A bridge: connects the neutron branch to a new, fully stable hybrid one. A tail: a short extension beyond the maximum of the stable hybrid branch. A tail-bridge combines features of the latter two.

The longest branches occur when the transition starts at relatively low pressure and the density jump is small. Stiff (poorly compressible) neutron matter and a high speed of sound in the quark phase also lengthen the branch. Interestingly, stiff equations of state for neutron matter, previously discarded due to the assumption of a rapid transition, now come back into play. They do not contradict observations or microphysical constraints. A slow transition opens up an entire region of parameters inaccessible with a fast one, like a new district on the map of stellar interiors.