Investigating signatures of phase transitions in neutron-star cores

Neutron stars explore matter at the highest densities in the universe such that their inner cores might undergo a phase transition from hadronic to exotic phases, e.g., quark matter. Such a transition could be associated with nontrivial structures in the density behavior of the speed of sound, such as jumps and sharp peaks. Here, we employ a physics-agnostic approach to model the density dependence of the speed of sound in neutron stars and study to what extent the existence of nontrivial structures can be inferred from existing astrophysical observations of neutron stars. For this, we exhaustively study different equations of state, including as well those with explicit first-order phase transitions. We obtain a large number of different equation of states which reproduce the same astrophysical observations and obey the same physical constraints, such as mechanical stability and causality. Among them, some have nontrivial structures in the sound speed whereas others do not. We conclude that astrophysical information to date do not require the existence of a phase transition to quark matter in the density range explored in the core of neutron stars.