Neutron stars are the densest astrophysical objects in the universe. Cores of neutron stars reach densities as high as those realized in ultrarelativistic heavy-ion collisions studied in particle accelerators. In these collisions ordinary nuclear matter melts into a new phase of elementary particle matter, quark matter. This naturally raises the question: does quark matter also exist inside neutron stars? In my talk, I describe how recent advancements in theory of superdense matter and in observations of neutron stars—such as the LIGO/Virgo detection of gravitational waves arising from a merger of two neutron stars—can inform us about what lies in the centers of neutron stars. I discuss how the different constraints point to the existence of quark matter cores in large neutron stars.
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