  Neutron-star cores contain matter at the highest densities in our Universe.
This highly compressed matter may undergo a phase transition where nuclear
matter melts into deconfined quark matter, liberating its constituent quarks
and gluons. Quark matter exhibits an approximate conformal symmetry, predicting
a specific form for its equation of state (EoS), but it is currently unknown
whether the transition takes place inside at least some physical neutron stars.
Here, we quantify this likelihood by combining information from astrophysical
observations and theoretical calculations. Using Bayesian inference, we
demonstrate that in the cores of maximally massive stars, the EoS is consistent
with quark matter. We do this by establishing approximate conformal symmetry
restoration with high credence at the highest densities probed and
demonstrating that the number of active degrees of freedom is consistent with
deconfined matter. The remaining likelihood is observed to correspond to EoSs
exhibiting phase-transition-like behavior, treated as arbitrarily rapid
crossovers in our framework.
