Nontrivial features in the speed of sound inside neutron stars

Measurements of neutron star masses, radii, and tidal deformability have direct connections to nuclear physics via the equation of state (EoS), which for the cold, catalyzed matter in neutron star cores is commonly represented as the pressure as a function of energy density. Microscopic models with exotic degrees of freedom display nontrivial structure in the speed of sound (${c}_{s}$) in the form of first-order phase transitions and bumps, oscillations, and plateaus in the case of crossovers and higher-order phase transitions. We present a procedure based on Gaussian processes to generate an ensemble of EoS that include nontrivial features. Using a Bayesian analysis incorporating measurements from x-ray sources, gravitational wave observations, and perturbative QCD results, we show that these features are compatible with current constraints. We investigate the possibility of a global maximum in ${c}_{s}$ that occurs within the densities realized in neutron stars---implying a softening of the EoS and possibly an exotic phase in the core of massive stars---and find that such a global maximum is consistent with, but not required by, current constraints.