The speed of sound of the matter within neutron stars may contain nonsmooth structure related to first- or higher-order phase transitions. Here we investigate what are the observable consequences of structure in the speed of sound, such as bumps, spikes, step functions, plateaus, and kinks. One of the main consequences is the possibility of ultraheavy neutron stars (with masses larger than 2.5 solar masses), mass twins in heavy (with masses larger than 2 solar masses) and ultraheavy neutron stars. These stars pass all observational and theoretical constraints, including those imposed by recent LIGO/Virgo gravitational-wave observations and NICER x-ray observations. We thoroughly investigate other consequences of this structure in the speed of sound to develop an understanding of how nonsmooth features affect astrophysical observables, such as stellar radii, tidal deformability, moment of inertia, and Love number. Our results have important implications for future gravitational wave and x-ray observations of neutron stars and their impact in nuclear astrophysics.

• Received 22 June 2021
• Accepted 18 November 2021

DOI:https://doi.org/10.1103/PhysRevD.105.023018