Abstract. We study the mass-radius curve of hybrid stars, assuming a single first-order phase transition between nuclear and quark matter, with a sharp interface between the quark matter core and nuclear matter mantle. We use a generic parameterization of the quark matter equation of state, which has a constant, i.e. density-independent, speed of sound ("CSS"). We argue that this parameterization provides a framework for comparison and empirical testing of models of quark matter. We obtain the phase diagram of possible forms of the hybrid star mass-radius relation, where the control parameters are the transition pressure, energy density discontinuity, and the quark matter speed of sound. We find that this diagram is sensitive to the quark matter parameters but fairly insensitive to details of the nuclear matter equation of state. We calculate the maximum hybrid star mass as a function of the parameters of the quark matter EoS, and find that there are reasonable values of those parameters that give rise to hybrid stars with mass above 2 M .

The neutron star tidal deformability is a critical parameter which determines the pre-merger gravitational-wave signal in a neutron star merger. In this article, we show how neutron star tidal deformabilities behave in the presence of one or two sharp phase transition(s). We characterize how the tidal deformability changes when the properties of these phase transitions are modified in dense matter equation of state (EoS). Sharp phase transitions lead to the smallest possible tidal deformabilities and also induce discontinuities in the relation between tidal deformability and gravitational mass. These results are qualitatively unmodified by a modest softening of the phase transition. Finally, we test two universal relations involving the tidal deformability and show that their accuracy is limited by sharp phase transitions. PACS numbers: 97.60.Jd, 95.30.Cq,

We analyze observations of eight quiescent low-mass X-ray binaries in globular clusters and combine them to determine the neutron star mass-radius curve and the equation of state of dense matter. We determine the effect that several uncertainties may have on our results, including uncertainties in the distance, the atmosphere composition, the neutron star maximum mass, the neutron star mass distribution, the possible presence of a hotspot on the neutron star surface, and the prior choice for the equation of state of dense matter. We find that the radius of a 1.4 solar mass neutron star is most likely from 10 to 14 km and that tighter constraints are only possible with stronger assumptions about the nature of the neutron stars, the systematics of the observations, or the nature of dense matter. Strong phase transitions are preferred over other models and interpretations of the data with a Bayes factor of 8 or more, and in this case, the radius is likely smaller than 12 km. However, radii larger than 12 km are preferred if the neutron stars have uneven temperature distributions.