We construct equilibrium models of uniformly and differentially rotating hybrid hadron-quark stars using equations of state (EOSs) with a first-order phase transition that gives rise to a third family of compact objects. We find that the ratio of the maximum possible mass of uniformly rotating configurationsthe supramassive limit -to the Tolman-Oppenheimer-Volkoff (TOV) limit mass is not EOS-independent, and is between 1.15 and 1.31, in contrast with the value of 1.20 previously found for hadronic EOSs. Therefore, some of the constraints placed on the EOS from the observation of the gravitational wave event GW170817 do not apply to hadron-quark EOSs. However, the supramassive limit mass for the family of EOSs we treat is consistent with limits set by GW170817, strengthening the possibility of interpreting GW170817 with a hybrid hadron-quark EOSs. We also find that along constant angular momentum sequences of uniformly rotating stars, the third family maximum and minimum mass models satisfy approximate EOS-independent relations, and the supramassive limit of the third family is approximately 16.5 % larger than the third family TOV limit. For differentially rotating spheroidal stars, we find that a lower-limit on the maximum supportable rest mass is 123 % more than the TOV limit rest mass. Finally, we verify that the recently discovered universal relations relating angular momentum, rest mass and gravitational mass for turning-point models hold for hybrid hadron-quark EOSs when uniform rotation is considered, but have a clear dependence on the degree of differential rotation. PACS. 04.40.Dg Relativistic stars: structure, and stability arXiv:1905.00028v1 [astro-ph.HE] 30 Apr 2019 4 Note that this result is in tension with what was found in [85] where different equations of state were adopted. M ↓ M TOV ↓ = 1 + 0.33 J J ↓,Kep 2 − 0.10 J J ↓,Kep 4 . (19)The spread in this equation is at most 2 %. 10 Moreover, we find that the bottom turning points can be described with the same Equations (18), but with a spread of 3 %. The universality becomes tighter if we consider top and bottom turning points separately. For the bottom turning points, the best-fitting functions are M ↓ M TOV ↓ = 1 + 0.35 J M TOV ↓ 2 2 − 0.12 J M TOV ↓ 2 4 , (20a) M 0,↓ M TOV 0,↓ = 1 + 0.58 J M TOV 0,↓ 2 2 − 0.35 J M TOV 0,↓ 2 4

We study the solution space of general relativistic, axisymmetric, equilibria of differentially rotating neutron stars with realistic, nuclear equations of state. We find that different types of stars, which were identified by earlier works for polytropic equations of state, arise for realistic equations of state, too. Scanning the solution space for the sample of realistic equations of state we treat, we find lower limits on the maximum rest masses supported by cold, differentially rotating stars for each type of stars. We often discover equilibrium configurations that can support more than 2 times the mass of a static star. We call these equilibria "übermassive", and in our survey we findübermassive stars that can support up to 2.5 times the maximum rest mass that can be supported by a cold, non-rotating star with the same equation of state. This is nearly two times larger than what previous studies employing realistic equations of state had found, and which did not uncoverübermassive neutron stars. Moreover, we find that the increase in the maximum rest mass with respect to the non-spinning stellar counterpart is larger for moderately stiff equations of state. These results may have implications for the lifetime and the gravitational wave and electromagnetic counterparts of hypermassive neutron stars formed following binary neutron star mergers. arXiv:1901.05479v1 [astro-ph.HE] 16 Jan 2019 T |W | Ωc Ωe J M 2 C M 0 M M 0 M T OV 0,max M 0 M sup 0,max M ADM M M ADM M T OV ADM,max M ADM M sup ADM,max T |W | Ωc Ωe J

We investigate the dynamical stability of relativistic, differentially rotating, quasi-toroidal models of neutron stars through hydrodynamical simulations in full general relativity. We find that all quasi-toroidal configurations studied in this work are dynamically unstable against the growth of non-axisymmetric modes. Both one-arm and bar mode instabilities grow during their evolution. We find that very high rest mass configurations collapse to form black holes. Our calculations suggest that configurations whose rest mass is less than the binary neutron star threshold mass for prompt collapse to black hole transition dynamically to spheroidal, differentially rotating stars that are dynamically stable, but secularly unstable. Our study shows that the existence of extreme quasi-toroidal neutron star equilibrium solutions does not imply that long-lived binary neutron star merger remnants can be much more massive than previously found. Finally, we find models that are initially supra-Kerr (J/M 2 > 1) and undergo catastrophic collapse on a dynamical timescale, in contrast to what was found in earlier works. However, cosmic censorship is respected in all of our cases. Our work explicitly demonstrates that exceeding the Kerr bound in rotating neutron star models does not imply dynamical stability.

Hybrid hadron-quark equations of state that give rise a third family of stable compact stars have been shown to be compatible with the LIGO-Virgo event GW170817. Stable configurations in the third family are called hybrid hadron-quark stars. The equilibrium stable hybrid hadron-quark star branch is separated by the stable neutron star branch with a branch of unstable hybrid hadronquark stars. The end-state of these unstable configurations has not been studied, yet, and it could have implications for the formation and existence of twin stars -hybrid stars with the same mass as neutron stars but different radii. We modify existing hybrid hadron-quark equations of state with a first-order phase transition in order to guarantee a well-posed initial value problem of the equations of general relativistic hydrodynamics, and study the dynamics of non-rotating or rotating unstable twin stars via 3-dimensional simulations in full general relativity. We find that unstable twin stars naturally migrate toward the hadronic branch. Before settling into the hadronic regime, these stars undergo (quasi)radial oscillations on a dynamical timescale while the core bounces between the two phases. Our study suggests that it may be difficult to form stable twin stars if the phase transition is sustained over a large jump in energy density, and hence it may be more likely that astrophysical hybrid hadron-quark stars have masses above the twin star regime. We also study the minimum-mass instability for hybrid stars, and find that these configurations do not explode, unlike the minimum-mass instability for neutron stars. Additionally, our results suggest that oscillations between the hadronic and quark phases could provide gravitational wave signals associated with such phase transitions in core-collapse supernovae and white dwarf-neutron star mergers.1 Henceforth we refer to EOSs which include both hadron and quark degrees of freedom as "hybrid EOSs", and stars that contain both hadronic and quark phases as "hybrid stars". Hybrid stars with the same mass as neutron stars are referred to as "twin stars.

Parametric equations of state (EoSs) provide an important tool for systematically studying EoS effects in neutron star merger simulations. In this work, we perform a numerical validation of the M*-framework for parametrically calculating finite-temperature EoS tables. The framework, introduced in Raithel et al. (2019), provides a model for generically extending any cold, β-equilibrium EoS to finite-temperatures and arbitrary electron fractions. In this work, we perform numerical evolutions of a binary neutron star merger with the SFHo finite-temperature EoS, as well as with the M*-approximation of this same EoS, where the approximation uses the zero-temperature, β-equilibrium  slice of SFHo and replaces the finite-temperature and composition-dependent parts with the M*-model. We find that the approximate version of the EoS is able to accurately recreate the temperature and thermal pressure profiles of the binary neutron star remnant, when compared to the results found using the full version of SFHo. We additionally find that the merger dynamics and gravitational wave signals agree well between both cases, with differences of $\lesssim 1-2{{\%}}$ introduced into the post-merger gravitational wave peak frequencies by the approximations of the EoS. We conclude the M*-framework can be reliably used to probe neutron star merger properties in numerical simulations.