Tidal Deformations of Hybrid Stars with Sharp Phase Transitions and Elastic Crusts

Abstract

Gravitational wave astronomy is expected to provide independent constraints on neutron star properties, such as their equation of state. This is possible with the measurements of binary components' tidal deformability, which alter the point-particle gravitational waveforms of neutron-star binaries. Here we provide a first study of the tidal deformability effects due to the elasticity/solidity of the crust (hadronic phase) in a hybrid neutron star, as well as the influence of a quark-hadronic phase density jump on tidal deformations. We employ the framework of nonradial perturbations with zero frequency and study hadronic phases presenting elastic aspects when perturbed (with the shear modulus approximately 1% of the pressure). We find that the relative tidal deformation change in a hybrid star with a perfect-fluid quark phase and a hadronic phase presenting an elastic part is never larger than about 2 − 4% (with respect to a perfect-fluid counterpart). These maximum changes occur when the elastic region of a hybrid star is larger than approximately 60% of the star's radius, which may happen when its quark phase is small and the density jump is large enough, or even when a hybrid star has an elastic mixed phase. For other cases, tidal deformation changes due to an elastic crust are negligible (10 −5 − 10 −1 %), therefore unlikely to be measured even with third generation detectors. Thus, only when the size of the elastic hadronic region of a hybrid star is over half of its radius, the effects of elasticity could have a noticeable impact on tidal deformations.

Neutron-star tidal deformability and equation-of-state constraints

“…At the same time, more and louder detections offer the opportunity of going beyond a single radius measurement [140] or even a characterization of features of the equation of state such as phase transitions [123]. Improved detector sensitivity will allow us to measure higher order terms beyond the = 2 tidal deformability [74], directly observe the postmerger signal [38], and study the properties of the neutron star crust in terms of its elastic properties [334,335], heating [336], and shattering [337]. Another effect of interest is the potential resonant excitation of different neutron star modes driven by the orbital motion [338,339].…”

Probing Elastic Quark Phases in Hybrid Stars with Radius Measurements

“…The baryon density jump at the quark-hadron interface is a free parameter, and chemical and mechanical equilibrium there imply a unique density jump and ρ å . For further details on this model, see Sieniawska et al (2019) and Pereira et al (2020).…”

Tidal deformations of neutron stars with elastic crusts

“…Of course, should one use an equation of state that involves discontinuities at such an interface, that would need to be taken into account. We do not consider such possibilities here, but will do so in upcoming work [37].…”

“…where C ≡ M/R is the star's compactness. Because H 0 and H 0 are continuous between the interior and the vacuum at the surface, we can use (37) to determine the ratio c 1 /c 2 in terms of the interior solutions at r = R. This gives the result [35]…”