Discontinuity gravity modes may arise in perturbed quark-hadron hybrid stars when a sharp density jump exists in the stellar interior, and they are a potential fingerprint to infer the existence of quark matter cores in compact objects. When a hybrid star is perturbed, conversion reactions may occur at the quarkhadron interface and may have a key role in global stellar properties such as the dynamic stability and the quasinormal mode spectrum. In this work we study the role of the conversion rate at the interface. To this end, we first derive the junction conditions that hold at the sharp interface of a nonradially perturbed hybrid star in the case of slow and rapid conversions. Then, we analyze the discontinuity g-mode in both cases. For rapid conversions, the discontinuity g-mode has zero frequency because a displaced fluid element near the phase splitting surface almost immediately adjusts its composition to its surroundings, and gravity cannot provide a buoyancy force. For slow conversions, a g-mode exists, and its properties are analyzed here using modern hadronic and quark equations of state. Moreover, it has been shown recently that in the case of slow conversions an extended branch of stable hybrid configurations arises for which ∂M=∂ϵ c < 0. We show that g-modes of the standard branch (that is, the one with ∂M=∂ϵ c > 0) have frequencies and damping times in agreement with previous results in the literature. However, g-modes of the extended branch have significantly larger frequencies (in the range 1-2 kHz) and much shorter damping times (a few seconds in some cases). We discuss the detectability of g-mode GWs with present and planned GW observatories.

The internal composition of neutron stars is currently largely unknown. Due to the possibility of phase transitions in quantum chromodynamics, stars could be hybrid and have quark cores. We investigate some imprints of elastic quark phases (only when perturbed) on the dynamical stability of hybrid stars. We show that they increase the dynamical stability window of hybrid stars in the sense that the onset of instabilities happens at larger central densities than the ones for maximum masses. In particular, when the shear modulus of a crystalline quark phase is taken at face value, the relative radius differences between elastic and perfect-fluid hybrid stars with null radial frequencies (onset of instability) would be up to 1%-2%. Roughly, this would imply a maximum relative radius dispersion (on top of the perfect-fluid predictions) of 2%-4% for stars in a given mass range exclusively due to the elasticity of the quark phase. In the more agnostic approach where the estimates for the quark shear modulus only suggest its possible order of magnitude (due to the many approximations taken in its calculation), the relative radius dispersion uniquely due to a quark phase elasticity might be as large as 5%-10%. Finally, we discuss possible implications of the above dispersion of radii for the constraint of the elasticity of a quark phase with electromagnetic missions such as NICER, eXTP, and ATHENA.Unified Astronomy Thesaurus concepts: General relativity (641); Neutron stars (1108); Stellar oscillations (1617)

We model neutron stars as magnetised hybrid stars with an abrupt hadron-quark phase transition in their cores, taking into account current constraints from nuclear experiments and multi-messenger observations. We include magnetic field effects considering the Landau level quantisation of charged particles and the anomalous magnetic moment of neutral particles. We construct the magnetised hybrid equation of state, and we compute the particle population, the matter magnetisation and the transverse and parallel pressure components. We integrate the stable stellar models, considering the dynamical stability for rapid or slow hadron-quark phase conversion. Finally, we calculate the frequencies and damping times of the fundamental and g non-radial oscillation modes. The latter, a key mode to learn about phase transitions in compact objects, is only obtained for stars with slow conversions. For low magnetic fields, we find that one of the objects of the GW170817 binary system might be a hybrid star belonging to the slow extended stability branch. For magnetars, we find that a stronger magnetic field always softens the hadronic equation of state. Besides, only for some parameter combinations a stronger magnetic field implies a higher hybrid star maximum mass. Contrary to previous results, the incorporation of anomalous magnetic moment does not affect the studied astrophysical quantities. We discuss possible imprints of the microphysics of the equation of state that could be tested observationally in the future, and that might help infer the nature of dense matter and hybrid stars.