Discontinuity gravity modes in hybrid stars: Assessing the role of rapid and slow phase conversions

Abstract

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.

Hybrid stars with sequential phase transitions: the emergence of the g2 mode

“…The error related to the fundamental mode is reduced as the compactness of the NS increase, but it is never larger than 20% [78]. On the other hand, if we focus on the error associated to the g modes, the difference is less than 10% [74,79]. Therefore, for the g modes, the results obtained using the relativistic Cowling approximation are qualitatively and quantitatively acceptable.…”

“…The presence of g modes in cold and non rotating stars, indicates that exist an abrupt phase transition in the interior of the star, because these modes are completely inhibited if the EoS is continuous [73]. Also, it is important to stress that the g modes associated with discontinuities in the EoS only exist in the slow conversion scenario: g modes does not appear if the conversion is rapid [74].…”

Probing Elastic Quark Phases in Hybrid Stars with Radius Measurements

“…As stressed previously, nucleation timescales can decrease significantly for hot NSs. It has been suggested that they may be smaller than typical perturbation timescales for temperatures around 20 MeV (Tonetto & Lugones 2020). In this case, conversions around a phase-splitting surface should be rapid.…”

Discontinuity g‐modes of hybrid stars: Effect of sequential phase transitions

“…In this work, we focus our attention on the study and analysis of the g-modes associated with discontinuous energy density profiles inside the compact star. For these modes, the relativistic Cowling approximation gives quantitatively accurate value of the frequencies, with errors not larger that ∼10% when compared to those calculated using linearized perturbation theory (Tonetto & Lugones 2020).…”