# Signatures of quark deconfinement through the r-modes of twin stars

## TL;DR

This paper explores how differences in r-mode instability windows and spin-down behavior of twin stars with identical mass but different radii can indicate quark deconfinement, using hybrid equations of state and analyzing observational data.

## Contribution

It introduces a systematic study of r-mode deviations in twin stars with hybrid equations of state, highlighting potential gravitational wave signatures of quark deconfinement.

## Key findings

- Twin stars can behave differently in r-mode instability despite similar mass and spin.
- Detection of gravitational waves from certain stars could indicate twin star existence.
- Hybrid equations of state can explain current pulsar data depending on parameters.

## Abstract

The observation and distinction of two compact stars with an identical mass but a different radius would be a clear sign of hadron-quark phase transition in nuclear matter. Motivated by studies searching for significant deviations in the observables of twin stars, we investigate the differences that manifest in their r-mode instability windows and spin-down evolution. Firstly, we obtain a set of hybrid equations of state (which predict the existence of a third stable branch of compact objects) by employing the well-known Maxwell construction within the phenomenological framework of constant speed of sound parametrization. Then, we systematically study the influence of certain parameters, such as the energy density jump (in the resulting hybrid equation of state) and the crust elasticity, on the deviations appearing in the r-mode instability windows and spin-down evolution of twin stars. We conclude that two stars with an identical mass and fairly similar spin frequency and temperature, may behave differently with respect to r-modes. Thus, the future possible detection of gravitational waves (due to unstable r-modes) from a star laying in the stable region of the frequency-temperature plane would be a strong indication for the existence of twin stars. Furthermore, we consider current data for the spin frequencies and temperatures of observed pulsars and compare them to the predictions made from equations of state employed in this study. We find that, depending on the transition density and the rigidness of the crust, hybrid equations of state may be a viable solution for the explanation of existing data.