# Maximum mass and universal relations of rotating relativistic hybrid hadron-quark stars

## TL;DR

This study models rotating hybrid hadron-quark stars with phase transitions, revealing that their maximum mass ratios vary with EOS and confirming universal relations under certain conditions, impacting gravitational wave interpretations.

## Contribution

It introduces new equilibrium models of hybrid stars with phase transitions, analyzing their maximum mass limits and universal relations, which differ from purely hadronic models and influence gravitational wave constraints.

## Key findings

- Maximum mass ratio for rotating hybrid stars varies between 1.15 and 1.31.
- Universal relations hold for uniform rotation but depend on differential rotation.
- GW170817 constraints do not fully apply to hybrid hadron-quark EOSs.

## Abstract

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 configurations - the 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.