A Detailed Analysis of the Special Points on $M-R$ Solutions of Hybrid (Twin) Stars

TL;DR

This study investigates the properties of hybrid neutron stars with hadron-quark phase transitions, revealing universal linear relations between special points and maximum masses across different models and parameters.

Contribution

It introduces universal linear relations between the special point mass and maximum mass of hybrid stars, independent of transition densities and bag model asymptotic values.

Findings

Existence of distinct special points on mass-radius diagrams of hybrid stars.

Universal linear relation between $M_{SP}$ and $M_{max}$ for various models.

Shift in the $M_{SP}-M_{max}$ relation with different bag model parameters.

Abstract

Hadron-quark phase transition in neutron star cores is achieved in the present work with the help of Maxwell construction. For the purpose we employ six different and well-known hadronic models for the pure hadronic phase. The quark phase is described with the MIT Bag model in which the density dependence of the bag pressure $B(\rho)$ is invoked for different asymptotic values ($B_{as}$) of $B(\rho)$. The resulting hybrid star (HS) configurations exhibit twin star characteristics and distinct special points (SPs) on the mass-radius diagram of the HSs irrespective of the transition densities and the value of $B_{as}$. We find that for any particular value of $B_{as}$, the mass corresponding to SP ($M_{SP}$) and the maximum mass ($M_{max}$) of the HSs, obtained with different hadronic models, follow a nearly linear (fitted) relationship where the slope is independent of the value of $B_{as}$. The $M_{SP}-M_{max}$ dependence of the HSs is found to be consistent with any hadronic equation of state (EoS) chosen to obtain the hybrid EoS and thus such relations can be considered as universal relations in the context of formation of SPs. A change in the value of $B_{as}$ shifts the position of the fitted line in the $M_{SP}-M_{max}$ plane, with the linearity, however, retained.