The role of finite value of strange quark mass $(m_s\ne 0)$ and baryon number density $(n)$ on the stability and maximum mass of strange stars

Abstract

This study describes the impact of non-zero value of strange quark mass $(m_s)$ and number density of baryons $(n)$ on the structure, stability and maximum mass of strange stars. We derive an exact relativistic solution of the Einstein field equation using the Tolman-IV metric potential and modified MIT bag model EoS, $p_r=\frac{1}{3}(\rho -4B^{\prime })$, where $B^{\prime }$ is a function of bag constant $B$, $m_s$ and baryon number density $(n)$. Following CERN's findings, transition of phase from hadronic matter to Quark-Gluon Plasma (QGP) may occur at high densities in presence of favourable conditions. The standard MIT bag model, with a constant $B$, fails to explain such transition properly. Introducing a finite $m_s$ and Wood-Saxon parametrisation for $B$, dependent on baryon number density $(n)$, provides a more realistic EoS to address such phase transition. Both $m_s$ and $n$ constrain the EoS, making it softer as $m_s$ increases. Solutions to the TOV equations reveal that for massless strange quarks, maximum mass is 2.01 $M_{\odot }$ and corresponding radius is 10.96 Km when $n=0.66f{m}^{-3}$. These values decrease to 1.99 $M_{\odot }$ and 1.96 $M_{\odot }$, with corresponding radii of 10.88 Km and 10.69 Km for $m_s=50$ and $100MeV$ respectively having same $n$ value. It is interesting to note that a corelation exists between $n$ and $m_s$. The hadronic to quark matter transition occurs at higher values of $n$, when $m_s$ increases such as $n\ge 0.484,0.489$ and $0.51f{m}^{-3}$ for $m_s=50$ and $100MeV$ respectively. Beyond these values, the energy per baryon $({\mathcal{E}}_{\mathcal{B}})$ drops below $930.4MeV$, indicating a complete transition to quark matter. For physical analysis, we have considered $n(=0.578f{m}^{-3})$ which lies in the stable region with $B(n)=70MeV/f{m}^3$. The model provides a viable description of strange stars, satisfying all necessary physical requirements.

Comments: 19 pages, 16 figures