The role of finite value of strange quark mass $(m_{s}\neq0)$ 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, $p_{r}=\frac{1}{3}(\rho-4B')$, where $B'$ 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 $n=0.66~fm^{-3}$. 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 $100~MeV$ 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 $n\geq0.484,~0.489$ and $0.51~fm^{-3}$ for $m_{s}=50$ and $100~MeV$ respectively. Beyond these values, the energy per baryon $(\mathcal{E_{B}})$ drops below $930.4~MeV$, indicating a complete transition to quark matter. For physical analysis, we have considered $n~(=0.578~fm^{-3})$ which lies in the stable region with $B(n)=70~MeV/fm^{3}$. The model provides a viable description of strange stars, satisfying all necessary physical requirements.