Hybrid compact stars model in Rastall gravity: a comparative study

Abstract

The purpose of present work is to provide a new mathematical model for hybrid compact stars composed of strange quark matter ($\mathit{SQM}$) and normal baryonic matter distribution in the modified Rastall theory of gravitation. The simplest form of phenomenological $\mathit{MIT}$ bag model equation of state ($P_{q}=\frac{1}{3}(\rho _{q}-4B_{g})$) has been used to correlate the density and pressure of strange quark matter in the stellar interior, whereas radial pressure and density are associated by the simple linear equation of state ($p_{r}=m\rho$) for normal matter distribution. In order to attain the solution of field equation, we used the static and spherically symmetric Krori and Barua ($\mathit{KB}$) type geometry and then arising arbitrary constants are obtained from some physical conditions. It has been manifested that for reasonable choice of the Rastall coupling parameter (i.e., $\chi =0$), the original results in the counterpart General Relativity ($\mathit{GR}$) can be reobtained. We examined the obtained model graphically and analytically in detail for physically plausible conditions and compare with the observational facts and counterpart $\mathit{GR}$. For the investigation of obtained results, we incorporate three different compact stars namely, $\mathit{Her} X-1$, $\mathit{SAX} J1808-3658 (\mathit{SSI})$ and $4U 1820-30$ with radii $7.7\mbox{ km}$, $7.07\mbox{ km}$, and $10\mbox{ km}$, respectively as strange quark star candidates. In order to check the validity of present model, we perform various physical tests analytically and graphically, namely, stability test, energy conditions, compactification and Buchdahl condition, dynamical equilibrium of applied forces and surface redshift etc. We found that our model meets necessary physical requirements for realistic model and more consonant with the observational facts as compared to the counterpart $\mathit{GR}$ which deviates from essential physical requirements for $\mathit{Her} X-1$. Therefore our model is more realistic and can be studied for strange quark stars.