Proto-strange quark star structure

In this paper, we investigate the newborn strange quark stars with constant entropy. We also use the MIT bag model to calculate the thermodynamic properties in two cases: the density-dependent bag constant and the fixed bag constant (B=90\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$B=90$$\end{document} MeV). We show that the equation of state becomes stiffer by using the density-dependent bag constant and by increasing the entropy. Furthermore, we indicate that the adiabatic index of the system reaches to 43\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{4}{3}$$\end{document} at high densities. Later, we calculate the structure of a strange quark star using the equation of state and the general relativistic equations of hydrostatic equilibrium, the Tolman–Oppenheimer–Volkoff (TOV) equations. We show that the gravitational mass of the star decreases by increasing the entropy and the maximum gravitational mass is larger when we use the density-dependent bag constant at fixed central energy density. It is shown that the mass–radius relation for this system obeys M∝R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$M\, \propto \, R^{3}$$\end{document} for different cases of the calculations. Finally, we see that for a given stellar mass considering the fixed bag constant, the maximum gravitational redshift of a strange quark star occurs at larger values of entropy.