Uniform models of neutron and quark (strange) stars in General Relativity

TL;DR

The paper develops uniform-density, general-relativistic models for cold neutron and strange stars, deriving an EOS-agnostic algebraic equilibrium relation that enables analytic mass estimates without integrating the TOV equations. For neutrons, it establishes a GR-based framework linking $P/( ho c^2)$ to a function of the compactness variable $x$, while for strange stars it provides closed-form solutions under the MIT bag EOS and shows the maximum state occurs at a universal $x_m$ independent of $B$. Comparisons with exact Oppenheimer-Volkoff solutions show the uniform-density approach reproduces the max mass within ~20% and highlights lower central densities. The work further connects the deconfinement boundary to constraints on strange-star masses, discusses experimental and theoretical QGP-density estimates, and concludes that strange stars are unlikely to form in standard stellar evolution, though primordial strange stars could be possible under high-density confinement conditions.

Abstract

Models of neutron and strange stars are considered in the approximation of a uniform density distribution. A universal algebraic equation, valid for any equation of state, is used to find the approximate mass of a star of a given density without resorting to the integration of differential equations. Equations of state for neutron stars had been taken for degenerate neutron gas and for more realistic ones, used by Bethe, Malone, Johnson (1975). Models of homogeneous strange stars for the equation of state in the "quark bag model" have a simple analytical solution. The solutions presented in the paper for various equations of state differ from the exact solutions obtained by the numerical integration of differential equations by at most $ \sim 20 \%$. The formation of strange stars is examined as a function of the deconfinement boundary (DB), at which quarks become deconfined. Existing experimental data indicate that matter reaches very high densities in the vicinity of the DB. This imposes strong constraints on the maximum mass of strange stars and prohibits their formation at the final stages of stellar evolution, because the limiting mass of neutron stars is substantially higher and corresponds to considerably lower matter densities.

Figures (10)

• Figure 1: (Solid line) Dependence of $\frac{P}{\rho c^2}$ on the parameter x , according to (\ref{['eq7']}). The abscissa of the vertical dashed line $x = x_l$ corresponds to the zero root of the denominator of (\ref{['eq7']}), $x_l = 0.9849$ . The horizontal dash-dotted line $\frac{P}{\rho c^2}=1$ separates the physically admissible region from the upper region where the principle of causality is violated.
• Figure 2: Degenerate neutron gas: dependence $M(\rho)$ in the case of a uniform density distribution (solid line), and the exact models (dash-dotted line); dependence $M_0(\rho)$ (dashed line) in the case of uniform density and (dotted line) the exact model.
• Figure 3: Degenerate neutron gas with a correction for nuclear interaction: the dependence $M(\rho)$ (solid line) in the case of a uniform density distribution and (dash-dotted line) the exact model; the dependence $M_0(\rho)$ (dashed line) in the case of uniform density and (dotted line) in the exact model.
• Figure 4: Model I H. The dependence $M(\rho)$ (solid line) in the case of a uniform density distribution and (dash-dotted line) in the exact model; the dependence $M_0(\rho)$ (dashed line) in the case of a uniform density and (dotted line) in the exact model. The vertical solid line shows at what density $v_s=c$ and $\rho = 2.2 \times10^{16}$ g/cm$^3$.
• Figure 5: Dependence of mass on density $M(\rho)$ for different values of the bag constant $B$ in the MIT bag model. Here $B$ is given in units MeV/fm$^3$. The curve maxima are indicated by crosses. The parameters of stars at maxima corresponding to critical states are presented in Table 1.