From neutron stars to quark stars in mimetic gravity

Realistic models of neutron and quark stars in the framework of mimetic gravity with a Lagrange multiplier constraint are presented. We discuss the effect of a mimetic scalar aiming to describe dark matter on the mass-radius relation and the moment of inertia for slowly rotating relativistic stars. The mass-radius relation and moment of inertia depend on the value of the mimetic scalar in the center of the star. This fact leads to the ambiguity in the mass-radius relation for a given equation of state. Such ambiguity allows us to explain some observational facts better than in standard general relativity. The case of mimetic potential $V(\varphi )\sim A{e}^{C{\varphi }^2}$ is considered in detail. The relative deviation of the maximal moment of inertia is approximately twice as large as the relative deviation of the maximal stellar mass. We also briefly discuss the mimetic $f(R)$ gravity. In the case of $f(R)=R+a{R}^2$ mimetic gravity, it is expected that the increase of maximal mass and maximal moment of inertia due to the mimetic scalar becomes much stronger with bigger parameter $a$. The influence of the scalar field in mimetic gravity can lead to the possible existence of extreme neutron stars with large masses.

Figure 1

The mass-radius diagram (left upper panel) and dependence of the neutron star mass on central density (right upper panel) for neutron stars in mimetic GR with $V(\varphi )=A{e}^{C{\varphi }^2}$ ($C=-0.5$) in comparison with GR by using the SLy4 equation of state for various values of $A$. The maximal masses and corresponding radii are $2.05M_{\odot }$ (9.98 km), $2.09M_{\odot }$ (10.19 km), $2.11M_{\odot }$ (10.24 km), and $2.13M_{\odot }$ (10.32 km) for GR, $A=0.02$, 0.03, and 0.04 correspondingly. In the lower panel, the relative deviation of the maximal star mass $\frac{M_{\max }-M_{\max }^{GR}}{M_{\max }^{GR}}$ as a function of $\varphi (0)={\varphi }_0$ is given.

Figure 2

The mass-number of particles diagram (left panel) and dependence of scalar field potential from the radial coordinate (right panel) for neutron stars in mimetic GR with $V(\varphi )=A{e}^{C{\varphi }^2}$ ($C=-0.5$) by using the SLy4 equation of state for various values of $A$. The mass-number particle diagram is depicted for each $A$ only in the vicinity of maximal mass. For stable star configurations we have $dM/d{\rho }_c>0$.

Figure 3

The dependence $e^{-2\lambda }=1-2m(r)/r$ (left) and $e^{2\psi }$ (right) from radial coordinate for stars with $M=1.4M_{\odot }$ in mimetic gravity and general relativity.

Figure 4

The mass profile (left) and density profile (right) for stars with ${\rho }_c=5\times 10^{14}\mathrm{g}/{\mathrm{cm}}^3$ (upper panel) and ${\rho }_c=10^{1}5\mathrm{g}/{\mathrm{cm}}^3$ in mimetic gravity and general relativity. For clarity we depicted the density profile in the interval $0<r<10\mathrm{km}$ only.

Figure 5

The mass-radius diagram, dependence of mass from the central density, and relative deviation of maximal star mass from $M_{\max }^{GR}$ as a function of $\varphi (0)={\varphi }_0$ for quark stars in mimetic GR with $V(\varphi )=A{e}^{C{\varphi }^2}$ ($C=-0.5$) in comparison with general relativity. Here we used the EOS (28) with $\alpha =0.28$, $B=B_0$ (left panels) and $\alpha =1/3$, $B=B_0$ (right panels). The maximal masses and corresponding radii for GR and $A=0.02$, 0.03, 0.04 are (a) $1.77M_{\odot }$ (10.23 km), $1.85M_{\odot }$ (10.50 km), $1.90M_{\odot }$ (10.67 km), $1.95M_{\odot }$ (10.75 km) for $\alpha =0.28$ and (b) $1.97M_{\odot }$ (10.76 km), $2.05M_{\odot }$ (10.99 km), $2.10M_{\odot }$ (11.11 km), $2.15M_{\odot }$ (11.28 km) for $\alpha =1/3$.

Figure 6

The mass-number of particles diagram for quark stars in mimetic GR with $V(\varphi )=A{e}^{C{\varphi }^2}$ ($C=-0.5$), with $\alpha =0.28$, $B=B_0$ (left panel) and $\alpha =1/3$, $B=B_0$ (right panel) for various values of $A$.

Figure 7

The relative deviation of the maximal moment of inertia from general relativity as a function of $\varphi (0)={\varphi }_0$ for some values of parameter $A$ for neutron stars using the SLy4 EOS (upper panel); quark stars [EOS (28) with $\alpha =0.28$, $B=B_0$] (left lower panel); and quark stars [EOS (28) with $\alpha =1/3$, $B=B_0$] (right lower panel).

Figure 8

Left panel: The dependence of the stellar moment of inertia (in units of $10^{45}\mathrm{g}·{\mathrm{cm}}^2$) from the mass in mimetic GR with $V(\varphi )=A{e}^{{\varphi }^2/2}$ in comparison with general relativity for (a) neutron stars using SLy4 EOS; (b) quark stars [EOS (28) with $\alpha =0.28$, $B=B_0$]; (c) quark stars [EOS (28) with $\alpha =1/3$, $B=B_0$]. Right panel: The normalized metric function $\omega (r)/\mathrm{\Omega }$ as a function of the radial coordinate for stars with masses $M=1.4M_{\odot }$ and close to maximal for corresponding EOS.