Hyperons in neutron stars within an Eddington-inspired Born-Infeld theory of gravity

We investigate the mass-radius relation of the neutron star (NS) with hyperons inside its core by using the Eddington-inspired Born-Infeld (EiBI) theory of gravity. The equation of state of the star is calculated by using the relativistic mean field model under which the standard SU(6) prescription and hyperon potential depths are used to determine the hyperon coupling constants. We found that, for $4\times {10}^6{\mathrm{m}}^2\lesssim \kappa \lesssim 6\times {10}^6{\mathrm{m}}^2$, the corresponding NS mass and radius predicted by the EiBI theory of gravity is compatible with observational constraints of maximum NS mass and radius. The corresponding $\kappa$ value is also compatible with the $\kappa$ range predicted by the astrophysical-cosmological constraints. We also found that the parameter $\kappa$ could control the size and the compactness of a neutron star.

Figure 1

EOS of neutron star matter based on the BSP parameter set of ERMF model with (NSM) and without hyperons (NSM-H).

Figure 2

Constituents fraction in neutron star core based on BSP parameter set of ERMF model.

Figure 3

Profiles of the exponential of metrics $e^{\nu }$, $e^{\beta }$ (left panel) and $e^{\lambda }$, $e^{\alpha }$ (right panel) as a function radius coordinate r for $\kappa =4,-4$ and 0 (GR). The black solid line represents the result of GR where in this case $e^{\nu }=e^{\beta }$ and $e^{\lambda }=e^{\alpha }$. These plots are taken for NS with the mass $M=1.4M_{\odot }$ case. Note that $\kappa$ is in unit ${10}^6{\mathrm{m}}^2$.

Figure 4

Profiles of parameter $a$ and $b$ in Eqs. (19) and (20) as a function of radius coordinate r. $\kappa$ is in unit ${10}^6{\mathrm{m}}^2$.

Figure 5

Pressure profile as a function radius coordinate r for a NS with several $\kappa$ values. The upper panel is for a NS with $P_c=200\mathrm{MeV}{\mathrm{fm}}^{-3}$, the middle panel for NS with $P_c=50\mathrm{MeV}{\mathrm{fm}}^{-3}$ and the lower panel for NS with $P_c=10\mathrm{MeV}{\mathrm{fm}}^{-3}$. $\kappa$ is in unit ${10}^6{\mathrm{m}}^2$.

Figure 6

Energy profile as a function radius coordinate r for a NS with several $\kappa$ values. Each panel uses exactly the same central pressure as those used in Fig 5. $\kappa$ is in unit ${10}^6{\mathrm{m}}^2$.

Figure 7

The relationship between NS $M/M_{\odot }$ and $\kappa$ for some particular fixed $R$.

Figure 8

The relationship between NS radius and $\kappa$ for particular fixed NS $M/M_{\odot }$.

Figure 9

NS mass-radius relation for some values of $\kappa$ where $\kappa =0$ corresponds to the GR result. The horizontal shaded band is the pulsar mass constraint from Ref. [7] and the vertical shaded band is the radius constraint from Ref. [16]. The combination of yellow and orange shaded bands is from astrophysical-cosmological constraints [30]. The constraint for $\kappa$ we get in this work, that is yellow shaded band only, is deducted both from astrophysical-cosmological constraint and maximum mass constraint in horizontal shaded band where $4\lesssim \kappa \lesssim 6$. The dotted line represents the limit of causality of GR from [44]. Note that $\kappa$ is in unit ${10}^6{\mathrm{m}}^2$.

Figure 10

Redshift $z$ as a function of $M/M_{\odot }$. The horizontal line is $z$ for low mass x-ray binary EXO 0748-676 NS [43]. $\kappa$ is in unit ${10}^6{\mathrm{m}}^2$.

Figure 11

Compactness of star $\xi$ as a function of $\kappa$ for several fixed central pressure $P_c$.