Magnetized relativistic stellar models in Eddington-inspired Born-Infeld gravity

We consider the structure of the magnetic fields inside the neutron stars in Eddington-inspired Born-Infeld (EiBI) gravity. In order to construct the magnetic fields, we derive the relativistic Grad-Shafranov equation in EiBI and numerically determine the magnetic distribution in such a way that the interior magnetic fields should be connected to the exterior distribution. Then, we find that the magnetic distribution inside the neutron stars in EiBI is qualitatively similar to that in general relativity, where the deviation of magnetic distribution in EiBI from that in general relativity is almost comparable to uncertainty due to the equation of state for the neutron star matter. However, we also find that the magnetic fields in the crust region are almost independent of the coupling constant in EiBI, which suggests a possibility of obtaining the information about the crust equation of state independent from the gravitational theory via the observations of the phenomena associated with the crust region. In any case, since the imprint of EiBI gravity on the magnetic fields is weak, the magnetic fields could be a poor probe of gravitational theories, considering the many magnetic uncertainties.

Figure 1

Neutron star models in EiBI with FPS EOS. The left panel corresponds to the stellar mass as a function of the central density normalized by the saturation density, while the right panel corresponds to the stellar mass as a function of the stellar radius. The solid line denotes the result in general relativity ($\kappa =0$) and the other lines denote the results in EiBI with various normalized coupling constant $8\pi \kappa {ϵ}_s$.

Figure 2

For the stellar models with $M=1.4M_{\odot }$ for FPS EOS, the tetrad components of the pure poloidal magnetic fields are plotted as a function of $r/R$, where the left and right panels correspond to the radial component on the symmetry axis ($\theta =0$) and the $\theta$ component on the equatorial plane ($\theta =\pi /2$), respectively. The both components are normalized by $B_p$, which is the magnetic field strength at the stellar surface of the poles. The solid line corresponds to the result in general relativity, while the broken and dotted lines correspond to the results in EiBI with various values of $8\pi \kappa {ϵ}_s$. The vertical lines denote the position of the stellar surface.

Figure 3

Relative deviation of $B_{[r]}/B_p$ in EiBI from that in general relativity for the stellar models with $M=1.4M_{\odot }$ constructed with FPS EOS, which corresponds to the left panel in Fig. 2. The labels in the figure denote the values of the coupling constant in EiBI.

Figure 4

Magnetic configurations on the meridional plane for the stellar models with $M=1.4M_{\odot }$ for FPS EOS in general relativity (middle panel) and in EiBI with $8\pi \kappa {ϵ}_s=-0.02$ (left panel) and 0.05 (right panel). The magnetic field strength is normalized by the magnetic dipole moment ${\mu }_b$.

Figure 5

Similar to Fig. 2, but for the stellar models constructed with SLy4 EOS.

Figure 6

The proportionality factor $\beta$ for the stellar models with various values of coupling constant in EiBI are shown as a function of the stellar mass, where the left and right panels correspond to the results for FPS and SLy4 EOSs, respectively. The labels in the figure denote the values of the coupling constant in EiBI.

Figure 7

The proportionality factor $\beta$ as a function of the coupling constant in EiBI for the fixed stellar mass, where the left and right panels correspond to the results for FPS and SLy4 EOSs, respectively.

Figure 8

For the stellar models in general relativity with $M=1.4M_{\odot }$ constructed with FPS EOS, the tetrad components of the mixed magnetic fields normalized by $B_p$ are plotted as a function of $r/R$, where the left, middle, and right panels are $B_{[r]}/B_p$ on the symmetry axis ($\theta =0$), $B_{[\theta ]}/B_p$ on the equatorial plane ($\theta =\pi /2$), and $B_{[\varphi ]}/B_p$ on the equatorial plane, respectively. The different lines in the figure correspond to the magnetic field distributions with different values of $\zeta R$, and the labels in the figure denote the value of $\zeta R$.

Figure 9

Similar to Fig. 8, but in EiBI with various coupling constants. Upper, middle, and lower panels correspond to the results in EiBI with $8\pi \kappa {ϵ}_s=-0.02$, 0.02, and 0.05, respectively.

Figure 10

Maximum value of $\zeta$ allowed for the stellar models with various coupling constants in EiBI are shown as a function of the stellar mass, where the left and right panels correspond to the results for FPS and SLy4 EOSs, respectively. The labels in the figure denote the values of the coupling constant in EiBI.