Massive neutron stars as mass gap candidates: Exploring equation of state and magnetic field

The densities in the cores of the neutron stars (NSs) can reach several times that of the nuclear saturation density. The exact nature of matter at these densities is still virtually unknown. We consider a number of proposed phenomenological, relativistic mean field equations of state to construct theoretical models of NSs. We find that, based on our selected set of models, the emergence of exotic matter at these high densities restricts the mass of NSs to $\simeq 2.2M_{\odot }$. However, the presence of magnetic fields and a model anisotropy significantly increases the star’s mass, placing it within the observational mass gap that separates the heaviest NSs from the lightest black holes. Therefore, we propose that gravitational wave observations, like GW190814 and other potential candidates within this mass gap, may actually represent massive, magnetized NSs.

Figure 1

Different RMF EOS: Here, the upper branch denotes the $npe\mu$ EOS, while the lower branch represents the hyperon-$\mathrm{\Delta }$ admixed $npe\mu -Y\mathrm{\Delta }$ EOS.

Figure 2

M-R curves for $npe\mu$ EOS (dotted) and $npe\mu -Y\mathrm{\Delta }$ EOS (solid). In each set, the top-to-bottom curves are sequentially for DDMEX, DD-ME2, DD-ME1, DD2, SWL, and GM1L.

Figure 3

Tidal deformability $\mathrm{\Lambda }$ as a function of M for $npe\mu$ EOS (dotted) and $npe\mu -Y\mathrm{\Delta }$ EOS (solid). The various curves are the same as Fig. 2.

Figure 4

Representative field profile within a star for $\eta =0.2$, $\gamma =2$.

Figure 5

M-R curves for varying $B_0$ and orientation in case of the profile corresponding to $\eta =0.2$, $\gamma =2$ for the DD-ME2 EOS. Anisotropic parameter $\kappa$ is set to 0.5 throughout.

Figure 6

M-R curves for varying $B_0$ and orientation in case of the profile corresponding to $\eta =0.2$, $\gamma =2$ for the DDMEX EOS. Anisotropic parameter $\kappa$ is set to 0.5 throughout.

Figure 7

Tidal deformability $\mathrm{\Lambda }$ as a function of M for varying $B_0$ in case of the profile corresponding to $\eta =0.2$, $\gamma =2$ for the DD-ME2 EOS. Anisotropic parameter $\kappa$ is set to 0.5 throughout.

Figure 8

Tidal deformability $\mathrm{\Lambda }$ as a function of M for varying $B_0$ in case of the profile corresponding to $\eta =0.2$, $\gamma =2$ for the DDMEX EOS. Anisotropic parameter $\kappa$ is set to 0.5 throughout.

Figure 9

Representative field profile within a star for $\eta =0.01$, $\gamma =2$.

Figure 10

M-R curves for varying $B_0$ in case of the field profile with $\eta =0.01$, $\gamma =2$ for the DDMEX EOS. Anisotropic parameter $\kappa$ is set to 0.5 throughout. Dotted lines indicate RO fields, dashed lines indicate TO fields.

Figure 11

Tidal deformability $\mathrm{\Lambda }$ as a function of M for varying $B_0$ in case of profile corresponding to $\eta =0.01$, $\gamma =2$ for the DDMEX EOS. Anisotropic parameter $\kappa$ is set to 0.5 throughout. The red dotted lines show the limits on ${\mathrm{\Lambda }}_{1.4}$ from GW190814. The various curves are the same as Fig. 10.

Figure 12

Change in the M-R curve of the DDMEX EOS due to varying anisotropy parameter $\kappa$. Three different $B_0$ have been considered: 0, $2\times {10}^{18}$, and $5\times {10}^{18}\mathrm{G}$. From top to bottom, each set corresponds to $\kappa =0.6$, 0.5, 0.4, 0.3, 0.2, and 0.1 sequentially.

Figure 13

Change in the M-R curve for EOS GM1L, DD-ME2, and DDMEX due to varying anisotropy parameter $\kappa$. $B_0$ has been fixed to 0 G throughout. From top to bottom, the curves for each EOS correspond to $\kappa =0.6$, 0.5, 0.4, 0.3, 0.2, and 0.1 sequentially.

Figure 14

Change in $\mathrm{\Lambda }-M$ relation of the DDMEX EOS due to varying anisotropy parameter $\kappa$. $B_0$ has been fixed to 0 G throughout.

Figure 15

$C-I$ relation for nonmagnetic NSs constructed under DDMEX EOS with varying $\kappa$. $I$ is normalized in units of the cube of the NS’s mass ($M^3$).

Figure 16

$C-\mathrm{\Lambda }$ relation for nonmagnetic NSs constructed under DDMEX EOS with varying $\kappa$.

Figure 17

$I-\mathrm{\Lambda }$ relation for nonmagnetic NSs constructed under DDMEX EOS with varying $\kappa$. $I$ is normalized in units of the cube of the NS’s mass ($M^3$).

Figure 18

$C-I$ relation for DDMEX EOS with fixed $\kappa =0.5$. Two values of $B_0$ are chosen along with the nonmagnetized case.

Figure 19

$C-\mathrm{\Lambda }$ relation for DDMEX EOS with fixed $\kappa =0.5$. Two values of $B_0$ are chosen along with the nonmagnetized case.

Figure 20

$I-\mathrm{\Lambda }$ relation for DDMEX EOS with fixed $\kappa =0.5$. Two values of $B_0$ are chosen along with the nonmagnetized case.

Figure 21

$C-I$ relation for NSs constructed by DDMEX, GM1L, and DD-ME2 EOS with fixed $\kappa =0.5$ and fixed $B_0=2\times {10}^{18}\mathrm{G}$.

Figure 22

$C-\mathrm{\Lambda }$ relation for NSs constructed by DDMEX, GM1L, and DD-ME2 EOS with fixed $\kappa =0.5$ and fixed $B_0=2\times {10}^{18}\mathrm{G}$.

Figure 23

$I-\mathrm{\Lambda }$ relation for NSs constructed by DDMEX, GM1L, and DD-ME2 EOS with fixed $\kappa =0.5$ and fixed $B_0=2\times {10}^{18}\mathrm{G}$.

Figure 24

M-R curves for varying dipole magnetic moment $\mu$ for the DDMEX EOS, where $\kappa =0.1$ throughout.

Figure 25

Tidal deformability $\mathrm{\Lambda }$ as a function of M for varying dipole magnetic moment $\mu$ for the DDMEX EOS, where $\kappa =0.1$ throughout.

Figure 26

Variation of the magnetic field within the star for varying $\mu$ based on the polynomial profile with the DDMEX EOS.