Realistic anisotropic neutron stars: Pressure effects

In this paper, we study the impact of anisotropy on neutron stars with different equations of state, which have been modeled by a piecewise polytropic function with continuous sound speed. Anisotropic pressure in neutron stars is often attributed to interior magnetic fields, rotation, and the presence of exotic matter or condensates. We quantify the presence of anisotropy within the star by assuming a quasilocal relationship. We find that the radial and tangential sound velocities constrain the range of anisotropy allowed within the star. As expected, the anisotropy affects the macroscopic properties of stars, and it can be introduced to reconcile them with astrophysical observations. For instance, the maximum mass of anisotropic neutron stars can be increased by up to 15% compared to the maximum mass of the corresponding isotropic configuration. This allows neutron stars to reach masses greater than $2.5M_{\odot }$, which may explain the secondary compact object of the GW190814 event. Additionally, we propose a universal relation for the binding energy of an anisotropic neutron star as a function of the star’s compactness and the degree of anisotropy.

Figure 1

Mass-radius relations for different equations of states with the GPP parametrization (see Table 2) The color scale corresponds to the value of the anisotropic parameter, ${\lambda }_a$. Positive values support more massive configurations. Configurations on the left of the solid black line are stable against radial perturbations. Configurations on the right of the dashed black lines satisfy the causality conditions for radial sound speed, while the configurations inside the region enclosed by the dotted black line satisfy it for tangential sound speed.

Figure 2

Fraction between the maximum mass for an anisotropic configuration, $M_{\mathrm{NS},\max }$, and the isotropic one, $M_{\mathrm{NS},\max }^{{\lambda }_a=0}$, as a function of the anisotropic parameter. Configuration with $M<M_{\mathrm{NS},\max }$ satisfies the stability and causality conditions. Colored lines correspond to the results of the EOS used, and black line is the fit given in Eq. (15).

Figure 3

Mass-radius relation of the isotropic configuration for all the EOS summarized in Table 2. In blue are the configurations composed of npem matter, in red the ones with hyperons and in black the ones with quarks. Colors bands indicate observational constrains given by the pulsar masses of PSR $\mathrm{J}0348+0432$ [62] and PSR J0952-0607, the mass and radius NICER constraints for the pulsars PSR $\mathrm{J}0030+0451$ [46, 47] and PSR $\mathrm{J}0740+662$ [48, 49], and the mass of the secondary compact object of the GW190814 event [64]. The dashed gray line corresponds to the faster observed pulsar, PSR J1748-2446ad [65], and the dotted gray line to the Buchdahl limit for the star compactness [66].

Figure 4

Same as Fig. 3 but for anisotropic NSs with, ${\lambda }_a$ $\epsilon (-2,2)$ for two selected EOSs: BHF and GM1Y6. Only models satisfying the stability and causality conditions are displayed.

Figure 5

Specific binding energy as a function of star compactness for all EOS summarized in Table 2. The color scale corresponds to the value of the anisotropic parameter. Only models satisfying the stability and causality conditions are displayed.

Figure 6

Fit for the specific binding energy as a function of star compactness [see Eq. (21)]. It is worth mentioning that all fits were done up to $\mathcal{C}=M_{\max }/R_{\max }$.

Figure 7

Pressure as function of mass density for the QHC21 EOS and its corresponding GPP parametrization. The dotted vertical lines correspond to the limiting densities of the zones shown.