Neutron stars with anisotropic matter

We have studied equilibrium, strongly gravitating configurations consisting of a neutron fluid with an anisotropic pressure. The fluid is described by two realistic equations of state (the softer SLy and the stiffer BSk21), and the anisotropy is modeled by the expression that takes into account both the local properties of the fluid (via the pressure) and the quasilocal properties of the configuration (via the compactness). Our purpose was to clarify how the presence of such an anisotropy influences the mass—radius relation and the internal structure of the models of neutron stars under consideration. In doing so, we have employed the recent astrophysical measurements of the mass and radius of neutron stars known from the literature. It enabled us to choose the anisotropy parameter $\alpha$ in such a way as to satisfy the allowed observational constraints.
It was shown that when one chooses negative values of the parameter $\alpha$ for the aforementioned equations of state, it is possible to shift the mass—radius curve in such a way as to satisfy the observational constraints well enough. This situation differs considerably from the isotropic case (when $\alpha=0$) where the mass—radius curve either falls just slightly in the region of the observational constraints (in the case of the SLy equation of state) or lies completely outside this region for the stiffer BSk21 equation of state.
Also, apart from the influence on the mass—radius relation, the presence of the anisotropy results in considerable changes in the distribution of the neutron matter energy density and pressure along the radius of the configurations. Namely, the greater (modulus) the value of the anisotropy parameter, a greater concentration of matter toward the center takes place. At the same time, for large negative $\alpha$ the difference between the tangential and radial pressures becomes greater, and, in the case of the stiff BSk21 equation of state, the tangential pressure can even become negative in the exterior regions of the star.
Using the linear stability analysis, we have determined the region of stable solutions for the anisotropic systems under consideration. It was shown that the inclusion of the anisotropy enables one to cover by stable branches of the mass—radius curves a considerable part of the region allowed by the observations.