From neutron stars to highly compact configurations

In this work, we deliver a comprehensive analysis of anisotropic fluids supporting self-gravitating spheres. Our research is grounded on anisotropic fluids that adhere to a well-behaved polytropic equation of state, with an appropriate anisotropy inspired by the conformally flat condition. We perform numerical integration of the generalized Lane–Emden equation over a broad spectrum of parameters, assessing the feasibility of the derived solution as a model for compact celestial objects. The findings are presented in color-coded diagrams, denoting the number of conditions met by the solutions based on the value of the parameters involved. Our study reveals that anisotropy is a pivotal factor in the interpretation of these models. Notably, the compactness of the solution falls within a range where the lower limit corresponds to neutron stars, and the upper limit relates to extremely compact configurations approaching Buchdhal’s limit.