Self-gravitating barotropic equilibrium configurations of rotating bodies with smoothed particle hydrodynamics

Context. Self-gravitational rotating bodies do not have spherically symmetric geometries. The study of physical events appearing in fast-spinning compact stars and accretion disks, for example those due to localized thermonuclear ignitions in white dwarfs or to the role played by hydrodynamic instabilities in stars and disks, often requires 3D simulations. When the numerical simulations are carried out with the smoothed particle hydrodynamics (SPH) technique a critical point arises as to how to build a stable initial model with rotation because there is no well-established method for that purpose.Aims. We want to provide a portable, easy-to-implement methodology for SPH simulations to procedurally generate physically sound, stable initial conditions for rotating bodies.Methods. We explain and validate an easy and versatile novel relaxation method to obtain 3D equilibrium configurations of rotating bodies with SPH. As detailed below, this method is able to relax barotropic, P (ρ ), structures either in rigid or differential rotation. The relaxation procedure strongly relies on the excellent conservation of angular momentum that characterizes the SPH technique.Results. We applied our proposal to obtain stable rotating structures of single white dwarfs, compact binaries harboring two white dwarfs, high-density stars approached as polytropes and accretion disks either in rigid or differential rotation.Conclusions. We present a novel relaxation method to build 3D rotating structures of barotropic bodies using the SPH technique. The method has been successfully applied to a variety of zero-temperature white dwarfs and polytropic self-gravitating structures. Our SPH results have been validated by comparing the main features (energies, central densities, and the polar-to-equatorial radius ratio) to those obtained with independent grid-based methods, for example, the self-consistent field method, showing that both methods agree within a few percent.