Evolutionary sequences of rotating protoneutron stars

¹ Departament d'Astronomia i Astrofísica, Universitat de València, 46100 Burjassot, Spain,
² Copernicus Astronomical Center (CAMK), Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland
³ Laboratoire de l'Univers et de ses Théories, UMR 8102 du CNRS, Observatoire de Paris – Section de Meudon, 92195 Meudon Cedex, France
⁴ Departament de Física Aplicada, Universitat d'Alacant, Apartat de correus 99, 03080 Alacant, Spain

Corresponding author: L. Villain, loic@camk.edu.pl

Received: 3 November 2003
Accepted: 19 January 2004

Abstract

We investigate the evolution of rigidly and differentially rotating protoneutron stars during the first twenty seconds of their life. We solve the equations describing stationary axisymmetric configurations in general relativity coupled to a finite temperature, relativistic equation of state, to obtain a sequence of quasi-equilibrium configurations describing the evolution of newly born neutron stars. The initial rotation profiles have been taken to mimic the situation found immediately following the gravitational collapse of rotating stellar cores. By analyzing the output of several models, we estimate that the scale of variation of the angular velocity in a newly born neutron star is of the order of 7-10 km. We obtain the maximum rotation frequency that can be reached as the protoneutron stars deleptonizes and cools down, as well as other relevant parameters such as total angular momentum or the instability parameter . Our study shows that imposing physical constraints (conservation of baryonic mass and angular momentum) and choosing reasonable thermodynamical profiles as the star evolves gives results consistent with the energetics of more complex simulations of non-rotating protoneutron stars. It appears to be unlikely that newly born protoneutron stars formed in nearly axisymmetric core collapses reach the critical angular velocity to undergo the bar mode instability. They could, however, undergo secular or low  rotational instabilities a few seconds after birth, resulting in a strong emission of gravitational waves retarded with respect to the neutrino luminosity peak. We also found that the geometry of strongly differentially rotating protoneutron stars can become toroidal-like for large values of the angular velocity, before reaching the mass shedding limit.