APPROXIMATE MATCHING OF ANALYTIC AND NUMERICAL SOLUTIONS FOR RAPIDLY ROTATING NEUTRON STARS

Emanuele Berti and Nikolaos Stergioulas

Department of Physics, Aristotle University of Thessaloniki
Abstract:

We investigate the properties of a closed-form analytic solution recently found by Manko et al. (2000) for the exterior spacetime of rapidly rotating neutron stars.  For selected equations of state we numerically solve the full Einstein equations to determine the neutron star spacetime along constant rest mass sequences. The analytic solution is then matched to the numerical solutions by imposing that the quadrupole moment of the numerical and analytic spacetimes be the same. For the analytic solution we consider, such a matching condition can be satisfied only for very rapidly rotating stars. When solutions to the matching condition exist, they belong to one of two branches.  For one branch the current octupole moment of the analytic solution is very close to the current octupole moment of the numerical spacetime; the other branch is more similar to the Kerr solution. We present an extensive comparison of the radii of innermost stable circular orbits (ISCO) obtained with a) the analytic solution, b) the Kerr metric, c) an analytic series expansion derived by Shibata and Sasaki (1998) and d) a highly accurate numerical code. In most cases where a corotating ISCO exists, the analytic solution has an accuracy consistently better than the Shibata-Sasaki expansion. The numerical code is used for tabulating the mass-quadrupole and current-octupole moments for several sequences of constant rest mass.

Mathematica 4.1 Notebook  and data for the most rapidly rotating FPS numerical model of 1.4Msun sequence
(replace SetDirectory with your own current working directory)

UPDATE:

Leonardo Pachón kindly sent us a mathematic notebook for a new 6-parameter solution by Pachón, Rueda & Sanabria-Gómez, PRD 73, 104038 (2006) . You can download the original file, as sent to us by L. Pachón, here.