Exploring the relativistic regime with Newtonian hydrodynamics

II. An effective gravitational potential for rapid rotation

¹ Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching, Germany e-mail: bjmuellr@mpa-garching.mpg.de
² Department of Physics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece

Received: 19 February 2008
Accepted: 12 June 2008

Abstract

We present the generalization of a recently introduced modified gravitational potential for self-gravitating fluids. The use of this potential allows for an accurate approximation of general relativistic effects in an otherwise Newtonian hydrodynamics code also in cases of rapid rotation. We test this approach in numerical simulations of astrophysical scenarios related to compact stars, like supernova core collapse with both a simplified and detailed microphysical description of matter, and rotating neutron stars in equilibrium. We assess the quality of the new potential, and demonstrate that it provides a significant improvement compared to previous formulations for such potentials. Newtonian simulations of compact objects employing such an effective relativistic potential predict inaccurate pulsation frequencies despite the excellent agreement of the collapse dynamics and structure of the compact objects with general relativistic results. We analyze and discuss the reason for this behavior.