ROXAS: a new pseudospectral non-linear code for general relativistic oscillations of fast rotating isolated neutron stars

Abstract Next-generation gravitational wave detectors are expected to increase their sensitivity in the kHz band where binary neutron star (NS) remnants are expected to emit. In this context, robust predictions of oscillation modes of the post-merger object are desirable. To that end, we present here our code R elativistic O scillations of non-a X isymmetric neutron st A r S ( ROXAS ) that is aimed at simulating isolated rotating NSs. It is based on our previously published formalism relying on primitive variables, along with the extended conformal-flatness condition formulation of Einstein equations. The equations are written under a well-balanced formulation. The code uses pseudospectral methods for both the metric and the hydrodynamics. Since standard test beds were already presented in a previous paper, we here mainly focus on presenting the numerical ingredients of ROXAS , as well as on the frequency extraction for axisymmetric and non-axisymmetric modes. We compare our results with semi-analytic perturbative methods. Spherically symmetric modes are also recovered. The code currently supports fast, rigidly rotating isolated NSs, described with a cold equation of state. We impose symmetries about the equatorial plane and by rotation of π around the vertical z axis. These symmetries include the dominant quadrupolar <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>ℓ</mml:mi> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mi>m</mml:mi> <mml:mrow> <mml:mo stretchy="false">|</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> mode. A notable feature of the code is its ability to follow the surface of the star at every step. It is very lightweight and can be run on office computers.