Rotating neutron stars: an invariant comparison of approximate and numerical space-time models

By Emanuele Berti, Frances White, A. Maniopoulou, M. Bruni. 2004

137 citations recorded by the source corpus.

We compare three different models of rotating neutron star spacetimes: i) the Hartle-Thorne (1968) slow-rotation approximation, keeping terms up to second order in the stellar angular velocity; ii) the exact analytic vacuum solution of Manko et al. (2000a, 2000b); and iii) a numerical solution of the full Einstein equations. In the first part of the paper we estimate the limits of validity of the slow-rotation expansion by computing relative errors in the spacetime’s quadrupole moment Q and in the corotating and counterrotating radii of Innermost Stable Circular Orbits (ISCOs) R±. We integrate the Hartle-Thorne structure equations for five representative equations of state. Then we match these models to numerical solutions of the Einstein equations, imposing the condition that the gravitational mass and angular momentum of the models be the same. We find that the Hartle-Thorne approximation gives very good predictions for the ISCO radii, with R± accurate to better than 1% even for the fastest millisecond pulsars. At these rotational rates the accuracy on Q is � 20%, and better for longer periods. In the second part of the paper we focus on the exterior vacuum spacetimes, comparing the Hartle-Thorne approximation and the Manko analytic solution to the numerical models using Newman-Penrose (NP) coordinateindependent quantities. For all three spacetimes we introduce a physically motivated ‘quasi-Kinnersley’ NP frame. In this frame we evaluate a quantity, the speciality index S, measuring the deviation of each stellar model from Petrov Type D. Deviations from speciality on the equatorial plane are smaller than 5% at star radii for the faster rotating models, and rapidly decrease for slower rotation rates and with distance. We find that, at leading order, the deviation from Type D is proportional to (Q QKerr). Our main conclusion is that the Hartle-Thorne approximation is very reliable for most astrophysical applications.

View Paper: https://www.semanticscholar.org/paper/ab2b7a8f0257aa3bc28b8388129d25815acb9468

Citations in the corpus

• Evidence for a maximum mass cut-off in the neutron star mass distribution and constraints on the equation of state (2017, background): “For reference, the fastest spinning pulsar in a binary, PSR J1748-2446ad (Hessels et al. 2006) has a spin period of ∼ 1.4ms, a factor of ∼ 1.5 larger than the gioulas & Friedman 1995; Berti & Stergioulas 2004; Berti et al. 2005; Yagi et al. 2014).”
• Approximate Universal Relations for Neutron Stars and Quark Stars (2016, methodology): “a can be used to automatically obtain the star’s quadrupole moment through the I-Q relations. In turn, this would provide a very precise description of the exterior gravitational eld of compact stars [90], allowing an extraordinarily precise prediction of the orbit of objects around such stars. Of c”