Universal relations for the Keplerian sequence of rotating neutron stars

Abstract

We investigate the Keplerian (mass-shedding) sequence of rotating neutron stars. Twelve different equations of state are used to describe the nuclear structure. We find four fitting relations which connect the rotating frequency, mass and radius of stars in the mass-shedding limit to the mass and radius of stars in the static sequence. We show the breakdown of approximate relation for the Keplerian frequency derived by Lattimer and Prakash [Science, 304, 536, (2004)] and then we present a new, EOS-independent and more accurate relation. This relation fits the Keplerian frequency of rotating neutron stars to about $2\%$ for a large range of the compactness $M_S/R_S$ of the reference non-rotating neutron star, namely the static star with the same central density as the rotating one. The performance of the fitting formula is close to $4\%$ for $M_S/R_S\le 0.05M_{\odot }$/km ($f_K\le 350$~Hz). We present additional EOS-independent relations for the Keplerian sequence including relations for $M_K{f}_K$ and $R_K{f}_K$ in terms of $M_S{f}_S$ and $R_S{f}_S$, respectively, one of $M_K/R_K$ as a function of $f_K/f_S$ and $M_S/R_S$, and a relation between the $M_K$, $R_K$ and $f_K$. These new fitting relations are approximately EOS-independent with an error in the worst case of $8\%$. The universality of the Keplerian sequence properties presented here add to the set of other neutron star universal relations in the literature such as the $I$-Love-$Q$ relation, the gravitational binding energy and the energy, angular momentum and radius of the last circular orbit of a test-particle around rotating neutron stars. This set of universal, analytic formulas, facilitate the inclusion of general relativistic effects in the description of relativistic astrophysical systems involving fast rotating neutron stars.

8 pages, 9 figures, Accepted for publication in Physical Review D

References in corpus (9)

• Shapiro delay measurement of a two solar mass neutron star
• A Massive Pulsar in a Compact Relativistic Binary
• Relativistic Mean-Field Hadronic Models under Nuclear Matter Constraints
• Equation of state and thickness of the inner crust of neutron stars
• Evidence for 1122 Hz X-Ray Burst Oscillations from the Neutron-Star X-Ray Transient XTE J1739-285
• Asymmetric nuclear matter and neutron-skin in extended relativistic mean field model
• Reconciling Nuclear and Astrophysical Constraints
• Low Densities Instability of Relativistic Mean Field Models
• Parameters of rotating neutron stars with and without hyperons

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• New quasi-universal relations for static and rapid rotating neutron stars
• Universal Relations for rapidly rotating neutron stars using supervised machine-learning techniques
• Properties of Rotating Neutron Star in Density-dependent Relativistic Mean-field Models
• Effect of symmetry energy on properties of rapidly rotating neutron stars and universal relations