# Universal relations for the Keplerian sequence of rotating neutron stars

## TL;DR

This paper derives and tests universal, EOS-independent relations for the properties of rotating neutron stars at the mass-shedding limit, improving the modeling of fast rotators in astrophysics.

## Contribution

It introduces new, more accurate universal relations connecting rotating neutron star parameters to static ones, including a revised relation for the Keplerian frequency.

## Key findings

- New fitting relations for the Keplerian frequency with about 2% accuracy.
- Relations for M_Kf_K, R_Kf_K, and other parameters with errors up to 8%.
- Breakdown of previous approximate relations and their improvements.

## 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 $M_{S}/R_{S}\leq 0.05~M_{\odot}$/km ($f_{K}\leq 350$~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.