Keplerian frequency of uniformly rotating neutron stars and strange stars

P. Haensel; J. L. Zdunik; M. Bejger; J. M. Lattimer

doi:10.1051/0004-6361/200811605

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Volume 502 / No 2 (August I 2009)

A&A, 502 2 (2009) 605-610

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Issue		A&A Volume 502, Number 2, August I 2009


Page(s)		605 - 610
Section		Stellar structure and evolution
DOI		https://doi.org/10.1051/0004-6361/200811605
Published online		22 June 2009

A&A 502, 605-610 (2009)

Keplerian frequency of uniformly rotating neutron stars and strange stars

P. Haensel¹, J. L. Zdunik¹, M. Bejger¹ and J. M. Lattimer²

¹ N. Copernicus Astronomical Center, Polish Academy of Sciences, Bartycka 18, 00-716 Warszawa, Poland e-mail: [haensel;jlz;bejger]@camk.edu.pl
² Department of Physics and Astronomy, State University of New York at Stony Brook, Stony Brook, NY 11794-3800, USA e-mail: lattimer@astro.sunysb.edu

Received: 30 December 2008
Accepted: 30 April 2009

Abstract

Aims. We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and strange stars with crusts. We check the validity of the empirical formula for Keplerian frequency, f_K, proposed by Lattimer & Prakash, $f_{\rm K}(M)=C\; (M/M_\odot)^{1/2}(R/10~{\rm km})^{-3/2}$ , where M is the (gravitational) mass of the Keplerian configuration, R is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and $C=1.04~$ kHz.

Methods. Numerical calculations are performed using precise 2D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars.

Results. We show that the empirical formula for $f_{\rm K}(M)$ holds within a few percent for neutron stars with realistic EOSs, provided $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$ , where $M_{\rm max}^{\rm stat}$ is the maximum allowable mass of non-rotating neutron stars for an EOS, and $C=C_{\rm NS}=1.08~$ kHz. Similar precision is obtained for strange stars with $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$ . For maximal crust masses we obtain $C_{\rm SS}=1.15$ kHz, and the value of C_SS is not very sensitive to the crust mass. All our Cs are significantly larger than the analytic value from the relativistic Roche model, $C_{\rm Roche}=1.00$ kHz. For $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$ , the equatorial radius of the Keplerian configuration of mass M, $R_{\rm K}(M)$ , is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, $R_{\rm K}(M)=a\;R(M)$ , with $a_{\rm NS}\approx a_{\rm SS} \approx 1.44$ . The value of a_SS is very weakly dependent on the mass of the crust of the strange star. Both a values are smaller than the analytic value $a_{\rm Roche}=1.5$ from the relativistic Roche model.

Key words: dense matter / equation of state / stars: neutron / stars: rotation

© ESO, 2009

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