A&A 381, L21-L24 (2002)

DOI: 10.1051/0004-6361:20011555

*Letter*

## Marginally stable orbits around Maclaurin spheroids and low-mass quark stars

**P. Amsterdamski**

^{1}, T. Bulik^{2}, D. Gondek-Rosinska^{3, 2}and W. Kluzniak^{1, 4}^{1}Institute of Astronomy, Zielona Góra University, ul. Lubuska 2, 65265 Zielona Góra, Poland

^{2}Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00716 Warszawa, Poland

^{3}Département d'Astrophysique Relativiste et de Cosmologie UMR 8629 du CNRS, Observatoire de Paris, 92195 Meudon Cedex, France

^{4}NORDITA, 17 Blegdamsvej, 2100 Copenhagen, Denmark

(Received 18 October 2001 / Accepted 8 November 2001)

** Abstract **

When the eccentricity of a Maclaurin spheroid
exceeds a critical value (
*e*>0.83458318), circular orbits
in the equatorial plane are unstable for a range of orbital radii
outside the stellar surface - this is a purely Newtonian effect
related to the oblateness of the star.
The orbital frequency in the marginally
stable orbit, and all other orbits, around Maclaurin spheroids
goes to zero in the limit
*e*=1.
The orbital and rotational frequencies in exact relativistic
numerical models of rotating, axially symmetric, quark stars
of very low mass (
) coincide
with those for Maclaurin spheroids. It is impossible to
determine the mass of a rapidly rotating quark star by measuring
the maximum orbital frequency alone.

**Key words:**dense matter

**--**equation of state

**--**stars: neutron

**--**stars: binaries: general

**--**X-rays: stars

Offprint request: W. Kluzniak, wlodek@camk.edu.pl

**©**

*ESO 2002*