Epicyclic frequencies of spheroidal stars with non-uniform density

Abstract

We consider the gravitational potential of a rotating star with non-uniform density to derive the orbital and epicyclic frequencies of the particles orbiting the star. We assume that the star is composed of concentric spheroids of constant density, with a global power-law distribution of density inside the star. At the lowest order approximation, we recover the known result for the Maclaurin spheroid that the maximum in the radial epicyclic frequency occurs at $r=\sqrt{2}ae$, for eccentricities $\ge 1/\sqrt{2}$. We find that the nature of these characteristic frequencies differs based on the geometry of the rotating star. For an oblate spheroid, the orbits resemble retrograde-Kerr orbits and the location of the radial epicyclic maximum approaches the stellar surface as the density variation inside the star becomes steeper. On the contrary, orbits around a prolate spheroid resemble prograde-Kerr orbits, but the marginally stable orbit does not exist for prolate-shaped stars. The orbital frequency is larger (smaller) than the Keplerian value for an oblate (prolate) star with the equality attained as $e\to 0$ or $r\to \infty$. The radial profiles of the angular velocity and the angular momentum allow for a stable accreting disc around any nature of oblate/prolate spheroid.

arXiv commentAccepted for publication in MNRAS

References in corpus (18)

• X-ray Properties of Black-Hole Binaries
• Magnetic fields in axisymmetric neutron stars
• Twisted-torus configurations with large toroidal magnetic fields in relativistic stars
• Rapid Oscillations in Cataclysmic Variables
• Dwarf Nova Oscillations and Quasi-Periodic Oscillations in Cataclysmic Variables: II. A Low Inertia Magnetic Accretor Model
• Tidal disruptions of main sequence stars -- III. Stellar mass dependence of the character of partial disruptions
• Correlation of the Quasi-Periodic Oscillation Frequencies of White Dwarf, Neutron Star, and Black Hole Binaries
• Angular Momentum Transport by Acoustic Modes Generated in the Boundary Layer I: Hydrodynamical Theory and Simulations
• Three-dimensional eccentric discs around Be stars
• Dwarf Nova Oscillations and Quasi-Periodic Oscillations in Cataclysmic Variables: I. Observations of VW Hyi
• Supersonic Shear Instabilities in Astrophysical Boundary Layers
• Low-mass quark stars as Maclaurin spheroids
• Roche tomography of cataclysmic variables - VIII: The irradiated and spotted dwarf nova, SS Cygni
• Quasi-Coherent Oscillations in the Extreme Ultraviolet Flux of the Dwarf Nova SS Cygni
• Boundary Layers of Accretion Disks: Wave-Driven Transport and Disk Evolution
• QPOs in Cataclysmic Variables and in X-ray Binaries
• Prolate stars due to meridional flows
• Geometrically thin accretion disk around Maclaurin spheroid

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