On the Relativistic Precession and Oscillation Frequencies of Test Particles Around Rapidly Rotating Compact Stars

Abstract

Whether or not analytic exact vacuum (electrovacuum) solutions of the Einstein (Einstein-Maxwell) field equations can accurately describe the exterior space-time of compact stars still remains an interesting open question in relativistic astrophysics. As an attempt to establish their level of accuracy, the radii of the innermost stable circular orbits (ISCOs) of test particles given by analytic exterior space-time geometries have been compared with those given by numerical solutions for neutron stars (NSs) obeying a realistic equation of state (EOS). It has been so shown that the six-parametric solution of Pachón et al. (PRS) more accurately describes the NS ISCO radii than other analytic models do. We propose here an additional test of accuracy for analytic exterior geometries based on the comparison of orbital frequencies of neutral test particles. We compute the Keplerian, frame-dragging, and precession and oscillation frequencies of the radial and vertical motions of neutral test particles for the Kerr and PRS geometries and then compare them with the numerical values obtained by Morsink & Stella for realistic NSs. We identify the role of high-order multipole moments such as the mass quadrupole and current octupole in the determination of the orbital frequencies, especially in the rapid rotation regime. The results of this work are relevant to cast a separatrix between black hole and NS signatures and to probe the nuclear-matter EOS and NS parameters from the quasi-periodic oscillations observed in low-mass X-ray binaries.

Appearance of innermost stable circular orbits of accretion discs around rotating neutron stars

“…Kluźniak et al 1990;Shibata & Sasaki 1998;Pachón et al 2006Pachón et al , 2012Bakala et al 2012;Gutierrez et al 2013). It has been shown that for geodesic motion, these are well described by formulae derived considering NS spacetime approximated by the Hartle-Thorne metric (Hartle & Thorne 1968;Abramowicz et al 2003;Berti et al 2005).…”

Geodesics in the field of a rotating deformed gravitational source

“…The importance of the quadrupole moment in the astrophysical context has been emphasized in several works. 9,[11][12][13][14][15] However, most analysis must be performed numerically due to the complexity of the exact metrics. The advantage of considering the HartleThorne approximate solution is that several physical quantities can be calculated analytically which facilitates their study.…”

Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin

“…The non-geodesic corrections to the radial epicyclic frequencies can be generated on the level of tens of percent for oscillating non-slender tori (Šrámková 2005;Blaes et al 2007;Straub & Šrámková 2009), or can do so by assuming a slightly charged internal part of the accretion disc interacting with the external dipole magnetic field of the neutron star when very strong effects can be obtained, on the level of hundred percent or higher Pachon et al 2012). We can consider several diverse possibilities to explain the behaviour of charged accretion discs.…”