Fundamental frequencies in the Schwarzschild Spacetime

Abstract

We consider the Keplerian, radial and vertical fundamental frequencies in the Schwarzschild spacetime to study the so-called kilohertz quasi-periodic oscillations from low-mass X-ray binary systems. We show that, within the Relativistic Precession Model, the interpretation of observed kilohertz quasi-periodic oscillations in terms of the fundamental frequencies of test particles in the Schwarzschild spacetime, allows one to infer the total mass M of the central object, the internal Rin and external Rex radii of accretion disks, and innermost stable circular orbits rISCO for test particles in a low-mass X-ray binary system. By constructing the relation between the upper and lower frequencies and exploiting the quasi-periodic oscillation data of the Z and Atoll sources we perform the nonlinear model fit procedure and estimate the mass of the central object. Knowing the value of the mass we calculate the internal Rin and external Rex radii of accretion disks and show that they are larger than rISCO, what was expected.