Fundamental Frequencies in the Schwarzschild Spacetime

TL;DR

This paper uses fundamental frequencies in Schwarzschild spacetime to interpret kilohertz quasi-periodic oscillations in X-ray binaries, enabling estimation of the central mass and accretion disk radii.

Contribution

It introduces a method to infer the mass and disk radii from QPO data using the Relativistic Precession Model in Schwarzschild spacetime.

Findings

Estimated the mass of the central object from QPO data.

Determined the inner and outer radii of accretion disks.

Confirmed that disk radii are larger than the innermost stable circular orbit.

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 $R_{in}$ and external $R_{ex}$ radii of accretion disks, and innermost stable circular orbits $r_{ISCO}$ 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 non-linear model fit analysis and estimate the mass of the central object. Knowing the value of the mass we calculate the internal $R_{in}$ and external $R_{ex}$ radii of accretion disks and show that they are larger than $r_{ISCO}$, what was expected.