Damped harmonic oscillator interpretation of the soft-state power spectra of Cyg X-1

TL;DR

This paper presents a damped harmonic oscillator model of accretion disc variability that explains Cyg X-1's soft-state power spectra and constrains the black hole mass to less than 20 solar masses.

Contribution

It introduces a simple, three-parameter model linking disc oscillations to observed X-ray variability, fitting observed spectra and constraining black hole mass.

Findings

Model explains Cyg X-1 soft-state power spectra

Constrains black hole mass to <16-20 solar masses

Preserves linear rms-flux relationship despite non-linear flux response

Abstract

We develop a model of an accretion disc in which the variability induced at a given radius is governed by a damped harmonic oscillator at the corresponding epicyclic frequency. That variability induces both linear and non-linear responses in the locally emitted radiation. The total observed variability of a source is the sum of these contributions over the disc radius weighted by the energy dissipation rate at each radius. It is shown that this simple model, which effectively has only three parameters including the normalization, can explain the range of the power spectra observed from Cyg X-1 in the soft state. Although a degeneracy between the black hole mass and the strength of the damping does not allow a unique determination of the mass, we can still constrain it to <16--20 solar masses. We also show that our model preserves the observed linear rms-flux relationship even in the presence of the non-linear flux response.