# Ultraluminous X-ray sources with flat-topped noise and QPO

## TL;DR

This study analyzes the timing properties of five ULXs displaying flat-topped noise and QPOs, revealing correlations with accretion rate and proposing a physical interpretation involving spherization radius and viscosity.

## Contribution

It introduces a model linking variability features to accretion rate and estimates black hole masses in ULXs, highlighting M82 X-1 as potentially more massive.

## Key findings

- FTN level is anti-correlated with QPO frequency.
- Fractional variability decreases as QPO frequency and luminosity increase.
- All ULXs likely have similar black hole masses, except M82 X-1.

## Abstract

We analyzed the X-ray power density spectra of five ultraluminous X-ray sources (ULXs) NGC5408 X-1, NGC6946 X-1, M82 X-1, NGC1313 X-1 and IC342 X-1 that are the only ULXs which display both flat-topped noise (FTN) and quasi-periodic oscillations (QPO). We studied the QPO frequencies, fractional root-mean-square (rms) variability, X-ray luminosity and spectral hardness. We found that the level of FTN is anti-correlated with the QPO frequency. As the frequency of the QPO and brightness of the sources increase, their fractional variability decreases. We propose a simple interpretation using the spherizarion radius, viscosity time and $\alpha$-parameter as basic properties of these systems. The main physical driver of the observed variability is the mass accretion rate which varies >3 between different observations of the same source. As the accretion rate decreases the spherization radius reduces and the FTN plus the QPO move toward higher frequencies resulting in a decrease of the fractional rms variability. We also propose that in all ULXs when the accretion rate is low enough (but still super-Eddington) the QPO and FTN disappear. Assuming that the maximum X-ray luminosity depends only on the black hole (BH) mass and not on the accretion rate (not considering the effects of either the inclination of the super-Eddington disc nor geometrical beaming of radiation) we estimate that all the ULXs have about similar BH masses, with the exception of M82 X-1, which might be 10 times more massive.