High-frequency X-ray variability as a mass estimator of stellar and supermassive black holes

TL;DR

This paper demonstrates that the amplitude of high-frequency X-ray variability in black holes inversely correlates with mass, providing a new, simple method to estimate black hole mass across stellar and supermassive scales.

Contribution

It introduces a universal high-frequency X-ray variability feature as a robust mass estimator for black holes, applicable from stellar to supermassive scales.

Findings

High-frequency X-ray variability amplitude scales as 1/Mass.

The high-frequency tail shape is universal and invariant.

C_M provides a reliable black hole mass estimate.

Abstract

There is increasing evidence that supermassive black holes in active galactic nuclei (AGN) are scaled-up versions of Galactic black holes. We show that the amplitude of high-frequency X-ray variability in the hard spectral state is inversely proportional to the black hole mass over eight orders of magnitude. We have analyzed all available hard-state data from RXTE of seven Galactic black holes. Their power density spectra change dramatically from observation to observation, except for the high-frequency (>10 Hz) tail, which seems to have a universal shape, roughly represented by a power law of index -2. The amplitude of the tail, C_M (extrapolated to 1 Hz), remains approximately constant for a given source, regardless of the luminosity, unlike the break or QPO frequencies, which are usually strongly correlated with luminosity. Comparison with a moderate-luminosity sample of AGN shows that the amplitude of the tail is a simple function of black hole mass, C_M = C/M, where C = 1.25 M_Sol / Hz. This makes C_M a robust estimator of the black hole mass which is easy to apply to low- to moderate-luminosity supermassive black holes. The high-frequency tail with its universal shape is an invariant feature of a black hole and, possibly, an imprint of the last stable orbit.