Extending the theory of propagating fluctuations: the first fully relativistic treatment and analytical Fourier-Green's functions

Abstract

The aperiodic variability ubiquitously observed from accreting black hole X-ray binary systems is generally analysed within the framework of the so-called ``theory of propagating fluctuations''. In this paper we derive the Fourier transforms of the Green's function solutions of the thin disc equations. These solutions suffice to describe all possible solutions through standard convolution techniques. Solutions are found for both Newtonian discs and general relativistic solutions with a vanishing ISCO stress. We use this new relativistic theory to highlight the Kerr black hole spin dependence of a number of observable variability properties of black hole discs. The phase lags, coherence, and power density spectra of Kerr discs are shown to be strong functions of black hole spin. Observations of the aperiodic variability of black hole accretion sources may now, at least in principle, offer a new avenue to directly constrain black hole spins.

arXiv comment20 pages, 19 Figures. Accepted for publication in MNRAS. Code available at https://github.com/andymummeryastro/GR_prop_fluc

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• A hidden quasi-periodic oscillation in Cygnus X-1 revealed by NICER
• A new 2D stochastic methodology for simulating variable accretion discs: propagating fluctuations and epicyclic motion
• The turbulent variability of accretion discs observed at high energies
• The X-ray variability of tidal disruption events