Bicoherence States from QPO-Accretion Flow Coupling in Black Hole X-ray Binaries

Abstract

We calculate the bispectrum of a black hole X-ray binary light curve model where lognormal fluctuations associated with the inner flow are multiplicatively modulated by a quasi-periodic oscillation (QPO) and its harmonic. The bispectrum is a third-order Fourier statistic which measures the strength of nonlinear relationships between frequencies in a timeseries. When applied to black hole X-ray binaries, the bispectrum reveals nonlinear coupling between QPOs and the broadband noise. These couplings are sorted into a small set of states and X-ray binaries are observed to transition between these states as they undergo spectral transitions. We show that the model we consider is able to reproduce all of the canonical bispectral states analytically. We consider other sources of incoherent variability which dilute this model light curve and find that changes in this dilution, together with changes in the QPO amplitude, drive the transitions between the bispectral states. We also show that the larger QPO amplitudes of high-inclination sources favor the cross state and the weaker QPOs of low-inclination sources favor the hypotenuse state, which can explain the empirically observed correlation. Additionally, any dilution by equatorial winds, which are seen mainly at high inclination, would push high-inclination sources further toward the cross state.