Seth Rowan Larner | Searcharxiv

arXiv2026

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

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.

astro-ph.HE↗

arXiv2026

Generation of Correlated Time Series for X-ray Astronomy Applications

Cross-spectral methods have become essential for studying accretion physics in X-ray binaries and active galactic nuclei, where coherence and phase lag measurements constrain physical models and reveal variability components invisible in power spectra alone. Recent multi-Lorentzian fitting techniques have uncovered new quasi-periodic features through joint analysis of power spectra and cross-spectra, but testing these methods requires synthetic data with realistic statistical properties. We present an algorithm for generating pairs of time series with arbitrary power spectra, coherence functions, and phase lag profiles. The method extends existing methods by decomposing the dependent time series into coherent and incoherent components, where the coherent part is constructed through a complex transfer function applied to a reference series. We derive the transfer function and normalization required to preserve target spectral shapes while achieving specified cross-spectral properties. We obtain approximate analytic expressions for the variance of coherence and phase lag estimators and construct the approximate covariance matrix relating these quantities to the underlying power and cross-spectra. When fitting models jointly to power and cross-spectra, these correlations must be incorporated into the likelihood. We apply the method to a two-Lorentzian model with component-specific phase lags and demonstrate close agreement between input models and generated power spectra, coherence function, and phase lag profile across four decades in frequency.

astro-ph.HE↗