Speaker
Description
The variability observed in stellar-mass black hole and neutron star binaries is highly complex and non-linear, exhibiting QPOs, stochastic and aperiodic components. Short-term variability, such as rapid flares, is commonly attributed to magnetic reconnection, plasmoid ejection and MHD turbulence, while long-term variability reflects changes in accretion states, jets, coronae, and their interactions. Decoding these non-linear variabilities can help us understand the dynamics of accretion disks, coronae, and relativistic jets, and potentially connect X-ray observations to GRMHD simulations. However, conventional Fourier-based methods, while powerful for detecting periodic signals in the frequency domain, have limitations in capturing the underlying non-linear evolution and state transitions. In this talk, I will introduce a new time-domain framework for accreting compact objects based on Koopman operator theory (KOT) and its modern, data-driven implementation, extended dynamic mode decomposition (EDMD). In this approach, the non-linear variability is embedded in a higher-dimensional linear space, where the Koopman operator decomposes light curve data into independently evolving dynamical modes with well-defined eigenvalues and eigenfunctions. KOT/EDMD is a well-developed yet actively evolving data-driven framework for analyzing and modeling complex nonlinear dynamical systems, with a growing range of real-world applications across science and engineering. I will present promising pilot-study applications of KOT/EDMD to X-ray lightcurve data of several BH and NS binaries, demonstrating its potential to provide new diagnostics for determining the physical processes that drive X-ray variability, and to predict future state transitions. By applying these modern time-domain analysis methods to multi-wavelength light-curve data, we may improve the interpretability and predictability of the many tones of accretion.