# Nonlinear Variability of Quasi-Periodic Oscillations in GX 339-4

## TL;DR

This paper investigates the nonlinear behavior of quasi-periodic oscillations in GX 339-4 using bicoherence analysis, revealing new coupling patterns and state-dependent waveform changes in black hole binary emissions.

## Contribution

It introduces the first observation of a new bicoherence pattern in type B QPOs and links nonlinear variability patterns to spectral state transitions.

## Key findings

- Confirmed hypotenuse and web patterns in type C QPOs
- Discovered a new pattern in type B QPOs
- Linked bicoherence pattern changes to spectral states

## Abstract

We examine the nonlinear variability of quasi-periodic oscillations (QPOs) using the bicoherence, a measure of phase coupling at different Fourier frequencies. We analyse several observations of RXTE/PCA archival data of the black hole binary GX 339-4 which show QPOs. In the type C QPOs, we confirm the presence of the 'hypotenuse' pattern where there is nonlinear coupling between low frequencies that sum to the QPO frequency as well as the 'web' pattern where in addition to the hypotenuse, nonlinear coupling between the QPO frequency and the broadband noise is present. We find that type B QPOs show a previously unknown pattern. We also show that the bicoherence pattern changes gradually from 'web' to 'hypotenuse' as the source moves from a hard intermediate state to a soft intermediate state. Additionally, we reconstruct the QPO waveforms from six observations using the biphase. Finally, we present a scenario by which a moderate increase in the optical depth of the hard X-ray emission region can explain the changes in the non-linearity seen during this transition.