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

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.Recently, attempts have been made to understand the non-linear variability in X-ray binaries. Nonlinearity has been shown by presence of a linear rms-flux relation (Uttley & McHardy 2001) and has also been seen in the hard state of Cygnus X-1 using the bispectrum and bicoherence,

A likely inclination dependence in the non-linear variability of quasi-periodic oscillations from black hole binaries

“…It has previously been shown in Arur & Maccarone (2019) that during the softening phase of the outburst, as GX 339-4 moves from HIMS to SIMS, a gradual change is seen in the bicoherence. The pattern moves from being a 'web' to a 'hypotenuse', as the strength of the bicoherence along the diagonal steadily increases, and that along the vertical and horizontal streaks falls off.…”

“…For the classification of the different phenomenological patterns seen in the bicoherence, we follow the conventions used in Maccarone et al (2011) and Arur & Maccarone (2019).…”

“…The bispectrum, a measure of phase coupling among triplets of frequencies, is a higher order time series analysis technique that can be used to break degeneracies between models that reproduce very similar power spectra (Maccarone & Schnittman 2005). The bispectrum has been used to de-tect the presence of non-linearity in the hard state of Cyg X-1 and GX 339-4 (Maccarone & Coppi 2002), detect the presence of coupling between broadband noise and QPO frequencies in GRS 1915+105 (Maccarone et al 2011) and to study the evolution of the type-C QPOs across state transitions in GX 339-4 (Arur & Maccarone 2019).…”

A review of quasi-periodic oscillations from black hole X-ray binaries: Observation and theory

“…The pattern exhibited by the source was found to correlate with the radio brightness and the QPO frequency. Recently, Arur and Maccarone [10] conducted a systematic analysis of GX 339-4 to find that the bi-spectrum transitions smoothly from the web to the hypotenuse pattern as the Type-C QPO frequency increases (no observations displayed the cross pattern for GX 339-4). Type-B QPOs only have bi-coherence peaks at ν j = ν k = ν qpo , and Type-A QPOs have low bi-coherence.…”

“…From this comparison, we can make two insights that were not appreciated by Ingram and van der Klis [94] at the time: i) the peak at half the QPO frequency for observation 1 corresponds to the ν k = ν qpo line in the cross pattern of the bi-coherence, and ii) the peak at a third of the QPO frequency in observation 2 indicates phase coupling between the QPO and the broadband noise. It is still rather unclear quite what this non-linear interaction between the QPO and broadband noise is, but some simple models are explored and discussed in [133] and [10]. The phase difference between harmonics, ψ, can also be related to the bi-spectrum, through the bi-phase [132].…”