A hidden quasi-periodic oscillation in Cygnus X-1 revealed by NICER

Context. Cygnus X-1 is a high-mass black hole binary system that has been extensively studied across multiple wavelengths since its discovery in 1964. Its rapid temporal and spectral variability in X-rays offer critical insights into the physics of accretion and the dynamics around black hole systems. The power spectra of Cygnus X-1 are generally featureless and often modelled with two broad Lorentzian functions without the need for narrow quasi-periodic oscillations, which are prevalent in other black hole X-ray binaries. Aims. We explore this phenomenon in light of the recent proposal that some variability components that are not detected in the power spectra may be significantly detected in the imaginary part of the cross spectra between two different energy bands and the coherence function. Specifically, we study the power, cross, and lag spectra and the coherence function of all available observations of Cygnus X-1 from the NICER mission up to Cycle 6 while looking for the so-called imaginary components. Methods. We simultaneously fitted the power spectra of the source in two energy bands, 0.3-2 keV and 2-12 keV, and the real and imaginary parts of the cross spectrum between the same energy bands with a multi-Lorentzian model. Under the assumption that each Lorentzian is coherent between the two energy bands while the Lorentzians are incoherent with one another, our fits predict the intrinsic coherence and phase lags. Results. The intrinsic coherence shows a narrow dip at a frequency that increases from ∼1 Hz to ∼6 Hz as the power-law index of the Comptonized component increases from ∼1.8 to ∼2.4. Simultaneously, the phase lags show a sudden and steep increase (hereafter referred to as the cliff) at the same frequencies. The dip and the cliff disappear if we use energy bands similar to those of the Rossi X-ray Timing Explorer mission (e.g. 3-5 keV and 5-12 keV) to compute the coherence and phase-lag spectrum. A narrow Lorentzian component with a low fractional root mean square amplitude and a large phase lag is required to effectively reproduce the drop of the intrinsic coherence. The rms and phase-lag spectra of this component change in a systematic way as the source moves in the hardness-intensity diagram. Conclusions. This component, referred to as the imaginary QPO, exhibits behaviour consistent with the canonical type-C QPO despite being undetectable in the power spectra alone. Comparison with a similar QPO found in MAXI J1348-630 and MAXI J1820+070 further supports this identification. If our interpretation is correct, this would be the first time that the type-C QPO is detected in Cygnus X-1.