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

Cygnus X-1 is a high-mass black hole binary extensively studied since its discovery in 1964. Its rapid X-ray variability provides insights into accretion physics. Unlike other black hole X-ray binaries, its power spectra are generally featureless and modeled with two broad Lorentzians, without requiring narrow quasi-periodic oscillations. We investigate the possibility that some undetected variability components in power spectra may appear in the imaginary part of the cross spectra and the coherence function. Using NICER observations up to Cycle 6, we study the power, cross, and lag spectra, along with the coherence function, searching for these "imaginary" components. We simultaneously fit the power spectra in two energy bands, 0.3-2 keV and 2-12 keV, and the real and imaginary parts of the cross-spectrum with a multi-Lorentzian model. Assuming each Lorentzian is coherent between the two bands but incoherent with others, we predict intrinsic coherence and phase lags. he intrinsic coherence shows a narrow dip at a frequency increasing 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 exhibit a steep increase (the "cliff") at the same frequencies. These features vanish when using energy bands similar to RXTE (e.g., 3-5 keV and 5-12 keV). A narrow Lorentzian component with low fractional rms and large phase lag is required to reproduce the coherence drop. Its rms and phase-lag spectra evolve systematically in the hardness-intensity diagram. This "imaginary" QPO behaves like a type-C QPO despite being undetectable in power spectra alone. Similar features in MAXI J1348-630 and MAXI J1820+070 support this interpretation, suggesting this may be the first detection of a type-C QPO in Cygnus X-1.