The nature of an imaginary quasi-periodic oscillation in the soft-to-hard transition of MAXI J1820+070

¹ Instituto Argentino de Radioastronomía (CCT La Plata, CONICET; CICPBA; UNLP), C.C.5, 1894 Villa Elisa, Argentina
² Facultad de Ciencias Astronómicas y Geofísicas, Universidad Nacional de La Plata, 1900 La Plata, Argentina
³ Kapteyn Astronomical Institute, University of Groningen, PO BOX 800 NL-9700 AV Groningen, The Netherlands
⁴ Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049 China
⁵ Dongguan Neutron Science Center, 1 Zhongziyuan Road, Dongguan, 523808 China
⁶ Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA, 02138 USA
⁷ Dr. Karl Remeis-Observatory and Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Sternwartstr. 7, 96049 Bamberg, Germany

^⋆ Corresponding author.

Received: 20 November 2024
Accepted: 14 February 2025

Abstract

A recent study shows that if the power spectra (PS) of accreting compact objects consist of a combination of Lorentzian functions that are coherent in different energy bands but incoherent with each other, the same is true for the real and imaginary parts of the cross spectrum (CS). Using this idea, we discovered imaginary quasi-periodic oscillations (QPOs) in NICER observations of the black hole candidate MAXI J1820+070. The imaginary QPOs appear as narrow features with a small real and large imaginary part in the CS but are not significantly detected in the PS when they overlap in frequency with other variability components. The coherence function drops and the phase lags increase abruptly at the frequency of the imaginary QPO. We show that the multi-Lorentzian model that fits the PS and CS of the source in two energy bands correctly reproduces the lags and the coherence, and that the narrow drop in the coherence is caused by the interaction of the imaginary QPO with other variability components. The imaginary QPO appears only in the decay of the outburst, during the transition from the high-soft to the low-hard state of MAXI J1820+070, and its frequency decreases from ∼5 Hz to ∼1 Hz as the source spectrum hardens. We also analysed the earlier observations of the transition, where no narrow features were seen, and we identified a QPO in the PS that appears to evolve into the imaginary QPO as the source hardens. As for the type-B and C QPOs in this source, the rms spectrum of the imaginary QPO increases with energy. The lags of the imaginary QPO are similar to those of the type-B and C QPOs above 2 keV but differ from the lags of those other QPOs below that energy. While the properties of this imaginary QPO resemble those of type-C QPOs, we cannot rule out that it is a new type of QPO.