A NICER view of the corona through time-dependent Comptonization of the quasi-periodic oscillations in nine black-hole X-ray binaries

Abstract

We present a systematic study of the evolution of the corona geometry in nine black hole X-ray binaries (BHXRBs) using archival data from NICER. We identify 171 observations exhibiting quasi-periodic oscillations (QPOs) across various spectral states and model the time-averaged energy spectra of the source, as well as the energy-dependent rms and phase-lag spectra of the QPO, with the time-dependent Comptonization model vKompthdk. This allows us to simultaneously constrain the corona size and feedback fraction during outbursts. By using the power color hue diagnostics, we identify different spectral states, and observe that the QPO frequency increases from $\sim$0.1 Hz to $\sim$10 Hz in the low-hard and hard-intermediate states (LHS and HIMS), and remains approximately constant at 4--5~Hz in the soft-intermediate state (SIMS). The corona size shows significant evolution: the corona is large ($\sim10^4$--$10^5$ km) in the LHS, contracts rapidly to $\sim10^3$ km in the HIMS, and exhibits a flare-like expansion near the HIMS-to-SIMS transition. In the SIMS and high-soft state (HSS), the corona becomes compact and stable (4000--8000~km). The feedback fraction of the corona photons increases during the periods in which the corona contracts and decreases during the periods in which the corona expands, indicating a change of the disk-corona coupling. Our results are consistent with previous QPO-based studies using vKompthdk on some individual sources. This work, however, provides the first view of the coronal evolution across outbursts for a diverse BHXRB sample, offering critical insights into coronal behavior as a function of the spectral state of the source.