2020ApJ...900..116H

We present phase-resolved spectroscopy based on the Hilbert-Huang transform (HHT) for millihertz quasi-periodic oscillations (mHz QPOs) in 4U 1636-53. The ∼8 mHz QPO can be detected approximately several thousand seconds before a type-I X-ray burst. It has been interpreted as marginally stable burning on the neutron-star surface. In this study, we use the HHT to analyze the data collected by XMM-Newton between 2007 and 2009. The HHT is a powerful tool that enables us to obtain instantaneous frequency, amplitude, and phase of phenomena with nonstationary periodicity, such as QPOs. With well-defined phases, the oscillation profile of the ∼8 mHz QPO for 4U 1636-53 can be precisely revealed. In addition to the oscillation profile, phase-resolved spectra for the complete cycle are constructed. From the correlation between spectral parameters and fluxes, we find that the oscillation is mainly attributed to variations in the area emitting blackbody radiation in three out of four observations with mHz QPO detections, whereas the other one shows a concurrent variation of temperature and flux with a constant emitting area. Although the cause of the difference is not clear, it might be related to the spectral state of the source that can be observed from a hard color difference in the color-color diagram.