  We present phase-resolved spectroscopies based on Hilbert-Huang transform
(HHT) for millihertz quasi-periodic oscillations (mHz QPOs) in 4U 1636-536.
This ~8 mHz QPO can be detected approximately several thousand seconds before a
type-I X-ray burst. It was interpreted as marginally stable burning on the
neutron-star surface. In this study, we used HHT to analyze the data collected
by XMM-Newton between 2007 and 2009. HHT is a powerful tool that enables us to
obtain instantaneous frequency, amplitude and phase of non-stationary
periodicity phenomena, 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 the variations of emitting
area of blackbody radiation in three out of four observations with mHz QPO
detections whereas the other one shows 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 hard color difference in color-color diagram.
