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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 atype-I X-ray burst. It was interpreted as marginally stable burning on theneutron-star surface. In this study, we used HHT to analyze the data collectedby XMM-Newton between 2007 and 2009. HHT is a powerful tool that enables us toobtain instantaneous frequency, amplitude and phase of non-stationaryperiodicity phenomena, such as QPOs. With well-defined phases, the oscillationprofile of the ~8 mHz QPO for 4U 1636-53 can be precisely revealed. In additionto the oscillation profile, phase-resolved spectra for the complete cycle areconstructed. From the correlation between spectral parameters and fluxes, wefind that the oscillation is mainly attributed to the variations of emittingarea of blackbody radiation in three out of four observations with mHz QPOdetections whereas the other one shows concurrent variation of temperature andflux with a constant emitting area. Although the cause of the difference is notclear, it might be related to the spectral state of the source that can beobserved from hard color difference in color-color diagram.

Phase-resolved analyses of mHz quasi-periodic oscillations in 4U 1636-53 using Hilbert-Huang transform