Analysis of Quasi-periodic Oscillations and Time Lag in Ultraluminous X-Ray Sources with XMM-Newton

We investigated the power density spectrum (PDS) and time lag of ultraluminous X-ray sources (ULXs) observed by XMM-Newton. We determined the PDSs for each ULX and found that five of them show intrinsic variability due to obvious quasi-periodic oscillations (QPOs) of mHz-1 Hz, consistent with previous reports. We further investigated these five ULXs to determine their possible time lag. The ULX QPOs exhibit a soft time lag that is linearly related to the QPO frequency. We discuss the likelihood of the ULX QPOs being type-C QPO analogs, and the time lag models. The ULXs might harbor intermediate-mass black holes if their. QPOs are type-C QPO analogs. We suggest that the soft lag and the linearity may be due to reverberation.