Determination of QPO properties in the presence of strong broad-band noise: a case study on the data of MAXI J1820+070

Accurate calculation of the phase lags of quasi-periodic oscillations (QPOs) will provide insight into their origin. In this paper, we investigate the phase lag correction method that has been applied to calculate the intrinsic phase lags of the QPOs in MAXI J1820+070. We find that the traditional additive model between broad-band noise (BBN) and QPOs in the time domain is rejected, but the convolution model is accepted. By introducing a convolution mechanism in the time domain, the Fourier cross-spectrum analysis shows that the phase lags between QPOs components in different energy bands will have a simple linear relationship with the phase lags between the total signals, so that the intrinsic phase lags of the QPOs can be obtained by linear correction. The power density spectrum (PDS) thus requires a multiplicative model to interpret the data. We briefly discuss a physical scenario for interpreting the convolution. In this scenario, the corona acts as a low-pass filter, Green's function containing the noise is convolved with the QPOs to form the low-frequency part of the PDS, while the high-frequency part requires an additive component. We use a multiplicative PDS model to fit the data observed by the Insight-Hard X-ray Modulation Telescope (HXMT). The overall fitting results are similar compared to the traditional additive PDS model. Neither the width nor the centroid frequency of the QPOs obtained from each of the two PDS models was significantly different, except for the rms of the QPOs. Our work thus provides a new perspective on the coupling of noise and QPOs.