X-ray time lag evaluation of MAXI J1820+070 with a differential cross-correlation analysis

MAXI J1820$+$070 is a transient black hole binary (BHB) discovered on 2018 March 11. The unprecedented rich statistics brought by the NICER X-ray telescope allows detailed timing analysis up to $\sim$1~kHz uncompromised by the photon shot noise. To estimate the time lags, the Fourier analysis was applied, which led to two different conclusions for the system configuration; one supporting the lamp-post configuration with a stable accretion disk extending close to the innermost stable circular orbit and the other supporting the truncated accretion disk contracting with time. Using the same data set, we present the results based on the cross-correlation function (CCF). The CCF is calculated between two different X-ray bands and one side is subtracted from the other side, which we call the differential CCF (dCCF). The soft and hard lags respectively of $\sim$0.03 and 3~s are clearly identified without being diluted by the spectral mixture, demonstrating the effectiveness of the dCCF analysis. The evolution of these lags is tracked, along with spectral changes for the first 120~days since the discovery. Both the dCCF and spectral fitting results are interpreted that the soft lag is a reverberation lag between the Comptonized emission and the soft excess emission and that the hard lag is between the disk black body emission and the Comptonized emission. The evolution of these lags is in line with the picture of the truncated disk contracting with time.