We performed time-lag analysis on the X-ray light curves of Centaurus A (Cen A) obtained by the Gas Slit Camera (GSC) aboard the Monitor of All-sky X-ray Image (MAXI) in three energy bands (2-4 keV, 4-10 keV, and 10-20 keV). We discovered a soft X-ray lag relative to higher energies (soft lag) on a timescale of days in a flaring episode by employing the discrete correlation function (DCF) and the z-transformed discrete correlation function (ZDCF) method. In the episode, a peak and a centroid in the DCF and the ZDCF was observed at a soft lag of ∼ 5 d in 2-4 keV versus 4-10 keV and in 4-10 keV versus 10-20 keV, and ∼ 10 d in 2-4 keV versus 10-20 keV. We found it difficult to explain the observed X-ray variation by a single energy injection with the one-zone synchrotron self-Compton (SSC) model, in which the soft lags in these three energy bands reflect the different cooling times of the relativistic electrons, by assuming the magnetic field and minimum Lorentz factor estimated from a broad-band spectral energy distribution. Alternatively, if the phenomenon is interpreted as cooling of Comptonizing electrons in a corona covering the accretion disk, the temperature of the corona producing the variable X-rays should be ∼ 10 keV for reconciliation with the soft lag in the energy range of 2-20 keV.
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