A reverberation mapping study of a highly variable AGN 6dFGS gJ022550.0-060145

We use LCOGT observations (MJD $59434-59600$) with a total exposure time of $\simeq 50$ hours and a median cadence of $0.5$ days to measure the inter-band time delays (with respect to $u$) in the $g$, $r$, and $i$ continua of a highly variable AGN, 6dFGS gJ022550.0-060145. We also calculate the expected time delays of the X-ray reprocessing of a static Shakura \& Sunyaev disk (SSD) according to the sources' luminosity and virial black-hole mass; the two parameters are measured from the optical spectrum of our spectroscopic observation via the Lijiang \SI{2.4}{\meter} telescope. It is found that the ratio of the measured time delays to the predicted ones is $2.6_{-1.3}^{+1.3}$. With optical light curves (MJD $53650-59880$) from our new LCOGT and archival ZTF, Pan-SATRRS, CSS, and ATLAS observations, and infrared (IR) WISE data (MJD $55214-59055$), we also measured time delays between WISE $W1$/$W2$ and the optical emission. $W1$ and $W2$ have time delays (with respect to V), $9.6^{+2.9}_{-1.6}\times 10^2$ days and $1.18^{+0.13}_{-0.10}\times 10^3$ days in the rest-frame, respectively; hence, the dusty torus of 6dFGS gJ022550.0-060145 should be compact. The time delays of $W1$ and $W2$ bands are higher than the dusty torus size-luminosity relationship of~\cite{Lyu2019}. By comparing the IR and optical variability amplitude, we find that the dust covering factors of $W1$ and $W2$ emission regions are 0.7 and 0.6, respectively. Future broad emission-line reverberation mapping of this target and the results of this work enable us to determine the sizes of the AGN main components simultaneously.