Detection of X-ray/UV delay in NGC 4051 using AstroSat observations

We study the connection between the variations in the far ultra-violet (FUV), near ultra-violet (NUV) and X-ray band emission from NGC 4051 using 4-days long AstroSat observations performed during 5-9 June 2016. NGC 4051 showed rapid variability in all three bands with the strongest variability amplitude in the X-ray band ($F_{var} \sim 37\%$) and much weaker variability in the UV bands ($F_{var} \sim 3 - 5\%$). Cross-correlation analysis performed using Interpolated cross-correlation Functions (ICCF) and Discrete cross-correlation Functions (DCF) revealed a robust correlation ($\sim 0.75$) between the UV and X-ray light curves. The variations in the X-ray band are found to lead those in the FUV and NUV bands by $\sim 7.4{\rm~ks}$ and $\sim 24.2{\rm~ks}$, respectively. The UV lags favour the thermal disc reprocessing model. The FUV and NUV bands are strongly correlated ($\sim 0.9$) and the variations in the FUV band lead those in the NUV band by $\sim 13{\rm~ks}$. Comparison of the UV lags found using the AstroSat observations with those reported earlier and the theoretical model for thermal reverberation time-lag suggests a possible change in either the geometry of the accretion disc/corona or the height of the corona.