Detection of time delay between UV and X-ray variability in Mrk 1044 using AstroSat observations

Active galactic nuclei are known to exhibit flux variations across the entire electromagnetic spectrum. Among these, correlations between UV/optical and X-ray flux variations serve as a key diagnostics for understanding the physical connection between the accretion disk and the corona. In this work, we present the results of analysis of ultraviolet (UV) and X-ray flux variations in the narrow line Seyfert 1 galaxy Mrk 1044. Simultaneous observations in the far-UV band (FUV: 1300$-$1800 \AA) and the X-ray band (0.5$-$7 keV) obtained during 31 August $-$ 8 September 2018 with the Ultraviolet Imaging Telescope and the Soft X-ray Telescope onboard \textit{AstroSat} were used for this study. Significant flux variability was detected in both FUV and X-ray bands. The fractional root mean square variability amplitude ($F_{\rm var}$) was found to be 0.036 $\pm$ 0.001 in the FUV band and 0.384 $\pm$ 0.004 in the X-ray band. To explore potential time lag between the two bands, cross-correlation analysis was performed using both the interpolated cross-correlation function (ICCF) and just another vehicle for estimating lags in nuclei (JAVELIN) methods. Results from both approaches are consistent within 2$\sigma$ uncertainty, indicating that X-ray variations lead the FUV variations, with measured lags of 2.25$\pm$0.05 days (ICCF) and $2.35_{-0.01}^{+0.02}$ days (JAVELIN). This is the first detection of a time delay between UV and X-ray variations in Mrk 1044. The observed UV lag supports the disk reprocessing scenario, wherein X-ray emission from the corona irradiates the accretion disk, driving the observed UV variability.