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Ultraviolet and X-ray variability of NGC 4051 over 45 days with XMM-Newton and Swift

We analyse 15 XMM-Newton observations of the Seyfert galaxy NGC 4051 obtained over 45 days to determine the ultraviolet (UV) light curve variability characteristics and search for correlated UV/X-ray emission. The UV light curve shows variability on all time scales, however with lower fractional rms than the 0.2-10 keV X-rays. On days-weeks timescales the fractional variability of the UV is Fvar ~ 8%, and on short (~ hours) timescales Fvar ~ 2%. The within-observation excess variance in 4 of the 15 UV observations was found be much higher than the remaining 11. This was caused by large systematic uncertainties in the count rate masking the intrinsic source variance. For the four "good" observations we fit an unbroken power-law model to the UV power spectra with slope -2.0 +/- 0.5. We compute the UV/X-ray Cross-correlation function for the "good" observations and find a correlation of ~ 0.5 at time lag of ~ 3 ks, where the UV lags the X-rays. We also compute for the first time the UV/X-ray Cross-spectrum in the range 0-28.5 ks, and find a low coherence and an average time lag of ~ 3 ks. Combining the 15 XMM-Newton and the Swift observations we compute the DCF over +/-40 days but are unable to recover a significant correlation. The magnitude and direction of the lag estimate from the 4 "good" observations indicates a scenario where ~ 25 % of the UV variance is caused by thermal reprocessing of the incident X-ray emission.