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.
