Lags measured from correlated X-ray/UV/optical monitoring of AGN allow us to determine whether UV/optical variability is driven by reprocessing of X-rays or X-ray variability is driven by UV/optical seed photon variations. We present the results of the largest study to date of the relationship between the X-ray, UV and optical variability in an AGN with 554 observations, over a 750d period, of the Seyfert 1 galaxy NGC 5548 with Swift. There is a good overall correlation between the X-ray and UV/optical bands, particularly on short timescales (tens of days). These bands lag the X-ray band with lags which are proportional to wavelength to the power 1.23+/-0.31. This power is very close to the power (4/3) expected if short timescale UV/optical variability is driven by reprocessing of X-rays by a surrounding accretion disc. The observed lags, however, are longer than expected from a standard Shakura-Sunyaev accretion disc with X-ray heating, given the currently accepted black hole mass and accretion rate values, but can be explained with a slightly larger mass and accretion rate, and a generally hotter disc. Some long term UV/optical variations are not paralleled exactly in the X-rays, suggesting an additional component to the UV/optical variability arising perhaps from accretion rate perturbations propagating inwards through the disc.
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