Twelve years of X-ray and optical variability in the Seyfert galaxy NGC 4051
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We discuss the origin of the optical variations in the Narrow line Seyfert 1 galaxy NGC 4051 and present the results of a cross-correlation study using X-ray and optical light curves spanning more than 12 years. The emission is highly variable in all wave- bands, and the amplitude of the optical variations is found to be smaller than that of the X-rays, even after correcting for the contaminating host galaxy flux falling inside the photometric aperture. The optical power spectrum is best described by an unbro- ken power law model with slope = 1.4+0.6 −0.2 and displays lower variability power than the 2–10 keV X-rays on all time-scales probed. We find the light curves to be signifi- cantly correlated at an optical delay of 1.2+1.0 −0.3 days behind the X-rays. This time-scale is consistent with the light travel time to the optical emitting region of the accretion disc, suggesting that the optical variations are driven by X-ray reprocessing.We show, however, that a model whereby the optical variations arise from reprocessing by a flat accretion disc cannot account for all the optical variability. There is also a second sig- nificant peak in the cross-correlation function, at an optical delay of 39+2.7 −8.4 days. The lag is consistent with the dust sublimation radius in this source, suggesting that there is a measurable amount of optical flux coming from the dust torus. We discuss the origin of the additional optical flux in terms of reprocessing of X-rays and reflection of optical light by the dust.