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 wavebands , 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 unbroken power law model with slope \alpha = 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 significantly 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 can not account for all the optical variability .
There is also a second significant 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 .