Testing disc reprocessing models for AGN optical variability by comparison of X-ray and optical power spectra of NGC 4395

It is generally thought that AGN optical variability is produced, at least in part, by reprocessing of central X-rays by a surrounding accretion disc, resulting in wavelength-dependent lags between bands. Any good model of AGN optical variability should explain not only these lags, but also the overall pattern of variability as quantified by the power spectral density (PSD). Here we present $\sim$daily g'-band monitoring of the low-mass AGN NGC\,4395 over 3 years. Together with previous TESS and GTC/HiPERCAM observations we produce an optical PSD covering an unprecedented frequency range of $\sim7$ decades allowing excellent determination of PSD parameters. The PSD is well fitted by a bending power law with low-frequency slope $\alpha_{L} = 1.0 \pm 0.2$, high-frequency slope $2.1^{+0.2}_{-0.4}$ and bend timescale $3.0^{+6.6}_{-1.7}\,$\,d. This timescale is close to that derived previously from a damped random walk (DRW) model fitted to just the TESS observations, although $\alpha_{L}$ is too steep to be consistent with a DRW. We compare the observed PSD with one made from light curves synthesized assuming reprocessing of X-rays, as observed by \xmm and Swift, in a disc defined by the observed lags. The simulated PSD is also well described by a bending power law but with a bend two decades higher in frequency. We conclude that the large-amplitude optical variations seen on long-timescales are not due to disc reprocessing but require a second source of variability whose origin is unknown but could be propagating disc accretion rate variations.