2025MNRAS.542.2572G

We present ground-based multiband light curves of the AGN Mrk 509, NGC 4151, and NGC 4593 obtained contemporaneously with Swift monitoring. We measure cross-correlation lags relative to Swift UVW2 (1928 Å) and test the standard prediction for disc reprocessing, which assumes a geometrically thin optically thick accretion disc where continuum interband delays follow the relation $\tau (\lambda) \propto \lambda ^{4/3}$. For Mrk 509 the 273-d Swift campaign gives well-defined lags that increase with wavelength as $\tau (\lambda)\propto \lambda ^{2.17\pm 0.2}$, steeper than the thin-disc prediction, and the optical lags are a factor of $\sim 5$ longer than expected for a simple disc-reprocessing model. This 'disc-size discrepancy' as well as excess lags in the u and r bands (which include the Balmer continuum and H $\alpha$, respectively) suggest a mix of short lags from the disc and longer lags from nebular continuum originating in the broad-line region. The shorter Swift campaigns, 69 d on NGC 4151 and 22 d on NGC 4593, yield less well-defined shorter lags $< 2$ d. The NGC 4593 lags are consistent with $\tau (\lambda) \propto \lambda ^{4/3}$ but with uncertainties too large for a strong test. For NGC 4151 the Swift lags match $\tau (\lambda) \propto \lambda ^{4/3}$, with a small U-band excess, but the ground-based lags in the r, i, and z bands are significantly shorter than the B and g lags, and also shorter than expected from the thin-disc prediction. The interpretation of this unusual lag spectrum is unclear. Overall these results indicate significant diversity in the $\tau \!-\!\lambda$ relation across the optical/UV/NIR, which differs from the more homogeneous behaviour seen in the Swift bands.