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Space Telescope and Optical Reverberation Mapping Project. III. Optical Continuum Emission and Broad-Band Time Delays in NGC 5548

We present ground-based optical photometric monitoring data for NGC 5548, part of an extended multi-wavelength reverberation mapping campaign. The light curves have nearly daily cadence from 2014 January to July in nine filters (\emph{BVRI} and \emph{ugriz}). Combined with ultraviolet data from the \emph{Hubble Space Telescope} and \emph{Swift}, we confirm significant time delays between the continuum bands as a function of wavelength, extending the wavelength coverage from 1158\,Å to the $z$ band ($\sim\!9160$\,Å). We find that the lags at wavelengths longer than the {\it V} band are equal to or greater than the lags of high-ionization-state emission lines (such as He\,{\sc ii}\,$λ1640$ and $λ4686$), suggesting that the continuum-emitting source is of a physical size comparable to the inner broad-line region (BLR). The trend of lag with wavelength is broadly consistent with the prediction for continuum reprocessing by an accretion disk with $τ\propto λ^{4/3}$. However, the lags also imply a disk radius that is 3 times larger than the prediction from standard thin-disk theory, assuming that the bolometric luminosity is 10\% of the Eddington luminosity ($L = 0.1L_{\rm Edd}$). Using optical spectra from the Large Binocular Telescope, we estimate the bias of the interband continuum lags due to BLR emission observed in the filters. We find that the bias for filters with high levels of BLR contamination ($\sim\! 20\%$) can be important for the shortest continuum lags, and likely has a significant impact on the {\it u} and {\it U} bands owing to Balmer continuum emission.