Information on the structure around active galactic nuclei (AGN) has long been derived from measuring lags in their varying light output at different wavelengths. In principle, infrared data would reach to larger radii, potentially even probing reprocessed radiation in any surrounding dusty torus. In practice, this has proved challenging because high quality data are required to detect such variability, and the observations must stretch over a long period to probe the likely month-scale lags in variability. In addition, large numbers of sources would need to be observed to start searching for any patterns in such lags. Here, we show that the UKIDSS Ultra Deep Survey, built up from repeated observations over almost a decade, provides an ideal data set for such a study. For 94 sources identified as strongly-varying AGN within its square-degree field, we find that the K-band light curves systematically lag the J-band light curves by an average of around a month. The lags become smaller at higher redshift, consistent with the band shift to optical rest-frame emission. The less luminous AGN also display shorter lags, as would be expected if their physical size scales with luminosity.
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