Temporal Correlations Between Optical and Gamma-ray Activity in Blazars

We have been using the 0.76-m Katzman Automatic Imaging Telescope (KAIT) at Lick Observatory to optically monitor a sample of 157 blazars that are bright in gamma rays, being detected with high significance ($ge 10sigma$) in one year by the Large Area Telescope (LAT) on the {it Fermi Gamma-ray Space Telescope}. We attempt to observe each source on a 3-day cadence with KAIT, subject to weather and seasonal visibility. The gamma-ray coverage is essentially continuous. KAIT observations extend over much of the 5-year {it Fermi} mission for several objects, and most have $>100$ optical measurements spanning the last three years. These blazars (flat-spectrum radio quasars and BL~Lac objects) exhibit a wide range of flaring behavior. Using the discrete correlation function (DCF), here we search for temporal relationships between optical and gamma-ray light curves in the 40 brightest sources in hopes of placing constraints on blazar acceleration and emission zones. We find strong optical--gamma-ray correlation in many of these sources at time delays of $sim 1$ to $sim 10$ days, ranging between $-40$ and +30 days. A stacked average DCF of the 40 sources verifies this correlation trend, with a peak above 99% significance indicating a characteristic time delay consistent with 0 days. These findings strongly support the widely accepted leptonic models of blazar emission. However, we also find examples of apparently uncorrelated flares (optical flares with no gamma-ray counterpart and gamma-ray flares with no optical counterpart) that challenge simple, one-zone models of blazar emission. Moreover, we find that flat-spectrum radio quasars tend to have gamma rays leading the optical, while intermediate and high synchrotron peak blazars with the most significant peaks have smaller lags/leads.