We have used the VLA to study radio variability among a sample of 18 low luminosity active galactic nuclei (LLAGNs), on time scales of a few hours to 10 days. The goal was to measure or limit the sizes of the LLAGN radio-emitting regions, in order to use the size measurements as input to models of the radio emission mechanisms in LLAGNs. We detect variability on typical time scales of a few days, at a confidence level of 99%, in half of the target galaxies. Either variability that is intrinsic to the radio emitting regions, or that is caused by scintillation in the Galactic interstellar medium, is consistent with the data. For either interpretation, the brightness temperature of the emission is below the inverse-Compton limit for all of our LLAGNs, and has a mean value of about 1E10 K. The variability measurements plus VLBI upper limits imply that the typical angular size of the LLAGN radio cores at 8.5 GHz is 0.2 milliarcseconds, plus or minus a factor of two. The ~ 1E10 K brightness temperature strongly suggests that a population of high-energy nonthermal electrons must be present, in addition to a hypothesized thermal population in an accretion flow, in order to produce the observed radio emission.

61 pages, 17 figures, 10 tables. Accepted for publication in the Astrophysical Journal