We have examined the compact structure in 250 flat-spectrum extragalactic radio sources using interferometric fringe visibilities obtained with the Very Long Baseline Array (VLBA) at 15 GHz. With projected baselines out to 440 M lambda, we are able to investigate source structure on typical angular scales as small as 0.05 mas. This scale is similar to the resolution of the VLBI Space Observatory Programme data obtained on longer baselines at a lower frequency and with somewhat poorer accuracy. For 171 sources in our sample, more than half of the total flux density seen by the VLBA remains unresolved on the longest baselines. There are 163 sources in our list with a median correlated flux density at 15 GHz in excess of 0.5 Jy on the longest baselines; these will be useful as fringe finders for short-wavelength VLBA observations. The total flux densities recovered in the VLBA images at 15 GHz are generally close to the values measured around the same epoch at the same frequency with the RATAN-600 and University of Michigan Radio Astronomy Observatory telescopes. We have modeled the core of each source with an elliptical Gaussian component. For about 60% of the sources, we have at least one observation in which the core component appears unresolved (generally smaller than 0.05 mas) in one direction, usually transverse to the direction into which the jet extends. BL Lac objects are on average more compact than quasars, while active galaxies are on average less compact. Also, in an active galaxy the sub-milliarcsecond core component tends to be less dominant. Intraday variability (IDV) sources typically have a more compact, more core-dominated structure on sub-milliarcsecond scales than non-IDV sources, and sources with a greater amplitude of intraday variations tend to have a greater unresolved VLBA flux density. The objects known to be GeV gamma-ray-loud appear to have a more compact VLBA structure than the other sources in our sample. This suggests that the mechanisms for the production of gamma-ray emission and for the generation of compact radio synchrotron-emitting features are related. The brightness temperature estimates and lower limits for the cores in our sample typically range between 1011 and 1013 K, but they extend up to 5; 1013 K, apparently in excess of the equipartition brightness temperature or the inverse Compton limit for stationary synchrotron sources. The largest component speeds are observed in radio sources with high observed brightness temperatures, as would be expected from relativistic beaming. Longer baselines, which can be obtained by space VLBI observations, will be needed to resolve the most compact high brightness temperature regions in these sources.
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