Atacama Cosmology Telescope: Dusty star-forming galaxies and active galactic nuclei in the equatorial survey.

We present a catalog of 510 radio-loud active galactic nuclei (AGNs, primarily blazars) and 287 dusty star-forming galaxies (DSFGs) detected by the Atacama Cosmology Telescope at significance in frequency bands centered on 148 GHz (2 mm), 218 GHz (1.4 mm), and 277 GHz (1.1 mm), from a 480 deg(2) strip centered at R.A. 00(h) on the celestial equator with additional 360 deg(2) shallower auxiliary fields at other longitudes. The combination of the deepest available 218 GHz wide-field imaging, our 277 GHz data, and multiband filtering results in the most sensitive wide-field millimeter-wave DSFG selection to date, with rms noise level referenced to 218 GHz reaching below 2 mJy. We have developed new techniques to remove Galactic contamination (including evidence for CO (2-1) line emission) from the extragalactic catalog, yielding a catalog of 321 Galactic sources in addition to the extragalactic catalog. We employ a new flux debiasing method that accounts for the heterogeneous sample selection in the presence of Galactic cuts. We present the spectral properties and source counts of the AGNs and DSFGs. The DSFG spectra depart from the Rayleigh-Jeans regime of an optically thin modified blackbody between 218 and 277 GHz, consistent with optically thick emission or an additional cold dust component. For AGNs with 148 and 218 GHz flux density >50 mJy, we estimate the interyear rms fractional deviation in flux density due to source variability to be 40% with a 0.98 interband correlation coefficient. We provide source counts for AGNs in the range of 8-2870 mJy and for DSFGs in the range of 8-90 mJy. Our DSFG counts probe both the brighter, lensed population and the fainter, unlensed population. At 277 GHz we report the first measurements of source counts at these flux densities, finding an excess above most model count predictions. Finally, we present 30 of the brightest DSFGs that were selected for multifrequency study as candidate high-z lensed systems.