BASS XXXII: Studying the Nuclear Millimeter-wave Continuum Emission of AGNs with ALMA at Scales <~100-200 pc

To understand the origin of nuclear (less than or similar to 100 pc) millimeter-wave (mm-wave) continuum emission in active galactic nuclei (AGNs), we systematically analyzed subarcsecond resolution Band-6 (211-275 GHz) Atacama Large Millimeter/submillimeter Array data of 98 nearby AGNs (z &lt; 0.05) from the 70 month Swift/BAT catalog. The sample, almost unbiased for obscured systems, provides the largest number of AGNs to date with high mm-wave spatial resolution sampling (similar to 1-200 pc), and spans broad ranges of 14-150 keV luminosity {40&lt; log [L-14(-150)/(erg s(-1))] &lt; 45}, black hole mass [5 &lt; log(M-BH/M-circle dot) &lt; 10], and Eddington ratio (-4 &lt; log lambda(Edd) &lt; 2). We find a significant correlation between 1.3 mm (230 GHz) and 14-150 keV luminosities. Its scatter is approximate to 0.36 dex, and the mm-wave emission may serve as a good proxy of the AGN luminosity, free of dust extinction up to N-H similar to 10(26) CM-2. While the mm-wave emission could be self-absorbed synchrotron radiation around the X-ray corona according to past works, we also discuss different possible origins of the mm-wave emission: AGN-related dust emission, outflow-driven shocks, and a small-scale (&lt;200 pc) jet. The dust emission is unlikely to be dominant, as the mm-wave slope is generally flatter than expected. Also, due to no increase in the mm-wave luminosity with the Eddington ratio, a radiation-driven outflow model is possibly not the common mechanism Furthermore, we find independence of the mm-wave luminosity on indicators of the inclination angle from the polar axis of the nuclear structure, which is inconsistent with a jet model whose luminosity depends only on the angle.