  Some luminous and ultraluminous infrared galaxies (LIRGs and ULIRGs) host
extremely compact and dusty nuclei. The intense infrared radiation arising from
warm dust in these sources is prone to excite vibrational levels of molecules
such as HCN. This results in emission from the rotational transitions of
vibrationally excited HCN (HCN-vib), with the brightest emission found in
compact obscured nuclei (CONs). We aim to establish how common CONs are in the
local Universe, and whether their prevalence depends on the luminosity or other
properties of the host galaxy. We have conducted an Atacama Large
Millimeter/submillimeter Array (ALMA) survey of the rotational J=3-2 transition
of HCN-vib in a sample of 46 far-infrared luminous galaxies. Compact obscured
nuclei are identified in 38 percent of ULIRGs, 21 percent of LIRGs, and 0
percent of lower luminosity galaxies. We find no dependence on the inclination
of the host galaxy, but strong evidence of lower IRAS 25 to 60 {\mu}m flux
density ratios (f25/f60) in CONs compared to the rest of the sample.
Furthermore, we find that CONs have stronger silicate features (s9.7{\mu}m) but
similar PAH equivalent widths (EQW6.2{\mu}m) compared to other galaxies. In the
local Universe, CONs are primarily found in (U)LIRGs. High resolution continuum
observations of the individual nuclei are required to determine if the CON
phenomenon is related to the inclinations of the nuclear disks. The lower
f25/f60 ratios in CONs as well as the results for the mid-infrared diagnostics
investigated are consistent with large dust columns shifting the nuclear
radiation to longer wavelengths, making the mid- and far-infrared
"photospheres" significantly cooler than the interior regions. To assess the
importance of CONs in the context of galaxy evolution, it is necessary to
extend this study to higher redshifts where (U)LIRGs are more common.
