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.
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