  A tight linear correlation is established between the HCN line luminosity and
the radio continuum (RC) luminosity for a sample of 65 galaxies (from Gao &
Solomon's HCN survey), including normal spiral galaxies and luminous and
ultraluminous infrared galaxies (LIRGs/ULIRGs). After analyzing the various
correlations among the global far-infrared (FIR), RC, CO, and HCN luminosities
and their various ratios, we conclude that the FIR-RC and FIR-HCN correlations
appear to be linear and are the tightest among all correlations. The
combination of these two correlations could result in the tight RC-HCN
correlation we observed. Meanwhile, the non-linear RC-CO correlation shows
slightly larger scatter as compared with the RC-HCN correlation, and there is
no correlation between ratios of either RC/HCN-CO/HCN or RC/FIR-CO/FIR. In
comparison, a meaningful correlation is still observed between ratios of
RC/CO-HCN/CO. Nevertheless, the correlation between RC/FIR and HCN/FIR also
disappears, reflecting again the two tightest FIR-RC and FIR-HCN correlations
as well as suggesting that FIR seems to be the bridge that connects HCN with
RC. Interestingly, despite obvious HCN-RC and RC-CO correlations,
multi-parameter fits hint that while both RC and HCN contribute significantly
(with no contribution from CO) to FIR, yet RC is primarily determined from FIR
with a very small contribution from CO and essentially no contribution from
HCN. These analyses confirm independently the former conclusions that it is
practical to use RC luminosity instead of FIR luminosity, at least globally, as
an indicator of star formation rate in galaxies including LIRGs/ULIRGs, and HCN
is a much better tracer of star-forming molecular gas and correlates with FIR
much better than that of CO.
