High-J CO Versus Far-Infrared Relations in Normal and Starburst Galaxies

Daizhong Liu, Yu Gao, Kate Isaak, Emanuele Daddi, Chentao Yang, Nanyao Lu, Paul van der Werf

Published 2015-04-22Version 1

We present correlations between 9 CO transition ($J=4-3$ to $12-11$) lines and beam-matched far-infrared (FIR) luminosities ($L_{\mathrm{FIR},\,b}$) among 167 local galaxies, using Herschel SPIRE/FTS spectroscopic data and PACS photometry data. We adopt entire-galaxy FIR luminosities ($L_{\mathrm{FIR},\,e}$) from the {\it{IRAS}} Revised Bright Galaxy Sample and correct to $L_{\mathrm{FIR},\,b}$ using PACS images to match the varying FTS beams. All 9 correlations between $L'_{\mathrm{CO}}$ and $L_{\mathrm{FIR},\,b}$ are essentially linear, even for the highest transition $J=12-11$. This supports the notion that dense molecular gas ($n_{\mathrm{H}_2}\gtrsim10^{4-6}\,cm^{-3}$) linearly correlates with the star formation rate (SFR). We divide the entire sample into three subsamples and find that smaller sample size can induce large difference in the correlation slopes. We also derive an average CO spectral line energy distribution (SLED) for the entire sample and discuss the implied average molecular gas properties for these local galaxies. We further extend our sample to high-z galaxies with literature CO($J=5-4$) data as an example, including submillimeter galaxies (SMGs) and "normal" star-forming BzKs. BzKs have similar FIR/CO(5-4) ratios as that of local galaxies, well following the local correlation, whereas SMGs roughly distribute around or slightly above local correlation with large uncertainties. Finally, by using Galactic CO($J=10-9$) data as well as very limited high-z CO($J=10-9$) data, we verify that the CO($J=10-9$) -- FIR correlation successfully extends to Galactic YSOs, suggesting that linear correlations are most likely valid over nearly 15 orders of magnitude.