We present correlations between 9 CO transitions ( J = 4 - 3 to 12 - 11 ) and beam-matched far-infrared ( far-IR ) luminosities ( L _ { \mathrm { FIR } , b } ) among 167 local galaxies , using Herschel Spectral and Photometric Imaging Receiverï‚ Fourier Transform Spectrometer ( SPIRE ; FTS ) spectroscopic data and Photoconductor Array Camera and Spectrometer ( PACS ) photometry data .
We adopt entire-galaxy FIR luminosities ( L _ { \mathrm { FIR } , e } ) from the IRAS Revised Bright Galaxy Sample and correct to L _ { \mathrm { FIR } , b } using PACS images to match the varying FTS beam sizes .
All 9 correlations between L ^ { \prime } _ { \mathrm { CO } } and L _ { \mathrm { FIR } , b } are essentially linear and tight ( \sigma = 0.2 - 0.3 dex dispersion ) , even for the highest transition , J = 12 - 11 .
This supports the notion that the star formation rate ( SFR ) is linearly correlated with the dense molecular gas ( n _ { \mathrm { H } _ { 2 } } \gtrsim 10 ^ { 4 - 6 } cm ^ { -3 } ) .
We divide the entire sample into three subsamples and find that smaller sample sizes can induce large differences 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 from the literature 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 , and follow well the locally-determined correlation , whereas SMG ratios fall around or slightly above the local correlation with large uncertainties .
Finally , by including 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 young stellar objects , suggesting that linear correlations are valid over 15 orders of magnitude .