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We have conducted two-component, non-LTE modeling of the CO lines from J =1-0 through J = 13-12 in 87 galaxies observed by the Herschel SPIRE FourierTransform Spectrometer (FTS). We find the average pressure of the coldmolecular gas, traced especially by CO J = 1-0, is $\sim 10^{5.0 \pm 0.5}$ Kcm$^{-3}$. The mid- to high-J lines of CO trace higher-pressure gas at $10^{6.5\pm 0.6}$ K cm$^{-3}$; this pressure is slightly correlated with LFIR. Twocomponents are often necessary to accurately fit the Spectral Line EnergyDistributions (SLEDs); a one-component fit often underestimates the flux of COJ = 1-0 and the mass. If low-J lines are not included, mass is underestimatedby an order of magnitude. Even when modeling the low-J lines alone or using an$\alpha_{CO}$ conversion factor, the mass should be considered to be uncertainto a factor of at least 0.4 dex, and the vast majority of the CO luminositywill be missed (median, 65%). We find a very large spread in our derived valuesof $\alpha_{CO}$, though they do not have a discernible trend with LFIR; thebest fit is a constant 0.7 M$_{\odot}$/ (K kms$^{-1}$ pc$^2$), with a standarddeviation of 0.36 dex, and a range of 0.3-1.6 M$_{\odot}$/ (K kms$^{-1}$pc$^2$). We find average molecular gas depletion times ($\tau_{dep}$) of $10^8$yr that decrease with increasing SFR. Finally, we note that the J = 11-10/J =1-0 line flux ratio is diagnostic of the warm component pressure, and discussthe implications of this comprehensive study of SPIRE FTS extragalactic spectrafor future study post-Herschel.

Warm and Cold Molecular Gas Conditions Modeled in 87 Galaxies Observed by the Herschel SPIRE Fourier Transform Spectrometer