Warm Molecular Gas in Luminous Infrared Galaxies
  We present our initial results on the CO rotational spectral line energy
distribution (SLED) of the $J$ to $J$$-$1 transitions from $J=4$ up to $13$
from Herschel SPIRE spectroscopic observations of 65 luminous infrared galaxies
(LIRGs) in the Great Observatories All-Sky LIRG Survey (GOALS). The observed
SLEDs change on average from one peaking at $J \le 4$ to a broad distribution
peaking around $J \sim\,$6$-$7 as the IRAS 60-to-100 um color, $C(60/100)$,
increases. However, the ratios of a CO line luminosity to the total infrared
luminosity, $L_{\rm IR}$, show the smallest variation for $J$ around 6 or 7.
This suggests that, for most LIRGs, ongoing star formation (SF) is also
responsible for a warm gas component that emits CO lines primarily in the
mid-$J$ regime ($5 \lesssim J \lesssim 10$). As a result, the logarithmic
ratios of the CO line luminosity summed over CO (5$-$4), (6$-$5), (7$-$6),
(8$-$7) and (10$-$9) transitions to $L_{\rm IR}$, $\log R_{\rm midCO}$, remain
largely independent of $C(60/100)$, and show a mean value of $-4.13$ ($\equiv
\log R^{\rm SF}_{\rm midCO}$) and a sample standard deviation of only 0.10 for
the SF-dominated galaxies. Including additional galaxies from the literature,
we show, albeit with small number of cases, the possibility that galaxies,
which bear powerful interstellar shocks unrelated to the current SF, and
galaxies, in which an energetic active galactic nucleus contributes
significantly to the bolometric luminosity, have their $R_{\rm midCO}$ higher
and lower than $R^{\rm SF}_{\rm midCO}$, respectively.
