  Surveying eighteen 12CO-bright galaxies from the ATLAS3D early-type galaxy
sample with the Institut de Radio Astronomie Millim\'etrique (IRAM) 30m
telescope, we detect 13CO(1-0) and 13CO(2-1) in all eighteen galaxies, HCN(1-0)
in 12/18 and HCO+(1-0) in 10/18. We find that the line ratios
12CO(1-0)/13CO(1-0) and 12CO(1-0)/HCN(1-0) are clearly correlated with several
galaxy properties: total stellar mass, luminosity-weighted mean stellar age,
molecular to atomic gas ratio, dust temperature and dust morphology. We suggest
that these correlations are primarily governed by the optical depth in the 12CO
lines; interacting, accreting and/or starbursting early-type galaxies have more
optically thin molecular gas while those with settled dust and gas discs host
optically thick molecular gas. The ranges of the integrated line intensity
ratios generally overlap with those of spirals, although we note some outliers
in the 12CO(1- 0)/13CO(1-0), 12CO(2-1)/13CO(2-1) and HCN/HCO+(1-0) ratios. In
particular, three galaxies are found to have very low 12CO(1-0)/13CO(1-0) and
12CO(2-1)/13CO(2-1) ratios. Such low ratios may signal particularly stable
molecular gas which creates stars less efficiently than 'normal' (i.e. below
Schmidt-Kennicutt prediction), consistent with the low dust temperatures seen
in these galaxies.
