In a pilot project to study the relationship between star formation and molecular gas properties in nearby normal early-type galaxies, we used the IRAM 30m telescope to observe the 13CO(J=1-0), 13CO(J=2-1), HCN(J=1-0) and HCO+(J=1-0) line emission in the four galaxies of the SAURON sample with the strongest 12CO emission. We report the detection of 13CO emission in all four SAURON sources and HCN emission in three sources, while no HCO+ emission was found to our detection limits in any of the four galaxies. We find that the 13CO/12CO ratios of three SAURON galaxies are somewhat higher than those in galaxies of different Hubble types. The HCN/12CO and HCN/13CO ratios of all four SAURON galaxies resemble those of nearby Seyfert and dwarf galaxies with normal star formation rates, rather than those of starburst galaxies. The HCN/HCO+ ratio is found to be relatively high (i.e., >1) in the three SAURON galaxies with detected HCN emission, mimicking the behaviour in other star-forming galaxies but being higher than in starburst galaxies. When compared to most galaxies, it thus appears that 13CO is enhanced (relative to 12CO) in three out of four SAURON galaxies and HCO+ is weak (relative to HCN) in three out of three galaxies. All three galaxies detected in HCN follow the standard HCN-infrared luminosity and dense gas fraction-star formation efficiency correlations. As already suggested by 12CO observations, when traced by infrared radiation, star formation in the three SAURON galaxies thus appears to follow the same physical laws as in galaxies of different Hubble types. The star formation rate and fraction of dense molecular gas however do not reach the high values found in nearby starburst galaxies, but rather resemble those of nearby normal star-forming galaxies.
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