We explore the relationship between gas, dust and star formation in a sample of 12 ultra-luminous infrared galaxies (ULIRGs) at high redshift compared to a similar sample of local galaxies. We present new CO observations and/or Spitzer mid-IR spectroscopy for 6 70 micron selected galaxies at z~1 in order to quantify the properties of the molecular gas reservoir, the contribution of an active galactic nuclei (AGN) to the mid-IR luminosity and the star formation efficiency (SFE=LIR/LCO). The mid-IR spectra show strong polycyclic aromatic hydrocarbon (PAH) emission and our spectral decomposition suggests that the AGN makes a minimal contribution (<25%) to the mid-IR luminosity. The 70 micron selected ULIRGs which we find to be spectroscopic close pairs, are observed to have high SFE, similar to local ULIRGs and high redshift submillimeter galaxies, consistent with enhanced IR luminosity due to an ongoing major merger. Combined with existing observations of local and high redshift ULIRGs, we further compare the PAH, IR and CO luminosities. We show that the ratio LPAH6.2/LIR decreases with increasing IR luminosity for both local and high redshift galaxies but the trend for high redshift galaxies is shifted to higher IR luminosities; the average LPAH6.2/LIR ratio at a given LIR is ~3 times higher at high redshift. When we normalize by the molecular gas, we find this trend to be uniform for galaxies at all redshifts and that the molecular gas is correlated with the PAH dust emission.The similar trends seen in the [CII] to molecular gas ratios in other studies suggests that PAH emission, like [CII], continues to be a good tracer of photodissociation regions even at high redshift. Together the CO, PAH and far-IR fine structure lines should be useful for constraining the interstellar medium conditions in high redshift galaxies.
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