Dense-gas tracers and carbon isotopes in five 2.5<z<4 lensed dusty star forming galaxies from the SPT SMG sample

The origin of the high SFR observed in high-z dusty star-forming galaxies is still unknown. Large fractions of dense molecular gas might provide part of the explanation, but there are few observational constraints on the amount of dense gas in high-z systems dominated by star formation. We present the results of our ALMA program targeting dense-gas tracers (HCN(5-4), HCO+(5-4), and HNC(5-4)) in 5 strongly lensed galaxies from the SPT SMG sample. We detected two of these lines (SNR>5) in SPT-125-47 at z=2.51 and tentatively detected all three (SNR~3) in SPT0551-50 at z=3.16. Since a significant fraction of our target lines is not detected, we developed a statistical method to derive unbiased mean properties taking into account both detections and non-detections. On average, the HCN(5-4) and HCO+(5-4) luminosities of our sources are a factor of ~1.7 fainter than expected, based on the local L'HCN(5-4)-LIR relation, but this offset corresponds to only ~2 sigma. We find that both the HCO+/HCN and HNC/HCN flux ratios are compatible with unity. The first ratio is expected for PDRs while the second is consistent with PDRs or XDRs and/or mid-IR pumping of HNC. Our sources are at the high end of the local relation between the star formation efficiency, determined using the LIR/[CI] and LIR/CO ratios, and the dense gas fraction, estimated using the HCN/[CI] and HCN/CO ratios. In SPT0125-47, we found that the velocity profiles of the lines tracing dense (HCN, HCO+) and lower-density (CO, [CI]) gas are similar. In addition to these lines, we obtained one robust and one tentative detection of 13CO(4-3) and found an average I12CO(4-3)/I13CO(4-3) flux ratio of 26.1$_{-3.5}^{+4.5}$, indicating a young but not pristine interstellar medium. We argue that the combination of large and slightly enriched gas reservoirs and high dense-gas fractions could explain the prodigious star formation in these systems.