2022A&A...667A..70R

Dusty star-forming galaxies (DSFGs) at redshift z ≥ 1 are among the most vigorously star-forming galaxies in the Universe. However, their dense (≥10⁵ cm^–3) gas phase - typically traced by HCN(1-0) - remains almost entirely unexplored: only two DSFGs have been detected in HCN(1-0) to date. We present the results of a Karl G. Jansky Very Large Array survey of the J = 1-0 transition of HCN, HCO⁺, and HNC(1-0) in six strongly lensed DSFGs at z = 2.5 - 3.3, effectively doubling the number of DSFGs with deep observations of these lines. We detect HCN(1-0) emission in one source (J1202+5354, 4.6 σ), with a tentative HCO⁺(1-0) detection in another (J1609+6045, 3.3σ). Spectral stacking yields strict upper limits on the HCN/FIR (≤3.6 × 10^–4) and HCN/CO(1-0) ratios (≤0.045). The inferred HCN/FIR ratios (a proxy for the star-formation efficiency) are consistent with those in z ∼ 0 far-infrared-luminous starbursts. However, the HCN/CO ratios - a proxy for the dense-gas fraction - are a factor of a few lower than suggested by the two previous DSFG detections. Our results imply that most DSFGs have low dense-gas fractions. A comparison with theoretical models of star-forming galaxies indicates that the bulk of gas in DSFGs is at lower densities (≈10² cm^–3), similar to 'normal' star-forming galaxies, rather than ultraluminous starbursts.