PRUSSIC: I. A JVLA survey of HCN, HCO+, and HNC (1–0) emission in z ∼ 3 dusty galaxies: Low dense-gas fractions in high-redshift star-forming galaxies

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