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 (>= 10(5) 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, e ffectively doubling the number of DSFGs with deep observations of these lines. We detect HCN(1-0) emission in one source (J1202 +5354, 4.6 sigma), with a tentative HCO+(1-0) detection in another (J1609 +6045, 3.3 sigma). Spectral stacking yields strict upper limits on the HCN /FIR (<= 3:6 x 10(-4)) and HCN /CO(1-0) ratios (<= 0.045). The inferred HCN /FIR ratios (a proxy for the star-formation e fficiency) are consistent with those in z similar to 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 (approximate to 10(2) cm(-3)), similar to 'normal' star-forming galaxies, rather than ultraluminous starbursts.