PRUSSIC

Dusty star-forming galaxies (DSFGs) at redshift z$\geq$1 are among the most vigorously in Universe. However, their dense ($\geq$10$^5$ cm$^{-3}$ ) gas phase - typically traced by HCN(1-0) remains almost entirely unexplored: only two DSFGs have been detected to date. We present results of a JVLA survey J=1-0 transition HCN, HCO+, and HNC(1-0) six strongly lensed z = 2.5 3.3, effectively doubling number with deep observations these lines. detect emission one source (J1202+5354, 4.4$\sigma$), tentative HCO+ (1-0) detection another (J1609+6045, 3.3$\sigma$). Spectral stacking yields strict upper limits on HCN/FIR ($\leq$3.6$\times$10$^{-4}$) HCN/CO(1-0) ratios ($\leq$0.045). The inferred (a proxy for star-formation efficiency) consistent those z$\sim$0 FIR-luminous starbursts. HCN/CO dense-gas fraction factor few lower than suggested previous DSFG detections. Our imply that low fractions. A comparison Krumholz & Thompson (2007) models indicates bulk is densities ($\approx$10$^2$ ), similar "normal" galaxies, rather ultraluminous