We present deep ALMA Band 3 observations of the HCN, HCO⁺, and HNC(4-3) emission in SDP.81, a well-studied z = 3.042; strongly lensed galaxy. These lines trace the high-density gas, which remains almost entirely unexplored in z ≥ 1 galaxies. Additionally, these dense-gas tracers are potentially powerful diagnostics of the mechanical heating of the interstellar medium. While the HCN(4-3) and HNC(4-3) lines are not detected, the HCO⁺(4-3) emission is clearly detected and resolved. This is the third detection of this line in a high-redshift star-forming galaxy. We find an unusually high HCO⁺/HCN intensity ratio of ≥2.2. Based on the modelling of the photodissociation region, the most likely explanation for the elevated HCO⁺/HCN ratio is that SDP.81 has low mechanical heating, making up less than 10% of the total energy budget, along with a sub-solar metallicity of Z ≈ 0.5 Z_⊙. While such conditions might not be representative of the general population of high-redshift dusty galaxies, a lower-than-solar metallicity might significantly impact gas masses inferred from CO observations. In addition, we report the detection of CO(0-1) absorption from the foreground lensing galaxy and CO(1-0) emission from a massive companion to the lensing galaxy, approximately 50 kpc to the south-east.

Dusty star-forming galaxies (DSFGs) at redshift z ≥ 1 are among the most vigorously star-forming galaxies in the Universe. However, their dense (≥10 ⁵cm ^-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, 3.3). 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 (≈10 ²cm ^-3), similar to normal star-forming galaxies, rather than ultraluminous starbursts.