Characterising the relationship between dense gas and star formation is critical for understanding the assembly of galaxies throughout cosmic history. However, due to the faintness of standard dense-gas tracers-HCN, HCO⁺, and HNC-dense gas in high-redshift galaxies remains largely unexplored. We present ALMA and NOEMA observations targeting HCN/HCO⁺/HNC (3–2) and (4–3) emission lines in 11 (mostly) gravitationally lensed dusty star-forming galaxies (DSFGs) at redshift z = 1.6 − 3.2. We detect at least one line in 10 out of 11 galaxies. Altogether, we detect 34 dense-gas transitions, more than quadrupling the number of extant high-redshift detections. Additionally, in two targets, we detect lower-abundance CO isotopologues ¹³CO and C¹⁸O, as well as CN emission. We derive excitation coefficients for HCN, HCO⁺, and HNC in DSFGs, finding them to be systematically higher than those in nearby luminous infrared galaxies. Assuming the canonical dense-mass conversion factor (α _HCN = 10), we find that DSFGs have shorter dense-gas depletion times (median 23 Myr) than nearby galaxies (≈60 Myr), with a star-forming efficiency per free-fall time of 1−2%, a factor of a few higher than in local galaxies. We find a wide range of dense-gas fractions, with HCN/CO ratios ranging between 0.01 and 0.15. Finally, we put the first constraints on the redshift evolution of the cosmic dense-gas density, which increases by a factor of 7 ± 4 between z = 0 and z = 2.5, consistent with the evolution of the cosmic molecular-gas density.

Massive star-forming galaxies at high redshift require a supply of molecular gas from their gas reservoirs that is replenished by infall from the surrounding circumgalactic medium to sustain their immense star formation rates. Our knowledge of the extent and morphology of cold-gas reservoirs of early galaxies is still in its infancy, however. We present the results of stacking more than 80 hours of JVLA observations of CO(1–0) emission, which traces the cold molecular gas, in 19 z = 2.0−4.5 dusty star-forming galaxies from the AS2VLA survey. The visibility-plane stack reveals extended emission with a half-light radius of 3.8 ± 0.5 kpc, which is a factor of 2–3 more extended than the dust-obscured star formation and 1.4 ± 0.2× more extended than the stellar emission revealed by the JWST. Stacking the [C i](1–0) observations for 10 galaxies from our parent sample yielded a half-light radius ≤2.6 kpc, which is marginally smaller than CO(1–0). The CO(1–0) size is also comparable to that of the [C ii] haloes detected around high-redshift star-forming galaxies. This suggests that these arise from molecular gas. Photo-dissociation region modelling indicates that the extended CO(1–0) emission arises from clumpy dense clouds and not from smooth diffuse gas. Our results show that the bulk (up to 80%) of the molecular gas in these galaxies resides outside the star-forming region with only a small part directly contributing to the star formation.

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.