PRUSSIC III -- ALMA and NOEMA survey of dense gas in high-redshift star-forming galaxies

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 eleven (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 13^CO and C^18O, 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 a canonical dense-mass conversion factor (alpha_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.

💡 Research Summary

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The PRUSSIC III paper presents the most extensive survey to date of dense‑gas tracers in high‑redshift dusty star‑forming galaxies (DSFGs). Using the Atacama Large Millimeter/sub‑millimeter Array (ALMA) and the Northern Extended Millimeter Array (NOEMA), the authors targeted the J = 3–2 and 4–3 rotational transitions of HCN, HCO⁺, and HNC in a sample of eleven gravitationally lensed DSFGs spanning 1.6 < z < 3.2 (median z ≈ 2.5). The galaxies were selected from Herschel‑ATLAS and Planck lens surveys and have intrinsic far‑infrared luminosities of 2.5 × 10¹²–2.2 × 10¹³ L⊙, corresponding to star‑formation rates of 400–4000 M⊙ yr⁻¹.

Observations were carried out in compact NOEMA configurations (D or C) with 9–12 antennas and in ALMA Band 3 with baselines up to 740 m. The spectral setup provided 2 MHz resolution (≈ 5 km s⁻¹) over two 7.744 GHz sidebands. After standard calibration (GILDAS for NOEMA, CASA pipeline for ALMA) the data were imaged with natural weighting to maximise sensitivity. Continuum was subtracted using line‑free channels, and spectra were extracted from apertures defined by the 2σ continuum contours. Narrow‑band images covering ±0.5 FWHM of the low‑J CO line were used to measure line fluxes, correcting for the fraction of flux outside this window assuming a Gaussian profile.

The survey detected at least one dense‑gas line in ten of the eleven galaxies, yielding a total of 34 line detections (HCN 3–2, HCN 4–3, HCO⁺ 3–2, HCO⁺ 4–3, HNC 3–2, HNC 4–3). This more than quadruples the number of high‑z dense‑gas detections previously available. In two sources, the authors also detected the rarer isotopologues ¹³CO and C¹⁸O as well as CN, providing a glimpse of the chemical richness of these systems.

Line ratios between the J = 4–3 and 3–2 transitions were used to derive excitation coefficients. The authors find that the excitation of HCN, HCO⁺ and HNC in DSFGs is systematically higher than in nearby luminous infrared galaxies (LIRGs), with typical HCN 4–3/3–2 ratios ∼1.5–2 times larger. Large‑velocity‑gradient (LVG) modelling suggests typical dense‑gas densities n(H₂) ≈ 10⁴·⁵–10⁵ cm⁻³ and kinetic temperatures Tₖ ≈ 50–80 K, consistent with the elevated CO excitation previously reported for similar objects.

To convert line luminosities into dense‑gas masses the authors adopt a canonical conversion factor α_HCN = 10 M⊙ (K km s⁻¹ pc²)⁻¹. Using this factor, the median dense‑gas depletion time (τ_dense = M_dense/SFR) is 23 Myr, substantially shorter than the ≈ 60 Myr typical of local galaxies. The implied star‑formation efficiency per free‑fall time (ε_ff) is 1–2 %, in line with theoretical expectations but a factor of a few higher than measured in nearby systems. The HCN/CO luminosity ratios span a wide range, 0.01–0.15, indicating that the fraction of molecular gas residing in the dense phase varies strongly from galaxy to galaxy.

A key result of the paper is the first empirical constraint on the cosmic evolution of the dense‑gas mass density, ρ_dense(z). By integrating the observed line luminosity functions and applying the same α_HCN, the authors infer that ρ_dense at z ≈ 2.5 is 7 ± 4 times larger than the present‑day value. This evolution mirrors that of the total molecular‑gas density derived from CO surveys, suggesting that the rise and fall of the cosmic star‑formation rate density is driven not only by the overall gas reservoir but also by a corresponding increase in the dense‑gas component.

The authors discuss several sources of systematic uncertainty. The assumed α_HCN may vary with metallicity, temperature, and optical depth; lensing magnification uncertainties could affect inferred intrinsic luminosities; and the use of mid‑J transitions introduces potential biases if excitation conditions differ from those in the local universe. Nevertheless, the consistency of the dense‑gas evolution with the well‑established CO‑based cosmic molecular‑gas evolution lends confidence to the main conclusions.

In summary, PRUSSIC III delivers a transformative dataset: (1) a four‑fold increase in high‑z dense‑gas detections, (2) robust measurements of excitation, density, and temperature of the dense phase, (3) evidence that high‑z DSFGs deplete their dense gas on ≈ 20 Myr timescales with ε_ff ≈ 1–2 %, (4) a broad distribution of dense‑gas fractions, and (5) the first quantitative estimate of the redshift evolution of the cosmic dense‑gas density. These results significantly advance our understanding of how the dense interstellar medium fuels the peak of cosmic star formation and provide a benchmark for future high‑resolution ALMA studies of the dense gas in the early universe.