Letter | Published:

Stellar populations dominated by massive stars in dusty starburst galaxies across cosmic time

Naturevolume 558pages260263 (2018) | Download Citation


All measurements of cosmic star formation must assume an initial distribution of stellar masses—the stellar initial mass function—in order to extrapolate from the star-formation rate measured for typically rare, massive stars (of more than eight solar masses) to the total star-formation rate across the full stellar mass spectrum1. The shape of the stellar initial mass function in various galaxy populations underpins our understanding of the formation and evolution of galaxies across cosmic time2. Classical determinations of the stellar initial mass function in local galaxies are traditionally made at ultraviolet, optical and near-infrared wavelengths, which cannot be probed in dust-obscured galaxies2,3, especially distant starbursts, whose apparent star-formation rates are hundreds to thousands of times higher than in the Milky Way, selected at submillimetre (rest-frame far-infrared) wavelengths4,5. The 13C/18O isotope abundance ratio in the cold molecular gas—which can be probed via the rotational transitions of the 13CO and C18O isotopologues—is a very sensitive index of the stellar initial mass function, with its determination immune to the pernicious effects of dust. Here we report observations of 13CO and C18O emission for a sample of four dust-enshrouded starbursts at redshifts of approximately two to three, and find unambiguous evidence for a top-heavy stellar initial mass function in all of them. A low 13CO/C18O ratio for all our targets—alongside a well tested, detailed chemical evolution model benchmarked on the Milky Way6—implies that there are considerably more massive stars in starburst events than in ordinary star-forming spiral galaxies. This can bring these extraordinary starbursts closer to the ‘main sequence’ of star-forming galaxies7, although such main-sequence galaxies may not be immune to changes in initial stellar mass function, depending on their star-formation densities.

  • Subscribe to Nature for full access:



Additional access options:

Already a subscriber?  Log in  now or  Register  for online access.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


  1. 1.

    Kennicutt, R. C. Jr. Star formation in galaxies along the Hubble sequence. Annu. Rev. Astron. Astrophys. 36, 189–231 (1998).

  2. 2.

    Bastian, N., Covey, K. R. & Meyer, M. R. A universal stellar initial mass function? A critical look at variations. Annu. Rev. Astron. Astrophys. 48, 339–389 (2010).

  3. 3.

    Kroupa, P. et al. The Stellar and Sub-Stellar Initial Mass Function of Simple and Composite Populations Ch. 4, 115–242 (Springer, Dordrecht, 2013).

  4. 4.

    Smail, I., Ivison, R. J. & Blain, A. W. A deep sub-millimeter survey of lensing clusters: a new window on galaxy formation and evolution. Astrophys. J. 490, L5–L8 (1997).

  5. 5.

    Hughes, D. H. et al. High-redshift star formation in the Hubble Deep Field revealed by a submillimetre-wavelength survey. Nature 394, 241–247 (1998).

  6. 6.

    Romano, D., Matteucci, F., Zhang, Z.-Y., Papadopoulos, P. P. & Ivison, R. J. The evolution of CNO isotopes: a new window on cosmic star formation history and the stellar IMF in the age of ALMA. Mon. Not. R. Astron. Soc. 470, 401–415 (2017).

  7. 7.

    Noeske, K. G. et al. Star formation in AEGIS field galaxies since z=1.1: the dominance of gradually declining star formation, and the main sequence of star-forming galaxies. Astrophys. J. 660, L43–L46 (2007).

  8. 8.

    Wilson, T. L. & Matteucci, F. Abundances in the interstellar medium. Astron. Astrophys. Rev. 4, 1–33 (1992).

  9. 9.

    Romano, D., Karakas, A. I., Tosi, M. & Matteucci, F. Quantifying the uncertainties of chemical evolution studies. II. Stellar yields. Astron. Astrophys. 522, A32 (2010).

  10. 10.

    Pagel, B. E. J. Nucleosynthesis and Chemical Evolution of Galaxies (Cambridge Univ. Press, Cambridge, 2009).

  11. 11.

    Henkel, C. et al. Carbon and oxygen isotope ratios in starburst galaxies: new data from NGC 253 and Mrk 231 and their implications. Astron. Astrophys. 565, A3 (2014).

  12. 12.

    Sliwa, K., Wilson, C. D., Aalto, S., Privon, G. C. & Extreme, C. O. Isotopic abundances in the ULIRG IRAS 13120–5453: an extremely young starburst or top-heavy initial mass function. Astrophys. J. 840, L11 (2017).

  13. 13.

    Danielson, A. L. R. et al. 13CO and C18O emission from a dense gas disc at z = 2.3: abundance variations, cosmic rays and the initial conditions for star formation. Mon. Not. R. Astron. Soc. 436, 2793–2809 (2013).

  14. 14.

    Barnes, P. J. et al. The three-mm ultimate Mopra Milky Way Survey. I. Survey overview, initial data releases, and first results. Astrophys. J. 812, 6 (2015).

  15. 15.

    Jiménez-Donaire, M. J. et al. 13CO/C18O gradients across the disks of nearby spiral galaxies. Astrophys. J. 836, L29 (2017).

  16. 16.

    Ballero, S. K., Matteucci, F., Origlia, L. & Rich, R. M. Formation and evolution of the Galactic bulge: constraints from stellar abundances. Astron. Astrophys. 467, 123–136 (2007).

  17. 17.

    Dabringhausen, J., Kroupa, P. & Baumgardt, H. A top-heavy stellar initial mass function in starbursts as an explanation for the high mass-to-light ratios of ultra-compact dwarf galaxies. Mon. Not. R. Astron. Soc. 394, 1529–1543 (2009).

  18. 18.

    Dabringhausen, J., Kroupa, P., Pflamm-Altenburg, J. & Mieske, S. Low-mass X-ray binaries indicate a top-heavy stellar initial mass function in ultracompact dwarf galaxies. Astrophys. J. 747, 72 (2012).

  19. 19.

    Peacock, M. B. et al. Further constraints on variations in the initial mass function from low-mass X-ray binary populations. Astrophys. J. 841, 28 (2017).

  20. 20.

    Schneider, F. R. N. et al. An excess of massive stars in the local 30 Doradus starburst. J. Sci. 359, 69–71 (2018).

  21. 21.

    Banerjee, S. & Kroupa, P. On the true shape of the upper end of the stellar initial mass function. The case of R136. Astron. Astrophys. 547, A23 (2012).

  22. 22.

    Kalari, V. M., Carraro, G., Evans, C. J. & Rubio, M. The Magellanic Bridge cluster NGC 796: deep optical AO imaging reveals the stellar content and initial mass function of a massive open cluster. Astrophys. J. 857, 132 (2018).

  23. 23.

    Lee, J. C. et al. Comparison of Hα and UV star formation rates in the local volume: systematic discrepancies for dwarf galaxies. Astrophys. J. 706, 599–613 (2009).

  24. 24.

    Pflamm-Altenburg, J. & Kroupa, P. Clustered star formation as a natural explanation for the Hα cut-off in disk galaxies. Nature 455, 641–643 (2008).

  25. 25.

    Speagle, J. S., Steinhardt, C. L., Capak, P. L. & Silverman, J. D. A highly consistent framework for the evolution of the star-forming “main sequence” from z ~ 0–6. Astrophys. J. Suppl . Ser. 214, 15 (2014).

  26. 26.

    Madau, P. et al. High-redshift galaxies in the Hubble deep field: colour selection and star formation history to z ~ 4. Mon. Not. R. Astron. Soc. 283, 1388–1404 (1996).

  27. 27.

    Pflamm-Altenburg, J. & Kroupa, P. The fundamental gas depletion and stellar-mass buildup times of star-forming galaxies. Astrophys. J. 706, 516–524 (2009).

  28. 28.

    Heikkila, A., Johansson, L. E. B. & Olofsson, H. The C18O/C17O ratio in the Large Magellanic Cloud. Astron. Astrophys. 332, 493–502 (1998).

  29. 29.

    Muraoka, K. et al. ALMA Observations of N83C in the early stage of star formation in the Small Magellanic Cloud. Astrophys. J. 844, 98 (2017).

  30. 30.

    Nishimura, Y. et al. Spectral line survey toward a molecular cloud in IC10. Astrophys. J. 829, 94 (2016).

  31. 31.

    Magain, P., Surdej, J., Swings, J.-P., Borgeest, U. & Kayser, R. Discovery of a quadruply lensed quasar—the ‘clover leaf’ H1413 + 117. Nature 334, 325–327 (1988).

  32. 32.

    Weiß, A. et al. ALMA redshifts of millimeter-selected galaxies from the SPT Survey: the redshift distribution of dusty star-forming galaxies. Astrophys. J. 767, 88 (2013).

  33. 33.

    Negrello, M. et al. The detection of a population of submillimeter-bright, strongly lensed galaxies. J. Sci. 330, 800 (2010).

  34. 34.

    Griffin, M. J. et al. The Herschel-SPIRE instrument and its in-flight performance. Astron. Astrophys. 518, L3 (2010).

  35. 35.

    Solomon, P., Vanden Bout, P., Carilli, C. & Guelin, M. The essential signature of a massive starburst in a distant quasar. Nature 426, 636–638 (2003).

  36. 36.

    McMullin, J. P., Waters, B., Schiebel, D., Young, W. & Golap, K. in Astronomical Data Analysis Software and Systems XVI (eds Shaw, R. A., Hill, F. & Bell, D. J.) Vol. 376, 127 (Astronomical Society of the Pacific Conference Series, ASP, 2007).

  37. 37.

    Mangum, J. G. & Shirley, Y. L. How to calculate molecular column density. Publ. Astron. Soc. Pacif. 127, 266 (2015).

  38. 38.

    Frerking, M. A., Langer, W. D. & Wilson, R. W. The relationship between carbon monoxide abundance and visual extinction in interstellar clouds. Astrophys. J. 262, 590–605 (1982).

  39. 39.

    Aalto, S., Booth, R. S., Black, J. H. & Johansson, L. E. B. Molecular gas in starburst galaxies: line intensities and physical conditions. Astron. Astrophys. 300, 369 (1995).

  40. 40.

    van der Tak, F. F. S., Black, J. H., Schöier, F. L., Jansen, D. J. & van Dishoeck, E. F. A computer program for fast non-LTE analysis of interstellar line spectra. With diagnostic plots to interpret observed line intensity ratios. Astron. Astrophys. 468, 627–635 (2007).

  41. 41.

    Yang, C. et al. Molecular gas in the Herschel-selected strongly lensed submillimeter galaxies at z ~ 2-4 as probed by multi-J CO lines. Astron. Astrophys. 608, A144 (2017).

  42. 42.

    Simpson, J. M. et al. The SCUBA-2 Cosmology Legacy Survey: multi-wavelength properties of ALMA-identified submillimeter galaxies in UKIDSS UDS. Astrophys. J. 839, 58 (2017).

  43. 43.

    Papadopoulos, P. P. et al. Molecular gas heating mechanisms, and star formation feedback in merger/starbursts: NGC 6240 and Arp 193 as case studies. Astrophys. J. 788, 153 (2014).

  44. 44.

    Wang, S. X. et al. An ALMA survey of submillimeter galaxies in the extended Chandra deep field-south: the AGN fraction and X-ray properties of submillimeter galaxies. Astrophys. J. 778, 179 (2013).

  45. 45.

    Spilker, J. S. et al. The rest-frame submillimeter spectrum of high-redshift, dusty, star-forming galaxies. Astrophys. J. 785, 149 (2014).

  46. 46.

    Chartas, G., Eracleous, M., Agol, E. & Gallagher, S. C. Chandra observations of the Cloverleaf quasar H1413+117: a unique laboratory for microlensing studies of a LoBAL quasar. Astrophys. J. 606, 78–84 (2004).

  47. 47.

    Martín, S., Martn-Pintado, J. & Mauersberger, R. HNCO abundances in galaxies: tracing the evolutionary state of starbursts. Astrophys. J. 694, 610–617 (2009).

  48. 48.

    Greve, T. R., Papadopoulos, P. P., Gao, Y. & Radford, S. J. E. Molecular gas in extreme star-forming environments: the starbursts Arp 220 and NGC 6240 as case studies. Astrophys. J. 692, 1432–1446 (2009).

  49. 49.

    Zinchenko, I., Henkel, C. & Mao, R. Q. HNCO in massive galactic dense cores. Astron. Astrophys. 361, 1079–1094 (2000).

  50. 50.

    Li, J., Wang, J. Z., Gu, Q. S. & Zheng, X. W. Distribution of HNCO 505-404 in massive star-forming regions. Astron. Astrophys. 555, A18 (2013).

  51. 51.

    Schöier, F. L., van der Tak, F. F. S., van Dishoeck, E. F. & Black, J. H. An atomic and molecular database for analysis of submillimetre line observations. Astron. Astrophys. 432, 369 (2005).

  52. 52.

    Matteucci, F. Chemical Evolution of Galaxies (Springer, Berlin, 2012).

  53. 53.

    Romano, D., Bellazzini, M., Starkenburg, E. & Leaman, R. Chemical enrichment in very low metallicity environments: Boötes I. Mon. Not. R. Astron. Soc. 446, 4220–4231 (2015).

  54. 54.

    Tinsley, B. M. Evolution of the stars and gas in galaxies. Fundamentals Cosm. Phys. 5, 287–388 (1980).

  55. 55.

    Pagel, B. E. J. Nucleosynthesis and Chemical Evolution of Galaxies (Cambridge Univ. Press, Cambridge, 1997).

  56. 56.

    Matteucci, F. (ed.) The Chemical Evolution of the Galaxy Vol. 253 (Springer, Netherlands, 2001).

  57. 57.

    Kennicutt, R. C. Jr. The global Schmidt law in star-forming galaxies. Astrophys. J. 498, 541–552 (1998).

  58. 58.

    Schaller, G., Schaerer, D., Meynet, G. & Maeder, A. New grids of stellar models from 0.8 to 120 solar masses at Z = 0.020 and Z = 0.001. Astron. Astrophys. Suppl. 96, 269–331 (1992).

  59. 59.

    Matteucci, F. & Greggio, L. Relative roles of type I and II supernovae in the chemical enrichment of the interstellar gas. Astron. Astrophys. 154, 279–287 (1986).

  60. 60.

    Henkel, C. & Mauersberger, R. C and O nucleosynthesis in starbursts - the connection between distant mergers, the Galaxy and the solar system. Astron. Astrophys. 274, 730–742 (1993).

  61. 61.

    Davis, T. A. Systematic variation of the 12CO/13CO ratio as a function of star formation rate surface density. Mon. Not. R. Astron. Soc. 445, 2378–2384 (2014).

  62. 62.

    Henkel, C., Downes, D., Weiß, A., Riechers, D. & Walter, F. Weak 13CO in the Cloverleaf quasar: evidence for a young, early generation starburst. Astron. Astrophys. 516, A111 (2010).

  63. 63.

    Hughes, G. L. et al. The evolution of carbon, sulphur and titanium isotopes from high redshift to the local Universe. Mon. Not. R. Astron. Soc. 390, 1710–1718 (2008).

  64. 64.

    Nomoto, K., Tominaga, N., Umeda, H., Kobayashi, C. & Maeda, K. Nucleosynthesis yields of core-collapse supernovae and hypernovae, and galactic chemical evolution. Nucl. Phys. A 777, 424–458 (2006).

  65. 65.

    Cescutti, G., Matteucci, F., McWilliam, A. & Chiappini, C. The evolution of carbon and oxygen in the bulge and disk of the Milky Way. Astron. Astrophys. 505, 605–612 (2009).

  66. 66.

    Carigi, L., Peimbert, M., Esteban, C. & Garca-Rojas, J. Carbon, nitrogen, and oxygen galactic gradients: a solution to the carbon enrichment problem. Astrophys. J. 623, 213–224 (2005).

  67. 67.

    Meyer, B. S., Nittler, L. R., Nguyen, A. N. & Messenger, S. Nucleosynthesis and chemical evolution of oxygen. Rev. Mineral. Geochem. 68, 31–53 (2008).

  68. 68.

    Sage, L. J., Henkel, C. & Mauersberger, R. Extragalactic O-18/O-17 ratios and star formation—high-mass stars preferred in starburst systems? Astron. Astrophys. 249, 31–35 (1991).

  69. 69.

    Kobayashi, C., Karakas, A. I. & Umeda, H. The evolution of isotope ratios in the Milky Way Galaxy. Mon. Not. R. Astron. Soc. 414, 3231–3250 (2011).

  70. 70.

    Timmes, F. X., Woosley, S. E. & Weaver, T. A. Galactic chemical evolution: hydrogen through zinc. Astrophys. J. Suppl . Ser. 98, 617–658 (1995).

  71. 71.

    Dye, S. et al. Herschel-ATLAS: modelling the first strong gravitational lenses. Mon. Not. R. Astron. Soc. 440, 2013–2025 (2014).

  72. 72.

    Aravena, M. et al. A survey of the cold molecular gas in gravitationally lensed star-forming galaxies at z ≥ 2. Mon. Not. R. Astron. Soc. 457, 4406–4420 (2016).

  73. 73.

    Venturini, S. & Solomon, P. M. The molecular disk in the Cloverleaf quasar. Astrophys. J. 590, 740–745 (2003).

  74. 74.

    Omont, A. et al. H2O emission in high-z ultra-luminous infrared galaxies. Astron. Astrophys. 551, A115 (2013).

  75. 75.

    Weiß, A., Henkel, C., Downes, D. & Walter, F. Gas and dust in the Cloverleaf quasar at redshift 2.5. Astron. Astrophys. 409, L41–L45 (2003).

  76. 76.

    Falgarone, E. et al. Large turbulent reservoirs of cold molecular gas around high-redshift starburst galaxies. Nature 548, 430–433 (2017).

  77. 77.

    Vieira, J. D. et al. Dusty starburst galaxies in the early Universe as revealed by gravitational lensing. Nature 495, 344–347 (2013).

  78. 78.

    Ferkinhoff, C. et al. Band-9 ALMA observations of the [N II] 122 μm line and FIR continuum in two high-z galaxies. Astrophys. J. 806, 260 (2015).

  79. 79.

    Ma, J. et al. Stellar masses and star formation rates of lensed, dusty, star-forming galaxies from the SPT survey. Astrophys. J. 812, 88 (2015).

  80. 80.

    Negrello, M. et al. Herschel-ATLAS: deep HST/WFC3 imaging of strongly lensed submillimetre galaxies. Mon. Not. R. Astron. Soc. 440, 1999–2012 (2014).

Download references


Z.-Y.Z. is grateful to X. Fu, H.-Y. B. Liu, Y. Shirley and P. Barnes for discussions. Z.-Y.Z., R.J.I. and P.P.P. acknowledge support from the European Research Council in the form of the Advanced Investigator Programme, 321302, COSMICISM. F.M. acknowledges financial funds from Trieste University, FRA2016. This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG cluster of excellence “Origin and Structure of the Universe”. This work also benefited from the International Space Science Institute (ISSI) in Bern, thanks to the funding of the team “The Formation and Evolution of the Galactic Halo” (Principal Investigator D.R.) This paper makes use of the ALMA data. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (South Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.

Reviewer information

Nature thanks C. Henkel, P. Kroupa and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Author information


  1. Institute for Astronomy, University of Edinburgh, Edinburgh, UK

    • Zhi-Yu Zhang
    • , R. J. Ivison
    •  & Padelis P. Papadopoulos
  2. European Southern Observatory, Garching, Germany

    • Zhi-Yu Zhang
    •  & R. J. Ivison
  3. INAF, Astrophysics and Space Science Observatory, Bologna, Italy

    • D. Romano
  4. Department of Physics, Section of Astrophysics, Astronomy and Mechanics, Aristotle University of Thessaloniki, Thessaloniki, Greece

    • Padelis P. Papadopoulos
  5. Research Center for Astronomy, Academy of Athens, Athens, Greece

    • Padelis P. Papadopoulos
  6. Department of Physics, Section of Astronomy, University of Trieste, Trieste, Italy

    • F. Matteucci
  7. INAF, Osservatorio Astronomico di Trieste, Trieste, Italy

    • F. Matteucci
  8. INFN, Sezione di Trieste, Trieste, Italy

    • F. Matteucci


  1. Search for Zhi-Yu Zhang in:

  2. Search for D. Romano in:

  3. Search for R. J. Ivison in:

  4. Search for Padelis P. Papadopoulos in:

  5. Search for F. Matteucci in:


Z.-Y.Z. is the Principal Investigator of the ALMA observing project. Z.-Y.Z. reduced the data and wrote the initial manuscript. R.J.I. and P.P.P. provided ideas to initialize the project and helped write the manuscript. Z.-Y.Z. and P.P.P. worked on molecular line modeling of isotopologue ratios and chemical/thermal effects on the abundances. D.R. and F.M. ran the chemical evolution models and provided theoretical interpretation of the data. All authors discussed and commented on the manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to R. J. Ivison.

Extended data figures and tables

  1. Extended Data Fig. 1 Velocity-integrated flux maps (moment 0) of 13CO and C18O for SDP 17b.

    Black contours show the high-resolution 250-GHz continuum image, obtained from the ALMA archive76, with levels of 3σ, 10σ and 50σ (σ = 0.6 × 10−1 mJy beam−1). Dashed red circles show the adopted apertures for extracting spectra. a, b, Images of 13CO and C18O for the J = 3 → 2 transition. White contours show the 95-GHz continuum, with levels of 3σ, 5σ and 10σ (σ = 1.7 × 10−2 mJy beam−1). c, d, Images of 13CO and C18O for the J = 4 → 3 transition. White contours show the 133-GHz continuum, with levels of 3σ, 5σ and 10σ (σ = 2.3 × 10−2 mJy beam−1). The corresponding synthesis beams (white for 13CO and C18O, and black for the 250-GHz continuum) are plotted in the bottom left.

  2. Extended Data Fig. 2 Velocity-integrated flux maps (moment 0) of 13CO and C18O J = 5 → 4 for SPT 0103−45 and the J = 3 → 2 transition in SPT 0125−47.

    Black contours show the high-resolution 336-GHz continuum image, obtained from the ALMA archive77, with levels of 3σ, 10σ and 30σ (σ = 2.3 × 10−2 mJy beam−1). Dashed red circles show the adopted apertures for extracting spectra. a, b, Images of 13CO and C18O J = 5 → 4 for SPT 0103−45. Blue contours show the narrow 12CO J = 4 → 3 emission, with levels of 3σ, 10σ and 30σ (σ = 0.14 Jy beam−1 km s−1). White contours show the 135-GHz continuum, with levels of 3σ, 10σ and 30σ (σ = 2 × 10−2 mJy beam−1). c, d, Images of 13CO and C18O for the J = 3 → 2 transition in SPT 0125−47. White contours show the 94-GHz continuum, with levels of 3σ, 5σ and 10σ (σ = 2.2 × 10−2 mJy beam−1). The corresponding synthesis beams (white for 13CO and C18O, and black for the 336-GHz continuum) are plotted in the bottom left.

  3. Extended Data Fig. 3 Velocity-integrated flux maps (moment 0) of 13CO and C18O for the J = 3 → 2 transition in the Cloverleaf quasar.

    a, Image of the 13CO J = 3 → 2 transition. b, Image of the C18O J = 3 → 2 transition. Black contours show the high-resolution 690-GHz continuum image, obtained from the ALMA archive78, with levels of 3σ, 5σ and 10σ (σ = 0.8 mJy beam−1). Dashed red circles show the adopted apertures for extracting spectra. White contours show the 92-GHz continuum, with levels of 3σ, 5σ and 10σ (σ = 2 × 10−2 mJy beam−1). The corresponding synthesis beams (white for 13CO and C18O, and black for the 690-GHz continuum) are plotted in the bottom left.

  4. Extended Data Fig. 4 ALMA spectra of the observed 12CO, 13CO and C18O transitions.

    a, ALMA spectra of 12CO in SPT 0125−47 and SPT 0103−45. Yellow shading shows the velocity range adopted from 12CO in the analysis. b, ALMA spectra of 13CO and C18O for all targets. All spectra are in black. Red lines show Gaussian fits to the observed lines. Velocities are labelled relative to their 12CO or 13CO transitions.

  5. Extended Data Fig. 5 I(13CO)/I(C18O) and I(12CO)/I(13CO) line ratios as a function of optical depth of 13CO, under LTE conditions.

    a, I(13CO)/I(C18O) line ratio as a function of optical depth of 13CO. b, I(12CO)/I(13CO) line ratio as a function of optical depth of 13CO. Both ratios assume LTE conditions. We assume the abundance ratios of 13CO/C18O and 12CO/13CO are 7 and 70, respectively, which are representative values found in the Milky Way. This shows that the I(13CO)/I(C18O) line ratio approaches unity (blue line) only when the optical depth of C18O is greater than or equal to 1 (and the corresponding optical depth τ13CO = 7). The bottom scale bar shows the corresponding N H 2 , assuming a CO/H2 abundance78  of 8.5 × 10−5. r and R are the intrinsic abundance ratio and measured line brigntness ratio, respectively.

  6. Extended Data Fig. 6 Optical depths, I(13CO)/I(C18O) and I(12CO)/I(13CO) line ratios as a function of H2 column density, under non-LTE conditions.

    a, Optical depths of 12CO, 13CO and C18O, for the = 3 → 2 transition; b, I(13CO)/I(C18O) line ratio, and c, I(12CO)/I(13CO) line ratio as a function of H2 column density,  N H 2 , and 13CO column density in various physical conditions, for non-LTE models calculated with RADEX40. For all models, we set the abundance ratios of 12CO, 13CO and C18O to be Galactic: 12CO/13CO = 70 and 13CO/C18O = 7, which are representative values of the Milky Way disk. Different line styles show the gas conditions of H2 volume densities, n H 2  = 103 cm−3, 104 cm−3 and 105 cm−3. The Tkin value for all models is set to 30 K, which is a typical dust temperature for the submillimetre galaxy population, and the lowest Tkin that H2 gas can reach for such intensive starburst conditions, due to cosmic ray heating43. In b and c, we also overlay the line ratios (in thick green lines) with the LTE assumption for comparison. All three panels show that for Galactic abundances the line ratio of 13CO/C18O can approach unity only when the 13CO column density is higher than 1019–1020 cm−2 (that is, H2 column density N H 2  > 1025–1026 cm−2).

  7. Extended Data Fig. 7 I(HNCO)/I(C18O) line ratio and normalized I(HNCO)/I(C18O) ratio as a function of H2 volume density.

    a, I(HNCO)/I(C18O) line ratio as a function of H2 volume density. b, I(HNCO)/I(C18O) line ratio as a function of H2 volume density, normalized with I(HNCO J = 5 → 4)/I(C18J = 1 → 0). Both ratios are calculated using RADEX40, in which we assume the same abundances as measured in Arp 22047. We assume Tkin = 30 K as the representative kinetic temperature of the H2 gas.

  8. Extended Data Table 1 Target properties
  9. Extended Data Table 2 ALMA observational information
  10. Extended Data Table 3 Observed targets, lines, frequencies, linewidths and fluxes

Source Data

About this article

Publication history






Rights and permissions

To obtain permission to re-use content from this article visit RightsLink.


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.