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

## Abstract

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.

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## Acknowledgements

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

### Affiliations

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

• Zhi-Yu Zhang
• , R. J. Ivison
2. #### European Southern Observatory, Garching, Germany

• Zhi-Yu Zhang
•  & R. J. Ivison

• D. Romano

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

### Contributions

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 $${N}_{{{\rm{H}}}_{2}}$$, 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, $${N}_{{{\rm{H}}}_{2}}$$, 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, $${n}_{{{\rm{H}}}_{2}}$$ = 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 $${N}_{{{\rm{H}}}_{2}}$$ > 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.