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i 21-centimetre emission from an ensemble of galaxies at an average redshift of one

An Author Correction to this article was published on 11 July 2022

This article has been updated


Baryonic processes in galaxy evolution include the infall of gas onto galaxies to form neutral atomic hydrogen, which is then converted to the molecular state (H2), and, finally, the conversion of H2 to stars. Understanding galaxy evolution thus requires an understanding of the evolution of stars and of neutral atomic and molecular hydrogen. For the stars, the cosmic star-formation rate density is known to peak at redshifts from 1 to 3, and to decline by an order of magnitude over approximately the subsequent 10 billion years1; the causes of this decline are not known. For the gas, the weakness of the hyperfine transition of H i at 21-centimetre wavelength—the main tracer of the H i content of galaxies—means that it has not hitherto been possible to measure the atomic gas mass of galaxies at redshifts higher than about 0.4; this is a critical gap in our understanding of galaxy evolution. Here we report a measurement of the average H i mass of star-forming galaxies at a redshift of about one, obtained by stacking2 their individual H i 21-centimetre emission signals. We obtain an average H i mass similar to the average stellar mass of the sample. We also estimate the average star-formation rate of the same galaxies from the 1.4-gigahertz radio continuum, and find that the H i mass can fuel the observed star-formation rates for only 1 to 2 billion years in the absence of fresh gas infall. This suggests that gas accretion onto galaxies at redshifts of less than one may have been insufficient to sustain high star-formation rates in star-forming galaxies. This is likely to be the cause of the decline in the cosmic star-formation rate density at redshifts below one.

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Fig. 1: The final stacked H i 21-cm emission image.
Fig. 2: The final stacked H i 21-cm spectrum.
Fig. 3: Redshift and temporal evolution of the cosmic H i mass density in galaxies, ΩHi.

Data availability

The raw data reported in this paper are available through the GMRT archive ( with project code 35_087. The analysed data files are large and are available from the corresponding author on reasonable request. The data displayed in Fig. 1 are publicly available at as a FITS file. Source data are provided with this paper.

Code availability

The custom code used to calibrate the GMRT data is publicly available at

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We thank the staff of the GMRT who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. N.K. acknowledges support from the Department of Science and Technology via a Swarnajayanti Fellowship (DST/SJF/PSA-01/2012-13). A.C., N.K. and J.N.C. also acknowledge support from the Department of Atomic Energy, under project 12-R&D-TFR-5.02-0700.

Author information

Authors and Affiliations



N.K. and A.C. wrote the GMRT proposal. A.C. carried out the analysis of the GMRT data, with N.K. and J.N.C. contributing to the data analysis. A.C., N.K. and J.N.C. contributed to the interpretation of the results. A.C. and N.K. wrote the manuscript. J.N.C., S.S. and K.S.D. contributed to the writing and the editing of the proposal and the manuscript.

Corresponding author

Correspondence to Nissim Kanekar.

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Competing interests

The authors declare no competing interests.

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Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work.

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

Extended data figures and tables

Extended Data Fig. 1 The fraction of data excised across the observing band.

This includes all data lost due to time-variable effects, including RFI, malfunctioning antennas and power failures. The plotted fraction of lost data was obtained by averaging over the approximately 67 h of on-source time on the five DEEP2 sub-fields.

Extended Data Fig. 2 Distribution of the spectral r.m.s. noise for the 7,653 target galaxies.

Shown is the r.m.s. noise per 30 km s−1 channel on the H i 21-cm spectra of the 7,653 galaxies of the final sample. Left panel, results for the galaxies in fields 31–33 and 42, each of which have about 900 min of on-source time. Right panel, results for field 41, where the on-source time was about 450 min. The red curve in each panel shows the predicted r.m.s. noise for the uGMRT array, after accounting for (1) the on-source time, (2) the fraction of data lost due to RFI and other effects, and (3) the smoothing of the H i 21-cm cubes to the same spatial resolution at all redshifts, that is, to coarser angular resolutions at higher frequencies.

Extended Data Fig. 3 Dependence of the stacked r.m.s. noise on the number of galaxies, N.

The figure shows the r.m.s. noise (in units of H i mass sensitivity) on the stacked H i 21-cm spectrum as a function of the number of galaxies whose H i 21-cm spectra have been stacked together, assuming a velocity width of 270 km s−1. Each red dot shows the r.m.s. noise from the spectrum of N galaxies (with N = 100, 200, 400, 800, 1,600, 3,200 and 6,400), randomly drawn from the full sample of 7,653 galaxies. The magenta star shows the r.m.s. noise on the final stacked spectrum of 7,653 galaxies. The dashed blue line indicates the relation r.m.s. noise N−0.5 (normalized to pass through the point with N = 100), as expected if the 7,653 H i 21-cm spectra contain no correlations. The relation r.m.s. noise N−0.5 is an excellent match to the data points, implying that the H i 21-cm spectra show no evidence for the presence of systematic correlated non-Gaussian effects.

Extended Data Fig. 4 The stacked 1.4-GHz continuum emission from our galaxies and offset positions.

a, b, The average rest-frame 1.4-GHz luminosity density of the 7,653 main-sequence DEEP2 galaxies, obtained by median-stacking the 1.4-GHz radio continuum emission at the location of each individual galaxy (a), and at a location 100″ offset from each galaxy (b). Dec., declination; RA, right ascension. A clear (29σ significance) detection is visible at the location of the DEEP2 galaxies, while the stack at offset positions shows no evidence for either emission or any systematic patterns. The circle in the bottom left corner of each panel represents the final 5.5″ beam of the continuum images, after convolution. The patterns visible in a around the central bright source arise from the effective point spread function of the stacked image.

Extended Data Fig. 5 The relation between H i mass and absolute blue magnitude.

The figure shows the relation between average H i mass and absolute B-band magnitude for galaxies with MB ≤ −20 at z = 1.06. The red points show the average H i mass, obtained by stacking the H i 21-cm emission, of blue galaxies in two MB bins (separated at the median, MB = −21.042) at z = 1.06. The solid blue curve shows the relation between MHi and MB in the local Universe40. Our measurements at z = 1.06 are consistent with the MBMHi relationship at z ≈ 0.

Extended Data Table 1 Summary of the uGMRT observations

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Chowdhury, A., Kanekar, N., Chengalur, J.N. et al.i 21-centimetre emission from an ensemble of galaxies at an average redshift of one. Nature 586, 369–372 (2020).

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