# A cold, massive, rotating disk galaxy 1.5 billion years after the Big Bang

## Abstract

Massive disk galaxies like the Milky Way are expected to form at late times in traditional models of galaxy formation1,2, but recent numerical simulations suggest that such galaxies could form as early as a billion years after the Big Bang through the accretion of cold material and mergers3,4. Observationally, it has been difficult to identify disk galaxies in emission at high redshift5,6 in order to discern between competing models of galaxy formation. Here we report imaging, with a resolution of about 1.3 kiloparsecs, of the 158-micrometre emission line from singly ionized carbon, the far-infrared dust continuum and the near-ultraviolet continuum emission from a galaxy at a redshift of 4.2603, identified by detecting its absorption of quasar light. These observations show that the emission arises from gas inside a cold, dusty, rotating disk with a rotational velocity of about 272 kilometres per second. The detection of emission from carbon monoxide in the galaxy yields a molecular mass that is consistent with the estimate from the ionized carbon emission of about 72 billion solar masses. The existence of such a massive, rotationally supported, cold disk galaxy when the Universe was only 1.5 billion years old favours formation through either cold-mode accretion or mergers, although its large rotational velocity and large content of cold gas remain challenging to reproduce with most numerical simulations7,8.

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## Data availability

The data reported in this paper are available though the ALMA archive:(http://almascience.eso.org/aq/) with project code 2017.1.01052.S, the JVLA archive:(https://science.nrao.edu/facilities/vla/archive/index) with project code 17A-279, and the HST/Mikulski Archive for Space Telescopes: (https://archive.stsci.edu/hst/) with project code 15410.

## Code availability

All of the code used to generate the kinematic modelling is available online at (https://github.com/mneeleman/qubefit).

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## Acknowledgements

This work would not have been possible without the insights of the late A. M. Wolfe. M.N. thanks F. Walter for discussions, and S. Simha for extracting effective radii from the HST and ALMA imaging. ALMA is a partnership of the European Southern Observatory (ESO; representing its member states), the National Science Foundation (NSF; United States) and the National Institutes of Natural Sciences (Japan), together with the National Research Council (Canada), the National Science Council and the Academia Sinica Institute of Astronomy and Astrophysics (Taiwan), and the Korean Astronomy and Space Science Institute (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, Associated Universities Incorporated (AUI) National Radio Astronomy Observatory (NRAO) and the National Astronomical Observatory of Japan. NRAO is a facility of the NSF operated under cooperative agreement by AUI. M.N. acknowledges support from the European Research Council advanced grant 740246 (Cosmic_Gas). N.K. acknowledges support from the Department of Science and Technology via a Swarnajayanti Fellowship (DST/SJF/PSA-01/2012-13), and from the Department of Atomic Energy under project 12-R&D-TFR-5.02-0700. Support for programme no. 15410 was provided by the National Aeronautics and Space Administration (NASA) through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy Incorporated, under NASA contract NAS 5-26555.

## Author information

Authors

### Contributions

M.N. is the PI of the observing programmes. M.N. and N.K. contributed to the analysis of the ALMA and JVLA data. M.R. reduced and analysed the HST data. All authors contributed to analysis of the data and writing and editing of the manuscript.

### Corresponding author

Correspondence to Marcel Neeleman.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Robert Grand and Alfred Tiley 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 Spectrum of the [C ii] line from DLA0817g.

The velocity is relative to the systemic velocity of the [C ii] line. The velocity range used to estimate the velocity-integrated [C ii] flux density and the integrated [C ii] contours is marked by the solid black bar. The 1σ (standard deviation) uncertainty of the measurements is indicated by the dotted red lines, and has been estimated by bootstrapping flux density measurements at random positions within each channel chosen to be devoid of any line emission. A double Gaussian model fit to the data is shown in green. Both the peak flux density of 16.8 ± 1.3 mJy and the velocity-integrated [C ii] line flux density of 5.8 ± 0.4 Jy km s−1 are consistent with values obtained from the lower-resolution data, indicating that no emission is resolved out by the higher-resolution observations.

### Extended Data Fig. 2 Channel maps of the [C ii] emission line from DLA0817g.

The plus symbol indicates the central position of the [C ii] emission derived from the kinematic analysis. This agrees within the uncertainties with the position derived from fitting a 2D-Gaussian profile to both the velocity-integrated [C ii] emission and the far-infrared continuum emission, using the imfit routine in CASA (Extended Data Table 1). The outer black contour is 3σ, where σ = 0.35 mJy per beam, with subsequent contours increasing in powers of $$\sqrt{2}$$. Velocities are relative to the kinematically derived [C ii] redshift, z = 4.2603. The synthesized beam is shown in the bottom left corner of the bottom left panel.

### Extended Data Fig. 3 Channel maps of the residuals, after subtracting the model from the data, of the [C ii] emission from DLA0817g.

The colour scaling, contour levels and annotations are the same as Extended Data Fig. 2. Little excess emission (at >3σ significance) is seen in the individual 25 km s−1 channels, indicating that the exponential thin disk model is a good approximation for the bulk of the [C ii] emission. Only two features are seen in the channel maps with >3σ emission in two or more consecutive channels: 2.8 kpc south of the centre at 88 km s−1 and 113 km s−1, and 3 kpc east of the centre at 113 km s−1, 138 km s−1 and 163 km s−1. This emission arises from clumps that are not rotating with the bulk of the gas, possibly arising in outflows or satellite galaxies.

### Extended Data Fig. 4 Position–velocity diagram for DLA0817g.

a, The pv diagram along the major axis of DLA0817g. b, The pv diagram along the minor axis. The contours in both panels are the pv diagrams derived from the rotating disk model with constant velocity. The outer contour is 2σ where σ = 0.35 mJy per beam, and the contours increase in powers of $$\sqrt{2}$$. Distances are given with respect to the kinematic centre of the emission (Fig. 1).

### Extended Data Fig. 5 Velocity dispersion profile for DLA0817g.

The observed velocity dispersion profile is measured from the standard deviation of a Gaussian fit to each pixel, and is shown by the data points where the data have been binned into bins equal to the size of the horizontal error bars. The vertical error bars reflect the 16 to 84 percentile spread in measurements per bin. The radius has been de-projected for the inclination of DLA0817g. The dashed line is the value derived from the kinematic modelling. The solid coloured region is the 16 to 84 percentile spread in the constant velocity dispersion model, showing that the increase in velocity dispersion at the galactic centre is due to beam-smearing.

### Extended Data Fig. 6 Light profile for dust continuum, [C ii] line and UV emission.

The light profiles are scaled by the emission at the kinematic centre. Distances from the kinematic centre are de-projected, taking into account the inclination of the disk. Both the dust continuum and the [C ii] emission are convolved with a Gaussian kernel to the slightly worse resolution of the UV observations. This increases the width of the surface density profile by about 10%. Vertical error bars give the 16 to 84 percentile range in the measurements within the bins defined by the horizontal error bars. The [C ii] surface density profile, the dust continuum profile and the UV surface density profile—within the uncertainties—are consistent with each other. This can also be seen by the effective radii (marked by solid vertical lines), whose 1σ uncertainties (marked by the vertical coloured regions) overlap at a value of approximately 3 kpc.

### Extended Data Fig. 7 The Toomre-Q parameter for DLA0817g.

a, The spatial distribution of the Toomre-Q parameter, assuming that the gas density is traced by the [C ii] emission. This spatial distribution is still convolved with the ALMA synthesized beam. Over the entire disk, Q is roughly constant and below 1, indicating that the disk is unstable against axisymmetric perturbations. The white cross shows the kinematic centre of the emission, and the inset shows the ALMA beam for the [C ii] emission. b, The radial profile of the Toomre-Q parameter. The solid dark line shows Q, assuming that the gas density falls off exponentially, at the same rate as the [C ii] emission. The coloured squares are the observed data, as in a, corrected for the projected radius. This panel shows that the observed data underestimate Q at large radii owing to beam smearing, which increases the emission, and thus the gas surface density.

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Neeleman, M., Prochaska, J.X., Kanekar, N. et al. A cold, massive, rotating disk galaxy 1.5 billion years after the Big Bang. Nature 581, 269–272 (2020). https://doi.org/10.1038/s41586-020-2276-y