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# A census of baryons in the Universe from localized fast radio bursts

## Abstract

More than three-quarters of the baryonic content of the Universe resides in a highly diffuse state that is difficult to detect, with only a small fraction directly observed in galaxies and galaxy clusters1,2. Censuses of the nearby Universe have used absorption line spectroscopy3,4 to observe the ‘invisible’ baryons, but these measurements rely on large and uncertain corrections and are insensitive to most of the Universe’s volume and probably most of its mass. In particular, quasar spectroscopy is sensitive either to the very small amounts of hydrogen that exist in the atomic state, or to highly ionized and enriched gas4,5,6 in denser regions near galaxies7. Other techniques to observe these invisible baryons also have limitations; Sunyaev–Zel’dovich analyses8,9 can provide evidence from gas within filamentary structures, and studies of X-ray emission are most sensitive to gas near galaxy clusters9,10. Here we report a measurement of the baryon content of the Universe using the dispersion of a sample of localized fast radio bursts; this technique determines the electron column density along each line of sight and accounts for every ionized baryon11,12,13. We augment the sample of reported arcsecond-localized14,15,16,17,18 fast radio bursts with four new localizations in host galaxies that have measured redshifts of 0.291, 0.118, 0.378 and 0.522. This completes a sample sufficiently large to account for dispersion variations along the lines of sight and in the host-galaxy environments11, and we derive a cosmic baryon density of $${\varOmega }_{{\rm{b}}}={0.051}_{-0.025}^{+0.021}{h}_{70}^{-1}$$ (95 per cent confidence; h70H0/(70 km s−1 Mpc−1) and H0 is Hubble’s constant). This independent measurement is consistent with values derived from the cosmic microwave background and from Big Bang nucleosynthesis19,20.

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## Data availability

The data sets generated during and/or analysed during this study are available at https://data-portal.hpc.swin.edu.au/dataset/observations-of-four-localised-fast-radio-bursts-and-their-host-galaxies.

## Code availability

Custom code is available at https://github.com/FRBs/FRB.

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## Acknowledgements

We thank H. Yang and L. Infante for providing IMACS imaging around FRB 190611 that informed the further follow-up observations on VLT and Gemini-S presented here. We are grateful to Australia Telescope National Facility (ATNF) operations staff and to Murchison Radio-astronomy Observatory staff for supporting our ASKAP operations, and the ATNF steering committee for allocating time for these observations. K.W.B., J.-P.M. and R.M.S. acknowledge support by Australian Research Council (ARC) grant DP180100857. A.T.D. and R.M.S. are the recipients of ARC Future Fellowships FT150100415 and FT190100155 respectively. S.O. and R.M.S. acknowledge support through ARC grant FL150100148. R.M.S. also acknowledges support through ARC grant CE170100004. N.T. acknowledges support from FONDECYT grant 11191217 and PUCV/VRIEA project 039.395/2019. The Australian Square Kilometre Array Pathfinder and Australia Telescope Compact Array are part of the Australia Telescope National Facility which is managed by CSIRO. Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. ASKAP uses the resources of the Pawsey Supercomputing Centre. Establishment of ASKAP, the Murchison Radio-astronomy Observatory and the Pawsey Supercomputing Centre are initiatives of the Australian Government, with support from the Government of Western Australia and the Science and Industry Endowment Fund. Part of this work was performed on the OzSTAR national facility at Swinburne University of Technology. OzSTAR is funded by Swinburne University of Technology and the National Collaborative Research Infrastructure Strategy (NCRIS). We acknowledge the Wajarri Yamatji as the traditional owners of the Murchison Radio-astronomy Observatory site. This work includes observations collected at the European Southern Observatory under ESO programmes 0102.A-0450(A), 0103.A-0101(A) and 0103.A-1010(B). This work includes data obtained from programme GS-2019B-Q-132 at the Gemini Observatory, acquired through the Gemini Observatory Archive and processed using the Gemini PYRAF package. Gemini Observatory is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (US), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), Ministério da Ciência, Tecnologia e Inovação (Brazil), and Korea Astronomy and Space Science Institute (Republic of Korea). PYRAF is a product of the Space Telescope Science Institute, which is operated by AURA for NASA.

## Author information

Authors

### Contributions

J.X.P., M.M. and J.P.M. framed the analysis approach and drafted the manuscript, with contributions from A.T.D., R.D.E. and R.M.S. K.W.B. developed the detection and localization pipelines, and with A.T.D. and C.P. jointly developed the correlation code and interferometry processing pipeline. D.R.S. made additional improvements to the performance of the detection pipeline. R.M.S. and S.B. detected the FRBs and performed follow-up astrometry. A.T.D. and C.K.D. derived the FRB positions from the CRAFT voltage data, and S.R., J.X.P., N.T. and L.M. obtained and reduced the optical data to derive the burst host-galaxy identifications and redshifts. M.M., J.X.B. and J.-P.M. developed the IGM model and analysis code, and S.O. adapted the code to run on the Swinburne supercomputer and collated the results. C.W.J. contributed to the maximum likelihood analysis and framed the approach to estimate parameter uncertainties.

### Corresponding authors

Correspondence to J.-P. Macquart or J. X. Prochaska.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Kiyoshi Masu, Fabrizio Nicastro and Anthony Walters 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 pulse profiles and host galaxy spectra of the four new FRBs presented here.

Top row, ASKAP data. The pulse profiles (upper subpanels, labelled A) and the radio dynamic spectra (lower subpanels, labelled B) show the detections by the ASKAP incoherent capture system (ICS) of FRB 190102 with a time resolution of 0.864 ms, and of FRBs 190608, 190611 and 190711 with a resolution of 1.728 ms. The spectral resolution is 1 MHz across the 336-MHz bandwidth. Bottom row, the SDSS (HG 190608) and VLT/FORS2 (HG 190102, HG 190611 and HG 190711) optical spectra of the host galaxies located at the respective FRB positions (see Table 1), and the spectral lines from which their redshifts are deduced.

### Extended Data Fig. 2 The shape of the distribution used to model the host-galaxy dispersion measure, DMhost.

The behaviour of the probability distribution phost(DMhost|μ, σhost) is shown for an illustrative set of parameters spanning the range of plausible values for μ and σhost.

### Extended Data Fig. 3 The expected contribution of the cosmic baryons to the dispersion measure.

The probability distribution of DMcosmic due to the cosmic baryons, p(DM), in semi-analytic models and simulations, as encoded in black, blue, red and green in order of increasing redshift (z; see key), is compared to the analytic form used in our analysis (DM; equation (4)). The thinner solid curves show semi-analytic models11 in which the minimum halo mass that can resist feedback and retain its gas is given by Mmin. The dashed curves are the best-fit analytic function, and the dot-dashed curves assume the σDM = Fz−1/2 scaling from the z = 0.5 best-fit for which F = 0.32, 0.15 and 0.09 for the top, middle and bottom panels, respectively. Because of the success of this Euclidean-space scaling, we adopt it in our analysis. The thicker green solid curve in the bottom panel is calculated from a hydrodynamic simulation63.

### Extended Data Fig. 4 The density of cosmic baryons derived from the extended FRB sample.

The constraints on the IGM parameters Ωbh70 and F, and on the host-galaxy parameters μ and σhost, for a log-normal host-galaxy DM distribution are shown in an identical manner to Fig. 3, but derived using the seven-burst sample (that is, including the five gold-standard bursts as well as FRBs 190523 and 190611).

### Extended Data Fig. 5 Constraints on the cosmic baryon density and FRB host-galaxy parameters derived using a Bayesian approach.

The results of a Markov Chain Monte Carlo (MCMC) analysis based on our five-FRB gold-standard sample presented in the main text demonstrate broad agreement with the results of the frequentist analysis presented in Fig. 3. The outermost vertical lines on the histogram denote the confidence region corresponding to that parameter, with the central line indicating the mean value.

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Macquart, JP., Prochaska, J.X., McQuinn, M. et al. A census of baryons in the Universe from localized fast radio bursts. Nature 581, 391–395 (2020). https://doi.org/10.1038/s41586-020-2300-2

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