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# The diffuse γ-ray background is dominated by star-forming galaxies

## Abstract

The Fermi Gamma-ray Space Telescope has revealed a diffuse γ-ray background at energies from 0.1 gigaelectronvolt to 1 teraelectronvolt, which can be separated into emission from our Galaxy and an isotropic, extragalactic component1. Previous efforts to understand the latter have been hampered by the lack of physical models capable of predicting the γ-ray emission produced by the many candidate sources, primarily active galactic nuclei2,3,4,5 and star-forming galaxies6,7,8,9,10, leaving their contributions poorly constrained. Here we present a calculation of the contribution of star-forming galaxies to the γ-ray background that does not rely on empirical scalings and is instead based on a physical model for the γ-ray emission produced when cosmic rays accelerated in supernova remnants interact with the interstellar medium11. After validating the model against local observations, we apply it to the observed cosmological star-forming galaxy population and recover an excellent match to both the total intensity and the spectral slope of the γ-ray background, demonstrating that star-forming galaxies alone can explain the full diffuse, isotropic γ-ray background.

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## Data availability

The data that were used to produce the figures and that support the findings of this study are available in Zenodo with the identifier https://doi.org/10.5281/zenodo.4764111. Source data are provided with this paper.

## Code availability

The code used to derive the key findings of this study is available in Zenodo with the identifier https://doi.org/10.5281/zenodo.4609628.

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## Acknowledgements

This research has made use of the NASA/IPAC Infrared Science Archive, which is funded by the National Aeronautics and Space Administration and operated by the California Institute of Technology. Funding for this work was provided by the Australian Government through the Australian Research Council, awards FT180100375 (M.R.K.) and DP190101258 (R.M.C. and M.R.K.), and the Australian National University through a research scholarship (M.A.R.). R.M.C. thanks O. Macias and S. Ando for conversations while a Kavli IPMU-funded guest of the GRAPPA Institute at the University of Amsterdam.

## Author information

Authors

### Contributions

All authors were involved in the design of the study and the interpretation of the results. M.A.R. performed the modelling and data analysis with input from M.R.K., R.M.C. and S.C. The manuscript was written by M.A.R., M.R.K. and R.M.C., and reviewed by all authors.

### Corresponding author

Correspondence to Matt A. Roth.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Paula Kornecki and the other, anonymous, reviewer(s) 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 effect of varying model parameters.

The plots presented here show the result of our calculations when varying the model parameters as discussed in the Supplementary Information. Our fiducial choice is plotted as a solid blue line, with the dashed and dash-dotted lines showing the spectrum for the upper and lower limits respectively of the varied parameter. The black points correspond to the Fermi data as in Fig. 4. Plot a shows MA plotted for reasonable values of 1.6 and 2.3, and extremal values of 1.1 and 3.0; b the ionization fraction χ for values of 10−2 and 10−6; c the injection index q for values 2.1 and 2.3; and finally d the conversion fraction of supernova energy to CR electrons for values of 1% and 3%, which is equivalent to 10% and 30% of the total energy injected in all cosmic ray species. Note that varying the total CR energy budget results in a trivial scaling of the result by the same fraction, and thus is not shown

### Extended Data Fig. 2 The contribution of SFGs in the $$\dot{{{\boldsymbol{M}}}_{\ast }}$$ - z plane.

The contribution of SFGs to the total γ-ray spectrum at selected energies in the star-formation rate $$(\dot{{M}_{\ast }})$$, redshift (z) plane. Coloured pixels show the fractional contribution (as indicated in the colourbar) from galaxies in each bin of $$\dot{{M}_{\ast }}$$ and z to the diffuse isotropic γ-ray background at the indicated energy; a fractional contribution of unity corresponds to that pixel producing all of the background, with no contribution from galaxies outside the pixel. Grey points show individual CANDELS galaxies in regions of $$\dot{{M}_{\ast }}$$ and z that contribute <10−3 of the total. Flanking histograms show the fractional contribution binned in one dimension – $$\dot{{M}_{\ast }}$$ (right) and z (top). We see that the background at lower energies is dominated by emission from galaxies on the high side of the star forming main sequence at z ~ 1−2, while at high energies it is dominated by the brightest systems at low redshift.

### Extended Data Fig. 3 The diffuse isotropic γ-ray and neutrino backgrounds.

The blue line and black points show the model-predicted and observed γ-ray background, and are identical to those shown in Fig. 4. The red lines show our model prediction for the neutrino background (single flavour) with Ecut = 100 PeV (solid line) and Ecut = 1 PeV (dashed line), computed as described in the Supplementary Information. We assume a neutrino flavour ratio at the detector of (νe:νμ:ντ) = (1:1:1). The red filled band shows a power-law fit73 to the single flavour astrophysical neutrino background with the 90% likelihood limit, as measured by IceCube, which is also shown as grey points, where the horizontal bars show the energy bin and the vertical bars the 1 σ uncertainty limit

### Extended Data Fig. 4 Cosmic ray calorimetry in the E - Σg plane.

Mean calorimetry fraction fcal(E) in the surface gas density Σg, cosmic ray energy E plane, binned in redshift intervals. This figure is constructed by deriving the gas surface density and energy dependent calorimetry fraction for each galaxy in the CANDELS sample using our model. The colour of each pixel gives the mean calorimetry fraction of all the galaxies within that particular range of Σg, E, and redshift. The horizontal white stripes correspond to ranges of Σg into which no CANDELS galaxies fall for the corresponding redshift range. Several physical processes contribute to the behaviour visible in the plot. At low Σg, galaxies have low fcal at all energies E because there are few targets for hadronic collisions with CRs. As Σg increases, the increased ISM density results in efficient calorimetry and conversion of CR energy into γ-rays for low CR energies; however, at higher energies the CR number density is low, yielding a high CR streaming velocity and rapid escape, resulting in low fcal. As Σg increases further, the increasing density results in the streaming instability being suppressed efficiently by ion-neutral damping towards lower energies, reducing the calorimetry fraction further. Finally, at the highest Σg, the streaming instability is suppressed completely by ion-neutral damping, but streaming is still limited to the speed of light. Consequently, increasing Σg further only results in increased collisions, and thus a higher calorimetry fraction.

### Extended Data Fig. 5 Cosmic ray calorimetry in the z - Σg plane.

Mean calorimetry fraction in the surface gas density (Σg), redshift (z) plane at CR energies E = 1 GeV, 10 GeV, 1 TeV and 10 TeV. To construct this figure, for each CANDELS sample galaxy, we apply our model to compute Σg and fcal(E) at the indicated energies. The colour indicates the average fcal(E) value computed over bins of (z, Σg), while contours indicate the density of the CANDELS sample in this plane. Note that the non-monotonic behaviour of fcal(E) with Σg that is most prominently visible in the 1 TeV panel is expected, for the reasons explained in the caption of Extended Data Fig. 4.

### Extended Data Fig. 6 Contributions to the diffuse isotropic γ-ray background.

The blue line and black points show the model-predicted and observed γ-ray background, and are identical to those shown in Fig. 4. The green line shows the contribution from π0 decay, the olive lines the contribution from bremsstrahlung emission, and the cyan lines the contribution from the inverse Compton emission. In both cases, dashed lines show the spectrum produced by primary CR electrons and the dash-dotted lines the spectrum from secondary electrons and positrons. The red line shows the contributions from the EBL cascade

## Supplementary information

### Supplementary Information

This file contains the following supplementary sections: Confidence intervals for source count distributions; Sensitivity of the result to model parameters; Comparison to earlier work; Neutrinos. Supplementary equations 1 – 10 are included within these sections.

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Roth, M.A., Krumholz, M.R., Crocker, R.M. et al. The diffuse γ-ray background is dominated by star-forming galaxies. Nature 597, 341–344 (2021). https://doi.org/10.1038/s41586-021-03802-x

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• DOI: https://doi.org/10.1038/s41586-021-03802-x