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# Neutrino tomography of Earth

## Abstract

Cosmic-ray interactions with the atmosphere produce a flux of neutrinos in all directions with energies extending above the TeV scale1. The Earth is not a fully transparent medium for neutrinos with energies above a few TeV, as the neutrino–nucleon cross-section is large enough to make the absorption probability non-negligible2. Since absorption depends on energy and distance travelled, studying the distribution of the TeV atmospheric neutrinos passing through the Earth offers an opportunity to infer its density profile3,4,5,6,7. This has never been done, however, due to the lack of relevant data. Here we perform a neutrino-based tomography of the Earth using actual data—one-year of through-going muon atmospheric neutrino data collected by the IceCube telescope8. Using only weak interactions, in a way that is completely independent of gravitational measurements, we are able to determine the mass of the Earth and its core, its moment of inertia, and to establish that the core is denser than the mantle. Our results demonstrate the feasibility of this approach to study the Earth’s internal structure, which is complementary to traditional geophysics methods. Neutrino tomography could become more competitive as soon as more statistics is available, provided that the sources of systematic uncertainties are fully under control.

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## Data availability

The IceCube data we consider in this paper are the same sample used by the collaboration to search for resonant matter effects induced by light sterile neutrinos8. The Monte Carlo results used to simulate the detector characteristics and all data are publicly available and can be downloaded from https://icecube.wisc.edu/science/data/IC86-sterile-neutrino.

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## Acknowledgements

A.D. thanks G. Cultrera, D. Errandonea, A. Kavner, C. Piromallo and G. Soldati for useful discussions. A.D. and J.S. were supported by the Generalitat Valenciana under grant PROMETEO II/2014/050 and by the Spanish MINECO grants FPA2014-57816-P and FPA2017-85985-P. S.P.-R. is supported by the Generalitat Valenciana under grant PROMETEOII/2014/049, by the Spanish MINECO grants FPA2014-54459-P and FPA2017-84543-P, by a Ramón y Cajal contract, and also partially by the Portuguese FCT through the CFTP-FCT Unit 777 (PEst-OE/FIS/UI0777/2013). The authors also acknowledge support by the Spanish MINECO under grant SEV-2014-0398. J.S. is also supported by the Spanish MINECO grant FPA2016-76005-C2-1-P, María de Maetzu program grant MDM-2014-0367 of ICCUB and research grant 2017-SGR-929. All authors are supported by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreements No. 690575 and 674896.

## Author information

The idea was conceived by A.D. The approach of the study was discussed by all authors. J.S. performed all the numerical calculations and prepared the figures. S.P.-R. wrote the text, with inputs from A.D. Bibliography selection was performed by A.D. and S.P.-R. All authors discussed the results and commented on the manuscript.

### Competing interests

The authors declare no competing interests.

Correspondence to Sergio Palomares-Ruiz.

## Supplementary information

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• #### DOI

https://doi.org/10.1038/s41567-018-0319-1