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.
Subscribe to Journal
Get full journal access for 1 year
only $14.08 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
Gaisser, T. K. & Honda, M. Flux of atmospheric neutrinos. Ann. Rev. Nucl. Part. Sci. 52, 153–199 (2002).
Gandhi, R., Quigg, C., Reno, M. H. & Sarcevic, I. Ultrahigh-energy neutrino interactions. Astropart. Phys. 5, 81–110 (1996).
González-García, M. C., Halzen, F., Maltoni, M. & Tanaka, H. K. M. Radiography of Earth’s core and mantle with atmospheric neutrinos. Phys. Rev. Lett. 100, 061802 (2008).
Borriello, E. et al. Sensitivity on Earth core and mantle densities using atmospheric neutrinos. J. Cosmol. Astropart. Phys. 0906, 030 (2009).
Borriello, E. et al. Studies on neutrino Earth radiography. Earth Planets Space 62, 211–214 (2010).
Takeuchi, N. Simulation of heterogeneity sections obtained by neutrino radiography. Earth Planets Space 62, 215–221 (2010).
Romero, I. & Sampayo, O. A. About the Earth density and the neutrino interaction. Eur. Phys. J. C 71, 1696 (2011).
Aartsen, M. G. et al. Searches for sterile neutrinos with the IceCube detector. Phys. Rev. Lett. 117, 071801 (2016).
Bolt, B. A. The precision of density estimation deep in the Earth. Q. J. R. Astron. Soc. 32, 367–388 (1991).
Kennett, B. L. N. On the density distribution within the Earth. Geophys. J. Int. 132, 374–382 (1998).
Masters, G. & Gubbins, D. On the resolution of density within the Earth. Phys. Earth Planet. Inter. 140, 159–167 (2003).
de Wit, R., Käufl, P., Valentine, A. & Trampert, J. Bayesian inversion of free oscillations for Earth’s radial (an)elastic structure. Phys. Earth Planet. Inter. 237, 1–17 (2014).
Williamson, E. & Adams, L. H. Density distribution in the Earth. J. Wash. Acad. Sci. 13, 413–428 (1923).
The USGS Earthquake Hazards Program (US Geological Survey, 2017); https://earthquake.usgs.gov/earthquakes/
Bellini, G. et al. Observation of geo-neutrinos. Phys. Lett. B 687, 299–304 (2010).
Gando, A. et al. Partial radiogenic heat model for Earth revealed by geoneutrino measurements. Nat. Geosci. 4, 647–651 (2011).
Winter, W. Neutrino tomography: Learning about the Earth’s interior using the propagation of neutrinos. Earth Moon Planets 99, 285–307 (2006).
Placci, A. & Zavattini, E. On the Possibility of Using High-Energy Neutrinos to Study the Earth’s Interior CERN Report (CERN, 1973); https://cds.cern.ch/record/2258764
Volkova, L. V. & Zatsepin, G. T. On the problem of neutrino penetration though the Earth. Izv. Akad. Nauk SSSR Ser. Fiz. 38, 1060–1063 (1974).
Hoshina, K. & Tanaka, H. K. M. Neutrino radiography with IceCube neutrino observatory. Poster at the XXV International Conference on Neutrino Physics and Astrophysics, 3–9 June 2012, Kyoto (Japan) (2012).
Dziewonski, A. M. & Anderson, D. L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981).
Luzum, B. et al. The IAU 2009 system of astronomical constants: the report of the IAU working group on numerical standards for fundamental astronomy. Celest. Mech. Dyn. Astron. 110, 293–304 (2011).
USAO, USNO, HMNAO and UKHO The Astronomical Almanac (US Navy, 2017); http://asa.usno.navy.mil/
Chen, W., Li, C. L., Ray, J., Shen, W. B. & Huang, C. L. Consistent estimates of the dynamic figure parameters of the Earth. J. Geod. 89, 179–188 (2015).
Adrián-Martínez, S. et al. Letter of intent for KM3NeT 2.0. J. Phys. G 43, 084001 (2016).
Gaisser, T. K., Stanev, T. & Tilav, S. Cosmic ray energy spectrum from measurements of air showers. Front. Phys. 8, 748–758 (2013).
Ostapchenko, S. Monte Carlo treatment of hadronic interactions in enhanced Pomeron scheme: I. QGSJET-II model. Phys. Rev. D 83, 014018 (2011).
Zatsepin, V. I. & Sokolskaya, N. V. Three component model of cosmic ray spectra from 100-GeV up to 100-PeV. Astron. Astrophys. 458, 1–5 (2006).
Riehn, F., Engel, R., Fedynitch, A., Gaisser, T. K. & Stanev, T. A new version of the event generator Sibyll. PoS ICRC2015, 558 (2016).
Barr, G. D., Gaisser, T. K., Robbins, S. & Stanev, T. Uncertainties in atmospheric neutrino fluxes. Phys. Rev. D 74, 094009 (2006).
Fedynitch, A., Becker Tjus, J. & Desiati, P. Influence of hadronic interaction models and the cosmic ray spectrum on the high energy atmospheric muon and neutrino flux. Phys. Rev. D 86, 114024 (2012).
Aartsen, M. G. et al. Measurement of the multi-TeV neutrino cross section with IceCube using Earth absorption. Nature 551, 596–600 (2017).
Cooper-Sarkar, A., Mertsch, P. & Sarkar, S. The high energy neutrino cross-section in the Standard Model and its uncertainty. J. High Ener. Phys. 08, 042 (2011).
Aaron, F. D. et al. Combined measurement and QCD analysis of the inclusive e + − p scattering cross sections at HERA. J. High Energy Phys. 01, 109 (2010).
Bustamante, M. & Connolly, A. Measurement of the energy-dependent neutrino-nucleon cross section above 10 TeV using IceCube showers. Preprint at https://arxiv.org/abs/1711.11043 (2017).
Argüelles Delgado, C. A., Salvado, J. & Weaver, C. N. A simple quantum integro-differential solver (SQuIDS). Comput. Phys. Commun. 196, 569–591 (2015).
González-García, M. C., Halzen, F. & Maltoni, M. Physics reach of high-energy and high-statistics IceCube atmospheric neutrino data. Phys. Rev. D 71, 093010 (2005).
Berezinsky, V. S., Gazizov, A. Z., Zatsepin, G. T. & Rozental, I. L. On penetration of high-energy neutrinos through Earth and a possibility of their detection by means of EAS. Sov. J. Nucl. Phys. 43, 406 (1986). [Yad. Fiz. 43, 637 (1986)].
Halzen, F. & Saltzberg, D. Tau-neutrino appearance with a 1000 megaparsec baseline. Phys. Rev. Lett. 81, 4305–4308 (1998).
Beacom, J. F., Crotty, P. & Kolb, E. W. Enhanced signal of astrophysical tau neutrinos propagating through Earth. Phys. Rev. D 66, 021302 (2002).
Dembinski, H. P. et al. Data-driven model of the cosmic-ray flux and mass composition from 10 GeV to 1011 GeV. PoS ICRC2017, 533 (2017).
Riehn, F. et al. The hadronic interaction model SIBYLL 2.3c and Feynman scaling. PoS ICRC2017, 301 (2017).
Ostapchenko, S. LHC results and hadronic interaction models. Preprint at https://arXiv.org/abs/1612.09461 (2016).
Aab, A. et al. Testing hadronic interactions at ultrahigh energies with air showers measured by the Pierre Auger Observatory. Phys. Rev. Lett. 117, 192001 (2016).
Dedenko, L. G., Lukyashin, A. V., Roganova, T. M. & Fedorova, G. F. Testing of the VENUS 4.12, DPMJET 2.55, QGSJET II-03 and SIBYLL 2.3 hadronic interaction models via help of the atmospheric vertical muon spectra. EPJ Web Conf. 158, 06006 (2017).
Dedenko, L. G., Lukyashin, A. V., Roganova, T. M. & Fedorova, G. F. Testing of the EPOS LHC, QGSJET01, QGSJETII-03 and QGSJETII-04 hadronic interaction models via help of the atmospheric vertical muon spectra. J. Phys. Conf. Ser. 934, 012017 (2017).
Pierog, T. Review of model predictions for extensive air showers. JPS Conf. Proc. 19, 011018 (2018).
Feroz, F. & Hobson, M. P. Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis. Mon. Not. R. Astron. Soc. 384, 449–463 (2008).
Feroz, F., Hobson, M. P. & Bridges, M. MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).
Feroz, F., Hobson, M. P., Cameron, E. & Pettitt, A. N. Importance nested sampling and the MultiNest algorithm. Preprint at https://arXiv.org/abs/1306.2144 (2013).
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.
The authors declare no competing interests.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Donini, A., Palomares-Ruiz, S. & Salvado, J. Neutrino tomography of Earth. Nature Phys 15, 37–40 (2019). https://doi.org/10.1038/s41567-018-0319-1
Physical Review D (2020)
JULOC: A local 3-D high-resolution crustal model in South China for forecasting geoneutrino measurements at JUNO
Physics of the Earth and Planetary Interiors (2020)
Physical Review C (2020)
Physical Review D (2020)
Nature Physics (2019)