High-Energy Neutrino Tomography of the Earth's Interior with IceCube

Technical Summary: High-Energy Neutrino Tomography of the Earth's Interior with IceCube

Problem and Motivation
The internal structure of the Earth, specifically its radial density distribution, is fundamental to understanding geological evolution, the geodynamo, and planetary formation. Historically, these properties have been inferred primarily through seismology (analyzing seismic wave propagation) and gravimetry, which probe the macroscopic response of matter to elastic and gravitational forces. While the Preliminary Reference Earth Model (PREM) provides a robust standard based on these methods, it relies on indirect inferences. A distinct physical approach involves probing the Earth's density using the weak interaction. High-energy neutrinos, which interact only via the weak force, traverse the Earth but experience attenuation dependent on the column density of matter they encounter. As neutrino energy increases, the interaction cross-section rises, making the Earth partially opaque to neutrinos above $\sim$10 TeV. This attenuation is sensitive to the density profile along the neutrino's trajectory, offering a novel, independent probe of planetary interiors.

Methodology
This study utilizes 10.7 years of data (2011–2022) from the IceCube Neutrino Observatory at the South Pole. The analysis focuses on 368,071 upgoing muon-neutrino events in the energy range of 500 GeV to 100 TeV. These events include both atmospheric neutrinos (produced by cosmic-ray interactions in the atmosphere) and a subdominant diffuse astrophysical flux.

The methodology proceeds as follows:

1. Event Selection: The dataset comprises "starting" and "throughgoing" muon tracks. Starting tracks (interactions within the instrumented volume) provide superior energy reconstruction, while throughgoing tracks (interactions outside the detector) offer high statistics.
2. Modeling: The Earth's density profile is parametrized as a set of concentric, uniform-density shells. The study primarily employs a five-shell configuration (inner core, outer core, and mantle/crust layers) and validates results with an eight-shell extension.
3. Simulation and Likelihood: Monte Carlo simulations model the IceCube detector's acceptance, systematic uncertainties (including glacial ice properties), and the expected neutrino flux. The analysis accounts for the Standard Model neutrino-nucleon cross-section, which is well-constrained by parton distribution functions (PDFs) and deep inelastic scattering data.
4. Inference: A joint fit is performed using a binned Poisson likelihood to constrain the densities of the shells, flux normalization, cross-section uncertainties, and detector nuisance parameters. The posterior distributions are sampled using a Markov Chain Monte Carlo (MCMC) algorithm.
5. Blind Analysis: To prevent bias, the analysis was conducted in two stages: a blind fit excluding near-horizontal events ($-1.0 < \cos\theta < -0.1$), where column depths are smallest and systematic mismodeling is most likely, followed by a fit using all available data ($-1.0 < \cos\theta < 0.0$).

Key Results
The analysis yields the following primary results:

• Density Profile: The inferred radial density profile, derived from the five-shell model, is consistent with the PREM model within the 68% highest-posterior-density (HPD) credible intervals. The results show no significant deviation from the PREM profile, validating the weak-interaction probe.
  • Shell 1 (Inner Core): Mode at 0.60–0.73 times the PREM density.
  • Shell 2 & 3 (Outer Core): Modes range from 0.72 to 1.1 times the PREM density.
  • Shell 4 & 5 (Mantle/Crust): Modes range from 1.3 to 1.6 times the PREM density.
  • The inclusion of near-horizontal events slightly shifts the posterior mode of the outermost shell (Shell 5) closer to unity, suggesting these events contribute constructively to the constraints.
• Derived Global Quantities:
  • Earth Mass: The posterior mode for the Earth's mass is $M = 7.25 \times 10^{24}$ kg, with a 68% HPD interval of $[6.31, 8.31] \times 10^{24}$ kg. While the mode is higher than the gravitational reference value ($5.97 \times 10^{24}$ kg), the reference value lies within the 95% HPD interval. The zero-mass hypothesis is excluded at $>5\sigma$.
  • Polar Moment of Inertia: The posterior mode is $I = 1.05 \times 10^{38}$ kg m$^2$ (68% HPD: $[9.04, 12.4] \times 10^{37}$ kg m$^2$). The reference value ($8.01 \times 10^{37}$ kg m$^2$) is contained within the 95% HPD interval. The normalized moment of inertia $I/(MR_\oplus^2)$ is calculated to be $\approx 0.357$, comparable to the PREM reference of 0.331.

Significance and Claims
The paper claims to present the most precise determination of the Earth's interior based on the weak interaction to date. By utilizing an order of magnitude more data than previous attempts and implementing a significantly updated systematic uncertainty treatment, the study demonstrates that neutrino attenuation can serve as a viable and complementary probe to seismology and gravimetry.

The results confirm that the Earth's density profile, as measured via neutrino attenuation, is consistent with established models derived from gravity and seismic waves. The authors emphasize that this work establishes neutrinos as a distinct physical tool for planetary tomography. While current uncertainties are dominated by flux modeling, cross-section knowledge, and detector/ice systematics, the paper posits that future improvements in detector calibration (e.g., IceCube Upgrade) and larger next-generation telescopes will transform this technique from a complementary cross-check into a precision probe of planetary structure.