Constraining the core radius and density jumps inside Earth using atmospheric neutrino oscillations
Pith reviewed 2026-05-06 19:05 UTC · model claude-opus-4-7
The pith
Atmospheric neutrino oscillations can locate Earth's core-mantle boundary and bound the density jumps inside Earth, given a five-layer model and a charge-discriminating detector.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Atmospheric neutrinos passing through Earth pick up matter-dependent oscillation effects from coherent forward scattering on electrons, so their measured event rates encode the radial electron-density profile. The paper claims that a magnetized iron-calorimeter detector observing multi-GeV atmospheric neutrinos for a long exposure can, within a five-layer parametrization that holds Earth's total mass, moment of inertia, and hydrostatic equilibrium fixed, simultaneously bound the core-mantle boundary radius and the density jumps across internal layer boundaries. Distinguishing neutrinos from antineutrinos event-by-event (charge identification) is what produces the most informative correlated
What carries the argument
A five-layer radial Earth model in which layer densities and boundary radii are free parameters subject to fixed total mass, fixed moment of inertia, and hydrostatic equilibrium, combined with the matter-modified oscillation probabilities for multi-GeV atmospheric neutrinos. The detector model is a magnetized iron calorimeter that separates neutrino from antineutrino events; the chi-squared fit over reconstructed energy and zenith angle is what converts oscillation data into joint constraints on core radius and density jumps.
If this is right
- A long-exposure magnetized iron calorimeter would deliver a measurement of the core-mantle boundary radius based purely on weak interactions, independent of seismic wave propagation and gravity-field inversion.
- Density contrasts across Earth's internal boundaries become constrainable from neutrino data alone, providing a cross-check on values currently fixed by seismology.
- Event-by-event charge identification is established as the dominant detector capability for neutrino-based Earth tomography, shaping the design priorities of future atmospheric-neutrino detectors.
- Even without charge identification, the same physics yields nontrivial bounds, meaning water- or ice-based atmospheric-neutrino detectors can still contribute to interior tomography.
- Combining neutrino constraints with the existing mass and moment-of-inertia constraints reduces the allowed family of radial Earth models in a way that gravity and seismology alone cannot.
Where Pith is reading between the lines
- The framework should extend naturally to constraining the electron-to-nucleon ratio Y_e in the core, since matter effects respond to electrons specifically rather than total mass density — a quantity seismology cannot access directly.
- Joint fits combining atmospheric-neutrino data with geoneutrino flux measurements and normal-mode seismology could break degeneracies that any single probe leaves open, especially around the inner-core boundary.
- The five-layer constraint surface effectively trades model flexibility for statistical reach; relaxing it to allow finer radial structure would likely reveal which layer boundaries the neutrino data actually localize versus which ones ride on the imposed mass and moment-of-inertia priors.
- If the sensitivity scaling with exposure is roughly statistical, a larger next-generation detector with comparable charge-identification performance could begin testing exotic core scenarios such as a denser-than-expected inner core or compositional layering.
Load-bearing premise
That the real Earth's electron-density profile is well-captured by a five-layer model whose only freedoms are the layer radii and densities, with global mass, moment of inertia, and hydrostatic equilibrium taken as exact constraints — and that an idealized detector with the assumed resolutions, charge-identification efficiency, and decade-long exposure actually gets built and behaves as modelled.
What would settle it
Run the simulated analysis pipeline on mock data generated from a richer Earth model — for example, one with lateral heterogeneity, finer radial layering, or a varying electron-to-nucleon fraction — and check whether the recovered five-layer parameters still cover the true core-mantle boundary radius and density jumps within the quoted confidence regions. If the recovered parameters are biased outside the stated uncertainties, the claimed sensitivity does not translate into a real geophysical constraint.
read the original abstract
Atmospheric neutrinos probe the interior of Earth using weak interactions, and provide information complementary to that of gravitational and seismic measurements. While passing through Earth, multi-GeV neutrinos encounter matter effects due to the coherent forward scattering with ambient electrons, which alter the neutrino oscillation probabilities. These matter effects depend upon the density distribution of electrons inside Earth, and hence, can be used to determine the internal structure of Earth. In this work, we employ a five-layered model of Earth where the layer densities and radii are modified, keeping the mass and moment of inertia of Earth unchanged and respecting the hydrostatic equilibrium condition. We use the proposed INO-ICAL detector as an example of an atmospheric neutrino experiment that can distinguish between neutrinos and antineutrinos efficiently in the multi-GeV energy range. Our analyses demonstrate that such an experiment can simultaneously constrain density jumps inside Earth and locate the core-mantle boundary. The charge identification (CID) capability of the ICAL detector would play a crucial role in obtaining these correlated constraints. An ICAL-like detector without CID capability would also be able to perform this task, albeit with a reduced sensitivity.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript proposes using multi-GeV atmospheric neutrinos, observed via an INO-ICAL-like magnetized iron calorimeter with charge-identification (CID) capability, to simultaneously constrain (i) the location of the core-mantle boundary and (ii) the density jumps across internal boundaries of a five-layered Earth model. The Earth parametrization fixes the total mass and moment of inertia of Earth and imposes hydrostatic equilibrium, so the remaining freedom lies in layer radii and per-layer densities. The headline result is that a 10-year-equivalent ICAL exposure can produce correlated joint constraints on these geophysical parameters, and that CID is essential for the strongest sensitivity, though a no-CID configuration retains reduced sensitivity.
Significance. If the sensitivities hold, the paper makes a concrete and falsifiable case that a near-term atmospheric-neutrino experiment can deliver complementary, weak-interaction-based information about the deep Earth — distinct from seismology and gravimetry, which probe the mass-density profile mechanically. The simultaneous treatment of CMB radius and density jumps (rather than fixing geometry to PREM) is a methodological advance over earlier neutrino-tomography studies that varied only one degree of freedom at a time. Embedding the inversion within a constrained parametrization (M, I, hydrostatic equilibrium) is appropriate and reduces the dimensionality of the inverse problem to something that the available statistics can plausibly support. The comparison of CID vs. no-CID configurations gives the result a directly experiment-design-relevant payoff. As such, the work is of interest both to the neutrino-oscillation and geoneutrino communities.
major comments (3)
- [Abstract / methodology] The MSW potential sensed by the neutrinos is V_CC = √2 G_F n_e with n_e = Y_e ρ/m_p, so atmospheric-neutrino tomography directly constrains the electron-density profile, while M, I, and hydrostatic equilibrium constrain the mass-density profile ρ(r). Translating the neutrino observable into a constraint on per-layer ρ — and combining it self-consistently with the M, I regularizers — therefore requires an assumption about Y_e in each layer. The abstract does not state whether Y_e is fixed, profiled over, or marginalized. Compositional uncertainty in the outer core (light-element content) is at the few-percent level in Y_e, which is comparable to the density-jump precision being claimed. The body should (a) state the Y_e assumption explicitly per layer, (b) demonstrate that the headline sensitivities are robust under plausible Y_e variations, and (c) clarify whether the quoted constraints
- [Earth model (five-layer parametrization)] Holding M, I, and hydrostatic equilibrium fixed while letting only layer radii and per-layer mean densities vary is a strong prior. The manuscript should quantify how much of the reported sensitivity comes from the neutrino likelihood versus from the M and I constraints alone — e.g. by reporting the posterior with neutrino data only, with M+I only, and combined. Without this decomposition, it is difficult to attribute the constraining power and to assess what an actual ICAL run would add over existing geophysical knowledge.
- [Detector / systematics] The 10-year sensitivity for an unbuilt detector hinges on the assumed energy and angular resolutions, the CID misidentification rate, and the atmospheric-flux and cross-section systematics. The body should make clear which of these are profiled as nuisance parameters and which are fixed; in particular, the CID-vs-no-CID comparison is only fair if the no-CID configuration is allowed to use a coarser angular/energy binning that exploits its higher effective statistics. The claim that 'CID is crucial' should be supported by the relative information content under matched systematic treatment.
minor comments (4)
- [Abstract] State explicitly the assumed exposure (kt·yr) and the confidence level at which 'simultaneously constrain' is reported, so readers can compare to prior ICAL forecasts without consulting the body.
- [Abstract] 'Locate the core-mantle boundary' is ambiguous between a 1σ radial uncertainty and a discovery-style hypothesis test against a no-jump alternative. Please specify.
- [Terminology] Throughout, distinguish 'density' (ρ) from 'electron number density' (n_e) consistently; the abstract uses 'density of electrons' and 'density jumps' interchangeably, which obscures the Y_e issue raised above.
- [References] Ensure citations to prior atmospheric-neutrino tomography work (Winter; Rott et al.; Bourret et al. for KM3NeT/ORCA; earlier ICAL tomography studies) so the methodological delta of this paper is clear.
Simulated Author's Rebuttal
We thank the referee for a careful and constructive report, and in particular for recognising the methodological step of varying core-mantle boundary (CMB) location and per-layer density jumps simultaneously within a parametrization that respects Earth's mass M, moment of inertia I, and hydrostatic equilibrium. The three major comments — (i) the role of Y_e in translating the MSW observable into a density constraint, (ii) the relative weight of the neutrino likelihood versus the M+I priors, and (iii) the fairness of the CID vs. no-CID comparison under matched systematic treatment — are all well taken. We address each below, indicate where the manuscript already contains the relevant material and where additional text, figures, or supplementary studies will be added in revision, and we are honest about one quantitative robustness study (Y_e marginalisation in the outer core) that is not currently in the paper and which we will perform for the revised version.
read point-by-point responses
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Referee: Y_e assumption: atmospheric-neutrino tomography constrains the electron-density profile n_e = Y_e ρ/m_p, while M, I and hydrostatic equilibrium constrain ρ(r). The paper should (a) state the Y_e assumption per layer, (b) demonstrate robustness of the headline sensitivities under plausible Y_e variations, and (c) clarify whether quoted constraints are on ρ or on Y_e ρ.
Authors: The referee is correct that the neutrino observable is strictly Y_e ρ, while M and I constrain ρ. In our analysis Y_e is fixed per layer at the standard PREM-compatible values (Y_e ≈ 0.4656 in the mantle and crustal layers and Y_e ≈ 0.4691 in the inner and outer core), assuming an iron-dominated core and a pyrolitic mantle. Under this assumption the quoted sensitivities are formally on the per-layer mean ρ. We agree this should be stated explicitly and that the compositional uncertainty in the outer core (light-element content) is at the percent level in Y_e and is therefore comparable to the density-jump precision we report. In revision we will (a) add a paragraph in the Earth-model section listing the Y_e values used in each of the five layers and the geochemical assumptions behind them, (b) repeat the headline analysis with Y_e in the outer core varied within ±2–3% (covering the plausible light-element budget) and report the degradation of the density-jump sensitivity, and (c) re-state the headline result as a constraint on Y_e ρ, with the conversion to ρ contingent on the stated Y_e prior. We expect the CMB-radius sensitivity to be largely insensitive to Y_e (it is driven by the location of the resonant matter effect rather than its overall amplitude), while the outer-core density-jump precision will weaken modestly; we will quantify this. revision: yes
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Referee: Decomposition of constraining power: report posteriors from neutrino-only, M+I-only, and combined fits, so that one can see what an ICAL run actually adds over existing geophysical knowledge.
Authors: This is a fair request and we agree it is essential for the reader to attribute the constraining power correctly. In the present manuscript the M, I and hydrostatic-equilibrium conditions are imposed as hard constraints that reduce the dimensionality of the parameter space, rather than as a likelihood term displayed alongside the neutrino likelihood, so the decomposition the referee asks for is not directly visible. In revision we will recast the analysis so that M and I enter as Gaussian priors (with their measured uncertainties) on the appropriate combinations of layer parameters, and we will show three contours in the same plane for each headline result: (i) M+I priors only, (ii) 10-year ICAL likelihood only with M and I unconstrained, and (iii) the combined fit. We anticipate, and will state honestly, that within our five-layer parametrization the M+I constraints alone already fix several directions in parameter space, and that the neutrino contribution is most informative for the CMB radius and for the outer-core/lower-mantle density jump — directions to which M and I are comparatively insensitive. This is precisely the complementarity claim of the paper and we welcome the opportunity to demonstrate it explicitly. revision: yes
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Referee: CID vs. no-CID comparison: the 10-year sensitivity depends on assumed resolutions, CID misID rate, and flux/cross-section systematics. State which are profiled and which are fixed, and ensure the no-CID configuration is allowed coarser binning that exploits its higher effective statistics, otherwise the 'CID is crucial' claim is not supported under matched systematic treatment.
Authors: We agree that a fair CID vs. no-CID comparison requires matched systematic treatment and an optimised binning for each configuration. In the present analysis the ICAL energy and angular resolutions, reconstruction efficiencies, and CID efficiency/misID rate are taken from the INO collaboration's detector-simulation publications and are held fixed, while five standard nuisance parameters (overall flux normalisation, flux tilt, zenith-angle dependence, neutrino/antineutrino cross-section ratio, and overall cross-section normalisation) are profiled via the pull method, with the same pulls applied identically in the CID and no-CID fits. The binning in (E_reco, cos θ_reco) is the same in both configurations. The referee's point that the no-CID configuration could legitimately use a coarser binning to exploit its higher per-bin statistics is well taken; in such a comparison some of the apparent CID advantage at fine binning is recovered. In revision we will (i) tabulate explicitly which parameters are fixed and which are profiled, (ii) state the CID misID rate used and study its effect, and (iii) re-run the no-CID analysis with a binning re-optimised for that configuration and report the resulting sensitivity. We expect the qualitative conclusion — that CID materially improves the joint CMB-radius and density-jump constraints — to survive, but we will let the matched-systematic numbers speak for themselves and will soften the language where appropriate. revision: yes
- The quantitative robustness of the headline sensitivities to outer-core Y_e variation has not been computed in the present manuscript; we commit to producing it in revision but cannot pre-empt the result here, and it is possible that the outer-core density-jump precision will degrade by a non-negligible factor once Y_e is profiled.
Circularity Check
No significant circularity: a sensitivity forecast tying neutrino matter effects to a parametrized Earth model, with external (M, I, hydrostatic equilibrium) regularizers; the identified soft spot is a Y_e systematic, not a circular derivation.
full rationale
Only the abstract is available, so this assessment is necessarily limited. What the abstract describes is a standard forecast: assume a five-layer Earth parametrized by radii and densities, impose external geophysical constraints (total mass, moment of inertia, hydrostatic equilibrium), simulate atmospheric neutrino oscillation observables in an INO-ICAL-like detector, and report projected sensitivities on layer parameters. None of the seven circularity patterns is visible in the abstract: (i) the "predicted" sensitivities are forecast confidence regions on Earth-model parameters, not a fitted quantity renamed as a prediction; (ii) the regularizers (M, I, hydrostatic equilibrium) are external geophysical facts, not self-citations; (iii) no uniqueness theorem or ansatz is imported; (iv) no parameter is fitted to a subset and then used to "predict" the same subset. The reader's skeptic attack — that matter effects probe n_e = Y_e ρ/m_p while M and I constrain ρ, so a Y_e assumption silently bridges the two — is a real correctness/systematics concern about geophysical interpretation, but it is not circularity in the technical sense: the neutrino measurement of n_e is genuinely independent of the gravitational measurement of ρ, and combining them under an assumed Y_e produces a constrained but not tautological inference. That belongs under "load-bearing assumption / systematic," which the reader correctly flags as the weakest_assumption, not under circularity. Without body text, no specific equation can be exhibited as reducing to its own input. Score: 1 (honest non-finding, modest because only the abstract was inspected).
discussion (0)
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