Galactic Substructure and Energetic Neutrinos from the Sun and the Earth

We consider the effects of Galactic substructure on energetic neutrinos from annihilation of weakly-interacting massive particles (WIMPs) that have been captured by the Sun and Earth. Substructure gives rise to a time-varying capture rate and thus to time variation in the annihilation rate and resulting energetic-neutrino flux. However, there may be a time lag between the capture and annihilation rates. The energetic-neutrino flux may then be determined by the density of dark matter in the Solar System’s past trajectory, rather than the local density. The signature of such an effect may be sought in the ratio of the direct- to indirect-detection rates.

💡 Research Summary

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The paper investigates how small‑scale dark‑matter substructures in the Milky Way affect the flux of high‑energy neutrinos produced by annihilation of weakly‑interacting massive particles (WIMPs) that have been captured by the Sun and the Earth. In the standard picture, the capture rate C is taken to be proportional to the local dark‑matter density ρ₀, the WIMP‑nucleon scattering cross‑section σₙ, and the inverse of the average WIMP velocity. Once captured, WIMPs sink to the core of the body, accumulate in number N, and annihilate at a rate A N², where A encodes the annihilation cross‑section and the core temperature. The time evolution obeys dN/dt = C − A N², and a steady‑state is reached after a characteristic equilibration time τ_eq = 1/√(C A).

The authors point out that Galactic substructures—dense clumps, streams, or tidally shredded mini‑halos—cause ρ(t) to vary as the Solar System traverses them. Consequently, C becomes a function of time, C(t). If τ_eq is long compared to the duration of a density enhancement, the WIMP population cannot adjust instantaneously; the annihilation rate at the present epoch retains a memory of past high‑density encounters. This “lag” effect is especially pronounced for the Earth, whose core temperature is lower than the Sun’s, making A smaller and τ_eq correspondingly larger.

Two illustrative substructure models are examined: (1) a modest overdensity (≈5 × ρ₀) lasting ~30 Myr, and (2) a strong overdensity (≈10 × ρ₀) lasting ~100 Myr. Numerical integration of the capture‑annihilation equation shows that for the Sun, whose τ_eq is of order 10 Myr, the neutrino flux can be enhanced by factors of 2–5, depending on the model. For the Earth, with τ_eq ≫ 100 Myr, the same encounters can boost the flux by an order of magnitude or more. In the latter case, the indirect neutrino signal may become comparable to or exceed the sensitivity of current detectors such as IceCube or KM3NeT, even when direct‑detection limits constrain σₙ to relatively low values.

A key diagnostic proposed is the ratio R = Φ_ν / R_direct, where Φ_ν is the observed neutrino flux and R_direct is the event rate measured by direct‑detection experiments (e.g., XENONnT, LZ). In a smooth halo, R is essentially constant, set by the particle physics parameters (σₙ, annihilation cross‑section) and the local density. Substructure introduces a time‑dependent C(t) that can raise R by factors of 10–100 for the Earth and by a few for the Sun. Detecting such deviations would constitute indirect evidence for past encounters with dark‑matter clumps.

The authors outline a practical strategy: (i) use the latest direct‑detection limits to compute the expected R under the assumption of a smooth halo; (ii) compare this prediction with the neutrino flux measured in the direction of the Sun and the Earth; (iii) if a statistically significant excess is found, infer the properties of the responsible substructure (overdensity factor, size, encounter duration) by fitting the time‑dependent capture model.

Finally, the paper proposes a unified analysis framework that combines high‑resolution Galactic simulations (providing substructure statistics and spatial distribution) with orbital integration of the Solar System through the simulated halo. This yields a probabilistic C(t) history for any given WIMP model. By confronting the predicted Φ_ν(t) with combined direct‑ and indirect‑detection data, one can simultaneously constrain particle‑physics parameters and the small‑scale structure of dark matter. The work thus opens a novel avenue for probing the granularity of the Milky Way’s dark halo using neutrino astronomy.