[Paper Review] Neutrino Flux Bounds and Prospects for High Energy and Ultrahigh Energy Neutrino Source Detection

Christian Hettlage, K. Mannheim|arXiv (Cornell University)|Feb 4, 2002

Astrophysics and Cosmic Phenomena6 references3 citations

TL;DR

This paper develops a generic framework to derive upper bounds on high-energy and ultrahigh-energy neutrino fluxes from hadronic sources, applying it to predict event rates in next-generation water-based Cherenkov detectors. It finds that while hundreds to thousands of events per year may be detectable, statistical uncertainties severely limit the feasibility of using neutrino telescopes for Earth tomography via neutrino attenuation.

ABSTRACT

After briefly reviewing various hadronic neutrino source models, we show how to construct generic upper flux bounds. We then turn to the problem of neutrino propagation through the inner Earth and neutrino detection in water-based Cerenkov detectors. Applying the formalism thus developed to the Mannheim-Protheroe-Rachen and the Waxman&Bahcall flux bounds, we find that event rates of several hundred to thousand events per year might be possible in next-generation neutrino telescopes. However, a tomography of the inner Earth will face severe constraints due to the statistical error of the event rates to be expected.

Motivation & Objective

• To establish generic upper bounds on high-energy and ultrahigh-energy neutrino fluxes from hadronic sources, independent of specific source models.
• To evaluate the detectability of these fluxes in next-generation water-based Cherenkov neutrino telescopes.
• To assess the potential of using neutrino event rates to perform tomography of the Earth's interior via neutrino attenuation.
• To quantify the impact of statistical uncertainties on the precision of such tomographic reconstructions.

Proposed method

• Derives generic neutrino flux bounds using particle physics constraints and observed cosmic ray proton spectra, assuming power-law forms for proton and target photon spectra.
• Applies the Mannheim-Protheroe-Rachen (MPR) and Waxman-Bahcall flux bounds as reference models for neutrino production in hadronic sources.
• Models neutrino propagation through the Earth using transport equations with energy degradation and flavor-dependent cross sections.
• Solves the cascade equations for neutrino interactions in water using CTEQ5DIS parton distribution functions and discretized transport equations.
• Estimates event rates in water-based Cherenkov detectors using a semi-analytical formula incorporating effective area, detector height, and matter density.
• Performs tomographic reconstruction of Earth's density using the Radon transform inversion method, accounting for statistical errors in event rates.

Experimental results

Research questions

• RQ1 What are the generic upper bounds on high-energy and ultrahigh-energy neutrino fluxes from hadronic sources, independent of specific source models?
• RQ2 How many neutrino events per year can be expected in next-generation water-based Cherenkov detectors for the MPR and Waxman-Bahcall flux bounds?
• RQ3 To what extent can neutrino event rates be used to reconstruct the internal density structure of the Earth via tomography?
• RQ4 How do statistical uncertainties in event rate measurements affect the precision of neutrino-based Earth tomography?

Key findings

• Next-generation neutrino telescopes could detect between several hundred and over a thousand muon neutrino events per year for the MPR and Waxman-Bahcall flux bounds, assuming a 100 GeV energy cutoff.
• The MPR flux bound with high neutron opacity predicts event rates peaking at around 1,000 events/year, while the Waxman-Bahcall bound yields slightly lower rates.
• Statistical errors in event rates—modeled as ±√N—significantly degrade the precision of tomographic reconstructions, making accurate density profiles difficult to recover.
• Tomography of the Earth's interior via neutrino attenuation is theoretically possible but practically constrained by statistical uncertainty, as shown by reconstruction errors in the radial density profile.
• The radial density reconstruction using the MPR bound shows substantial deviation from the Dziewonski-Anderson model when statistical errors are included, especially for tauon events.
• The event rate dependence on nadir angle reflects neutrino attenuation through the Earth, providing a direct link between observed rates and column density, but this link is weakened by statistical noise.