Diffuse Astrophysical Neutrino Flux

• Diffuse astrophysical neutrino flux is the widespread high-energy signal from cosmic accelerators beyond the solar system.
• Detection employs muon tracks and cascades with advanced veto and machine learning methods to effectively separate cosmic signals from atmospheric backgrounds.
• Global analyses from IceCube and Baikal-GVD reveal a power-law spectrum with nearly equal flavor ratios, underscoring contributions from both Galactic and extragalactic sources.

The diffuse astrophysical neutrino flux refers to the all-sky, non-pointlike component of high-energy neutrinos originating from astrophysical processes beyond the solar system. Unlike targeted searches for emission from individual sources, the paper of the diffuse flux focuses on detecting and characterizing an excess of neutrino events above the known backgrounds—primarily from atmospheric interactions—across large fractions of the sky and over a broad energy range, typically extending from several TeV to the PeV scale and beyond. This flux is a critical probe of high-energy cosmic accelerators and has become a cornerstone of modern astroparticle physics, enabled by the advent of kilometer-scale detectors such as IceCube and Baikal-GVD.

1. Physical Basis and Theoretical Expectations

Theoretical models predict that the diffuse astrophysical neutrino flux arises from the interactions of accelerated cosmic rays with matter (pp interactions) or radiation fields (pγ interactions) in energetic astrophysical environments such as active galactic nuclei (AGN), gamma-ray bursts (GRBs), starburst galaxies, supernova remnants (SNRs), and the Galactic plane itself. For sources in which protons are efficiently confined, photopion production is dominated by processes like:

$$p + \gamma \rightarrow \Delta^+ \rightarrow n + \pi^+,$$

followed by

$$\pi^+ \rightarrow \mu^+ + \nu_\mu \rightarrow e^+ + \nu_e + \bar{\nu}_\mu + \nu_\mu.$$

The Waxman–Bahcall (WB) upper bound—derived for sources where cosmic-ray protons escape to contribute to the observed ultra-high-energy cosmic ray flux—proposes an all-flavor neutrino flux scaling as $E^{-2}$, often written as:

$$E^2 \Phi_\nu \lesssim \text{a few} \times 10^{-8}~\text{GeV cm}^{-2} \text{s}^{-1} \text{sr}^{-1}.$$

After propagation over cosmic distances, standard neutrino oscillations yield an observed flavor ratio at Earth close to $1:1:1$ for $(\nu_e:\nu_\mu:\nu_\tau)$ (Brunner, 2011).

2. Experimental Methodologies and Channel Complementarity

Detection of the diffuse astrophysical neutrino flux relies on two primary event topologies:

• Muon Tracks: Mainly from $\nu_\mu$ charged-current (CC) interactions. Tracks offer superb angular resolution and leverage the large effective volume set by the long range of muons in the medium (ice or water). Upward-going tracks maximize background rejection from atmospheric muons.
• Cascades (Showers): Resulting from $\nu_e$ and $\nu_\tau$ CC as well as neutral current (NC) interactions of all flavors. Cascades deposit energy locally with good (10–30%) energy resolution but inferior angular resolution.

Modern analyses employ starting event samples (requiring the neutrino vertex to be contained within the detector), extended veto methods, and advanced machine learning (e.g., boosted decision trees and DNN classifiers) to suppress atmospheric backgrounds, particularly in the southern sky where the Galactic plane resides (Abbasi et al., 28 Feb 2024, Silva et al., 2023, Osborn et al., 10 Jul 2025).

Table: Key Detection Channels

Channel	Main Flavor Sensitivity	Energy Resolution	Angular Resolution
Muon Tracks	$\nu_\mu$	Moderate	$\lesssim1^\circ$
Cascades	$\nu_e$, $\nu_\tau$	10–30%	2–10$^\circ$ (IceCube)
Double Cascades	$\nu_\tau$ CC	Cascade-like	Cascade-like

3. Empirical Results and Spectral Characterization

The diffuse flux has now been robustly detected with statistical significances exceeding $5\sigma$ in both IceCube and Baikal-GVD (Collaboration et al., 2 Jul 2025). Analyses converge on a power-law spectral shape, parameterized as

$$\frac{d\Phi}{dE_\nu} = \phi_\mathrm{astro} \left( \frac{E_\nu}{100~\mathrm{TeV}} \right)^{-\gamma_\mathrm{astro}},$$

with global fits yielding:

• IceCube Starting Tracks: $\gamma_\mathrm{astro} = 2.58^{+0.10}_{-0.09}$, $$\phi_\mathrm{astro} = 1.68^{+0.19}_{-0.22} \times 10^{-18}$$ GeV$^{-1}$cm$^{-2}$s$^{-1}$sr$^{-1}$ (per flavor at 100 TeV) (Abbasi et al., 28 Feb 2024, Silva et al., 2023, Jeong, 23 Jul 2024).
• Baikal-GVD Cascades: $\gamma_\mathrm{astro} = 2.64^{+0.09}_{-0.11}$, $$\phi_\mathrm{astro} = 4.42^{+2.31}_{-1.29} \times 10^{-18}$$ GeV$^{-1}$cm$^{-2}$s$^{-1}$sr$^{-1}$ (per flavor at 100 TeV) (Collaboration et al., 2 Jul 2025).

Combining different channels via global or forward-folding fits provides cross-validation of flux parameters and tight control over systematics (Naab et al., 2023). No statistically significant evidence is found for a low-energy break (down to 3–16 TeV); the spectrum is consistent with a single, unbroken power law within current sensitivity (Abbasi et al., 28 Feb 2024).

4. Source Populations and Spectral Features

Extragalactic SNRs, hypernova remnants (HNRs), and GRB remnants contribute via $pp$ interactions, with SNRs predicted to dominate the diffuse flux up to $100-150$ TeV. This leads to a strong prediction for a spectral break at $E_\nu \sim 100-150$ TeV, with higher energies requiring contribution from rarer, higher-energy sources (Chakraborty et al., 2015).

Multi-component models combine residual atmospheric backgrounds, a Galactic $pp$ component (spectral index $\sim2.6$, cut off at $E_\nu \sim 150$ TeV), extragalactic $pp$ sources (canonical $E^{-2}$), and a hard $p\gamma$ extragalactic component (e.g., TDEs, AGN; index $<2$) to account for observed anisotropies, flavor ratios, and the lack of resolved point sources (Palladino et al., 2018).

Constraints from the extragalactic $\gamma$-ray background measured by Fermi-LAT require that persistent extragalactic $pp$ sources (e.g., starburst galaxies) cannot overshoot the non-blazar $\gamma$-ray contribution, thereby favoring scenarios where the dominant neutrino sources are “$\gamma$-dark” (optically thick to high-energy photons) (Collaboration et al., 2020, Fang et al., 2022).

Point source analyses firmly constrain blazars to contribute no more than $\sim15\%$ of the diffuse flux, with non-blazar AGN and starburst galaxies remaining viable contributors, particularly at lower energies (Smith et al., 2020, Kochocki et al., 2020).

5. Galactic Plane Emission and Anisotropy

The most recent joint analyses utilizing throughgoing tracks, starting tracks, and cascades over 12.1 years have achieved a $4.5\sigma$ detection of diffuse neutrino emission from the Galactic plane, confirming that the Milky Way is itself a high-energy neutrino source. The Galactic component is observed as a band (e.g., $|b|<10^\circ$ in Galactic latitude) and exhibits a slightly softer spectrum than the isotropic component (e.g., spectral index $\sim2.7$ for the Galactic band compared to $\sim2.5$ for the isotropic flux). However, its normalization is subdominant, with at most a 10% effect on the total isotropic normalization (Osborn et al., 10 Jul 2025, Silva et al., 2023).

Spectral studies indicate that while the Galactic plane provides an important baseline, the extragalactic isotropic flux remains the dominant contribution at energies above tens of TeV.

6. Flavor Composition and Event Topologies

Standard oscillation theory predicts a nearly equal flavor composition at Earth. IceCube analyses using double cascade event identification and machine learning-based selection algorithms have firmly detected the presence of astrophysical $\nu_\tau$ at $>5\sigma$ significance, and combined fits to HESE, tracks, and cascades robustly support the canonical $1:1:1$ flavor ratio. The absence of strong deviations disfavors exotic production or propagation scenarios (Lad et al., 2023).

7. Future Prospects, Instrumentation, and Theoretical Impact

The ongoing expansion of Baikal-GVD and the planned IceCube-Gen2 array will enhance neutrino detection volumes by factors of several, improving the sensitivity to subdominant Galactic components, enabling more refined point source searches, and facilitating detailed spectral and regional analyses across the sky (Collaboration et al., 2 Jul 2025, Xu, 2017).

Spectral measurements across channels, coupled with advanced likelihood methods and robust detector modeling (e.g., “SnowStorm”), will continue to reduce systematic uncertainties. The combined multi-channel, long-exposure analysis has provided statistically independent, corroborating measurements of all-flavor diffuse fluxes and their spectral properties (Naab et al., 2023, Jeong, 23 Jul 2024).

Empirical evidence excludes many optimistic source classes (e.g., canonical long GRBs contribute less than 10% at $E_\nu \sim 100$ TeV) (Collaboration et al., 2020), and stacking limits and the diffuse $\gamma$-ray background shape the allowed population demographics and energetics of cosmogenic cosmic accelerators (Palladino et al., 2018, Dey et al., 2022).

The diffuse astrophysical neutrino flux is now an established probe of high-energy cosmic ray acceleration and propagation, the physical environments of extragalactic sources, and the Galactic interstellar medium, providing ongoing constraints on the landscape of ultra-high-energy particle astrophysics.