Neutrino anisotropy as a probe of extreme astrophysical accelerators

TL;DR

The paper argues that if astrophysical neutrino sources trace the local large-scale structure, the observed neutrino sky should exhibit a measurable large-scale anisotropy whose strength depends on the effective horizon set by the neutrino spectrum and energy threshold, as well as the cosmological evolution of source luminosity. It develops a semi-analytic model using the CosmicFlows-2 density field to compute per-pixel flux and employs a maximum-likelihood framework to extract an anisotropy parameter $\alpha$ from data. The results show the anisotropy is sensitive to the evolution parameter $m$, can be enhanced by higher energy thresholds, and is detectable with current and future detectors given sufficient event statistics, offering a novel probe of UHECR/neutrino source evolution and their connection to the local matter distribution. The approach remains robust to reasonable systematic variations (energy resolution, $E_{\max}$ variance, and multiple populations) and provides a complementary pathway to study the origin of the diffuse neutrino flux and the UHECR dipole, with practical implications for IceCube and IceCube-Gen2.

Abstract

We predict that neutrino sources following the matter distribution of the universe result in an anisotropy in the neutrino sky imprinted by the local large-scale structure. We calculate the level of this anisotropy and explore how it depends on the cosmological evolution of neutrino sources. We show how the level of anisotropy can be amplified when a cutoff in the neutrino spectrum is considered, introducing an effective neutrino horizon. This effect might allow for future neutrino detectors to measure a neutrino anisotropy associated with the local large-scale structure. Measurement of the level of this anisotropy along with features of the neutrino spectrum will allow observers to constrain the cosmological evolution of neutrino sources, which at ultrahigh energies (UHEs) are also expected to be the sources of UHE cosmic rays.

Figures (10)

• Figure 1: Predicted neutrino skymaps (in Galactic coordinates) with threshold energies at the maximum neutrino energy for two different source evolution indices: $m=-5$ (top) and $m=0$ (bottom). The color scale indicates the predicted neutrino flux relative to the all-sky average. We assume $z_0=2$ [roughly the peak of star-formation Robertson:2015uda] and $\gamma=-2.53$. The top skymap serves as the template map for our maximum likelihood analysis. For the reader's convenience, these maps can be found in equatorial coordinates in Appendix \ref{['app:raDec']}.
• Figure 2: Anisotropy measure $\alpha$ as a function of source evolution power law index $m$ for various threshold energies (colored lines). All lines assume $\gamma=-2.53$, and $z_0=2$ (solid) or $z_0=4$ (dashed) to demonstrate the sensitivity to $z_0$. Dashed black lines indicate the $90\%$ confidence level upper-limit on $\alpha$ given a number of observed events for a truly isotropic distribution. Note that $\alpha$ saturates to $1$$(0)$ once the level of anisotropy is maximized (minimized).
• Figure 3: Relative difference of the inferred anisotropy level using a template with fixed spectral index, $\alpha$, compared to that obtained when using a template matching the true spectral index, $\alpha_\gamma$, as a function of the true spectral index. $\alpha$ is calculated with a template using $\gamma=-2.53$ and both templates assume $m=-5$. Results are shown for several true source evolutions ($z_0=2$ fixed): $m=-3$ (top), $m=0$ (middle), and $m=+3$ (bottom). Various $E_\mathrm{th}/E_\mathrm{max}$ ratios are shown as colored lines.
• Figure 4: The minimal anisotropy level $\alpha$ to which a detector is sensitive (dashed line) or has the potential to measure with $3\sigma$ significance (solid line) as a function of the number of observed neutrino events.
• Figure 5: Anisotropy measure $\alpha$ as a function of source evolution power law index $m$ for various threshold energies (colored lines) with perfect (solid) and $30\%$ (dashed) energy resolutions. All lines assume $\gamma=-2.53$ and $z_0=2$. Dashed black lines same as in Fig. \ref{['fig:alpha_evo']}.