Energy-dependent anisotropy of cosmic-ray muons: A twelve-year study with IceCube Neutrino Observatory

The anisotropy of cosmic rays offers insights into their origin, propagation, and interaction with galactic magnetic fields. Using twelve years (2011–2023) of data from the IceCube Neutrino Observatory, we present an energy-resolved analysis of cosmic-ray muon anisotropy based on 7.92 × 1011 reconstructed events between 13 TeV and 5.3 PeV. The spectrum is divided at log10(Ereco/GeV) = 5 corresponding approximately to 100 Tev and to explore low and high energy regimes. Analyses include sidereal modulation, angular distributions, Fourier power spectra, and HEALPix intensity mapping. Gaussian and power-law fits were assessed using χ2, χ2v, and BIC metrics. Low-energy muons (≤ 100 TeV) show strong dipolar modulation and large-scale anisotropy, while high-energy muons (> 100 TeV) exhibit localized, directionally coherent features, suggesting reduced magnetic scattering and source related origins. The results confirm a statistically significant energy-dependent anisotropy consistent with diffusion based cosmic-ray transport, establishing IceCube as a precision probe of PeV scale anisotropy.