The Energy Spectrum of Ultra-High Energy Cosmic Rays across Declinations $-90^\circ$ to $+44.8^\circ$ as measured at the Pierre Auger Observatory

TL;DR

The study tests whether the ultra-high-energy cosmic ray energy spectrum depends on declination by combining vertical and inclined observations from the Pierre Auger Observatory across $-90^ obreak o +44.8^ obreak o$. It employs a forward-folding, multi-break power-law model $J(E;\mathbf{p})$ and cross-calibrates two energy estimators, $S_{38}$ and $N_{68}$, via correlated shifts $(\delta A,\delta B,\delta C)$ to produce a single, sky-wide spectrum. The analysis finds no significant declination dependence beyond the known dipole modulation and robustly confirms the instep at about $10~\mathrm{EeV}$ with a significance around $5.5\sigma$, arguing against an origin from a small number of foreground sources. These results tighten constraints on the origin and propagation of ultra-high-energy cosmic rays and demonstrate the value of combining vertical and inclined data with careful energy calibration for accurate, all-sky spectral measurements.

Abstract

The energy spectrum of cosmic rays above 2.5 EeV has been measured across the declination range $-90^\circ \leqδ\leq +44.8^\circ$ using data from $\sim 310{,}000$ events accrued at the Pierre Auger Observatory from an exposure of $(104{,}900\pm 3{,}100)$ km$^2\,$sr$\,$yr. No significant variations of energy spectra with declination are observed, after allowing or not for non-uniformities across the sky arising from the well-established dipolar anisotropies in the arrival directions of ultra-high energy cosmic rays. Additionally, the instep feature in the spectrum at $\simeq$ 10 EeV reported previously is now established at a significance above $5\,σ$. The quasi-uniformity of the energy spectrum across declinations disfavors an origin for the instep from a few distinctive sources.

Figures (4)

• Figure 1: Individual energy spectra scaled by $E^3$ inferred from $S_{38}$- and $N_{68}$-based analyses before (top panel) and after (bottom panel) correcting the energies of inclined events to a best-fit common energy scale. The declination range after combination is reduced to $[-84.8^\circ,+24.8^\circ]$ to guarantee observation of the same sky. Upper limits at 90% confidence level are shown in empty bins. The gray line is the best-fit to data points after combination.
• Figure 2: Top: Energy spectra in five declination ranges. The dotted reference lines are the best-fit function for the spectrum combined over $[-84.8^\circ,+24.8^\circ]$; the full lines account for the impact of dipole anisotropies in each band. Bottom: Corresponding residuals. Artificial shifts are applied for visualization purpose. An alternative view of the residuals is provided in the Supplemental material.
• Figure 3: Energy spectrum scaled by $E^2$ (energy flux) across declinations $[-90^\circ,+44.8^\circ]$. The number of events corrected for detector effects is indicated in each bin. The red band stands for the systematic uncertainties while the dotted line indicates the best-fit function described by the spectral features given with their statistical and systematic uncertainties.
• Figure 4: Energy-spectra residuals zoomed within $\pm25\%$ in the five declination bands.