# How isotropic can the UHECR flux be?

## TL;DR

This paper investigates the apparent isotropy of ultra-high energy cosmic ray (UHECR) arrival directions and explores how their anisotropy can reveal information about source distribution, magnetic fields, and composition, with implications for future observations.

## Contribution

It provides a model-independent analysis showing that source inhomogeneity should produce detectable anisotropies, and uses current data to constrain UHECR composition and magnetic field models.

## Key findings

- Expected dipole and quadrupole anisotropies at energies above 30 EeV if sources follow matter distribution.
- Current data's lack of quadrupole above 10 EeV disfavors pure proton composition.
- Future measurements of anisotropies above 60 EeV can inform UHECR mass composition.

## Abstract

Modern observatories of ultra-high energy cosmic rays (UHECR) have collected over 10^4 events with energies above 10 EeV, whose arrival directions appear to be nearly isotropically distributed. On the other hand, the distribution of matter in the nearby Universe -- and, therefore, presumably also that of UHECR sources -- is not homogeneous. This is expected to leave an imprint on the angular distribution of UHECR arrival directions, though deflections by cosmic magnetic fields can confound the picture. In this work, we investigate quantitatively this apparent inconsistency. To this end we study observables sensitive to UHECR source inhomogeneities but robust to uncertainties on magnetic fields and the UHECR mass composition. We show, in a rather model-independent way, that if the source distribution tracks the overall matter distribution, the arrival directions at energies above 30 EeV should exhibit a sizeable dipole and quadrupole anisotropy, detectable by UHECR observatories in the very near future. Were it not the case, one would have to seriously reconsider the present understanding of cosmic magnetic fields and/or the UHECR composition. Also, we show that the lack of a strong quadrupole moment above 10 EeV in the current data already disfavours a pure proton composition, and that in the very near future measurements of the dipole and quadrupole moment above 60 EeV will be able to provide evidence about the UHECR mass composition at those energies.