Detecting ultra-high-energy cosmic ray anisotropies through harmonic cross-correlations

¹ CEICO, Institute of Physics of the Czech Academy of Sciences, Na Slovance 1999/2, 182 21 Prague, Czech Republic
e-mail: federico.urban@fzu.cz
² Dipartimento di Fisica, Università degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy
³ INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy
⁴ Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK

Received: 21 May 2020
Accepted: 2 May 2021

Abstract

We propose an observable for ultra-high-energy cosmic ray (UHECR) physics: the harmonic-space cross-correlation power spectrum between the arrival directions of UHECRs and the large-scale cosmic structure mapped by galaxies. This cross-correlation has not yet been considered in the literature, and it permits a direct theoretical modelling of the main astrophysical components. We describe the expected form of the cross-correlation and show how, if the distribution of UHECR sources traces the large-scale cosmic structure, it could be easier to detect with current data than the UHECR auto-correlation. Moreover, the cross-correlation is more sensitive to UHECR anisotropies on smaller angular scales, it is more robust to systematic uncertainties, and it could be used to determine the redshift distribution of UHECR sources, making it a valuable tool for determining their origins and properties.