Constraints on UHECR sources and extragalactic magnetic fields from directional anisotropies

A dipole anisotropy in ultra-high-energy cosmic ray (UHECR) arrival directions, of extragalactic origin, is now firmly established at energies E > 8 EeV. Furthermore, the UHECR angular power spectrum shows no power at smaller angular scales than the dipole, apart from hints of possible individual hot or warm spots for energy thresholds $\gtrsim$40 EeV. Here, we exploit the magnitude of the dipole and the limits on smaller-scale anisotropies to place constraints on two quantities: the extragalactic magnetic field (EGMF) and the number density of UHECR sources or the volumetric event rate if UHECR sources are transient. We also vary the bias between the extragalactic matter and the UHECR source densities, reflecting whether UHECR sources are preferentially found in over- or under-dense regions, and find that little or no bias is favored. We follow Ding et al. (2021) in using the Cosmic Flows 2 density distribution of the local universe as our baseline distribution of UHECR sources, but we improve and extend that work by employing an accurate and self-consistent treatment of interactions and energy losses during propagation. Deflections in the Galactic magnetic field are treated using both the full JF12 magnetic field model, with random as well as coherent components, or just the coherent part, to bracket the impact of the GMF on the dipole anisotropy. This Large Scale Structure (LSS) model gives good agreement with both the direction and magnitude of the measured dipole anisotropy and forms the basis for simulations of discrete sources and the inclusion of EGMF effects.