High energy electromagnetic cascades in extragalactic space: physics and features

TL;DR

This paper models electromagnetic cascades in space, revealing universal spectral features and providing new limits on cascade energy density by comparing analytic results with Fermi LAT data.

Contribution

It introduces the concept of 'strong universality' in cascade spectra and the '$E_{ m max}$ rule', advancing understanding of cascade properties and constraints on their energy density.

Findings

Cascade spectrum has two components with specific energy dependencies.

Derived upper limits on cascade energy density are more stringent than previous estimates.

Identified conditions under which cascade properties exhibit universality.

Abstract

Using the analytic modeling of the electromagnetic cascades compared with more precise numerical simulations we describe the physical properties of electromagnetic cascades developing in the universe on CMB and EBL background radiations. A cascade is initiated by very high energy photon or electron and the remnant photons at large distance have two-component energy spectrum, $\propto E^{-2}$ ($\propto E^{-1.9}$ in numerical simulations) produced at cascade multiplication stage, and $\propto E^{-3/2}$ from Inverse Compton electron cooling at low energies. The most noticeable property of the cascade spectrum in analytic modeling is 'strong universality', which includes the standard energy spectrum and the energy density of the cascade $\omega_{\rm cas}$ as its only numerical parameter. Using numerical simulations of the cascade spectrum and comparing it with recent Fermi LAT spectrum we obtained the upper limit on $\omega_{\rm cas}$ stronger than in previous works. The new feature of the analysis is "$E_{\max}$ rule". We investigate the dependence of $\omega_{\rm cas}$ on the distribution of sources, distinguishing two cases of universality: the strong and weak ones.