Fast and “lossless” propagation of relativistic electrons along magnetized nonthermal filaments in galaxy clusters and the Galactic Center region

¹ Max Planck Institute for Astrophysics Karl-Schwarzschild-Str. 1 D-85741 Garching, Germany
² Space Research Institute (IKI) Profsoyuznaya 84/32 Moscow 117997, Russia
³ Minnesota Institute for Astrophysics, University of Minnesota 116 Church St SE Minneapolis MN 55455, USA
⁴ Universitäts-Sternwarte, Fakultät für Physik, Ludwig-Maximilians-Universität München Scheinerstr.1 81679 München, Germany
⁵ Istituto Nazionale di Astrofisica (INAF) – Istituto di Radioastronomia (IRA) Via Gobetti 101 40129 Bologna, Italy
⁶ Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford Oxford OX1 3PU, United Kingdom
⁷ Merton College Oxford OX1 4JD, United Kingdom

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 27 July 2025
Accepted: 17 November 2025

Abstract

Relativistic leptons in galaxy clusters lose their energy via radiation (synchrotron and inverse Compton losses) and interactions with the ambient plasma. At z ∼ 0, pure radiative losses limit the lifetime of electrons emitting at ∼GHz frequencies to t_r ≲ 100 Myr. Adiabatic losses can further lower Lorentz factors of electrons trapped in an expanding medium. If the propagation speed of electrons relative to the ambient weakly magnetized (plasma β ∼ 10²) intracluster medium (ICM) is limited by the Alfvén speed (v_a,ICM = c_s,ICM/β^1/2 ∼ 10⁷ cm s⁻¹), GHz-emitting electrons can travel only 1 ∼ v_a,ICMt_r ∼ 10 kpc relative to the underlying plasma. However, elongated structures spanning hundreds of kiloparsecs (or even a megaparsec) have been observed, requiring either a re-acceleration mechanism or another form of synchronization (e.g., via a large-scale shock). We argue that filaments with ordered magnetic fields supported by nonthermal pressure are characterized by v_a ≫ v_a,ICM and, thus, they can provide such a synchronization even without re-acceleration or shocks. In particular, along quasi-stationary filaments, electrons can propagate without experiencing adiabatic losses, and their velocity is not limited by the Alfvén or sound speeds of the ambient thermal plasma. This model predicts that along filaments that span significant pressure gradients (e.g., in the cores of galaxy clusters), the synchrotron break frequency, ν_b ∝ B, scales with the ambient gas pressure as P^1/2. The emission from such filaments should be strongly polarized due to the magnetic field being ordered along them. While some of these structures can be observed as “filaments” (i.e., long and narrow bright structures), others can be unresolved and appear as a diffuse emission. They could also be too faint to be detected, while continuing to provide channels for electron propagation. We examine several cases of filamentary structures in tailed radio galaxies and in a cluster relic, where “lossless” propagation provides an attractive alternative to other mechanisms for explaining the observed spectral behaviors.