Fast and "lossless" propagation of relativistic electrons along magnetized non-thermal filaments in galaxy clusters and the Galactic Center region

TL;DR

This work proposes that lossless propagation of relativistic electrons along magnetized, low‑beta filaments can reconcile the presence of extended, filamentary synchrotron structures with the rapid radiative aging expected in the intracluster medium. By arguing that filaments can reach Alfvén speeds far exceeding ambient values, the authors show that electrons can traverse hundreds of kiloparsecs with minimal adiabatic and radiative losses, leading to a break frequency that scales as $\nu_b \propto B$ and potentially as $\nu_b \propto P_t^{1/2}$ when magnetic and gas pressures are in equipartition. The paper supports its position with observational constraints from tailed radio galaxies and cluster relics, which imply high transverse transport velocities (e.g., $v_{\min}$ ranging from a few thousand to ~15,000 km/s) to explain spectral uniformity along filaments. It also outlines concrete, testable predictions for magnetic-field topology, polarization, spectral shapes, and possible IC signals, and discusses plausible formation channels via AGN-driven bubbles and large-scale flows. If validated, this framework would imply that long-lived, magnetically dominated filaments are a common, albeit often unresolved, component of cluster cores and Galactic Center environments, significantly impacting our understanding of relativistic particle transport and non-thermal pressure in these systems.

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<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 $β\sim10^2$) Intracluster Medium (ICM) is limited by the Alfvén speed, $v_{a,ICM}=c_{s,ICM}/β^{1/2}\sim 10^7\,{\rm cm\,s^{-1}}$, GHz-emitting electrons can travel only $l \sim v_{a,ICM}t_r\sim 10\,kpc$ relative to the underlying plasma. Yet, elongated structures spanning hundreds of kpc or even a few Mpc are observed, requiring either a re-acceleration mechanism or another form of synchronization, e.g., by a large-scale shock. We argue that filaments with ordered magnetic fields supported by non-thermal pressure have $v_{a}\gg v_{a,{\rm ICM}}$ and so 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 $ν_b\propto B$ should scale with the ambient gas pressure as $P^{1/2}$, and the emission from such filaments should be strongly polarized. While some of these structures can be observed as "filaments", i.e., long and narrow bright structures, others can be unresolved and have a collective appearance of a diffuse structure, or be too faint to be detected, while still providing channels for electrons' propagation.

Figures (5)

• Figure 1: Examples of radio-bright filaments in clusters and the Galactic Center, where fast propagation of relativistic electrons might be important. Top panel; the core of Nest200047 group, (left, 2021NatAs...5.1261B, LOFAR image at 144 MHz) and the Galactic Center Non-thermal filaments (right, 2019Natur.573..235H, MeerKAT image at 1.3 GHz).Middle panel: the peripheral radio relic at the edge of the X-ray halo in Abell 2256 (2014ApJ...794...24O, VLA image at 1.5 GHz). In all cases, the filaments are long, comparable to the characteristic size of the system. They appear "laminar", and from the polarization measurements in the GC and Abell 2256, the magnetic fields are oriented along the filaments 2019ApJ...884..170P2006AJ....131.2900C. In the case of the Galactic Center, we also know that the field is dynamically strong 2006JPhCS..54....1M. Bottom: the tailed radio galaxy, MysTail in Abell 3266, showing three parallel 40-50 kpc long filaments embedded in the tail. The host position is marked with an "X".
• Figure 2: Expected steepening of synchrotron spectra as particles move from the cluster core in the radial direction from 20 to 140 kpc. All spectra are normalized to unity at $\nu=5\times 10^7\,{\rm GHz}$. The magnetic energy density is assumed to follow the ICM pressure profile $P_t(r)$, i.e., $B_f^2/8\pi=P_t(r)$. For these simulations, we adopted a simple power law pressure profile $P_t\approx 2\times 10^{-10} (r/{\rm kpc})^{-1}\,{\rm erg\, cm^{-3}}$, derived from X-ray observation of the NEST200047 group 2025AA...699A.375M. The solid back curve (marked with "A") shows the synchrotron spectrum at the initial position at $r_1=20\,{\rm kpc}$. It has a low-frequency slope $\alpha_0=-0.5$ and is "aged" in the $15\,\mu{\rm G}$ field for $3\times 10^7\,{\rm yr}$ so that a break develops in the spectrum. The spectra marked with "B" and "C" show the evolved spectra at the final position at $r_2=140\,{\rm kpc}$. These spectra represent two extreme limits. Namely, for "C", the electrons are moving "in a bubble" from $r_1$ to $r_2$ with the velocity $\varv=500\,{\rm km\,s^{-1}}$ (just below the sound speed in the group ICM $c_s\sim700 \,{\rm km\,s^{-1}}$) and suffer from the adiabatic and radiative losses. In addition to the evolution of the particle spectrum, the magnetic field is lower at $r_2$. All these effects combined lead to a very steep spectrum at the final position. In contrast, for the spectrum "B", we assume that electrons quickly propagate "along a static filament" and do not suffer from any losses. The only reason why the spectrum "B" is steeper than "A" is that the magnetic field is lower at the final position, hence a lower critical frequency $\nu_c\propto B$. For each curve, the position of the break frequency (defined here as a frequency where the spectral slope is $\alpha=\alpha_0-1$) is shown with a small vertical magenta bar. This plot illustrates that if the initial spectrum has a break around 1 GHz, and no re-acceleration is present, any "subsonic" regime of propagation (blue lines) will result in a very steep spectrum at 100 MHz. If "fast-track" routes are available for a fraction of electrons, this might reduce the apparent steepening dramatically.
• Figure 3: Top: Map of Tail C in Abell 2256 at 6.8 resolution at 149 MHz, (LOFAR reference), color-coded by its spectral index to 1.5 GHz 2014ApJ...794...24O. Bottom: Observed spectral index between 149 and 1515 MHz, and the corresponding maximum age for relativistic electrons at each location, based on the cutoff frequency calculated from the spectral index, as described in the text. The red line corresponds to an electron transport velocity of 4500 ${\rm km\,s^{-1}}$.
• Figure 4: The spectral index of the GReET tail in A1033 tail as a function of distance from the host, from Fig. 3 in 2017SciA....3E1634D. The red points show the expected steepening of an $\alpha_0= -0.65$ spectrum with a low velocity for the radiating plasma, while the very modest amount of steepening in the final portion of the tail is consistent with a much higher transport velocity of 15,000 km/s, as shown in blue. The bottom plot, in solid black, shows the inferred direction of the host's motion at each position in the tail, assuming the tail is left behind material. The variation in direction around 400 kpc is assumed to arise from a transverse flow, not from a change in the host velocity.
• Figure 5: Top: NW relic of Abell 3667 from 2017SciA....3E1634D. Colors indicate the spectral indices, and different filaments show different characteristic indices. Bottom: spectral indices along five of the filaments, showing how the variations along them are significantly smaller than the differences between them. Numbers on the right indicate the equivalent Mach numbers (and their scatter) if these indices were due to DSA. Errors per measured point are just slightly smaller than the variations, so the intrinsic variations are significantly smaller than observed.