Quasi-perpendicular shocks of galaxy clusters in kinetic simulation

Illustration 1: A Hubble image of the galaxy cluster Abell 1689. Radio observations of the intracluster medium in these giant clusters reveal galaxy halos and other structures of hot gas produced by the intracluster magnetic fields. Astronomers successfully modeled the intracluster fields in the merging cluster Abell 2345, and found more complex turbulence present than had been previously predicted. Credit: N. Benitez, T. Broadhurst, H. Ford, M. Clampin, G. Hartig, G. Illingworth (UCO/Lick), ACS Science Team, ESA, NASA, APOD.

Galaxy clusters – vast collections of galaxies, hot gas, and dark matter bound together with gravitational forces – often host numerous shock waves, including large-scale merger shocks generated during the collision and merging of clusters, when the gas clouds within them collide, creating shock waves propagating through the gas and heating it to high temperatures. Previous observations of radio relics have provided compelling evidence for the acceleration of relativistic electrons at merger shocks. Such radio relics in clusters are up to megaparsec-sized regions of radio emission, typically with an arc-like morphology. This emission shows strong polarization and steep integrated radio spectra. The high polarization in radio relics is attributed to the compression of the perpendicular component of preshock magnetic fields across shocks. Conversely, radio halos, which are formed by electrons accelerated through turbulence, exhibit notably lower polarization. Furthermore, spectral steepening within these relics primarily arises from the postshock aging of cosmic ray electrons due to synchrotron and inverse Compton losses. This allows us to gain insights into the interaction between magnetic fields and high-energy particles.

Merger shocks are also found to propagate in the intracluster medium: hot, dilute, and weakly magnetized, with the magnetic field strength on the order of 1 μG. Correspondingly, hot plasma in this medium is characterized by a high plasma beta parameter, β, representing the ratio of thermal to magnetic pressures. Due to high temperatures, even the most energetic merger shocks typically have low sonic Mach numbers (usually less than 5).

So-called diffusive shock acceleration (DSA), also known as the first-order Fermi process, is considered the most plausible mechanism responsible for particle acceleration to high energies. In this process, particles gain energy by repeatedly crossing the shock front while being scattered between upstream and downstream regions. The essential element of DSA is the particle injection mechanism. DSA is effective only for particles with Larmor radii larger than the shock thickness, typically a few gyroradii of thermal ions. Therefore, thermal particles should be somehow pre-accelerated to suprathermal momenta. This injection is more difficult for electrons than ions due to the lower mass and smaller Larmor radii of electrons. Thus, electron injection to DSA requires some interactions with the waves in the shock that provide their pre-acceleration. However, for the conditions of low-Mach-number shocks in the hot ICM, such mechanisms are not fully understood.

Supercomputer simulations can provide a great help. Fully kinetic particle-in-cell (so-called PIC) simulations are constrained by severe limitations, restricting their applicability to large-scale systems due to significant computational demands. On the contrary, hybrid kinetic simulations, which combine kinetic ions and fluid electrons, can handle much larger macroscopic systems, which makes them particularly valuable for advancing our understanding of the ion DSA process and the ion-scale turbulence in shocks. A combined hybrid kinetic and test-particle model was recently developed by Trotta & Burgess (2019) to study 2D and 3D turbulent structures at low-Mach-number shocks in low-beta solar-wind plasmas. This approach allowed to study the influence of the shock surface fluctuations on the acceleration of suprathermal electrons.

Using the particle-in-cell approach, the Authors previously showed that electrons are energized through the stochastic shock-drift acceleration process facilitated by multi-scale turbulence, including ion-scale shock surface rippling. In the present work our team performed hybrid-kinetic simulations in a range of various quasi-perpendicular foreshock conditions, including plasma beta, magnetic obliquity, and the shock Mach number. We studied the ion kinetic physics responsible for the shock structure and wave turbulence, that in turn affects the particle acceleration processes. The study covers the spatial and temporal scales, allowing the development of large-scale ion turbulence modes in the system. We applied a recently developed generalized fluid-particle hybrid numerical code that can combine fluid modeling for both electrons and ions with an arbitrary number of kinetic species. This model has been limited to a standard hybrid simulation configuration with kinetic ions and fluid electrons. It utilizes the exact form of the generalized Ohm’s law, allowing for an arbitrary choice of mass and energy densities, as well as the charge-to-mass ratio of the kinetic species.

The results show that the properties of ion-driven multi-scale magnetic turbulence in merger shocks are in agreement with the ion structures observed in PIC simulations. In typical shocks with the sonic Mach number M_s=3, the magnetic structures and shock front density ripples grow and saturate at wavelengths reaching approximately four ion Larmor radii. Moreover, only shocks with Mach number > 2.3 develop ripples. At very weak shocks with Mach number ≲ 2.3, weak turbulence is formed downstream of the shock. We observed a moderate dependence of the strength of magnetic field fluctuations on the quasi-perpendicular magnetic field obliquity. However, as the field obliquity decreases, the shock front ripples exhibit longer wavelengths. Finally, we note that the steady-state structure of M_s=3 shocks in high-beta plasmas shows evidence that there is little difference between 2D and 3D simulations. The turbulence near the shock front seems to be a 2D-like structure in 3D simulations.




Original publication: S. S. Boula, J. Niemiec, T. Amano, O. Kobzar, Quasi-perpendicular shocks of galaxy clusters in hybrid kinetic simulations, Astronomy & Astrophysics, 684, A129 (2024).


The research was conducted at the Department of High Energy Astrophysics of the Jagiellonian University’s Astronomical Observatory (OA UJ). The work was carried out thanks to the financial support of the National Science Center through grant 2016/22/E/ST9/00061. The Authors acknowledge Polish high-performance computing infrastructure PLGrid (ACK Cyfronet AGH) for providing computer facilities and support within computational grant no. PLG/2022/015967.



Contact:

Oleh Kobzar Astronomical Observatory Jagiellonian University O.Kobzar [at] oa.uj.edu.pl