Shocks

High-resolution simulations of shocks in galaxy clusters

Collisions of galaxy clusters are the most energetic events in the Universe since the Big Bang. The shocks they drive are observable as spectacular arcs in the radio sky, the so-called radio relics.

MeerKAT radio image of the radio relics in Abell 3667
The radio relics in the cluster Abell 3667 as seen by MeerKAT. Image taken from de Gasperin et al. (2022).

This radio emission is thought to originate from relativistic electrons accelerated at the shock, which lose their energy as synchrotron radiation in the magnetic field of the intra-cluster medium (ICM).

Further, recent observations show an increasing number of radio relics with complex morphologies. These relics are deformed, patchy and of strongly varying surface brightness.

Shock structures in a simulated galaxy cluster from the COMPASS simulation set
Shock structures found in the COMPASS simulation set.

To study the origin of this deformation and patchiness I work with state-of-the-art MHD zoom-in simulations of galaxy clusters. These simulations contain an on-the-fly shock finder (Beck et al. 2016), which identifies shock surfaces and allows us to estimate the acceleration of CR electrons based on recent results from small-scale plasma simulations.

Shock surfaces in a simulated galaxy cluster, labelled by Virgo
Shock surfaces in a simulated galaxy cluster, classified by Virgo. Each color marks an individual shock surface, the right panel additionally shows particles classified as non-shock (gray). Image taken from Lamparth et al. (2022).

While the on-the-fly shock finder allows us to mark tracer particles that experience a shock, it cannot easily disentangle colliding or overlapping shock waves from simultaneous merger events. To this end I contributed to the development of Virgo, a scalable, unsupervised machine learning pipeline which identifies individual shock surfaces and classifies their associated tracer particles. We presented the package and its application to the COMPASS simulation set in Lamparth et al. (2022).

Surface density, temperature and dissipated shock energy in the Box4 simulation for SPH and MFM
Surface density, temperature and dissipated shock energy in the Box4 simulation, run with SPH (top) and MFM (bottom). Image taken from Böss et al. (2026).

The on-the-fly shock finder described above was built for smoothed particle hydrodynamics (SPH). Fully Lagrangian methods like SPH have historically had a hard time capturing shocks as accurately as grid-based or moving-mesh codes. This is especially true in galaxy clusters, where shocks overlap and collide while being embedded in strong shear flows. To remedy this I developed the first shock finder with shock surface reconstruction for meshless finite mass (MFM) hydrodynamics, using the MFM implementation in OpenGadget3 (Groth et al. 2023). It identifies shocked cells from converging flows, reconstructs the shock surface by walking along the kernel neighbors, and evaluates the Rankine-Hugoniot jump conditions across that surface to obtain the sonic Mach number.

We tested the new shock finder against analytic solutions for hydrodynamic, magnetized and CR-modified shock tubes, as well as Sedov-Taylor blast waves. In cosmological simulations it captures more than three orders of magnitude more dissipated shock energy than the legacy SPH shock finder in the Box4 galaxy group, converges at much lower resolution, and produces CR protons that fill almost the entire volume of our galaxy cluster zoom-in simulations. We presented the method in Böss et al. (2026).