Rotation Measure Analysis of Shocks and Sloshing Fronts in a Galaxy Cluster Merger Simulation

TL;DR

This study introduces analytical and full polarized radiative transfer (PRT) analyses of background radio sources behind a FLASH-based galaxy cluster merger simulation to investigate RM signatures from shocks and sloshing fronts. The authors find a local RM enhancement of about $56\%$ behind the shock front and a $\sim 23.3\%$ RM decrease near the sloshing center due to tangled magnetic fields, with beam depolarization amplified by magnetic fluctuations in both scenarios. Full PRT results validate the analytical expectations and reveal that background intensity and intrinsic polarization of the background sources significantly modulate observed polarization, particularly near the cluster core where RM gradients are steep. These results highlight the potential of RM and polarization grids as powerful diagnostics of ICM magnetization and turbulence, with direct relevance to interpreting Fornax-like observations.

Abstract

Recent observations of the Fornax cluster show depolarization signatures on megaparsec scales, which may be associated with shocks and/or sloshing motions during cluster merger and/or in-fall. To investigate the possible reasons behind the depolarization, we carry out analytical and full polarized radiative transfer (PRT) calculations of radio point sources behind a merging galaxy cluster simulated using the FLASH code. With uniform background light, we analyzed the rotation measure (RM) morphology near the shock front and the cluster center, where sloshing cold fronts appear. For the shock scenario, we find a local RM enhancement by $\sim56\%$ behind the shock front on megaparsec scales, arising from the compression of hot gas and magnetic field lines. Behind the sloshing cold front, the cluster center shows decrement in RM magnitude by $\sim23.3\%$, as a result of the cancellation effect of randomly-oriented magnetic fields induced by sloshing-driven turbulence. We find that beam depolarization increases behind shock fronts and across sloshing cold fronts, indicating enhanced magnetic field fluctuations across the plane of the sky in both scenarios. By fully accounting for all radiative transfer coefficients in the PRT calculations, the uniform background light becomes more depolarized near the cluster center, with the effect growing more pronounced as background intensity decreases. This suggests that synchrotron emission and Faraday rotation of the intracluster medium can significantly influence the polarization of background sources.

Figures (11)

• Figure 1: Projected X-ray emissivity in energy band $0.5 - 7$ keV (left column) and RM (right column) zoomed-in towards the shock front at 1.6 Gyr (pre-shock; first row) and at 2 Gyr (post-shock; second row). Contours represent evenly-spaced X-ray surface brightness from -5 to -7.5, with a step size of $d=-0.5$ on a logarithmic scale. We find RM enhancement behind the shock front, while the depolarization effect is not apparent.
• Figure 2: Slice plot of gas density across the shock front, with gravitational potential contours (cyan dashed lines) overlaid with magnetic field vectors (black arrows). The subcluster's central position (dip in the gravitational potential) coincides with the tip of the shock front, indicating the lack of separation between the shock front and the contact discontinuity in our merger simulation.
• Figure 3: The left and right columns show DOLP maps at 1.6 Gyr (before shock passage) and 2 Gyr (after shock passage), respectively. The DOLP maps are smoothed by sigma (FWHM) of 0 (no smoothing; top row), $0.5\times 0.5$ pixels (middle row) and $1\times 1$ pixels (bottom row). The overlaid contours of X-ray surface brightness in cyan dashed lines represent evenly-spaced values from -5 to -7, with a step size of $d=-1$ on a logarithmic scale. Beam depolarization occurs behind the shock front due to an enhance in magnetic field fluctuations across the plane of the sky, with the effect becoming more pronounced as the beam size increases.
• Figure 4: Projected X-ray emissivity in energy band $0.5 - 7$ keV (left column) and RM (right column) zoomed-in towards the sloshing cold front at 1.2 Gyr (at the onset of sloshing; first row) and at 2.7 Gyr (after sloshing occurs; second row) Contours in the top and bottom panels represent evenly-spaced X-ray surface brightness from -2.1 to -3.6 and -2.5 to -3.75, with their respective step sizes being -0.3 and -0.25 on a logarithmic scale. The RM at cold front has in general decreased after sloshing occurs, as a result of strong magnetic field entanglement along the line of sight.
• Figure 5: Spatial evolution of the magnetic field’s Z component ($B_z$) along the Z axis, sampled across the X axis from $x = -200~\rm{kpc}$ to $x = 200~\rm{kpc}$, with each color representing different line of sight. This region is experiencing sloshing motions. The left and right panels display $B_z$ profiles at 1.2 Gyr and 2.7 Gyr, respectively. As sloshing progresses, the magnetic field becomes more tangled on smaller scales, as indicated by an increased standard deviation ($\sigma$) of $B_z$. This increased tangling leads to stronger cancellation effects in the RM.