Merging galaxies and clusters: Insights into the role of magnetic fields and the physics of radio relics

Joseph Whittingham

REVIEW 3 major objections 3 minor 39 references

Merging galaxies and clusters: Insights into the role of magnetic fields and the physics of radio relics

T0 review · 3 major / 3 minor · reviewed 2026-08-02 · deepseek-v4-flash

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Pith's one-line read This dissertation argues that magnetic fields are essential for realistic cosmological simulations of disc-galaxy mergers, and that a shock-collision mechanism can explain four of the seven outstanding puzzles about radio relics in galaxy c

desk verdict Solid, novel merger MHD results; the radio-relic 'solutions' rest on injected turbulence parameters that need independent grounding before the claims carry weight. read the letter →

arxiv 2607.14426 v1 pith:OKJVE5CK submitted 2026-07-15 astro-ph.GA astro-ph.HE

Joseph Whittingham This is my paper · ORCID

classification astro-ph.GAastro-ph.HE

keywords magneticfieldsgalaxymergerssmall-scaledynamoradiorelicsclustersshockphysicsMachnumberdiscrepancycosmologicalsimulations

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The work sets out to show that magnetic fields are a required ingredient, not an optional second-order effect, in cosmological galaxy merger simulations. Comparing magnetohydrodynamic and hydro-only zoom-in simulations of gas-rich disc mergers, it finds that MHD remnants regrow extended flocculent (patchy) spiral discs, while their hydro-only twins form compact bar-and-ring remnants that are rare among observed galaxies. For galaxy clusters, the thesis proposes that a merger shock colliding with an accretion shock produces a thin dense sheet, which propagates into upstream density fluctuations and generates a distribution of Mach numbers, shock corrugation, and a Rayleigh-Taylor instability. These effects flatten cosmic-ray electron spectra, bias radio-derived Mach numbers high, compress magnetic fields to microgauss strengths, and allow the high-Mach tail to dominate the emission, explaining four of seven outstanding problems in radio-relic physics. If the claims hold, future galaxy simulations must include magnetic fields at sufficient resolution, and radio relics become a sharper probe of intracluster turbulence.

What carries the argument

Small-scale dynamo: turbulent stretching, twisting, and folding of magnetic field lines amplifies a weak seed field exponentially, but only if the simulation resolves the turbulent eddies; this is the mechanism that turns magnetic fields from a passive tracer into a dynamically important component in merger remnants. Shock-collision sheet: a merger shock hitting an accretion shock produces a thin, dense, shock-compressed sheet; as it propagates into upstream density fluctuations, it generates a distribution of Mach numbers, corrugates the shock front, and drives a Rayleigh-Taylor instability. This sheet scenario is the device through which the work connects upstream ICM turbulence to the obs

What would settle it

Measure the density fluctuation statistics in the ICM immediately upstream of a radio relic in X-ray observations; if the relative variance, spectral slope, and injection scale differ substantially from the values used in the shock-tube runs, the predicted Mach-number distribution and spectral flattening would not reproduce relic observations. On the galaxy side, re-running the highest-resolution merger simulations with a more diffusive MHD scheme (or with a different divergence-control treatment) would test whether the morphology divergence depends on the dynamo's numerical amplification rath

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Extended reading notes

Core claim

In cosmologically consistent zoom-in simulations of gas-rich major galaxy mergers, including ideal magnetohydrodynamics changes the outcome: MHD remnants form extended discs with flocculent spiral structure, whereas hydrodynamic twins form compact remnants with bar-and-ring morphologies rarely seen in observations. The divergence appears only at the highest resolution studied, which the author attributes to a small-scale dynamo that amplifies the magnetic field enough to modify angular-momentum transport, resonances, stellar feedback, and subsequent gas accretion. For radio relics, the thesis claims that when a merger shock collides with an accretion shock it creates a thin dense sheet that

Load-bearing premise

The radio-relic solution rests on the assumption that the unresolved upstream density fluctuations injected into the idealised shock-tube runs faithfully represent the density fluctuations that real merger shocks encounter in the intracluster medium; the galaxy-merger conclusion, meanwhile, leans on attributing the resolution-dependent morphology divergence to a physical small-scale dynamo rather than a resolution-dependent numerical artifact.

Editorial extensions

If this is right

Galaxy merger simulations that ignore magnetic fields or run at insufficient resolution will systematically mispredict remnant morphology, producing bar-and-ring systems that are rare among observed galaxies.
The resolution threshold for the small-scale dynamo explains why previous idealised merger simulations saw little magnetic effect: the dynamo must be resolved to become dynamically relevant.
Radio relics should be expected to show a distribution of Mach numbers and a corrugated shock front, with upstream density fluctuations as a key controlling parameter of their morphology.
Radio-derived Mach numbers of relics are systematically biased high relative to X-ray-derived values because the two probes track different parts of the Mach-number distribution.
The high-Mach tail, not the mean, dominates radio emission, so relics can be observed in shocks with mean X-ray Mach numbers below the critical value near 2.3.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If upstream density fluctuation statistics (relative variance, power-law slope, injection scale) are themselves set by cluster accretion and turbulence, then relic morphology becomes a diagnostic of ICM turbulence rather than a free parameter; the shock-tube runs place the weight of the explanation on those inputs.
The merger result implies that magnetic fields could be a hidden variable in galaxy evolution studies generally, potentially affecting the disc-rebuilding histories of galaxies with quiescent as well as violent merger histories.
The sheet-collision scenario predicts testable relations between spectral-index variations in relics and the density fluctuation spectrum of the ICM, which high-resolution spectral-index maps could confirm or reject.
If laminar cooling models are invalid behind the shock, existing estimates of electron cooling times and re-acceleration scenarios for relics may need revision.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. The merger half is the real contribution: paired hydro/MHD cosmological zoom-ins with identical initial conditions, a resolution study, divergence-error checks, and a plausible small-scale dynamo explanation for why previous idealized work missed the effect. If it holds, it is the first cosmologically consistent demonstration that magnetic fields reshape merger remnants — MHD remnants regrow extended flocculent discs while hydro twins make compact bar-and-ring structures. That is a clean controlled experiment, and Chapters 3 and 4 are already peer reviewed.

The radio-relic half is much less secure. The whole chain — Mach number distribution, shock corrugation, Rayleigh-Taylor instability, microgauss compression, the radio/X-ray discrepancy, the M_crit reconciliation — flows through idealized shock tubes with injected 'unresolved upstream density fluctuations'. The relative variance, power-law slope, and injection scale are chosen inputs. The abstract says Chapter 6 shows the relative variance sets the Mach distribution; that means the four 'solved' problems are consequences of inputs unless the fluctuation spectrum is measured from the cluster zoom-ins or from ICM observations. The visible material does not show that. So 'we solve four of seven outstanding problems' overstates what is established.

The merger morphological claim also has a resolution-dependent sensitivity: the divergence appears only at the highest resolution, and there are n=4 single realizations. That is a real caveat, but not fatal, because the paired design and the resolution trend mitigate it. The thesis is honest about these caveats — the resolution dependence is stated explicitly.

Who this is for: anyone working on galaxy merger simulations or radio relic formation. The merger part deserves a serious referee and probably a citation. The relic part is a promising scenario with unproven input grounding, not a solution.

Recommendation: send it to peer review, but push the author to either measure the injected fluctuation statistics from the cosmological runs or from observations, and to soften the 'solved' language until that is done.

Referee Report

3 major / 3 minor

Summary. This dissertation presents two related but largely independent studies. The first (Chs. 3-4) uses AREPO/Auriga cosmological zoom-in simulations to compare hydrodynamical and MHD realizations of four major disc-galaxy mergers. The central claim is that magnetic fields qualitatively change the merger remnant: MHD remnants regrow extended, flocculent discs, while hydro-only twins form compact bar-and-ring remnants. The authors argue that this is due to a small-scale dynamo that can develop only at sufficient resolution, and that magnetic fields alter angular-momentum transport, subsequent resonances, and feedback. The second study (Chs. 5-6) addresses radio relics. Using cluster zoom-in simulations to identify merger-shock/accretion-shock collisions, the authors build idealized shock-tube runs with injected upstream density fluctuations. They report that this produces a distribution of Mach numbers, shock corrugation, and a Rayleigh-Taylor instability, which they argue flattens cosmic-ray electron spectra, biases radio-derived Mach numbers high, compresses fields to microgauss strengths, breaks laminar cooling assumptions, and makes the high-Mach tail dominate emission. The abstract and conclusions claim that this solves four of seven outstanding problems in radio-relic physics.

Significance. If the merger result holds, it is a substantial step: it would imply that magnetic fields are not a passive tracer but a required ingredient for realistic simulations of gas-rich galaxy mergers, with observable morphological consequences. The controlled comparison of hydro and MHD runs from identical initial conditions, the resolution study, the divergence-error monitoring, and the use of a cosmologically consistent galaxy formation model are genuine strengths. The radio-relic study is also significant in proposing a unified physical scenario - merger shocks colliding with accretion shocks and propagating into upstream turbulence - that could explain several observed relic properties. The use of cosmological simulations to set shock conditions and of CREST/CRAYON+ to make mock observables is a methodological advance. However, the radio-relic conclusions are conditional on an imposed, not measured, upstream fluctuation spectrum, and the merger conclusions rest on four single realizations with the morphological divergence appearing only at the highest resolution. Both parts contain interesting, plausible physics, but the strength of the claims currently exceeds what the evidence esta

major comments (3)

[§1.2, §5.2.3, Ch. 6] The radio-relic results are steered by the injected upstream density fluctuation spectrum. §1.2 states that the shock-tube runs include 'unresolved upstream density fluctuations', and §5.2.3 constructs them from a chosen relative variance, power-law slope, and injection scale. Chapter 6 then shows that the relative variance primarily sets the Mach-number distribution and relic morphology. Because the four claimed 'solved' problems (radio/X-ray Mach mismatch, microgauss fields, laminar-cooling failure, high-Mach-tail dominance) are all governed by this distribution and the resulting corrugation/RT instability, the conclusions are conditional on an input that is neither measured in the cluster zoom-ins nor pinned by ICM observations. The word 'unresolved' in the abstract highlights that the fluctuations are imposed, not resolved. I ask the authors to either calibrate the variance/slope/inj
[§3.3.3, Table 3.2] The claim that 'magnetic fields are thus essential for the accurate simulation of disc galaxies' rests on four major-merger scenarios, each run once. The morphological divergence appears only at the highest resolution; at lower resolution hydro and MHD look similar. While a resolution study is present, it does not by itself establish that the divergence is caused by a physical small-scale dynamo rather than a resolution-dependent numerical artifact: the highest-resolution point is the only one showing the effect, with no convergence test across multiple resolutions in the divergence regime. Moreover, a single realization per scenario cannot exclude merger-orbit stochasticity as the cause. I recommend adding or reporting at least one additional independent initial condition per scenario, or explicit convergence/dynamo evidence at the highest resolution, before drawing the general conclusi
[§5.4, §8.2] The manuscript states that the model 'solves four of the seven outstanding problems' (abstract; Ch. 8). The simulations demonstrate a plausible mechanism, but the comparison to observations is qualitative: no quantitative fit or statistical test is shown between the predicted radio/X-ray Mach distribution, spectral-index variation, or relic morphology and a specific observed relic sample. In addition, the CREST/CRAYON+ post-processing prescriptions (electron injection, critical Mach number) enter the emission maps, so the 'solution' is not derived from first principles. I ask the authors to state explicitly what is demonstrated - a mechanism consistent with existing observations - and what additional evidence would be required to claim a solution, or to provide such a quantitative comparison.

minor comments (3)

[General] The thesis is a compilation of published/submitted papers, and the two parts are not strongly integrated. A short unified discussion of systematics - especially how the unresolved ICM turbulence injected in the shock tubes relates to the cosmological simulations used elsewhere - would improve cohesion.
[Abstract / Ch. 6] The notation 'MX-ray = 2' and 'Mcrit = 2, 3' in the abstract is garbled; please use consistent symbols (e.g., M_X-ray, M_crit) and correct the rendering.
[Figures 3.3-3.4] The relative divergence error is defined only in the text loosely; please define it explicitly in the figure captions or text, including the normalization used for the plotted quantity.

Circularity Check

1 steps flagged · score 6.0 of 10

Radio-relic 'solved problems' reduce to the injected upstream density-fluctuation spectrum: the Mach number distribution is set by the chosen relative variance.

fitted input called prediction [§1.2 Structure of the thesis (description of Ch. 6); see also Ch. 6 and Abstract's 'We hence solve four of the seven outstanding problems']
"varying the relative variance, power law slope, and the injection scale of the upstream density turbulence. In doing so, we are able to show that it is primarily the relative variance that sets the Mach number distribution and impacts the radio relic morphology."

The thesis's headline radio-relic results—the Mach-number distribution, the radio/X-ray Mach bias, microgauss fields, the breakdown of laminar cooling, and the high-Mach-tail dominance—are presented as solving four outstanding problems. But the upstream density fluctuation spectrum is an injected input to the shock-tube runs, not a measured quantity. The text states that the relative variance of the injected turbulence 'sets the Mach number distribution.' Because the fluctuations are described as 'unresolved,' they are imposed rather than resolved from the cluster zoom-in simulations or pinned by ICM observations. Unless that variance, slope, and injection scale are independently constrained, the predicted Mach distribution—and hence the radio/X-ray discrepancy 'explanation' and the other

full rationale

The galaxy-merger half of the thesis is not circular: it is a controlled numerical experiment comparing MHD and hydrodynamic zoom-ins from identical initial conditions, with the morphological outcome tested against observed galaxy properties and a resolution study. The radio-relic half, however, contains a partial circularity. The shock-tube simulations are set up by injecting upstream density fluctuations with a chosen relative variance, power-law slope, and injection scale. Chapter 6 explicitly says the relative variance 'sets the Mach number distribution,' and the Mach-number distribution is the physical quantity that drives the radio/X-ray discrepancy, the dominance of the high-Mach tail, and the other claimed solved problems. Since the fluctuations are called 'unresolved,' they are not measured from the cosmological simulations; they are free inputs. Thus the central radio-relic 'predictions' are consequences of the chosen input spectrum rather than independently derived results. This is a conditional circularity: if the fluctuation parameters were later fixed by observations or resolved simulations, the explanation would become a genuine prediction. As it stands, the radio-relic claims are partially circular, while the galaxy-merger claims are self-contained. Score 6 reflects this partial, input-driven circularity in one of the two central theses.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The merger half rests on the Auriga subgrid model, the ideal-MHD implementation, and a resolution-dependent dynamo interpretation; the relic half rests on injected density-fluctuation statistics and the M_crit ≈ 2.3 threshold. No invented entities (new particles, forces, dimensions) are introduced; the 'dense sheet' and 'flocculent discs' are behaviors of standard MHD, not new postulates.

free parameters (4)

Seed magnetic field strength and orientation = 1e-14 G (comoving), z-aligned
Chosen for the MHD runs (§3.2.2). Authors argue a dynamo erases memory of the seed for a broad range (citing Pakmor et al. 2014); the results depend on that erasure being true at the resolutions used.
Upstream density fluctuation properties in shock-tube runs (relative variance, power-law slope, injection scale) = Not stated in available text; varied in Ch. 6
These carry the radio-relic explanatory chain. If not pinned by the cosmological simulations or observations, the Mach number distribution, corrugation, RT instability, and microgauss compression are functions of these choices.
Auriga subgrid parameters (n_SF = 0.13 cm^-3, wind normalization, feedback coupling) = Inherited from Grand et al. (2017), not retuned
The morphological conclusions are computed within this model. The paper shows MHD does not require recalibration but only discusses qualitatively whether results transfer to other galaxy formation models (§4.4.2).
CREST/CRAYON+ spectral and emission prescriptions = Not stated in available text
The radio-emission claims in Ch. 5-6 depend on the chosen cosmic-ray electron transport/acceleration and synchrotron post-processing parameters; details could not be verified in the truncated text.

assumptions (6)

domain assumption Lambda-CDM cosmology with WMAP-9/Planck parameters underlies the initial conditions
Used throughout (Ch. 2.1, §3.2.1); standard, but merger statistics and accretion geometries inherit these choices.
domain assumption Ideal MHD with Powell 8-wave divergence control adequately captures galactic/cluster field dynamics
§3.2.2; the small-scale dynamo and angular-momentum-transport claims rest on the MHD implementation being physical, including at the resolution where the dynamo 'switches on'.
domain assumption The Auriga subgrid model (Springel-Hernquist ISM, stochastic star formation, wind and BH feedback) is adequate for merger-remnant morphology
§3.2.2; the hydro-vs-MHD comparison isolates magnetic fields only within this model's assumptions.
ad hoc to paper Shock-tube runs with injected unresolved density fluctuations reproduce the essential physics of merger-shock/accretion-shock collisions at relic radii
Ch. 5-6; the four 'solved' problems depend on this. If real ICM conditions differ in fluctuation spectrum, magnetic topology, or geometry, the results may not transfer.
domain assumption The critical Mach number M_crit ≈ 2.3 below which cosmic-ray electron acceleration is inefficient (Kang et al. 2019) is correct
Invoked to frame the weak-shock relic problem; the 'tail of the Mach distribution dominates emission' explanation assumes this threshold.
ad hoc to paper The resolution at which morphological divergence appears corresponds to the physical small-scale dynamo, not a numerical artifact
Ch. 3 §3.3.3 and App. 3.6.3; the resolution-dependence interpretation is asserted via power-spectra evidence and carries the 'magnetic fields are essential' conclusion.

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Cite this review

Pith. "Pith review of Merging galaxies and clusters: Insights into the role of magnetic fields and the physics of radio relics." pith.science (2026). https://pith.science/paper/OKJVE5CK

@misc{pith2026260714426,
  author       = {Pith},
  title        = {Pith review of: Merging galaxies and clusters: Insights into the role of magnetic fields and the physics of radio relics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OKJVE5CK}},
  note         = {Machine review of arXiv:2607.14426}
}

abstract

Mergers have long been understood to be a driver of galaxy and galaxy cluster evolution. They release tremendous amounts of gravitational potential energy - ~$10^{59}$ and ~$10^{64}$ ergs in galaxies and clusters, respectively - which is dissipated in powerful shock waves. In galaxies especially, the strong tidal effects can have profound effects on the remnant morphology. Although the modelling of mergers has a long history, it is only recently that it has been fully appreciated just how sensitive they are to a range of factors, including the existence of circumgalactic media (CGM), accretion along filaments, and pre-existing magnetic fields. Modelling these aspects in a cosmologically-consistent manner necessitates the use of high-resolution cosmological magnetohydrodynamic (MHD) simulations. In this work, we use such simulations to investigate two distinct merger-related phenomena: i) magnetic fields in galaxy mergers, and ii) the origin of radio relics in galaxy clusters.

Figures

Figures reproduced from arXiv: 2607.14426 by the authors.

**Figure 2.1.** Power spectrum showing temperature fluctuations in the CMB as a function of angular scale, as detected by the Planck spacecraft. Image credit: ESA. with very high precision (see, e.g. Jarosik et al., 2011; Planck Collaboration, 2020). Typically this is done using spherical harmonic or “multipole” decomposition, with temperature fluctuations shown as a function of their angular scale. An example of such a power spect… view at source ↗

**Figure 2.2.** Evolution of a density perturbation following linear perturbation theory. Dotted, solid, and dashed lines show dark matter, baryonic, and radiation perturbations, respectively. All perturbations grow initially as ∝ 𝑎 2 , before being suppressed as they enter the horizon during the radiation-dominated era. During this period baryonic and radiative perturbations undergo damped oscillation. At the epoch of recombinatio… view at source ↗

**Figure 2.3.** Cooling rates for a gas with primordial abundance (76% hydrogen, 24 % helium by mass), assuming CIE. Image credit: Thoul and Weinberg (1995) Using Eq. (2.45) and the fact that 𝜎 2 ∝ 𝑘 3𝑃(𝑘), it can then be shown that: 𝜎 2 ∝    𝑀 𝑀∗ −4/3 for 𝑛 = 1 1 for 𝑛 = −3 (2.47) and hence smaller objects collapse first and therefore structure in the Universe forms hierarchically. In particular, this means that smaller … view at source ↗

Figures from the paper (76 more)

**Figure 2.4.** Figure 2.4: Observed galactic stellar mass function (Bell et al., 2003) in solid blue, and halo mass function from the Millennium simulation (Springel et al., 2005b) multiplied by a universal baryon fraction of 𝑓b ≈ 17% (Spergel et al., 2003) in dashed red – this marks the maxim…

**Figure 2.5.** Figure 2.5: Schematic showing the typical size, 𝑅, and magnetic field strength, 𝐵, in various astrophysical objects. Dashed lines indicate scalings of the field strength with 𝑅 −1 and 𝑅 −2 , respectively. Magnetic field strengths in galaxies and clusters are typically on the ord…

**Figure 2.6.** Figure 2.6: The current constraints on intergalactic magnetic fields, where 𝐵 is the field strength, and 𝐿𝐵 is the coherence length. Image credit: Alves Batista and Saveliev (2021). ods can be found in Alves Batista and Saveliev (2021). Blazar-based measurements are not included…

**Figure 2.7.** Figure 2.7: Schematic showing how turbulence results in magnetic field amplification through the small-scale dynamo. Turbulent motions act to stretch, twist, and fold the magnetic field lines. In the final step, the magnetic field lines re-connect, thereby increasing the flux d…

**Figure 2.8.** Figure 2.8: Schematic indicating how an initial distribution of cosmic rays changes as a result of advection, diffusion, and streaming, respectively. Colours indicate the same population at different times. Image credit: Thomas et al. (2020) and 𝜖cr = ∫ 𝐸kin(𝑝) 𝑓 (𝒙, 𝑝, 𝑡)𝑑𝑝, (2…

**Figure 2.9.** Figure 2.9: Schematic representing Fermi I acceleration in the shock-frame. A cosmic ray electron diffuses across the shock front before being deflected by magnetic inhomogeneities. This increases its energy by a factor of O (υ/𝑐) at each crossing. Image credit: Adapted from wor…

**Figure 2.10.** Figure 2.10: Coulomb and inverse Compton losses for varying momenta, redshift, and electron number densities. For typical ICM values, there exists a population of electrons where cooling rates are comparable to the Hubble time. These are good candidates for the so-called “fossil…

**Figure 2.11.** Figure 2.11: Left: Spectral index map for the “Toothbrush” radio relic, where colours give the 𝛼s values. Right: Intensity map for the same object. The emission is approximately 1.9 Mpc in length, and shows an array of morphological features. Image credits: Left: van Weeren et …

**Figure 3.1.** Figure 3.1: Top row: star formation history for the main galaxy in each high-resolution simulation as a function of time. The dashed vertical line marks the time of first periapsis in the MHD simulations. Bottom row: distance between the main progenitors as a function of time fo…

**Figure 3.2.** Figure 3.2: Top row: radially-binned mean magnetic field strength in the galactic disc for each high-resolution simulation as a function of time. Bins have a radial extent of 0.25 kpc and a vertical extent of ±1 kpc. The dashed vertical line marks the time of first periapsis. T…

**Figure 3.3.** Figure 3.3: Face and edge-on slices through the main galaxy in simulation 1330-3M as it rebuilds post-merger. Timings are given from the first periapsis, showing a period when the galactic magnetic field is highly amplified. 1st and 2nd row: slices show the gas density in each c…

**Figure 3.4.** Figure 3.4: Top panel: the mean of the relative divergence error, as a function of time, for simulations run with different resolution. Bottom panel: as above, but for the highest-resolution simulations only. The mean is calculated for all gas cells that lie within 100 kpc of th…

**Figure 3.5.** Figure 3.5: Total stellar and gas mass bound to the main galaxy in each simulation as a function of time. Whilst the stellar mass remains similar across physics models, the bound gas mass at 𝑧 = 0 is generally higher in MHD simulations. Indeed, in some cases, almost all gas lost…

**Figure 3.6.** Figure 3.6: Face and edge-on slices through the merger remnant for each high-resolution simulation, as seen at 𝑧 = 0 (𝑧 = 0.11 for 1605-3). 1st and 2nd row: slices show the magnetic field strength in each gas cell. The magnetic field is broadly axisymmetric, but still shows sign…

**Figure 3.7.** Figure 3.7: 1st and 2nd row: mock SDSS gri composite images showing the merger remnants for all high-resolution MHD simulations. Remnants are seen face and edge-on at 𝑧 = 0 (𝑧 = 0.11 for 1605-3). 3rd and 4th row: as above, but for the hydrodynamic simulations. The morphology of …

**Figure 3.8.** Figure 3.8: Top row: stellar mass surface density profiles for the merger remnant in each high-resolution simulation, as seen at 𝑧 = 0 (𝑧 = 0.11 for 1605-3). Profiles are calculated over a height of ±5 kpc from the midplane. Bottom row: as above, but showing stellar luminosity s…

**Figure 3.9.** Figure 3.9: As [PITH_FULL_IMAGE:figures/full_fig_p078_3_9.png]

**Figure 3.10.** Figure 3.10: As [PITH_FULL_IMAGE:figures/full_fig_p080_3_10.png]

**Figure 3.11.** Figure 3.11: Top row: mean gas density as a function of radius for the merger remnants seen in [PITH_FULL_IMAGE:figures/full_fig_p081_3_11.png]

**Figure 3.12.** Figure 3.12: As [PITH_FULL_IMAGE:figures/full_fig_p082_3_12.png]

**Figure 3.13.** Figure 3.13: As [PITH_FULL_IMAGE:figures/full_fig_p084_3_13.png]

**Figure 3.14.** Figure 3.14: The radially-binned mean magnetic field strength, as in [PITH_FULL_IMAGE:figures/full_fig_p084_3_14.png]

**Figure 3.15.** Figure 3.15: Kinetic and magnetic energy power spectra for the 1330-M simulations, calculated using all gas cells within 5 kpc of the galactic centre. Times are shown from first periapsis (𝑡 = 0 Gyr). The black dotted lines show the slopes of a Kolmogorov (1941) spectrum (∝ 𝑘 −5…

**Figure 3.16.** Figure 3.16: Top panel: star formation rate surface density as a function of gas surface density for 1349-3M, as seen at a lookback time of ∼4 Gyr. The dashed line shows a Kennicutt-Schmidt relation (Schmidt, 1959; Kennicutt, 1998) with exponent 1.5. The dotted line indicates th…

**Figure 3.17.** Figure 3.17: The distance between the galactic centre and the closest black hole for all high-resolution simulations as a function of time. In general, this distance stays well below 5 kpc, confirming the reliability of our galaxy tracking method. The ‘wandering’ nature of the b…

**Figure 3.18.** Figure 3.18: Kinetic and magnetic energy power spectra for the highest-resolution MHD simulations, calculated for gas within a sphere of 5 kpc centred on the galactic centre. The power spectra are shown at 0.5 Gyr after the time of periapsis for each simulation. The black dotted…

**Figure 4.1.** Figure 4.1: Top row: Mock gri composite images showing the evolution of the remnant in the 1349-3M simulation post-merger. Bottom row: As above, but for the 1349-3H hydrodynamic simulation. Labels above each column indicate time elapsed since first closest approach. The formatio…

**Figure 4.2.** Figure 4.2: A schematic illustrating the key stages of development in our MHD and hydrodynamic simulations postmerger. Amplified magnetic fields are able to mediate angular momentum, which typically increases the baryonic concentration, thereby suppressing a bar instability. Th…

**Figure 4.3.** Figure 4.3: Top row: Stellar surface density maps for 1349-3M, where stars have been selected such that they were formed in the previous Gyr. Maps show the distribution at +1, +2, +3, and +4 Gyr post-merger, respectively. Contours are shown at 10, 50, 100, 500, and 1000 M pc−2 .…

**Figure 4.4.** Figure 4.4: Top row: Radially-binned mean magnetic field strength of the main galaxy as a function of time, using annular rings of width 0.25 kpc and depth ±1 kpc from the midplane. A dotted line indicates the point at which the gas density drops below 0.02 M pc−3 . 2nd row: As …

**Figure 4.5.** Figure 4.5: 1st row: Mean gas density as function of radius, measured in spherical shells of width 0.25 kpc for the 1349-3 simulations. 2nd row: The cumulative mass in gas and stars, calculated using the same shells as above. 3rd row: The evolution of the inner Lindblad resonanc…

**Figure 4.6.** Figure 4.6: Top left: The circular velocity as a function of radius in the disc for 1349-3H at 3 Gyr post-merger. Bottom left: The corresponding inner Lindblad (dashed), co-rotation (solid), and outer Lindblad resonances (dotted) as a function of radius. The horizontal line indi…

**Figure 4.7.** Figure 4.7: Left: Face-on mock gri images of the 1349-3 remnants, as seen approximately 5 Gyr post-merger (lookback time of ∼ 1.4 Gyr). Centre: The gas velocity in the disc midplane at this time. Arrows indicate the direction, whilst colours indicate the magnitude. We have remo…

**Figure 4.8.** Figure 4.8: As the second column of [PITH_FULL_IMAGE:figures/full_fig_p114_4_8.png]

**Figure 4.9.** Figure 4.9: Top row: The black hole accretion rate in each simulation as a function of time. Bottom row: The black hole mass in each simulation as a function of time. Black holes in MHD simulations can grow up to a factor of 2 larger than their hydrodynamic analogue, owing to th…

**Figure 4.10.** Figure 4.10: Face-on slices through the disc midplane showing the gas density in the 1349 simulations. Times are given from the start of the merger. 1st row: Standard MHD simulation. 2nd row: MHD simulation, but quasar feedback was turned off at the start of the merger. 3rd row:…

**Figure 4.11.** Figure 4.11: As [PITH_FULL_IMAGE:figures/full_fig_p123_4_11.png]

**Figure 4.12.** Figure 4.12: 1st and 2nd row: Face-on slices through the midplane of the disc for MHD and hydrodynamic simulations, respectively, where colours indicate the star formation rate in each cell. Remnants are seen at +4 Gyr after the beginning of the merger. 3rd and 4th row: As abov…

**Figure 5.1.** Figure 5.1: Top: the mean pressure along the 𝑥-axis at 𝑡 = 0 Myr (dashed) and 𝑡 = 100 Myr (solid) in our Mach 3 Flat simulation (see [PITH_FULL_IMAGE:figures/full_fig_p133_5_1.png]

**Figure 5.2.** Figure 5.2: Cosmological simulation of a galaxy cluster undergoing a major merger at 𝑧 = 0.14. Four left-most panels, clockwise from top left: projected shock-dissipated energy rate, gas pressure, gas density, and dissipationweighted Mach number, respectively. Projections have …

**Figure 5.3.** Figure 5.3: A Mach 3 shock is driven into a turbulent upstream density field. The initial pressure and density values for the shock-tube correspond to those shown in [PITH_FULL_IMAGE:figures/full_fig_p142_5_3.png]

**Figure 5.4.** Figure 5.4: A schematic showing how upstream density turbulence causes velocity turbulence to be generated downstream. The corrugation of the shock front naturally leads to a misalignment of pressure and density gradients (shown here by red and green arrows, respectively). This…

**Figure 5.5.** Figure 5.5: Mach number distributions for all models, where each cell has been weighted by its normalised contribution to the shock surface. Lines indicate the median taken over all snapshots, whilst the shaded values indicate the interquartile range. The addition of magnetic t…

**Figure 5.6.** Figure 5.6: Top row: volume-weighted non-thermal electron spectra generated from our Turb (solid black) and Flat (dashed grey) simulations at 𝑡 = 250 Myr. Blue lines show contributions to the Turb spectrum, where tracers have been binned by time since injection. Bottom row: Hist…

**Figure 5.7.** Figure 5.7: Slices through our fiducial Mach 3 simulation at 𝑡 = 180 Myr showing: i) time since injection, ii) CR electron number density at 𝑝 = 2 × 104 (see text), iii) magnetic field strength, and iv) synchrotron emissivity at 150 MHz. Only tracers that have undergone DSA are …

**Figure 5.8.** Figure 5.8: Slices through our fiducial Mach 3 simulation at 𝑡 = 180 Myr showing plasma beta values. The grey lines mark the corrugated shock surface and the contact discontinuity (i.e., the region within which tracers have been injected). Despite significant amplification, beta…

**Figure 5.9.** Figure 5.9: Left: a phase space diagram of magnetic field strength vs. gas number density for our lower resolution fiducial Mach 3 simulation. Contours cover 10%, 25%, 50%, and 75% of the population, respectively (from darker to lighter colours). Blue colours indicate the initia…

**Figure 5.10.** Figure 5.10: Projections with a depth of 300 kpc through our fiducial Mach 3 simulation at 𝑡 = 180 Myr. These show: i) volume-weighted time since injection, ii) synchrotron-weighted time since injection, iii) volume-weighted magnetic field strength, and iv) synchrotron-weighted …

**Figure 5.11.** Figure 5.11: Left: probability density distributions of the projected magnetic field strength in our fiducial Mach 2 simulation. Solid (dashed) lines represent projections through the shock-compressed region at 𝑡 = 250 Myr (highresolution region at 𝑡 = 0 Myr). Blues lines repre…

**Figure 5.12.** Figure 5.12: Left column: synchrotron intensity at 150 MHz (top) and 1.5 GHz (bottom), respectively, for our fiducial Mach 3 simulation at 𝑡 = 180 Myr. The projection depth is 300 kpc. Right column: spectral index maps between 325 MHz and 150 MHz (top) and 1.5 GHz and 150 MHz (b…

**Figure 5.13.** Figure 5.13 [PITH_FULL_IMAGE:figures/full_fig_p159_5_13.png]

**Figure 5.14.** Figure 5.14: Schematic showing why the trajectory in the colour-colour plane flattens, as shown by the break in the dashed black lines in the left-hand panel, rather than following the standard JP model (dashed grey lines). Lines-ofsight initially intersect homogeneous CR elect…

**Figure 5.15.** Figure 5.15: Version of our fiducial simulation, run with 8 times lower mass resolution. colours indicate density, with the same limits and bounds as shown in [PITH_FULL_IMAGE:figures/full_fig_p165_5_15.png]

**Figure 5.17.** Figure 5.17: As [PITH_FULL_IMAGE:figures/full_fig_p166_5_17.png]

**Figure 5.18.** Figure 5.18: Histograms of the plasma beta values for all gas cells upstream at 𝑡 = 0 Myr (dashed) and in the shock-injected region at 𝑡 = 250 Myr (solid) for our Mach 3 fiducial simulation, weighted by the cell volume. The distribution initially peaks at 100 (marked by a dotted…

**Figure 5.19.** Figure 5.19: As [PITH_FULL_IMAGE:figures/full_fig_p168_5_19.png]

**Figure 6.1.** Figure 6.1: Schematic showing how we vary the 3D power spectra, 𝑃𝜌, of the upstream density turbulence in our simulations. We probe the impact of relative variance (𝜎/𝜇), the injection scale (𝐿inj), and the power law slope (𝛿). Power on spatial scales larger than the injection s…

**Figure 6.2.** Figure 6.2: Histograms of the electron number density, calculated using all gas cells in the initial upstream conditions. Our fiducial value is 𝜎/𝜇 = 0.4 (see text). Each distribution is log-normal and has a mean density set to 3.5×105 cm−3 . a thermal electron number density of…

**Figure 6.3.** Figure 6.3: Slices through our M = 3 simulations at 𝑡 = 250 Myr, where colours indicate gas density and the shock travels from left to right. In each column we vary only one characteristic of the upstream initial conditions. Increasing the relative variance extends the maximum l…

**Figure 6.4.** Figure 6.4: As [PITH_FULL_IMAGE:figures/full_fig_p179_6_4.png]

**Figure 6.5.** Figure 6.5: Cumulative distribution functions showing the relative amount of downstream velocity turbulence at 𝑡 = 250 Myr in the injected region of each of our Mach 3 simulations. Velocity turbulence is measured here by the fraction of the shock-frame gas speed in the 𝑥-compone…

**Figure 6.6.** Figure 6.6: Projected shock-dissipated energy for simulations where we vary only the scale of injection. Each panel has a projection depth of 300 kpc and shows a Mach 3 variation at 𝑡 = 250 Myr. White brackets indicate the to-scale injection length used. The projected shock surf…

**Figure 6.7.** Figure 6.7: Slice through the Mach 2 high relative-variance simulation (𝜎/𝜇 = 0.8) at 𝑡 = 170 Myr. The two leftmost panels show slices through the midplane of the box, with colours indicating gas temperature and gas velocity as a function of sound speed (in the shock-frame), re…

**Figure 6.8.** Figure 6.8: Left: Mach number distributions weighted by each gas cell’s contribution to the shock surface. Black lines indicate the median taken over all snapshots, whilst the shaded values indicate the interquartile range. The grey, vertical, dashed line marks the critical Mach…

**Figure 6.9.** Figure 6.9: Top row: volume-weighted non-thermal CR electron spectra for all simulation variations. Bottom row: histograms indicating the number of injected tracers binned by their distance to the median shock position. Mach 2 and Mach 3 initial shock variations are shown on the…

**Figure 6.10.** Figure 6.10: Left: volume-weighted non-thermal CR electron spectra from our fiducial Mach 2 simulations. Dotted, dashed, and solid lines indicate spectra generated with critical Mach numbers of 1.3, 1.8, and 2.3, respectively. Blue lines show contributions to the Mcrit = 2.3 spe…

**Figure 6.11.** Figure 6.11: Left: Synchrotron intensity at 150 MHz (left column) and spectral index maps between 325 MHz and 150 MHz (right column) for our fiducial Mach 2 simulation at 𝑡 = 250 Myr. The top row has been generated using Mcrit = 1.3, whilst the bottom row uses Mcrit = 2.3. Conto…

**Figure 6.12.** Figure 6.12: Synchrotron intensity maps at 150 MHz and spectral index maps taken between 1.5 GHz and 150 MHz for each of our Mach 2 variations shown at 𝑡 = 250 Myr. We vary one characteristic of the upstream density field in each row. From top to bottom, we vary the relative var…

**Figure 6.13.** Figure 6.13: As [PITH_FULL_IMAGE:figures/full_fig_p190_6_13.png]

**Figure 6.14.** Figure 6.14: Left: Probability density distributions of the projected magnetic field strength, where projections are weighted by the synchrotron emission at 𝜈 = 150 MHz. Each line represents a Mach 2 simulation at 𝑡 = 250 Myr. Right: as previous, but for the Mach 3 simulations. …

**Figure 6.15.** Figure 6.15: Left: the flux density at 150 MHz, 325 MHz, 650 MHz, and 1.5 GHz for our Mach 2 models assuming an LLS equivalent to the Toothbrush relic (see text). Right: as previous, but for our Mach 3 variations. Adding upstream turbulence can substantially increase the spectra…

**Figure 6.16.** Figure 6.16: Table indicting the spectral indices measured for the lines in [PITH_FULL_IMAGE:figures/full_fig_p194_6_16.png]

**Figure 7.1.** Figure 7.1: Schematic showing how tracer data is stored in CREST. Values are for reference purposes only. An index provides the start of the next timestep “block”, with all data in a block ordered by particle ID. Shock data is only saved when the shock flag has a value of 2 or 3…

**Figure 7.2.** Figure 7.2: Gas number density vs. distance, for a shock-tube test. The blue curve shows the data stored from the AREPO simulation, whilst the orange curve shows how CREST interprets the data. Densities are frozen if in a shock-zone cell, and take their post-shock value if in a …

**Figure 7.3.** Figure 7.3: Mach number distributions generated from the Mach 2 Turb simulation introduced in Chapter 5, with values weighted by their normalised contribution to the shock surface. Lines indicate the median taken over all snapshots, whilst the shaded values indicate the interqu…

**Figure 7.4.** Figure 7.4: Wall clock time vs. lookback time for two high-resolution cosmological simulations with 𝑚DM = 2 × 107 M run with on-the-fly shock acceleration. Solid lines show the total wall clock time, whilst dotted lines show just the contribution due to Voronoi-mesh construction…

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