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REVIEW 3 major objections 3 minor 39 references

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

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-02 02:07 UTC pith:OKJVE5CK

load-bearing objection Solid, novel merger MHD results; the radio-relic 'solutions' rest on injected turbulence parameters that need independent grounding before the claims carry weight. the 3 major comments →

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

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

Joseph Whittingham This is my paper
classification astro-ph.GA astro-ph.HE
keywords magnetic fieldsgalaxy mergerssmall-scale dynamoradio relicsgalaxy clustersshock physicsMach number discrepancycosmological simulations
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

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.

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

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

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.

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

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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.

Where Pith is reading between the lines

These are 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.

Editorial analysis

A structured set of objections, weighed in public.

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

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. [§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
  2. [§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
  3. [§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)
  1. [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.
  2. [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.
  3. [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

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

specific steps
  1. 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.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 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.
axioms (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.

pith-pipeline@v1.3.0-alltime-deepseek · 55202 in / 19267 out tokens · 188585 ms · 2026-08-02T02:07:00.866580+00:00 · methodology

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read the original 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 Joseph Whittingham.

Figure 2.1
Figure 2.1. 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… view at source ↗
Figure 2.2
Figure 2.2. 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 … view at source ↗
Figure 2.3
Figure 2.3. 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 t… view at source ↗
Figure 2.4
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 maximum possible stellar content as a function of halo mass. Star formation is heavily suppressed at the low and high halo-mass ends due to feedb… view at source ↗
Figure 2.5
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 order of µG, although this varies depending on the exact conditions and spatial scale observed. Image credit: Akahori et al. (2018). because th… view at source ↗
Figure 2.6
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 in [PITH_FULL_IMAGE:figures/full_fig_p040_2_6.png] view at source ↗
Figure 2.7
Figure 2.7. Figure 2.7: Schematic showing how turbulence results in magnetic field amplification through the small-scale dy￾namo. 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 density by a factor of two. This process continues, leading to exponential growth in the kinematic phase. Image credit: J. Schober. arrive at… view at source ↗
Figure 2.8
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, (2.89) respectively, where 𝐸kin = ( p 𝑝 2 + 1 − 1)𝑚e𝑐 2 is the kinetic energy of a particle. 2.6.3 Transport The transport of cosmic rays foll… view at source ↗
Figure 2.9
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 work by M. Pulupa Streaming When scatterings are sufficiently frequent, the cosmic rays distribution is isotropised in the rest frame of the Al… view at source ↗
Figure 2.10
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” electrons, which help boost radio relic surface brightnesses to observed values through Fermi I re-acceleration. Image credit: Pinzke et a… view at source ↗
Figure 2.11
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 morpho￾logical features. Image credits: Left: van Weeren et al. (2012a). Right: Rajpurohit et al. (2020a). shocks driven by AGN jets (see, e.g., Hardcastle and Croston, 2020, and references therein), … view at source ↗
Figure 3.1
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 for the same simulations. The star formation history of the galaxy does not change significantly with the inclusion of MHD physics. cold gas i… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Top row: radially-binned mean magnetic field strength in the galactic disc for each high-resolution simu￾lation 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. The merger in each simulation is able to substantially amplify the magnetic field in the inner 5 kpc by up to an order of magnitude, with eff… view at source ↗
Figure 3.3
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 cell. 3rd and 4th row: slices show the magnetic field strength in each cell. 5th and 6th row: slices show the relative divergence error in ea… view at source ↗
Figure 3.4
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 the main galaxy. It stays well below 1 per cent in each simulation and decreases with increased simulation resolution. error is seen to altern… view at source ↗
Figure 3.5
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 can be accounted for by a comparable increase in stellar mass. time, as well as the sum of these quantities. For each simulation, the merge… view at source ↗
Figure 3.6
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 significant amounts of small-scale structure. This roughly mirrors the corresponding gas distribution. 3rd and 4th row: slices show gas density … view at source ↗
Figure 3.7
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 the merger remnant is once again systematically different between MHD and hydrodynamic runs. Whilst MHD simulations generally produce MW-lik… view at source ↗
Figure 3.8
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 surface density profiles for the mock SDSS 𝑔-band. Data from MHD simulations are fit simultaneously with exponential and Sérsic profiles usin… view at source ↗
Figure 3.9
Figure 3.9. Figure 3.9: As [PITH_FULL_IMAGE:figures/full_fig_p078_3_9.png] view at source ↗
Figure 3.10
Figure 3.10. Figure 3.10: As [PITH_FULL_IMAGE:figures/full_fig_p080_3_10.png] view at source ↗
Figure 3.11
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] view at source ↗
Figure 3.12
Figure 3.12. Figure 3.12: As [PITH_FULL_IMAGE:figures/full_fig_p082_3_12.png] view at source ↗
Figure 3.13
Figure 3.13. Figure 3.13: As [PITH_FULL_IMAGE:figures/full_fig_p084_3_13.png] view at source ↗
Figure 3.14
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] view at source ↗
Figure 3.15
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 −5/3 ) and a Kazantsev (1968) spectrum (∝ 𝑘 3/2 ), which are theoretically expected for a small-scale dynamo resulting from incompressible tur… view at source ↗
Figure 3.16
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 the approximate position of the cut-off in the star formation rate. Bottom panel: as above, but for 1349-3H. Both follow the same relation, de… view at source ↗
Figure 3.17
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 black hole in simulation 1526-3H likely contributes to the unusual morphology displayed by the corresponding merger remnant. the Kennicutt-Sc… view at source ↗
Figure 3.18
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 lines show the slopes of a Kolmogorov spectrum (∝ 𝑘 −5/3 ) (Kol￾mogorov, 1941), which is theoretically expected for a small-scale dynamo re… view at source ↗
Figure 4.1
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 formation of a strong bar in the hydrodynamic simulation is associated with the development of a stellar ring. The absence of a bar in the MHD simul… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: A schematic illustrating the key stages of development in our MHD and hydrodynamic simulations post￾merger. Amplified magnetic fields are able to mediate angular momentum, which typically increases the baryonic concentration, thereby suppressing a bar instability. This leads to a fundamentally different stellar distribution and manifestation of feedback. A full description of each stage can be found in S… view at source ↗
Figure 4.3
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 . The projection has a vertical extent of ±5 kpc from the midplane. Bottom row: As above, but for 1349-3H. Star formation between 1 and 2 Gyr… view at source ↗
Figure 4.4
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 above, but showing the magnetic to thermal energy ratio in each ring. 3rd row: The absolute value of the total angular momentum for all gas … view at source ↗
Figure 4.5
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 resonance profile over time. Labels above each column indicate time elapsed since the start of the merger. The increased concentration of gas in the… view at source ↗
Figure 4.6
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 indicates the bar pattern speed measured for this galaxy. The intersection of this line with the profiles marks the radial position of the reson… view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Left: Face-on mock gri images of the 1349-3 remnants, as seen approximately 5 Gyr post-merger (look￾back 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 removed arrows from the approximate area of the disc. Right: The surface density of Monte-Carlo tracers that will end up in the disc at 𝑧 = 0, w… view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: As the second column of [PITH_FULL_IMAGE:figures/full_fig_p114_4_8.png] view at source ↗
Figure 4.9
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 the increased gas concentration in these simulations. however, the density of tracers drops strongly, with tracers only evident in thin filame… view at source ↗
Figure 4.10
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: Hydrodynamic simulation, but quasar feedback was turned off at the start of the merger. 4th row: Standard hydrodynamic simulation. It is ap… view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: As [PITH_FULL_IMAGE:figures/full_fig_p123_4_11.png] view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: 1st and 2nd row: Face-on slices through the midplane of the disc for MHD and hydrodynamic simu￾lations, 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 above, but colours indicate gas velocity, with arrows indicating the projected velocity in the CGM. The bar-and-ring structure observed for 1349… view at source ↗
Figure 5.1
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] view at source ↗
Figure 5.2
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 dissipation￾weighted Mach number, respectively. Projections have a depth of ±7.5 Mpc from the cluster centre. Right-most panels: enlarged cut-outs showing slices through the midplane of the projection. The… view at source ↗
Figure 5.3
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] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: A schematic showing how upstream density turbulence causes velocity turbulence to be generated down￾stream. 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 results in a baroclinic term, which in turn induces vorticity, causing the contact discontinuity to become Rayleigh-Taylor unstable. once a… view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Mach number distributions for all models, where each cell has been weighted by its normalised contri￾bution to the shock surface. Lines indicate the median taken over all snapshots, whilst the shaded values indicate the interquartile range. The addition of magnetic turbulence (Flat) to a homogeneous density distribution (Flat-ConstB) broadens the distribution only very mildly. By contrast, the addition o… view at source ↗
Figure 5.6
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: Histograms indicating the total number of injected tracers relative to the shock front, where bins have a width of 2 kpc. Blue and grey colours … view at source ↗
Figure 5.7
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 shown. A Rayleigh-Taylor instability induces a counter-streaming plume (in the shock rest frame) that brings aged, and therefore cooled, ele… view at source ↗
Figure 5.8
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 values are typically well above 10, limiting the ability of the magnetic field to affect dynamics. emission19. Older electrons have had mor… view at source ↗
Figure 5.9
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 initial upstream distribution, whilst red colours show the final state in the injected region at 𝑡 = 250 Myr. A cross marks the median of the dist… view at source ↗
Figure 5.10
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 magnetic field strength. Regions with no injected tracers have been masked (see text for further details). Synchrotron emission is calculate… view at source ↗
Figure 5.11
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 (high￾resolution region at 𝑡 = 0 Myr). Blues lines represent volume-weighting, whilst orange lines represent synchrotron￾weighting, where the synchrotron emission is calculated at 𝜈 = 150 MHz. Arr… view at source ↗
Figure 5.12
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 (bottom), respectively. Intensity fluctuations in this region are a consequence of Mach number variations, whilst spectral index variations to… view at source ↗
Figure 5.13
Figure 5.13. Figure 5.13 [PITH_FULL_IMAGE:figures/full_fig_p159_5_13.png] view at source ↗
Figure 5.14
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-of￾sight initially intersect homogeneous CR electron populations (top right panel), with the same steep spectral curvature. Due to turbulence, later lines-of-sight intersect inhomogeneous p… view at source ↗
Figure 5.15
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] view at source ↗
Figure 5.17
Figure 5.17. Figure 5.17: As [PITH_FULL_IMAGE:figures/full_fig_p166_5_17.png] view at source ↗
Figure 5.18
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, grey line), but shifts towards higher values as cells experience increased gas pressure behind the shock front. Amplification downstream i… view at source ↗
Figure 5.19
Figure 5.19. Figure 5.19: As [PITH_FULL_IMAGE:figures/full_fig_p168_5_19.png] view at source ↗
Figure 6.1
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 scale is set to white noise. 10−6 10−5 10−4 10−3 ne [cm−3 ] 100 101 102 103 104 Counts σ/µ = 0.2 0.4 0.8 [PITH_FULL_IMAGE:figures/full_fig_p… view at source ↗
Figure 6.2
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 𝑛e = 3.5 × 10−5 cm−3 ) and choose the initial upstream pressure to be 𝑃1 = 1 × 10−13 dyne cm−2 . Shocks in observed radio relics cover a ra… view at source ↗
Figure 6.3
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 length of the downstream, but can also bring material behind the contact discontinuity closer to the shock front. Steepening the power spectr… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: As [PITH_FULL_IMAGE:figures/full_fig_p179_6_4.png] view at source ↗
Figure 6.5
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-component, where decreasing values of this fraction indicate higher levels of turbulence. Increasing the relative variance has the greatest impact … view at source ↗
Figure 6.6
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 surface shows “thread” and “knot” features, similar to those observed in real radio relics. The injection scale sets the size of these features.… view at source ↗
Figure 6.7
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 left￾most 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), respectively. The right-most panel is a thin projection with depth 35 kpc, where colours indicate the emission-weighted Mach number. Higher te… view at source ↗
Figure 6.8
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 number above which we inject CR electrons. Colours indicate the simulation variation, with data in the top and bottom panels coming from ou… view at source ↗
Figure 6.9
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 left and right, respectively. Adding a turbulent upstream density field results in flatter spectra (relative to 𝛼e, flat). This is especial… view at source ↗
Figure 6.10
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 spectrum, where tracers have been binned by the highest Mach number they encountered. Vertical, grey lines indicate momenta that contribute mos… view at source ↗
Figure 6.11
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. Contours in the bottom row indicate the previous extent of the emission. Right: as previous, but data is from our lowest relative-variance (𝜎/𝜇 =… view at source ↗
Figure 6.12
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 variance, the power law slope, and the injection scale, respectively. Increasing the relative variance both extends the emission and increases … view at source ↗
Figure 6.13
Figure 6.13. Figure 6.13: As [PITH_FULL_IMAGE:figures/full_fig_p190_6_13.png] view at source ↗
Figure 6.14
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. Relative variance has the greatest impact on the distribution. In many cases, the tail end of the distribution easily reaches µG-strength. t… view at source ↗
Figure 6.15
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 spectral flux density; this is especially true of low-Mach number shocks. Nonetheless, Fermi-I re-acceleration of a fossil CR electron population i… view at source ↗
Figure 6.16
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] view at source ↗
Figure 7.1
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 (indicating shock-surface and post-shock cells, respectively.). In this way, the data saved is kept to a minimum. Ellipses represent array … view at source ↗
Figure 7.2
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 shock-surface or post-shock cell. This helps prevents spurious adiabatic effects during the shock and produces more accurate cooling. • Corr… view at source ↗
Figure 7.3
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 snap￾shots, whilst the shaded values indicate the interquartile range. The dotted (solid) line shows the values produced by the original (updated) shock finder. The original algorithm was unstable … view at source ↗
Figure 7.4
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. The simulation run before the shock-finder update (blue) needed to be stopped at 𝑡lt ≈ 6 Gyr due to the increasingly unaffordable computat… view at source ↗

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