arXiv subjects

Maria Werhahn

Publications and source records attributed to Maria Werhahn.

At least 19 recordsLinked to original sources

arXiv2026

Same galaxy, different CGM: how the metal loading of galactic winds regulates the baryon cycle in Milky Way-mass galaxies

The circumgalactic medium (CGM) is both the reservoir of gas that fuels star formation and galaxy growth, and the repository for the mass, energy, and metals expelled through stellar evolution and feedback. We present a controlled experiment using a suite of five cosmological magnetohydrodynamical simulations of a Milky Way-mass halo from the Auriga suite, where we vary the metal content and energy loading of galactic winds driven by stellar feedback. We chose these parameters in combination such that all five runs obtain very similar (within $\approx$10\%) $z=0$ stellar masses and morphologies and thus produce similar amounts of metals throughout their lifetimes. Our simulations differ substantially in where these metals end up, spatially within the halo and across the different baryonic components (stars, gas disc, CGM, and the intergalactic medium). The metal content affects the cooling efficiency of the halo gas, regulating the CGM cool gas fraction and the accretion rates onto the galaxy. Between our two extreme models, we report an order of magnitude difference in the median gas metallicity at vertical heights $|z| \gtrsim 30$ kpc above the disc plane. Current constraints on the metallicity of the Milky Way halo gas from absorption-line measurements of intermediate- and high-velocity clouds at $|z| \lesssim 15$ kpc are broadly consistent with our simulations, though a direct comparison is limited by differences in the adopted methods. Our findings show that galaxies with nearly identical stellar content and morphology can differ substantially in their CGM, which offers a promising avenue for constraining feedback physics within galaxy formation models.

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arXiv2026

Simulating realistic radio morphologies of Fanaroff-Riley I jets in a self-regulating cool-core cluster

Active galactic nucleus (AGN) jets radiate radio synchrotron emission displaying a wide range of morphologies. At the same time, they provide heat to prevent cooling flows in cool-core galaxy clusters. We produce mock radio observations of AGN jets in a self-regulating cool-core galaxy cluster. To this end, we employ magneto-hydrodynamical simulations of an idealised Perseus-like galaxy cluster, in which accretion-powered low-density jets accelerate cosmic ray protons and electrons by means of a sub-grid model. Cosmic ray electron spectra are spatially and temporally evolved along Lagrangian tracer trajectories using the Fokker-Planck solver Crest to produce radio synchrotron emission. Self-regulated AGN jets stabilize the cool-core cluster against cooling flows and produce realistic Fanaroff-Riley I (FRI) and disturbed lobe morphologies, in contrast to symmetrical lobe structures obtained with a single jet outburst of fixed power. Our mock radio observations are viewed in a blazar configuration - along the jet axis - and exhibit complex radio-emitting lobe structures despite this. This highlights the strong deflection of light jets by cold gas structures and suggests that small-scale black hole and jet properties cannot be inferred from kpc-scale FRI radio lobe morphologies. Combining self-consistently evolved magnetic fields and electron spectra enables us to explain a known observational phenomenon, whereby radio observations of AGN lobes on galaxy cluster scales occasionally display similar spatial extents at different frequencies: in 1-50 $\mu$G magnetic fields obtained in our cool-core environment, both freshly accelerated and hundreds-of-Myr-old electrons are able to contribute to the 150 MHz - 1.4 GHz frequency range.

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arXiv2026

Revisiting radio synchrotron diagnostics in star-forming galaxies

Radio continuum observations are widely used to study cosmic ray (CR) electron populations and transport processes in star-forming galaxies, but their interpretation relies on several simplifying assumptions. Here, we revisit three common assumptions: that some vertical radio profiles can be explained by CR advection alone, that radio spectra directly trace the galaxy-wide CR electron spectrum, and that bremsstrahlung and Coulomb losses are negligible for radio-emitting electrons. We model radio emission using time-dependent CR electron evolution in a magnetohydrodynamical simulation of an isolated Milky Way-mass galaxy. CR electron spectra are evolved self-consistently along Lagrangian tracer particles with the CREST framework, including injection at supernova remnants, advection with the gas, and spatially and temporally varying radiative losses. We compare these results to commonly adopted steady-state models. We find that advection-only transport in self-consistently driven galactic winds fails to reproduce the extended vertical radio intensity profiles observed in edge-on galaxies, despite reproducing the observed steepening of spectral indices with height. This is because slowly accelerating winds keep electrons in strong cooling environments for too long. Matching observed radio haloes with advection alone requires unrealistically high midplane wind velocities, implying that additional transport or re-acceleration processes are required. Although galaxy-integrated CR electron spectra at radio-emitting energies are similar across models, the resulting synchrotron spectra differ systematically because radio emission is biased toward young electrons in dense, strongly magnetised regions. Finally, we show that bremsstrahlung and Coulomb losses significantly shape radio spectra even when their loss rate is subdominant and therefore cannot be neglected.

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arXiv2026

Zooming in on radio relics -- II. How relic morphology probes density fluctuations at the edge of galaxy clusters

Gas properties in the outer intracluster medium (ICM) are not well-constrained, as traditional probes lose sensitivity at Mpc distances. We show that the morphology of radio relics effectively encodes the power spectrum of the surrounding density fluctuations, and that they hence represent a new observational window. To demonstrate this, we use cosmologically motivated shock-tube simulations in which we systematically vary the coherence length, amplitude, and power-law slope of the upstream density power spectra. We then post-process our simulations with the cosmic ray electron spectral solver, Crest, thereby producing a suite of mock radio relics. We find that the downstream morphology of our simulated relics is independently sensitive to each of the aforementioned parameters. Specifically, we show that observed 'double strand' features can be formed by curved shock fronts in projection, and that the scale of these features maps directly to the fluctuation coherence length. Increasing the fluctuation amplitude, meanwhile, progressively lengthens the downstream extent of the relic, thus explaining why relics are observed to be broader than the idealised expectation. It also broadens the Mach number distribution across the shock, which simultaneously increases the integrated radio flux density and produces patchier emission. Finally, steepening the power-law slope makes 'double strand' features more likely, and additionally increases both the number of radio filaments oriented parallel to the shock front and their spacing. At higher Mach numbers, steepening the power-law slope can further lead to the production of curved radio filaments, which trace large eddies. We apply our analysis to the Toothbrush and Sausage relics, and find evidence for a typical fluctuation coherence length of ~500 kpc, a non-uniform amplitude, and power spectra that are steeper than a Kolmogorov-like scaling.

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arXiv2026

The diffuse gamma-ray sky of a Milky Way analogue: Local diversity and global constraints

Diffuse gamma-ray emission is a key tracer of cosmic rays (CRs) in galaxies, encoding information about their transport, energetics, and interactions with the interstellar medium. Interpreting the Milky Way gamma-ray sky is challenging because the observed emission depends on the three-dimensional distributions of CRs and gas, as well as the observer location within the Galaxy. Using the Rhea suite of CR-MHD simulations of a Milky Way analogue, we study how pion-decay gamma-ray emission varies with galactic environment, local conditions, and CR transport physics. Emission is computed in post-processing under steady-state assumptions, enabling analysis of luminosities, spectra, full-sky maps, and angular power spectra (APS) for multiple observer positions, including those inside Local-Bubble-like cavities. The simulated galaxy reproduces Milky Way-like gamma-ray luminosities and spectral slopes without parameter tuning. While total luminosity is relatively stable, the morphology of the gamma-ray sky varies strongly with observer location due to the complex local gas distribution, consistent with observations. For all observers, the APS traces gas column density rather than the smoother CR energy density, in agreement with previous studies. Comparisons with Fermi-LAT data show good agreement in both the all-sky spectrum and APS, with a diffusion coefficient scaling proportional to E^0.5 providing the best match. These results show that key features of Galactic gamma-ray emission arise naturally in self-consistent CR-MHD simulations. Gas density fluctuations primarily shape emission morphology, while CR transport governs spectral and structural properties. The Rhea simulations provide a physically grounded framework for interpreting diffuse gamma-ray observations and highlight the importance of local environment in tracing Galactic CR physics.

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arXiv2026

Simulating cosmic ray electron spectra and radio emission from an AGN jet outburst in a cool-core cluster

Active galactic nucleus (AGN) powered jets can accelerate cosmic ray electrons, leading to the observed radio synchrotron emission. To simulate this emission, jet dynamics in galaxy clusters must be coupled to electron spectral modelling. We run magneto-hydrodynamic (MHD) simulations of a single AGN jet outburst in a Perseus-like galaxy cluster and adopt a sub-grid model for the acceleration of cosmic ray protons and electrons at unresolved internal shocks in the jet. We evolve cosmic ray electron spectra along Lagrangian trajectories using the Fokker-Planck solver Crest and compute the non-thermal emission using Crayon+. The resulting total electron spectrum reaches a steady-state slope at high momenta, with a gradually decreasing normalization over time, while the lower-momentum portion continues to resemble a freely cooling spectrum. The interaction of the jets with the turbulent cluster environment inflates lobes which rise buoyantly, induce amplification of the magnetic fields and uplift old cosmic ray populations in the wake of the bubbles. We connect radio spectral indices to electron injection ages: at a given radio frequency, weaker magnetic fields are illuminated by higher momenta electrons, whose age is determined by the last injection event. On the other hand, stronger magnetic fields are illuminated by lower momenta electrons, whose age is determined by the maximum energy injection event in the past. This powerful approach allows us to relate the underlying MHD properties to electron spectra and the resulting radio synchrotron emission, thereby enabling us to infer the underlying physics from observed radio properties.

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arXiv2025

Steady-State or Not? The Evolution of Cosmic Ray Electron Spectra in Galaxies

Cosmic ray (CR) electrons are key tracers of non-thermal processes in galaxies, yet their spectra are often modelled under the untested assumption of steady state between injection and cooling. In this work, we present a time-dependent modelling of CR electron spectra in a galactic context using the CREST code, applied to magnetohydrodynamical simulations of an isolated Milky Way-mass galaxy performed with AREPO. CR electrons are injected at supernova sites and evolved with adiabatic changes and cooling processes on Lagrangian tracer particles, including losses from synchrotron, inverse Compton, bremsstrahlung, and Coulomb interactions. We compare these fully time-dependent spectra to local and global steady-state models computed with CRAYON+, as well as to one-zone analytic steady-state solutions. We find that the global CR electron spectrum in the simulated galactic disk closely resembles a steady-state solution up to energies of 500 GeV, with deviations only at higher energies where cooling times become shorter than injection timescales. High-energy electrons are dominated by recently injected populations that have not yet reached equilibrium, however, producing a steeper spectrum and lower normalisation than a steady-state model predicts. Spatially, the electrons modelled on-the-fly with CREST are more confined to the star-forming disk, in contrast to the more extended distributions from steady-state post-processing models. Our results demonstrate that while steady-state assumptions capture the bulk CR electron population in star-forming disks, a time-dependent treatment is essential to describe the high-energy and outflowing components.

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arXiv2025

Robust magnetic field estimates in star-forming galaxies with the equipartition formula in the absence of equipartition

The equipartition model is widely used to estimate magnetic field strength from synchrotron intensity in radio galaxies, yet the validity of its underlying assumptions remains uncertain. Using an Arepo simulation which incorporates a two-moment cosmic ray (CR) transport scheme and a multiphase interstellar medium, we compare magnetic fields inferred from synthetic synchrotron emission maps with the true fields in the simulation. Starting from the derivation of the equipartition formula, we find that the deviation between the equipartition magnetic field and the true magnetic field depends only weakly on the ratio of the magnetic to the CR energy density. In practice, for both face-on and edge-on projections, the equipartition model slightly overestimates the total synchrotron-weighted magnetic field with mean offsets of 32% (0.17 dex) and 36% (0.2 dex), even though the energy equipartition between CR protons and magnetic fields does not hold locally. Beyond these average offsets, a clear trend emerges in edge-on projections that the model underestimates the field in the disk and overestimates it in the halo. Our results demonstrate that the validity of the equipartition model depends only weakly on the strict fulfillment of energy equipartition, and that the equipartition model remains a practical method for estimating magnetic field strengths in face-on projection maps based on our CR-magnetohydrodynamics simulation.

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arXiv2025

Unveiling the Impact of Cosmic Rays on the Disc Sizes and Outflows from Dwarf Scales to Galaxy Groups

Cosmic rays (CRs) are a non-thermal energy component in the interstellar and circumgalactic medium (CGM) that can act as an additional feedback channel beyond thermal and kinetic feedback from stars and AGN. They influence galaxy evolution by altering gas properties, regulating star formation, and shaping galactic outflows. We investigate these effects using a suite of cosmological zoom-in simulations, which incorporate CR transport and feedback on top of the Auriga galaxy formation model. Our simulations span a wide range of halo masses, from dwarf galaxies to small groups ($M_{200\mathrm{c}}= 10^{10} - 10^{13}~\mathrm{M}_\odot$), allowing us to assess the mass-dependent impact of CRs in a cosmological setting. We find that CRs have the strongest impact in lower-mass galaxies ($M_{200\mathrm{c}} < 10^{12}~\mathrm{M}_\odot$), where they suppress star formation rates by up to 50\%, reduce gas and stellar half-light radii, and drive outflows that reach higher velocities at the virial radius compared to simulations without CRs. These CR-enhanced outflows also transport more metals and magnetic fields into the CGM, leading to higher CGM metallicities, stronger magnetisation, and lower CGM temperatures. In more massive galaxies, CRs do not significantly affect star formation or outflow properties, likely because thermal and kinetic feedback from stars and AGN dominate in this regime. However, CRs still influence galaxy morphology across all halo masses by reducing the gas half-mass radius and stellar half-light radius. Finally, variations in CR transport properties, such as different diffusion coefficients or the exclusion of Alfv\'en cooling, significantly affect star formation, CGM properties, and outflows in lower-mass galaxies. This sensitivity makes these galaxies key environments for testing CR transport models and refining our understanding of their role in galaxy evolution.

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arXiv2025

Auriga Superstars: Improving the resolution and fidelity of stellar dynamics in cosmological galaxy simulations

Cosmological hydrodynamical simulations have become an indispensable tool to understand galaxies. However, computational constraints still severely limit their numerical resolution. This not only restricts the sampling of the stellar component and its direct comparison to detailed observations, but also the precision with which it is evolved. To overcome these problems we introduce the \emph{Superstars} method. This method increases the stellar mass resolution in cosmological galaxy simulations in a computationally inexpensive way for a fixed dark matter and gas resolution without altering any global properties of the simulated galaxies. We demonstrate the \emph{Superstars} method for a Milky Way-like galaxy of the Auriga project, improving the stellar mass resolution by factors of $8$ and $64$ at an additional cost of only $10\%$ and $500\%$, respectively. We show and quantify that this improves the sampling of the stellar population in the disc and halo without changing the properties of the central galaxy or its satellites, unlike simulations that change the resolution of all components (gas, dark matter, stars). Moreover, the better stellar mass resolution reduces numerical heating of the stellar disc in its outskirts and keeps substructures in the stellar disc and inner halo more coherent. It also makes lower mass and lower surface brightness structures in the stellar halo more visible. The \emph{Superstars} method is straightforward to incorporate in any cosmological galaxy simulation that does not resolve individual stars.

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arXiv2025

Quantifying the intrinsic variability due to randomness of the Auriga galaxy formation model

Numerical simulations have become an indispensable tool in astrophysics. To interpret their results, it is critical to understand their intrinsic variability, that is, how much the results change with numerical noise or inherent stochasticity of the physics model. We present a set of seven realisations of high-resolution cosmological zoom-in simulations of a Milky Way-like galaxy with the Auriga galaxy formation model. All realisations share the same initial conditions and code parameters, but draw different random numbers for the inherently stochastic parts of the model. We show that global galaxy properties at $z=0$, including stellar mass, star formation history, masses of stellar bulge and stellar disc, the radius and height of the stellar disk change by less than $10\%$ between the different realisations, and that magnetic field structures in the disc and the halo are very similar. In contrast, the star formation rate today can vary by a factor of two and the internal morphological structure of the stellar disc can change. The time and orbit of satellite galaxies and their galaxy properties when falling into the main halo are again very similar, but their orbits start to deviate after first pericenter passage. Finally, we show that changing the mass resolution of all matter components by a factor of $8$ in the Auriga model changes galaxy properties significantly more than the intrinsic variability of the model, and that these changes are systematic. This limits detailed comparisons between simulations at different numerical resolutions.

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arXiv2025

The role of magnetic fields in ram pressure stripping of satellite galaxies in the circumgalactic medium around massive galaxies

The presence of magnetic fields in galaxies and their haloes could have important consequences for satellite galaxies moving through the magnetised circumgalactic medium (CGM) of their host. We therefore study the effect of magnetic fields on ram pressure stripping of satellites in the CGM of massive galaxies. We use cosmological `zoom-in' simulations of three massive galaxy haloes ($M_{\rm{200c}} = 10^{12.5-13}$ M$_\odot$), each simulated with and without magnetic fields. Across our full sample of satellite galaxies (11 with magnetic fields and 10 without), we find that the fraction of gas retained after infall through the CGM shows no population-wide impact of magnetic fields. However, for the most massive satellites, we find that twice as much gas is stripped without magnetic fields. The evolution of a galaxy's stripped tail is also strongly affected. Magnetic fields reduce turbulent mixing, inhibiting the dispersion of metals into the host CGM. This suppressed mixing greatly reduces condensation from the CGM onto the stripped tail. By studying the magnetic field structure, we find evidence of magnetic draping and attribute differences in the stripping rate to the draping layer. Differences in CGM condensation are attributed to magnetic field lines aligned with the tail suppressing turbulent mixing. We simulate one halo with enhanced resolution in the CGM and show these results are converged with resolution, though the structure of the cool gas in the tail is not. Our results show that magnetic fields can play an important role in ram pressure stripping in galaxy haloes and should be included in simulations of galaxy formation.

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arXiv2025

The dynamical impact of cosmic rays in the Rhea magnetohydrodynamics simulations

This study explores the dynamical impact of cosmic rays (CRs) in Milky Way-like galaxies using the Rhea simulation suite. Cosmic rays, with their substantial energy density, influence the interstellar medium (ISM) by supporting galactic winds, modulating star formation, and shaping ISM energetics. The simulations incorporate a multi-phase ISM, self-consistent CR transport in the advection-diffusion approximation, and interactions with magnetic fields to study their effect on galaxy evolution. Key findings reveal that CRs reduce star formation rates, and drive weak but sustained outflows with mass loading factors of $\sim0.2$, transporting a substantial fraction (20%-60%) of the injected CR energy. These CR-driven outflows are launched not just from the galactic center but across the entire disk, illustrating their pervasive dynamical influence. Galactic disks supported by CRs exhibit broader vertical structures compared to magnetic-field-dominated setups, though the scale heights are similar. CR feedback enhances magnetic flux transport to the circumgalactic medium (CGM), leading to a magnetically enriched CGM with field strengths of $\sim0.5\mu\mathrm{G}$ while reducing gas temperatures to $\lesssim10^5\,\mathrm{K}$. The CR energy is relatively smoothly distributed in the disk, with gradient lengths exceeding the typical size of molecular clouds, indicating that the CR behavior is not adiabatic.

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arXiv2024

Zooming-in on cluster radio relics -- I. How density fluctuations explain the Mach number discrepancy, microgauss magnetic fields, and spectral index variations

It is generally accepted that radio relics are the result of synchrotron emission from shock-accelerated electrons. Current models, however, are still unable to explain several aspects of their formation. In this paper, we focus on three outstanding problems: i) Mach number estimates derived from radio data do not agree with those derived from X-ray data, ii) cooling length arguments imply a magnetic field that is at least an order of magnitude larger than the surrounding intracluster medium (ICM), and iii) spectral index variations do not agree with standard cooling models. To solve these problems, we first identify typical shock conditions in cosmological simulations, using the results to inform significantly higher resolution shock-tube simulations. We apply the cosmic ray electron spectra code CREST and the emission code CRAYON+ to these, thereby generating mock observables ab-initio. We identify that upon running into an accretion shock, merger shocks generate a shock-compressed sheet, which, in turn, runs into upstream density fluctuations in pressure equilibrium. This mechanism directly gives rise to solutions to the three problems: it creates a distribution of Mach numbers at the shock-front, which flattens cosmic ray electron spectra, thereby biasing radio-derived Mach number estimates to higher values. We show that this effect is particularly strong in weaker shocks. Secondly, the density sheet becomes Rayleigh-Taylor unstable at the contact discontinuity, causing turbulence and additional compression downstream. This amplifies the magnetic field from ICM-like conditions up to microgauss levels. We show that synchrotron-based measurements are strongly biased by the tail of the distribution here too. Finally, the same instability also breaks the common assumption that matter is advected at the post-shock velocity downstream, thus invalidating laminar-flow based cooling models.

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arXiv2024

Anisotropic thermal conduction on a moving mesh for cosmological simulations

In weakly collisional, strongly magnetised plasmas such as the intracluster medium (ICM), hot accretion flows and the solar corona, the transport of heat and momentum occurs primarily along magnetic field lines. In this paper we present a new scheme for modelling anisotropic thermal conduction which we have implemented in the moving mesh code AREPO. Our implementation uses a semi-implicit time integration scheme which works accurately and efficiently with individual timestepping, making the scheme highly suitable for use in cosmological simulations. We apply the scheme to a number of test-problems including the diffusion of a hot patch of gas in a circular magnetic field, the progression of a point explosion in the presence of thermal conduction, and the evolution and saturation of buoyancy instabilities in anisotropically conducting plasmas. We use these idealised tests to demonstrate the accuracy and stability of the solver and highlight the ways in which anisotropic conduction can fundamentally change the behaviour of the system. Finally, we demonstrate the solver's capability when applied to highly non-linear problems with deep timestep hierarchies by performing high-resolution cosmological zoom-in simulations of a galaxy cluster with conduction. We show that anisotropic thermal conduction can have a significant impact on the temperature distribution of the ICM and that whistler suppression may be relevant on cluster scales. The new scheme is, therefore, well suited for future work which will explore the role of anisotropic thermal conduction in a range of astrophysical contexts including the ICM of clusters and the circumgalactic medium of galaxies.

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arXiv2024

Environment matters: stronger magnetic fields in satellite galaxies

Magnetic fields are ubiquitous in the universe and an important component of the interstellar medium. It is crucial to accurately model and understand their properties in different environments and across all mass ranges of galaxies to interpret observables related to magnetic fields correctly. However, the assessment of the role of magnetic fields in galaxy evolution is often hampered by limited numerical resolution in cosmological simulations, in particular for satellite galaxies. To this end, we study the magnetic fields in high-resolution cosmological zoom simulations of disk galaxies (with $M_{200}\approx10^{10}$ to $10^{13}\,\mathrm{M}_\odot$) and their satellites within the Auriga galaxy formation model including cosmic rays. We find significantly higher magnetic field strengths in satellite galaxies compared to isolated dwarfs with a similar mass or star-formation rate, in particular after they had their first close encounter with their host galaxy. These are stronger on average by factors of 2-8 when compared at the same total mass, with a large scatter, ranging up to factors of $\sim$15. While this result is ubiquitous and independent of resolution in the satellites that are past their first infall, there seems to be a wide range of amplification mechanisms acting together. Our result highlights the importance of considering the environment of dwarf galaxies when interpreting their magnetic field properties as well as related observables such as their gamma-ray and radio emission, the latter being particularly relevant for future observations such as with the SKA observatory.

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arXiv2024

Simulating Radio Synchrotron Morphology, Spectra, and Polarization of Cosmic Ray Driven Galactic Winds

The formation of galaxies is significantly influenced by galactic winds, possibly driven by cosmic rays due to their long cooling times and better coupling to plasma compared to radiation. In this study, we compare the radio observations of the edge-on galaxy NGC 4217 from the CHANG-ES collaboration catalog with a mock observation of an isolated galaxy based on the arepo simulation that adopts the state-of-the-art two-moment cosmic ray transport treatment and multiphase interstellar medium model. We find significant agreement between the simulated and observed images and spectroscopic data for reasonable model parameters. Specifically, we find that (i) the shape of the intensity profiles depends weakly on the magnitude of the magnetic field, the distance of the simulated galaxy, and the normalization of the CR electron spectrum. The agreement between the mock and actual observations is degenerate with respect to these factors; (ii) the multi-wavelength spectrum above 0.1 GHz is in agreement with the radio observations and its slope is also only weakly sensitive to the magnetic field strength; (iii) the magnetic field direction exhibits X-shaped morphology, often seen in edge-on galaxies, which is consistent with the observations and indicates the presence of a galactic-scale outflow. Our results highlight the importance of incorporating advanced cosmic ray transport models in simulations and provide a deeper understanding of galactic wind dynamics and its impact on galaxy evolution.

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arXiv2023

Magnetic field amplification in cosmological zoom simulations from dwarf galaxies to galaxy groups

Magnetic fields are ubiquitous in the Universe. Recently, cosmological simulations of galaxies have successfully begun to incorporate magnetic fields and their evolution in galaxies and their haloes. However, so far they have mostly focused on Milky Way-like galaxies. Here we analyse a sample of high resolution cosmological zoom simulations of disc galaxies in haloes with mass $M_\mathrm{200c}$ from $10^{10}\,\mathrm{M}_\odot$ to $10^{13}\,\mathrm{M}_\odot$, simulated with the Auriga galaxy formation model. We show that with sufficient numerical resolution the magnetic field amplification and saturation is converged. The magnetic field strength reaches equipartition with turbulent energy density for galaxies in haloes with $M_\mathrm{200c}\gtrsim 10^{11.5}\,\mathrm{M_\odot}$. For galaxies in less massive haloes, the magnetic field strength saturates at a fraction of equipartition that decreases with decreasing halo mass. For our lowest mass haloes, the magnetic field saturates significantly below $10\%$ of equipartition. We quantify the resolution we need to obtain converged magnetic field strengths and discuss our resolution requirements also in the context of the IllustrisTNG cosmological box simulations. We show that, at $z=0$, rotation-dominated galaxies in our sample exhibit for the most part an ordered large scale magnetic field, with fewer field reversals in more massive galaxies. Finally, we compare the magnetic fields in our cosmological galaxies at $z=0$ with simulations of isolated galaxies in a collapsing halo setup. Our results pave the way for detailed studies of cosmic rays and other physical processes in similar cosmological galaxy simulations that crucially depend on the strength and structure of magnetic fields.

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