arXiv subjects

Chris Power

Publications and source records attributed to Chris Power.

At least 37 records · Page 2Linked to original sources

arXiv2025

On the Use of WGANs for Super-Resolution in Dark-Matter Simulations

Super-resolution techniques have the potential to reduce the computational cost of cosmological and astrophysical simulations. This can be achieved by enabling traditional simulation methods to run at lower resolution and then efficiently computing high-resolution data corresponding to the simulated low-resolution data. In this work, we investigate the application of a Wasserstein Generative Adversarial Network (WGAN) model, previously proposed in the literature, to increase the particle resolution of dark-matter-only simulations. We reproduce prior results, showing the WGAN model successfully generates high-resolution data with summary statistics, including the power spectrum and halo mass function, that closely match those of true high-resolution simulations. However, we also identify a limitation of the WGAN model in the form of smeared features in generated high-resolution data, particularly in the shapes of dark-matter halos and filaments. This limitation points to a potential weakness of the proposed WGAN-based super-resolution method in capturing the detailed structure of halos, and underscores the need for further development in applying such models to cosmological data.

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arXiv2025

Jet outbursts, non-thermal pressure and the AGN jet duty cycle

We predict the non-thermal pressure (NTP) induced in the cores of galaxy clusters by kinetic jet feedback from an active galactic nucleus (AGN). We model a population of Fanaroff-Riley type I jets when sampling power-law distributions in jet power and age, which we evolve in time with a two-phase jet-lobe model. We couple the energy of each jet outburst to the surrounding gas inside spherical shells, allowing us to estimate the fraction of NTP to total pressure induced in the cluster. We predict the mean profile for this NTP fraction over the source population in a variety of cluster environments and for different AGN jet duty cycles. For typical gas and dark matter profiles, the mean NTP fraction peaks at ~4-6% when the AGN jets are active for 10-30% of the total AGN lifecycle. These predictions are in good agreement with observational constraints, suggesting that AGN feedback imparts only small non-thermal contributions to the cluster's core. Furthermore, we find a relationship between the peak in the mean NTP fraction and the AGN jet duty cycle in a given cluster environment. Applying this to Hitomi measurements of the NTP in the Perseus cluster, we infer an AGN jet duty cycle that is consistent with independent evidence of Perseus' AGN jet activity. We propose this as a novel approach for observationally inferring the past AGN activity of real clusters from their observed NTP fraction and environmental profiles.

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arXiv2025

On the accuracy of dark matter halo merger trees and the consequences for semi-analytic models of galaxy formation

Galaxy formation and evolution models, such as semi-analytic models, are powerful theoretical tools for predicting how galaxies evolve across cosmic time. These models follow the evolution of galaxies based on the halo assembly histories inferred from large $N$-body cosmological simulations. This process requires codes to identify halos ("halo finder") and to track their time evolution ("tree builder"). While these codes generally perform well, they encounter numerical issues when handling dense environments. In this paper, we present how relevant these issues are in state-of-the-art cosmological simulations. We characterize two major numerical artefacts in halo assembly histories: (i) the non-physical swapping of large amounts of mass between subhalos, and (ii) the sudden formation of already massive subhalos at late cosmic times. We quantify these artefacts for different combinations of halo finder (SUBFIND, VELOCIRAPTOR, HBT-HERONS) and tree builder codes (D-TRESS+DHALO, TREEFROG, HBT-HERONS), finding that in general more than $50\%$ ($80\%$) of the more massive subhalos with $>10^{3}$ ($>10^{4}$) particles at $z=0$ inherit them in most cases. However, HBT-HERONS, which explicitly incorporates temporal information, effectively reduces the occurrence of these artefacts to $5\%$ ($10\%$). We then use the semi-analytic models SHARK and GALFORM to explore how these artefacts impact galaxy formation predictions. We demonstrate that the issues above lead to non-physical predictions in galaxies hosted by affected halos, particularly in SHARK where the modelling of baryons relies on subhalo information. Finally, we propose and implement fixes for the numerical artefacts at the semi-analytic model level, and use SHARK to show the improvements, especially at the high-mass end, after applying them.

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arXiv2024

Using dust to constrain dark matter models

In this paper, we use hydrodynamic zoom-in simulations of Milky Way-type haloes to explore using dust as an observational tracer to discriminate between cold and warm dark matter (WDM) universes. Comparing a cold and 3.5 keV WDM particle model, we tune the efficiency of galaxy formation in our simulations using a variable supernova rate to create Milky Way systems with similar satellite galaxy populations while keeping all other simulation parameters the same. Cold dark matter (CDM), having more substructure, requires a higher supernova efficiency than WDM to achieve the same satellite galaxy number. These different supernova efficiencies create different dust distributions around their host galaxies, which we generate by post-processing the simulation output with the \powderday{} codebase. Analysing the resulting dust in each simulation, we find $\sim$4.5 times more dust in our CDM Milky Way haloes compared with WDM. The distribution of dust out to $R_{200\text{c}}$ is then explored, revealing that the WDM simulations are noticeably less concentrated than their CDM counterparts, although differences in substructure complicate the comparison. Our results indicate that dust is a possible unique probe to test theories of dark matter.

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arXiv2024

The Three Hundred: The existence of massive dark matter-deficient satellite galaxies in cosmological simulations

The observation of a massive galaxy with an extremely low dark matter content (i.e. NGC 1277) has posed questions about how such objects form and evolve in a hierarchical universe. We here report on the finding of several massive, dark matter-deficient galaxies in a set of 324 galaxy clusters theoretically modelled by means of full-physics hydrodynamical simulations. We first focus on two example galaxies selected amongst the most massive and dark matter-deficient ones. By tracing the evolution of these galaxies, we find that their lack of dark matter is a result of multiple pericentre passages. While orbiting their host halo, tidal interactions gradually strip away dark matter while preserving the stellar component. A statistical analysis of all massive satellite galaxies in the simulated clusters shows that the stellar-to-total mass ratio today is strongly influenced by the number of orbits and the distance at pericentres. Galaxies with more orbits and closer pericentres are more dark matter-deficient. Additionally, we find that massive, dark matter-deficient galaxies at the present day are either the remnants of very massive galaxies at infall or former central galaxies of infalling groups. We conclude that such massive yet dark matter-deficient galaxies exist and are natural by-products of typical cluster galaxy evolution, with no specific requirement for an exotic formation scenario.

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arXiv2024

Predicting the Non-Thermal Pressure in Galaxy Clusters

We investigate the relationship between a galaxy cluster's hydrostatic equilibrium state, the entropy profile, $K$, of the intracluster gas, and the system's non-thermal pressure (NTP), within an analytic model of cluster structures. When NTP is neglected from the cluster's hydrostatic state, we find that the gas' logarithmic entropy slope, $k\equiv \mathrm{d}\ln K/\mathrm{d}\ln r$, converges at large halocentric radius, $r$, to a value that is systematically higher than the value $k\simeq1.1$ that is found in observations and simulations. By applying a constraint on these `pristine equilibrium' slopes, $k_\mathrm{eq}$, we are able to predict the required NTP that must be introduced into the hydrostatic state of the cluster. We solve for the fraction, $\mathcal{F}\equiv p_\mathrm{nt}/p$, of NTP, $p_\mathrm{nt}$, to total pressure, $p$, of the cluster, and we find $\mathcal{F}(r)$ to be an increasing function of halocentric radius, $r$, that can be parameterised by its value in the cluster's core, $\mathcal{F}_0$, with this prediction able to be fit to the functional form proposed in numerical simulations. The minimum NTP fraction, as the solution with zero NTP in the core, $\mathcal{F}_0=0$, we find to be in excellent agreement with the mean NTP predicted in non-radiative simulations, beyond halocentric radii of $r\gtrsim0.7r_{500}$, and in tension with observational constraints derived at similar radii. For this minimum NTP profile, we predict $\mathcal{F}\simeq0.20$ at $r_{500}$, and $\mathcal{F}\simeq0.34$ at $2r_{500}$; this amount of NTP leads to a hydrostatic bias of $b\simeq0.12$ in the cluster mass $M_{500}$ when measured within $r_{500}$. Our results suggest that the NTP of galaxy clusters contributes a significant amount to their hydrostatic state near the virial radius, and must be accounted for when estimating the cluster's halo mass using hydrostatic equilibrium approaches.

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arXiv2024

Constraining cosmological parameters using the splashback radius of galaxy clusters

Cosmological parameters such as $Ω_{\rm{M}}$ and $σ_{8}$ can be measured indirectly using various methods, including galaxy cluster abundance and cosmic shear. These measurements constrain the composite parameter $S_{8}$, leading to degeneracy between $Ω_{\rm{M}}$ and $σ_{8}$. However, some structural properties of galaxy clusters also correlate with cosmological parameters, due to their dependence on a cluster's accretion history. In this work, we focus on the splashback radius, an observable cluster feature that represents a boundary between a cluster and the surrounding Universe. Using a suite of cosmological simulations with a range of values for $Ω_{\rm{M}}$ and $σ_{8}$, we show that the position of the splashback radius around cluster-mass halos is greater in cosmologies with smaller values of $Ω_{\rm{M}}$ or larger values of $σ_{8}$. This variation breaks the degeneracy between $Ω_{\rm{M}}$ and $σ_{8}$ that comes from measurements of the $S_{8}$ parameter. We also show that this variation is, in principle, measurable in observations. As the splashback radius can be determined from the same weak lensing analysis already used to estimate $S_{8}$, this new approach can tighten low-redshift constraints on cosmological parameters, either using existing data, or using upcoming data such as that from Euclid and LSST.

astro-ph.CO↗

arXiv2024

Reconsidering the dynamical states of galaxy clusters using PCA and UMAP

Numerous metrics exist to quantify the dynamical state of galaxy clusters, both observationally and within simulations. Many of these correlate strongly with one another, but it is not clear whether all of these measures probe the same intrinsic properties. In this work, we use two different statistical approaches -- principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) -- to investigate which dynamical properties of a cluster are in fact the best descriptors of its dynamical state. We use measurements taken directly from The Three Hundred suite of galaxy cluster simulations, as well as morphological properties calculated using mock X-ray and SZ maps of the same simulated clusters. We find that four descriptions of dynamical state naturally arise, and although correlations exist between these, a given cluster can be "dynamically relaxed" according to all, none, or some of these four descriptions. These results demonstrate that it is highly important for future observational and theoretical studies to consider in which sense clusters are dynamically relaxed. Cluster dynamical states are complex and multi-dimensional, and so it is not meaningful to classify them simply as "relaxed" and "unrelaxed" based on a single linear scale.

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arXiv2024

On bursty star formation during cosmological reionization - how does it influence the baryon mass content of dark matter halos?

The baryon mass content of dark matter halos in the early Universe depends on global factors - e.g. ionising ultraviolet (UV) radiation background - and local factors - e.g. star formation efficiency and assembly history. We use a lightweight semi-analytical model to investigate how local and global factors impact halo baryon mass content at redshifts of $z\geq 5$. Our model incorporates a time delay between when stars form and when they produce feedback, which drive bursts of star formation, and a mass and redshift dependent UV background, which captures the influence of cosmological reionization on gas accretion onto halos. We use statistically representative halo assembly histories and assume that the cosmological gas accretion rate is proportional to the halo mass accretion rate. Delayed feedback leads to oscillations in gas mass with cosmic time, behaviour that cannot be captured with instantaneous feedback. Highly efficient star formation drives stronger oscillations, while strong feedback impacts when oscillations occur; in contrast, inefficient star formation and weak feedback produce similar long-term behaviour to that observed in instantaneous feedback models. If the delayed feedback timescale is too long, a halo retains its gas reservoir but the feedback suppresses star formation. Our model predicts that lower mass systems ($\leq 10^7 \text{M}_\odot$) at $z \leq 10$ should be strongly gas deficient, whereas higher mass systems retain their gas reservoirs because they are sufficiently massive to continue accreting gas through cosmological reionization. Interestingly, in higher mass halos, the median $m_\star/(m_\star+m_\text{g}) \simeq 0.01-0.05$, but is a factor of 3-5 smaller when feedback is delayed. Our model does not include seed supermassive black hole feedback, which is necessary to explain massive quenched galaxies in the early Universe.

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arXiv2024

Quenching massive galaxies across cosmic time with the semi-analytic model SHARK v2.0

We introduce version 2.0 of the SHARK semi-analytic model of galaxy formation after many improvements to the physics included. The most significant being: (i) a model describing the exchange of angular momentum (AM) between the interstellar medium and stars; (ii) a new active galactic nuclei feedback model which has two modes, a wind and a jet mode, with the jet mode tied to the jet energy production; (iii) a model tracking the development of black hole (BH) spins; (iv) more sophisticated modelling of environmental effects on satellite galaxies; and (v) automatic parameter exploration using Particle Swarm Optimisation. We focus on two timely research topics: the structural properties of galaxies and the quenching of massive galaxies. For the former, SHARK v2.0 is capable of producing a more realistic stellar size-mass relation with a plateau marking the transition from disk- to bulge-dominated galaxies, and scaling relations between specific AM and mass that agree well with observations. For the quenching of massive galaxies, SHARK v2.0 produces massive galaxies that are more quenched than the previous version, reproducing well the observed relations between star formation rate (SFR) and stellar mass, and specific SFR and BH mass at $z=0$. SHARK v2.0 produces a number density of massive-quiescent galaxies >1dex higher than the previous version, in good agreement with JWST observations at $z\le 5$; predicts a stellar mass function of passive galaxies in reasonably good agreement with observations at $0.5<z<5$; and environmental quenching to already be effective at $z=5$.

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arXiv2024

Predicting the Scaling Relations between the Dark Matter Halo Mass and Observables from Generalised Profiles II: Intracluster Gas Emission

We investigate the connection between a cluster's structural configuration and observable measures of its gas emission that can be obtained in X-ray and Sunyaev-Zeldovich (SZ) surveys. We present an analytic model for the intracluster gas density profile: parameterised by the dark matter halo's inner logarithmic density slope, $α$, the concentration, $c$, the gas profile's inner logarithmic density slope, $\varepsilon$, the dilution, $d$, and the gas fraction, $η$, normalised to cosmological content. We predict four probes of the gas emission: the emission-weighted, $T_\mathrm{X}$, and mean gas mass-weighted, $T_\mathrm{m_g}$, temperatures, and the spherically, $Y_\mathrm{sph}$, and cylindrically, $Y_\mathrm{cyl}$, integrated Compton parameters. Over a parameter space of clusters, we constrain the X-ray temperature scaling relations, $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$, within $57.3\%$ and $41.6\%$, and $M_{200} - T_\mathrm{m_g}$ and $M_{500} - T_\mathrm{m_g}$, within $25.7\%$ and $7.0\%$, all respectively. When excising the cluster's core, the $M_{200} - T_\mathrm{X}$ and $M_{500} - T_\mathrm{X}$ relations are further constrained, to within $31.3\%$ and $17.1\%$, respectively. Similarly, we constrain the SZ scaling relations, $M_{200} - Y_\mathrm{sph}$ and $M_{500} - Y_\mathrm{sph}$, within $31.1\%$ and $17.7\%$, and $M_{200} - Y_\mathrm{cyl}$ and $M_{500} - Y_\mathrm{cyl}$, within $25.2\%$ and $22.0\%$, all respectively. The temperature observable $T_\mathrm{m_g}$ places the strongest constraint on the halo mass, whilst $T_\mathrm{X}$ is more sensitive to the parameter space. The SZ constraints are sensitive to the gas fraction, whilst insensitive to the form of the gas profile itself. In all cases, the halo mass is recovered with an uncertainty that suggests the cluster's structural profiles only contribute a minor uncertainty in its scaling relations.

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arXiv2024

Predicting the Scaling Relations between the Dark Matter Halo Mass and Observables from Generalised Profiles I: Kinematic Tracers

We investigate the relationship between a dark matter halo's mass profile and measures of the velocity dispersion of kinematic tracers within its gravitational potential. By predicting the scaling relation of the halo mass with the aperture velocity dispersion, $M_\mathrm{vir} - σ_\mathrm{ap}$, we present the expected form and dependence of this halo mass tracer on physical parameters within our analytic halo model: parameterised by the halo's negative inner logarithmic density slope, $α$, its concentration parameter, $c$, and its velocity anisotropy parameter, $β$. For these idealised halos, we obtain a general solution to the Jeans equation, which is projected over the line of sight and averaged within an aperture to form the corresponding aperture velocity dispersion profile. Through dimensional analysis, the $M_\mathrm{vir} - σ_\mathrm{ap}$ scaling relation is devised explicitly in terms of analytical bounds for these aperture velocity dispersion profiles: allowing constraints to be placed on this relation for motivated parameter choices. We predict the $M_{200} - σ_\mathrm{ap}$ and $M_{500} - σ_\mathrm{ap}$ scaling relations, each with an uncertainty of $60.5\%$ and $56.2\%$, respectively. These halo mass estimates are found to be weakly sensitive to the halo's concentration and mass scale, and most sensitive to the size of the aperture radius in which the aperture velocity dispersion is measured, the maximum value for the halo's inner slope, and the minimum and maximum values of the velocity anisotropy. Our results show that a halo's structural and kinematic profiles impose only a minor uncertainty in estimating its mass. Consequently, spectroscopic surveys aimed at constraining the halo mass using kinematic tracers can focus on characterising other, more complex sources of uncertainty and observational systematics.

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arXiv2024

Are Odd Radio Circles phoenixes of powerful radio galaxies?

Odd Radio Circles (ORCs) are a class of low surface brightness, circular objects approximately one arcminute in diameter. ORCs were recently discovered in the Australian Square Kilometre Array Pathfinder (ASKAP) data, and subsequently confirmed with follow-up observations on other instruments, yet their origins remain uncertain. In this paper, we suggest that ORCs could be remnant lobes of powerful radio galaxies, re-energised by the passage of a shock. Using relativistic hydrodynamic simulations with synchrotron emission calculated in post-processing, we show that buoyant evolution of remnant radio lobes is alone too slow to produce the observed ORC morphology. However, the passage of a shock can produce both filled and edge-brightnened ORC-like morphologies for a wide variety of shock and observing orientations. Circular ORCs are predicted to have host galaxies near the geometric centre of the radio emission, consistent with observations of these objects. Significantly offset hosts are possible for elliptical ORCs, potentially causing challenges for accurate host galaxy identification. Observed ORC number counts are broadly consistent with a paradigm in which moderately powerful radio galaxies are their progenitors.

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arXiv2023

Faraday rotation as a probe of radio galaxy environment in RMHD AGN jet simulations

Active galactic nuclei (AGN) play an integral role in galaxy formation and evolution by influencing galaxies and their environments through radio jet feedback. Historically, interpreting observations of radio galaxies and quantifying radio jet feedback has been challenging due to degeneracies between their physical parameters. In particular, it is well-established that different combinations of jet kinetic power and environment density can yield indistinguishable radio continuum properties, including apparent size and Stokes I luminosity. We present an approach to breaking this degeneracy by probing the line-of-sight environment with Faraday rotation. We study this effect in simulations of three-dimensional relativistic magnetohydrodynamic AGN jets in idealised environments with turbulent magnetic fields. We generate synthetic Stokes I emission and Faraday rotation measure (RM) maps, which enable us to distinguish between our simulated sources. We find enhanced RMs near the jet head and lobe edges and an RM reversal across the jet axis. We show that increasing the environment density and the average cluster magnetic field strength broadens the distribution of Faraday rotation measure values. We study the depolarisation properties of our sources, finding that the hotspot regions depolarise at lower frequencies than the lobes. We quantify the effect of depolarisation on the RM distribution, finding that the frequency at which the source is too depolarised to measure the RM distribution accurately is a probe of environmental properties. This technique offers a range of new opportunities for upcoming surveys, including probing radio galaxy environments and determining more accurate estimates of the AGN feedback budget.

astro-ph.HE↗

arXiv2023

CosmoDRAGoN simulations -- I. Dynamics and observable signatures of radio jets in cosmological environments

We present the Cosmological Double Radio Active Galactic Nuclei (CosmoDRAGoN) project: a large suite of simulated AGN jets in cosmological environments. These environments sample the intra-cluster media of galaxy clusters that form in cosmological smooth particle hydrodynamics (SPH) simulations, which we then use as inputs for grid-based hydrodynamic simulations of radio jets. Initially conical jets are injected with a range of jet powers, speeds (both relativistic and non-relativistic), and opening angles; we follow their collimation and propagation on scales of tens to hundreds of kiloparsecs, and calculate spatially-resolved synthetic radio spectra in post-processing. In this paper, we present a technical overview of the project, and key early science results from six representative simulations which produce radio sources with both core- (Fanaroff-Riley Type I) and edge-brightened (Fanaroff-Riley Type II) radio morphologies. Our simulations highlight the importance of accurate representation of both jets and environments for radio morphology, radio spectra, and feedback the jets provide to their surroundings.

astro-ph.HE↗

arXiv2023

Thermal and Reionisation History within a Large-Volume Semi-Analytic Galaxy Formation Simulation

We predict the 21-cm global signal and power spectra during the Epoch of Reionisation using the MERAXES semi-analytic galaxy formation and reionisation model, updated to include X-ray heating and thermal evolution of the intergalactic medium. Studying the formation and evolution of galaxies together with the reionisation of cosmic hydrogen using semi-analytic models (such as MERAXES) requires N-body simulations within large volumes and high mass resolutions. For this, we use a simulation of side-length $210~h^{-1}$ Mpc with $4320^3$ particles resolving dark matter haloes to masses of $5\times10^8~h^{-1}~M_\odot$. To reach the mass resolution of atomically cooled galaxies, thought to be the dominant population contributing to reionisation, at $z=20$ of $\sim 2\times10^7~h^{-1}~M_\odot$, we augment this simulation using the DARKFOREST Monte-Carlo merger tree algorithm (achieving an effective particle count of $\sim10^{12}$). Using this augmented simulation we explore the impact of mass resolution on the predicted reionisation history as well as the impact of X-ray heating on the 21-cm global signal and the 21-cm power spectra. We also explore the cosmic variance of 21-cm statistics within $70^{3}$ $h^{-3}$ Mpc$^3$ sub-volumes. We find that the midpoint of reionisation varies by $Δz\sim0.8$ and that the cosmic variance on the power spectrum is underestimated by a factor of $2-4$ at $k\sim 0.1-0.4$ Mpc$^{-1}$ due to the non-Gaussian nature of the 21-cm signal. To our knowledge, this work represents the first model of both reionisation and galaxy formation which resolves low-mass atomically cooled galaxies while simultaneously sampling sufficiently large scales necessary for exploring the effects of X-rays in the early Universe.

astro-ph.CO↗

arXiv2022

SAMI-HI: the connection between global asymmetry in the ionised and neutral atomic hydrogen gas in galaxies

Observations of the neutral atomic hydrogen (HI) gas in galaxies are predominantly spatially unresolved, in the form of a global HI spectral line. There has been substantial work on quantifying asymmetry in global HI spectra (`global HI asymmetry'), but due to being spatially unresolved, it remains unknown what physical regions of galaxies the asymmetry traces, and whether the other gas phases are affected. Using optical integral field spectrograph (IFS) observations from the Sydney AAO Multi-object IFS (SAMI) survey for which global HI spectra are also available (SAMI-HI), we study the connection between asymmetry in galaxies' ionised and neutral gas reservoirs to test if and how they can help us better understand the origin of global HI asymmetry. We reconstruct the global H$α$ spectral line from the IFS observations and find that, while some global H$α$ asymmetries can arise from disturbed ionised gas kinematics, the majority of asymmetric cases are driven by the distribution of H$α$-emitting gas. When compared to the HI, we find no evidence for a relationship between the global H$α$ and HI asymmetry. Further, a visual inspection reveals that cases where galaxies have qualitatively similar H$α$ and HI spectral profiles can be spurious, with the similarity originating from an irregular 2D H$α$ flux distribution. Our results highlight that comparisons between global H$α$ and HI asymmetry are not straightforward, and that many global HI asymmetries trace disturbances that do not significantly impact the central regions of galaxies.

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arXiv2022

A stochastic model to reproduce the star-formation history of individual galaxies in hydrodynamic simulations

The star formation history (SFH) of galaxies is critical for understanding galaxy evolution. Hydrodynamical simulations enable us to precisely reconstruct the SFH of galaxies and establish a link to the underlying physical processes. In this work, we present a model to describe individual galaxies' SFHs from three simulations: TheThreeHundred, Illustris-1 and TNG100-1. This model divides the galaxy SFH into two distinct components: the "main sequence" and the "variation". The "main sequence" part is generated by tracing the history of the $SFR-M_*$ main sequence of galaxies across time. The "variation" part consists of the scatter around the main sequence, which is reproduced by fractional Brownian motions. We find that: 1) The evolution of the main sequence varies between simulations; 2) fractional Brownian motions can reproduce many features of SFHs, however, discrepancies still exist; 3) The variations and mass-loss rate are crucial for reconstructing the SFHs of the simulations. This model provides a fair description of the SFHs in simulations. On the other hand, by correlating the fractional Brownian motion model to simulation data, we provide a 'standard' against which to compare simulations.

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