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Klaus Dolag

Publications and source records attributed to Klaus Dolag.

At least 55 records · Page 3Linked to original sources

General Implicit Runge-Kutta Integrators for Multifluid Gas-Dust Aerodynamic Drag

The integration of aerodynamic drag is a fundamental step in simulating dust dynamics in hydrodynamical simulations. We propose a novel integration scheme, designed to be compatible with Strang splitting techniques, which allows for the straightforward integration of external forces and hydrodynamic fluxes in general-purpose hydrodynamic simulation codes. Moreover, this solver leverages an analytical solution to the problem of drag acceleration, ensuring linear complexity even in cases with multiple dust grain sizes, as opposed to the cubic scaling of methods that require a matrix inversion step. This new General Implicit Runge-Kutta integrator (GIRK) is evaluated using standard benchmarks for dust dynamics such as DUSTYBOX, DUSTYWAVE, and DUSTYSHOCK. The results demonstrate not only the accuracy of the method but also the expected scalings in terms of accuracy, convergence to equilibrium, and execution time. GIRK can be easily implemented in hydrodynamical simulations alongside hydrodynamical steps and external forces, and is especially useful in simulations with a large number of dust grain sizes.

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Modeling dust dynamics in OpenGadget3 -- I. SPH implementation of the One-Fluid model

Dust dynamics plays a critical role in astrophysical processes and has been modeled in hydrodynamical simulations using various approaches. Among particle-based methods like Smoothed Particle Hydrodynamics (SPH), the One-Fluid model has proven to be highly effective for simulating gas-dust mixtures. This study presents the implementation of the One-Fluid model in OpenGadget3, introducing improvements to the original formulation. These enhancements include time-dependent artificial viscosity and conductivity, as well as a novel treatment of dust diffusion using a pressure-like term. The improved model is tested using a suite of dust dynamics benchmark problems: DUSTYBOX, DUSTYWAVE, and DUSTYSHOCK, with the latter extended to multidimensional scenarios, as well as a dusty Sedov-Taylor blast wave. Additional tests include simulations of Cold Keplerian Disks, dusty protoplanetary disks, and Kelvin-Helmholtz instabilities to evaluate the model's robustness in more complex flows. The implementation successfully passes all standard benchmark tests. It demonstrates stability and accuracy in both simple and complex simulations. The new diffusion term improves the handling of flows with large dust-to-gas ratios and low drag coefficients, although limitations of the One-Fluid model in these regimes remain. The enhanced One-Fluid model is a reliable and robust tool for simulating dust dynamics in OpenGadget3. While it retains some limitations inherent to the original formulation, the introduced improvements expand its applicability and address some challenges in gas-dust dynamics.

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Towards Exascale Computing for Astrophysical Simulation Leveraging the Leonardo EuroHPC System

Developing and redesigning astrophysical, cosmological, and space plasma numerical codes for existing and next-generation accelerators is critical for enabling large-scale simulations. To address these challenges, the SPACE Center of Excellence (SPACE-CoE) fosters collaboration between scientists, code developers, and high-performance computing experts to optimize applications for the exascale era. This paper presents our strategy and initial results on the Leonardo system at CINECA for three flagship codes, namely gPLUTO, OpenGadget3 and iPIC3D, using profiling tools to analyze performance on single and multiple nodes. Preliminary tests show all three codes scale efficiently, reaching 80% scalability up to 1,024 GPUs.

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Analysis of Galaxies at the Extremes: Failed Galaxy Progenitors in the MAGNETICUM Simulations

There is increasing observational evidence for a failed galaxy formation pathway for some ultradiffuse galaxies (UDGs) at low redshift however they currently lack simulated counterparts. We attempt to identify dark matter halos at high redshift within the MAGNETICUM cosmological simulations that could plausibly be their progenitors. We build a toy model of passive galaxy evolution within the stellar mass-halo mass relation to trace z = 0 observations of UDGs back to their z = 2 locations. We identify a population of 443 galaxies that match these parameter space positions within the simulation. We build two comparison samples within the simulation that follow the stellar mass-halo mass relationship at z = 2, one of which is stellar mass matched (with varying smaller halo masses) and the other is halo mass matched (with varying larger stellar masses) to our sample. We identify that our failed galaxy progenitor candidates have 1) flatter, cored dark matter halos; 2) more extended stellar bodies; 3) a larger fraction of their gas in the outskirts of their halos; 4) lower metallicities and 5) higher star formation rates than the control samples. Findings 1) and 2) are similar to low redshift observations of UDGs. Finding 3) will aid the removal of gas and permanent quenching of star formation which is a requirement of the failed galaxy formation scenario. The low metallicities of finding 4) match those observed in low redshift failed galaxy UDGs. Comparing the high star formation rates of finding 5) to recent JWST observations suggests that a starburst would naturally explain the high globular cluster richness of the UDGs. Many of the properties we find for these failed galaxy progenitors can be explained by an assembly bias of their dark matter halo to later formation times. We conclude by proposing that the fraction of failed galaxy UDGs is expected to increase with environmental density.

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Living the stream: Properties and progenitors of tidal shells and streams around galaxies from Magneticum

Stellar shells and streams are remnants of satellite galaxies visible around galaxies. Advances in low-surface-brightness observations and increasing resolution of cosmological simulations now allow investigating the properties and origin of these features. The metallicity, age, and velocity dispersion of shells and streams are investigated to infer their progenitor galaxies properties. We employed the hydrodynamical cosmological simulations Magneticum Pathfinder to extract these properties and identify the progenitors of the shells and streams. We compared to observational results from surveys and individual galaxies, matching and testing the methodology used in observations. Mock observations of shells and streams agree well with observational data regarding their morphology and spatial distribution. We find that both types of features are associated with localized depressions in stellar velocity dispersion compared to the surrounding regions. They are not as clearly distinct in metallicity and ages, though overall shells and more metal rich and streams are younger. We confirm results from idealized models that shells form commonly from radial major mergers but also through minor mergers, while streams usually form from minor mergers on circular orbits. We do not find the widths of streams to correlate with the half-mass radii of their progenitors, but the progenitors follow the mass-metallicity relation. On average, the masses measured for shells and streams approximately corresponds to 20% of the progenitor mass. We introduce a class of star-forming streams, which originate from in-situ star formation rather than the disruption of a satellite galaxy. Measuring stellar population properties of shells and streams provides the means to reconstruct the progenitor properties, and especially distinguish those streams that are not made through the disruption of a galaxy but formed in-situ.

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Why Cosmic Voids Matter: Pristine Evolution

We utilize the Magneticum suite of hydrodynamical simulations to investigate the formation and evolution of cosmic voids from $z = 5.04$ to present day, using cold dark matter and (sub-) halo tracers in high-density samples. This includes the evolution of their global properties, such as size, shape, inner density, and average density, as well as their radial density profiles. Our results provide several key conclusions for void analyses in modern surveys. We demonstrate that a relative size framework is required, mitigating methodological selection effects and revealing the true physical evolution of densities around halo-defined voids. This necessity arises from our findings that a void's properties are more fundamentally tied to its rank within its contemporary population than to its absolute size. Using this framework, we show that the evolution of halo voids stabilizes at redshifts below $z \simeq 1$, driven primarily by cosmic expansion rather than ongoing halo formation. We further find that the matter evolution around these stable voids is remarkably well-described by linear growth theory, with deviations appearing as non-linear growth on small scales and suppressed growth in the largest voids, potentially driven by the influence of dark energy. This late-time stability and the predictable evolution confirm voids as pristine laboratories for probing the nature of dark energy with upcoming surveys.

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Simulating the LOcal Web (SLOW) V. Thermodynamic Properties and Evolution of Local Galaxy Clusters

The intracluster medium (ICM), composed of hot plasma, dominates the baryonic content of galaxy clusters and is primarily observable in X-rays. Its thermodynamic properties, pressure, temperature, entropy, and electron density, offer crucial insight into the physical processes shaping clusters, from accretion and mergers to radiative cooling and feedback. We investigate the thermodynamic properties of galaxy clusters in the Simulating the LOcal Web (SLOW) constrained simulations, which reproduce the observed large-scale structure of the local Universe. We assess how well these simulations reproduce observed ICM profiles and explore the connection between cluster formation history and core classification. Three-dimensional thermodynamic profiles are extracted and compared to deprojected X-ray and Sunyaev - Zel'dovich (SZ) data for local clusters classified as solid cool-core (SCC), weakly cool-core (WCC), and non-cool-core (NCC) systems. We also examine the mass assembly history of the simulated counterparts to link their formation to present-day ICM properties. The simulations reproduce global thermodynamic profiles for clusters such as Perseus, Coma, A85, A119, A1644, A2029, A3158, and A3266. Moreover, they show that CC clusters typically assemble their mass earlier, while NCC systems grow through more extended, late-time merger-driven histories. WCC clusters show intermediate behavior, suggesting an evolutionary transition. Our results demonstrate that constrained simulations provide a powerful tool for linking cluster formation history to present-day ICM properties and point to possible refinements in subgrid physics as well as in resolution that could improve the agreement in cluster core regions.

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N-body simulations of dark matter-baryon interactions

Dark matter (DM) particles can interact with particles of the standard model. Although there are a number of constraints derived from direct and indirect detection experiments, the evolution of astrophysical objects could offer a promising probe. Obtaining predictions is challenging and primarily limited by our ability to simulate scattering between DM and baryonic particles within N-body and hydrodynamics simulations. We have developed the first scheme allowing for the simulation of these interacting dark matter (IDM) models, accurately accounting for their angular and velocity dependence, as well as the mass ratio between the DM and baryonic scattering partners. To describe DM-baryon interactions, we used an N-body code together with its implementation of smoothed-particle hydrodynamics and meshless finite mass. The interaction is realised in a pairwise fashion by creating a virtual scattering partner from the baryonic particle and allowing it to interact with a DM particle using a scattering routine initially developed for self-interacting dark matter (SIDM). After the interaction, the virtual particle is rejoined with the baryonic particle, fulfilling the requirements of energy and momentum conservation. Through several test problems, we demonstrated that we are able to reproduce the analytic solutions with our IDM scheme. This includes a test for scattering with a physical mass ratio of 1:1000, which is beyond the limits of SIDM simulations. We comment on various numerical aspects and challenges, and we describe the limitations of our numerical scheme. Furthermore, we study the impact of IDM on halo formation with a collapsing over-density. We find that it is possible to accurately model IDM within N-body and hydrodynamics simulations commonly used in astrophysics. Finally, our scheme allows for novel predictions to be made and new constraints on DM-baryon scattering to be set.

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Two intersecting radio shells: relics of galaxy merger shocks ?

We present the discovery of two intersecting radio shells, likely radio relics, surrounding a compact galaxy group dominated by a massive elliptical galaxy. The shells present as partial, edge-brightened rings with diameters of about 240" (720 kpc) each and resemble a pair of odd radio circles. The central galaxy, WISEA J184105.19-654753.8, which shows signs of interactions, is radio bright, has a stellar mass of 3.1 x 10^11 Msun (for a redshift of zphot = 0.18) and is located in the intersect region. The double radio shell system, which we refer to as ORC J1841-6547 (also known as ORC 6), was detected in 944 MHz radio continuum images obtained with Phased Array Feeds on the Australian Square Kilometre Array Pathfinder (ASKAP). The more prominent, north-western shell may be associated with an X-ray detection, while the weaker, south-eastern shell has no counterpart at non-radio wavelength. We propose outwards moving shocks from galaxy mergers driving into the intragroup medium, re-energising relic radio lobes, as a possible formation scenario for the observed radio shells. We conclude that at least some ORCs are shock-energised relics in the outskirts of galaxy groups, which originate during the merger evolution of the brightest group galaxy.

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Multi-cloud crushing -- the collective survival of cold clouds in galactic outflows

The ram-pressure acceleration of cold gas by hot outflows plays a crucial role in the dynamics of multiphase galactic winds. Recent numerical studies incorporating radiative cooling have identified a size threshold for idealized cold clouds to survive within high-velocity outflows. This study extends the investigation to a more complex morphology of cold gas as observed in the interstellar medium. We conduct three-dimensional hydrodynamic simulations of ensembles of individual spherical clouds to systematically explore under which conditions the cold clouds can survive. We find that cloud ensembles can survive collectively -- even when individual clouds, if isolated, would be rapidly destroyed. Our results indicate that, besides the morphology, factors such as tight packing, small inter-cloud distance and higher fragmentation facilitate survival. We propose a novel multi-cloud survival criterion that accounts for collective properties of the cloud system, including total gas mass and the geometric configuration based on an effective volume filling fraction of the cold gas $F_V$. This fraction is computed by constructing a composite volume from individual enclosing conical boxes aligned with the wind, incorporating spatial overlap and cloud-tail spreading. The box dimensions scale with the critical survival radius $r_{\rm crit}$ from the single-cloud criterion. We find a universal threshold $F_{V,{\rm crit}}\approx 0.24$ that robustly separates surviving from destroyed systems across diverse geometric configurations. Our findings emphasize the critical importance of initial cloud distribution and fragmentation in governing the long-term evolution and survival of cold gas structures, providing insight into observed multiphase outflows and CGM dynamics.

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The Three Hundred Project: Modeling Baryon and Hot-Gas Fraction Evolution in Simulated Clusters

The baryon fraction of galaxy clusters is a powerful tool to inform on the cosmological parameters while the hot-gas fraction provides indications on the physics of the intracluster plasma and its interplay with the processes driving galaxy formation. Using cosmological hydrodynamical simulations from The Three Hundred collaboration of about 300 simulated massive galaxy clusters with median mass $M_{500}\approx7 \times 10^{14}$M$_{\odot}$ at $z=0$, we model the relations between total mass and either baryon fraction or the hot gas fractions at overdensities $Δ= 2500$, $500$, and $200$ with respect to the cosmic critical density, and their evolution from $z\sim 0$ to $z\sim 1.3$. We fit the simulation results for such scaling relations against three analytic forms (linear, quadratic, and logarithmic in a logarithmic plane) and three forms for the redshift dependence, considering as a variable both the inverse of cosmic scale factor, $(1+z)$, and the Hubble expansion rate, $E(z)$. We show that power-law dependencies on cluster mass poorly describe the investigated relations. A power-law fails to simultaneously capture the flattening of the total baryon and gas fractions at high masses, their drop at the low masses, and the transition between these two regimes. The other two functional forms provide a more accurate description of the curvature in mass scaling. The fractions measured within smaller radii exhibit a stronger evolution than those measured within larger radii. From the analysis of these simulations, we conclude that as long as we include systems in the mass range herein investigated, the baryon or gas fraction can be accurately related to the total mass through either a parabola or a logarithm in the logarithmic plane. The trends are common to all modern hydro simulations, although the amplitude of the drop at low masses might differ [Abridged].

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The full iron budget in simulated galaxy clusters: The chemistry between gas and stars

Heavy chemical elements such as iron in the intra-cluster medium (ICM) of galaxy clusters are a signpost of the interaction between the gas and stellar components. Observations of the ICM metallicity in present-day massive systems, however, pose a challenge to the underlying assumption that the cluster galaxies have produced the amount of iron that enriches the ICM. We evaluate the iron share between ICM and stars within simulated galaxy clusters with the twofold aim of investigating the origin of possible differences with respect to observational findings and of shedding light on the observed excess of iron on the ICM with respect to expectations based on the observed stellar population. We evaluated the iron mass in gas and stars in a sample of 448 simulated systems with masses M500 > 1e14 Msun at z=0.07. These were extracted from the high-resolution (352 cMpc/h)^3 volume of the Magneticum cosmological hydrodynamical simulations. We compared our results with observational data of low-redshift galaxy clusters. The iron share in simulated clusters features a shallow dependence on the total mass, and its value is close to unity on average. In the most massive simulated systems, the iron share is thus smaller than observational values by almost an order of magnitude. The dominant contribution to this difference is related to the stellar component, whereas the chemical properties of the ICM agree well overall with the observations. We find larger stellar mass fractions in simulated massive clusters, which in turn yield higher stellar iron masses, than in observational data. Consistently with the modelling, we confirm that the stellar content within simulated present-day massive systems causes the metal enrichment in the ICM. It will be crucial to alleviate the stellar mass discrepancy between simulations and observations to definitely assess the iron budget in galaxy clusters.

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Intra-Cluster Light as a Dynamical Clock for Galaxy Clusters: Insights from the MAGNETICUM, IllustrisTNG, Hydrangea and Horizon-AGN Simulations

As the most massive nodes of the cosmic web, galaxy clusters represent the best probes of structure formation. Over time, they grow by accreting and disrupting satellite galaxies, adding those stars to the brightest cluster galaxy (BCG) and the intra-cluster light (ICL). However, the formation pathways of different galaxy clusters can vary significantly. To inform upcoming large surveys, we aim to identify observables that can distinguish galaxy cluster formation pathways. Using four different hydrodynamical simulations, Magneticum, TNG100 of IllustrisTNG, Horizon-AGN, and Hydrangea, we study how the fraction of stellar mass in the BCG and ICL ($f_{ICL+BCG}$) relates to the galaxy cluster mass assembly history. For all simulations, $f_{ICL+BCG}$ is the best tracer for the time at which the cluster has accumulated 50% of its mass ($z_{f}$), performing better than other typical dynamical tracers, such as the subhalo mass fraction, the halo mass, and the center shift. More relaxed clusters have higher $f_{ICL+BCG}$, in rare cases up to 90%, while dynamically active clusters have lower fractions, down to 20%, which we find to be independent of the exact implemented baryonic physics. We determine the average increase in $f_{ICL+BCG}$ from stripping and mergers to be between 3-4% per Gyr. $f_{ICL+BCG}$ is tightly traced by the stellar mass ratio between the BCG and both the second (M12) and fourth (M14) most massive cluster galaxy. The average galaxy cluster has assembled half of its halo mass by $z_{f}=0.67$ (about 6 Gyr ago), though individual histories vary significantly from $z_{f}=0.06$ to $z_{f}=1.77$ (0.8 to 10 Gyr ago). As all four cosmological simulations consistently find that $f_{ICL+BCG}$ is an excellent tracer of the cluster dynamical state, upcoming surveys can leverage measurements of $f_{ICL+BCG}$ to statistically quantify the assembly of the most massive structures.

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Go with the Flow: The Self-Similar and Non-Linear Behaviour of Large-Scale In- and Outflows and the Impact of Accretion Shocks from Galaxies to Galaxy Clusters

From the scale-free nature of gravity, the structure in the universe is expected to be self-similar on large scales. However, this self-similarity will eventually break down due to small-scale gas physics such as star formation, AGN and stellar feedback as well as non-linear effects gaining importance relative to linear structure formation. In this work we investigate the large-scale matter flows that connect collapsed structures to their cosmic environments specifically for their agreement with self-similarity in various properties. For this purpose we use the full power of the hydrodynamical cosmological simulation suite Magneticum Pathfinder to calculate the in- and outflow rates for haloes on a large range of masses and redshifts. We find a striking self-similarity across the whole mass range and cosmic epochs that only breaks in the outflowing regime due to the different outflow driving mechanisms for galaxies vs. galaxy clusters. Geometrical analysis of the patterns of in vs. outflow demonstrate how the inflows organize into anisotropic filaments driven by the tidal environment, while the outflows are isotropic due to their thermal nature. This also manifests in the thermal and chemical properties of the gas: While the inflowing gas is pristine and colder, encountering the accretion shocks and entering the influence region of AGN and stellar feedback heats the gas up into a diffuse, metal enriched and hot atmosphere. Overall the differences between outflowing and infalling gas are enhanced at the galaxy cluster scale compared to the galaxy scale due to the accretion shocks that reach out to large radii for these objects. An individual study of the gas motions in the outskirts of one of the most massive clusters in the simulations illustrates these results: Gas found in the outer hot atmosphere at z=0 falls in and is completely enriched early before being shock heated and expanding.

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Hydrodynamic methods and sub-resolution models for cosmological simulations

Cosmological simulations are powerful tools in the context of structure formation. They allow us to explore the assembly and clustering of dark matter halos, to validate or reject possible scenarios of structure formation, and to investigate the physical properties of evolving galaxies across time. Cosmological hydrodynamical simulations are especially key to study how the complex interstellar medium of forming galaxies responds to the most energetic processes during galaxy evolution, such as stellar feedback ensuing supernova explosions and feedback from AGN. Given the huge dynamical range of physical scales spanned by the astrophysical processes involved in cosmic structure formation and evolution, cosmological simulations resort to sub-resolution models to capture processes occurring below their resolution limit. The impact of different sub-grid prescriptions accounting for the same process is striking, though often overlooked. Some among the main aforementioned processes include: hot gas cooling, star formation and stellar feedback, stellar evolution and chemical enrichment, black hole growth and feedback. Producing simulations of cosmic structure formation and galaxy evolution in large computational volumes is key to shed light on what drives the formation of the first structures in the Universe, and their subsequent evolution. Not only are predictions from simulations crucial to compare with data from ongoing observational instruments, but they can also guide future observational campaigns. Besides, since we have entered the era of high-performance computing, it is fundamental to have numerical codes which are very efficient from the computational point of view. In this chapter, we review the main hydrodynamic methods used in cosmological simulations and the most common techniques adopted to include the astrophysical processes which drive galaxy formation and evolution (abridged).

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Cosmological Inference with Cosmic Voids and Neural Network Emulators

Cosmic Voids are a promising probe of cosmology for spectroscopic galaxy surveys due to their unique response to cosmological parameters. Their combination with other probes promises to break parameter degeneracies. Due to simplifying assumptions, analytical models for void statistics are only representative of a subset of the full void population. We present a set of neural-based emulators for void summary statistics of watershed voids, which retain more information about the full void population than simplified analytical models. We build emulators for the void size function and void density profiles traced by the halo number density using the Quijote suite of simulations for a broad range of the $Λ\mathrm{CDM}$ parameter space. The emulators replace the computation of these statistics from computationally expensive cosmological simulations. We demonstrate the cosmological constraining power of voids using our emulators, which offer orders-of-magnitude acceleration in parameter estimation, capture more cosmological information compared to analytic models, and produce more realistic posteriors compared to Fisher forecasts. We find that the parameters $Ω_m$ and $σ_8$ in this Quijote setup can be recovered to $14.4\%$ and $8.4\%$ accuracy respectively using void density profiles; including the additional information in the void size function improves the accuracy on $σ_8$ to $6.8\%$. We demonstrate the robustness of our approach to two important variables in the underlying simulations, the resolution, and the inclusion of baryons. We find that our pipeline is robust to variations in resolution, and we show that the posteriors derived from the emulated void statistics are unaffected by the inclusion of baryons with the Magneticum hydrodynamic simulations. This opens up the possibility of a baryon-independent probe of the large-scale structure.

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Field-level simulation-based inference with galaxy catalogs: the impact of systematic effects

It has been recently shown that a powerful way to constrain cosmological parameters from galaxy redshift surveys is to train graph neural networks to perform field-level likelihood-free inference without imposing cuts on scale. In particular, de Santi et al. (2023) developed models that could accurately infer the value of $Ω_{\rm m}$ from catalogs that only contain the positions and radial velocities of galaxies that are robust to uncertainties in astrophysics and subgrid models. However, observations are affected by many effects, including 1) masking, 2) uncertainties in peculiar velocities and radial distances, and 3) different galaxy selections. Moreover, observations only allow us to measure redshift, intertwining galaxies' radial positions and velocities. In this paper we train and test our models on galaxy catalogs, created from thousands of state-of-the-art hydrodynamic simulations run with different codes from the CAMELS project, that incorporate these observational effects. We find that, although the presence of these effects degrades the precision and accuracy of the models, and increases the fraction of catalogs where the model breaks down, the fraction of galaxy catalogs where the model performs well is over 90 %, demonstrating the potential of these models to constrain cosmological parameters even when applied to real data.

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Turbulent Pressure Support in Galaxy Clusters -- Impact of the Hydrodynamical Solver

The amount of turbulent pressure in galaxy clusters is still debated, especially as for the impact of the dynamical state and the hydro-method used for simulations. We study the turbulent pressure fraction in the intra cluster medium of massive galaxy clusters. We aim to understand the impact of the hydrodynamical scheme, analysis method, and dynamical state on the final properties of galaxy clusters from cosmological simulations. We perform non-radiative simulations of a set of zoom-in regions of seven galaxy clusters with Meshless Finite Mass (MFM) and Smoothed Particle Hydrodynamics (SPH). We use three different analysis methods based on: $(i)$ the deviation from hydrostatic equilibrium, $(ii)$ the solenoidal velocity component obtained by a Helmholtz-Hodge decomposition, and $(iii)$ the small-scale velocity obtained through a multi-scale filtering approach. We split the sample of simulated clusters into active and relaxed clusters. Our simulations predict an increased turbulent pressure fraction for active compared to relaxed clusters. This is especially visible for the velocity-based methods. For these, we also find increased turbulence for the MFM simulations compared to SPH, consistent with findings from more idealized simulations. The predicted non-thermal pressure fraction varies between a few percent for relaxed clusters and $\approx13\%$ for active ones within the cluster center and increases towards the outskirts. No clear trend with redshift is visible. Our analysis quantitatively assesses the importance played by the hydrodynamical scheme and the analysis method to determine the non-thermal/turbulent pressure fraction. While our setup is relatively simple (non-radiative runs), our simulations show agreement with previous, more idealized simulations, and make a step further toward the understanding of turbulence.

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