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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).

In cosmological simulations of large-scale structure star formation and feedback in galaxies are modelled by so-called sub-grid models, that represent a physically motivated approximation of processes occurring below the resolution limit. However, when additional physical processes are considered in these simulations, for instance, magnetic fields or cosmic rays, they are often not consistently coupled within the descriptions of the underlying sub-grid star formation models. Here, we present a careful study on how one of the most commonly used sub-grid models for star formation in current large-scale cosmological simulations can be modified to self consistently include the effects of non-thermal components (e.g., magnetic fields) within the fluid. We demonstrate that our new modelling approach, that includes the magnetic pressure as an additional regulation on star formation, can reproduce global properties of the magnetic field within galaxies in a setup of an isolated Milky Way-like galaxy simulation, but is also successful in reproducing local properties such as the anti-correlation between the local magnetic field strength with the local star formation rate as observed in galaxies (i.e. NGC 1097). This reveals how crucial a consistent treatment of different physical processes is within cosmological simulations and gives guidance for future simulations.

Subsonic turbulence plays a major role in determining properties of the intra cluster medium (ICM). We introduce a new Meshless Finite Mass (MFM) implementation in OpenGadget3 and apply it to this specific problem. To this end, we present a set of test cases to validate our implementation of the MFM framework in our code. These include but are not limited to: the soundwave and Kepler disk as smooth situations to probe the stability, a Rayleigh-Taylor and Kelvin-Helmholtz instability as popular mixing instabilities, a blob test as more complex example including both mixing and shocks, shock tubes with various Mach numbers, a Sedov blast wave, different tests including self-gravity such as gravitational freefall, a hydrostatic sphere, the Zeldovich-pancake, and a \\(10^{15}M_{\\odot}\\) galaxy cluster as cosmological application. Advantages over SPH include increased mixing and a better convergence behavior. We demonstrate that the MFM-solver is robust, also in a cosmological context. We show evidence that the solver performs extraordinarily well when applied to decaying subsonic turbulence, a problem very difficult to handle for many methods. MFM captures the expected velocity power spectrum with high accuracy and shows a good convergence behavior. Using MFM or SPH within OpenGadget3 leads to a comparable decay in turbulent energy due to numerical dissipation. When studying the energy decay for different initial turbulent energy fractions, we find that MFM performs well down to Mach numbers \\(\\mathcal{M}\\approx 0.01\\). Finally, we show how important the slope limiter and the energy-entropy switch are to control the behavior and the evolution of the fluids.

We investigate the orbital decay of a massive BH embedded in a dark matter halo and a stellar bulge, using both analytical and numerical simulations with the aim of developing and validating a reliable dynamical friction (DF) correction across simulation resolutions. We develop a Python-based library to solve the equations of motion of the BH and provide an analytical framework for the numerical results. Then, we carry out simulations at different resolutions and for different softening choices using the Tree-PM code OpenGADGET3, where we implement an improved DF correction based on a kernel-weighted local density estimation. Our results demonstrate that the DF correction significantly accelerates BH sinking and ensures convergence with increasing resolution, closely matching analytical predictions. We find that in low-resolution regimes - particularly when the BH mass is smaller than that of the background particles - our DF model still effectively controls BH dynamics. Contrary to expectations, the inclusion of a stellar bulge can delay sinking due to numerical heating, an effect partially mitigated by the DF correction. We conclude that our refined DF implementation provides a robust framework for modeling BH dynamics both in controlled simulation setups of galaxies and in large-scale cosmological simulations. This will be crucial for future simulation campaigns, to enable more accurate predictions of AGN accretion and feedback, and to estimate gravitational-wave event rates.

The XRISM Resolve X-ray spectrometer allows to gain detailed insight into gas motions of the intra cluster medium (ICM) of galaxy clusters. Current simulation studies focus mainly on statistical comparisons, making the comparison to the currently still small number of clusters difficult due to unknown selection effects. This study aims to bridge this gap, using simulated counterparts of Coma, Virgo, and Perseus from the SLOW constrained simulations. These clusters show excellent agreement in their properties and dynamical state with observations, thus providing an ideal testbed to understand the processes shaping the properties of the ICM. We find that the simulations match the order of the amount of turbulence for the three considered clusters, Coma being the most active, followed by Perseus, while Virgo is very relaxed. Typical turbulent velocities are a few \\(\\approx100\\) km s\\(^{-1}\\), very close to observed values. The resulting turbulent pressure support is \\(\\approx1\\%\\) for Virgo, \\(\\approx 6\\%\\) for Perseus, and \\(\\approx 8\\%\\) for Coma within the central \\(1-2\\%\\) of \\(R_{200}\\). Compared to previous simulations and observations, measured velocities and turbulent pressure support are on average lower, in line with XRISM findings, thus indicating the importance of selection effects.

The properties of quasar-host galaxies might be determined by the growth and feedback of their supermassive (SMBH, \\(10^{8-10}\\) M\\(_{\\odot}\\)) black holes. We investigate such connection with a suite of cosmological simulations of massive (halo mass \\(\\approx 10^{12}\\) M\\(_{\\odot}\\)) galaxies at \\(z\\simeq 6\\) which include a detailed sub-grid multiphase gas and accretion model. BH seeds of initial mass \\(10^5\\) M\\(_{\\odot}\\) grow mostly by gas accretion, and become SMBH by \\(z=6\\) setting on the observed \\(M_{\\rm BH} - M_{\\star}\\) relation without the need for a boost factor. Although quasar feedback crucially controls the SMBH growth, its impact on the properties of the host galaxy at \\(z=6\\) is negligible. In our model, quasar activity can both quench (via gas heating) or enhance (by ISM over-pressurization) star formation. However, we find that the star formation history is insensitive to such modulation as it is largely dominated, at least at \\(z>6\\), by cold gas accretion from the environment that cannot be hindered by the quasar energy deposition. Although quasar-driven outflows can achieve velocities \\(> 1000~\\rm km~s^{-1}\\), only \\(\\approx 4\\)% of the outflowing gas mass can actually escape from the host galaxy. These findings are only loosely constrained by available data, but can guide observational campaigns searching for signatures of quasar feedback in early galaxies.

The impact of viscosity in the Intracluster Medium (ICM) is still an open question in astrophysics. To address this problem, we have run a set of cosmological simulations of three galaxy clusters with a mass larger than \\(M_{\\mathrm{Vir}} > 10^{15} \\)M\\(_{\\odot}\\) at \\(z=0\\) using the SPMHD-code OpenGadget3. We aim to quantify the influence of viscosity and constrain its value in the ICM. Our results show significant morphological differences at small scales, temperature variations, and density fluctuations induced by viscosity. We observe a suppression of instabilities at small scales, resulting in a more filamentary structure and a larger amount of small structures due to the lack of mixing with the medium. The conversion of kinetic to internal energy leads to an increase of the virial temperature of the cluster of \\(\\sim\\)5% - 10%, while the denser regions remain cold. The amplitude of density and velocity fluctuations are found to increase with viscosity. However, comparison with observational data indicates that the simulations, regardless of the viscosity, match the observed slope of the amplitude of density fluctuations, challenging the direct constraint of viscosity solely through density fluctuations. Furthermore, the ratio of density to velocity fluctuations remains close to 1 regardless of the amount of viscosity, in agreement with the theoretical expectations. Our results show for the first time in a cosmological simulation of a galaxy cluster the effect of viscosity in the ICM, a study that is currently missing in the literature.

The evolution of the Kelvin-Helmholtz Instability (KHI) is widely used to assess the performance of numerical methods. We employ this instability to test both the smoothed particle hydrodynamics (SPH) and the meshless finite mass (MFM) implementation in OpenGadget3. We quantify the accuracy of SPH and MFM in reproducing the linear growth of the KHI with different numerical and physical set-ups. Among them, we consider: \\(i)\\) numerical induced viscosity, and \\(ii)\\) physically motivated, Braginskii viscosity, and compare their effect on the growth of the KHI. We find that the changes of the inferred numerical viscosity when varying nuisance parameters such as the set-up or the number of neighbours in our SPH code are comparable to the differences obtained when using different hydrodynamical solvers, i.e. MFM. SPH reproduces the expected reduction of the growth rate in the presence of physical viscosity and recovers well the threshold level of physical viscosity needed to fully suppress the instability. In the case of galaxy clusters with a virial temperature of \\(3\\times10^7\\) K, this level corresponds to a suppression factor of \\(\\approx10^{-3}\\) of the classical Braginskii value. The intrinsic, numerical viscosity of our SPH implementation in such an environment is inferred to be at least an order of magnitude smaller (i.e. \\(\\approx10^ {-4}\\)), re-ensuring that modern SPH methods are suitable to study the effect of physical viscosity in galaxy clusters.

The study of protoclusters at cosmic noon is essential to understand the impact on galaxies of the environment and of the transformational processes occurring in this epoch. This work tests the predictions of the DIANOGA cosmological hydrodynamical simulations of cluster progenitors at z=2.2, comparing them with observations, and investigates the environmental effects on galaxies by comparing protoclusters with an average volume of the Universe. We analyze 14 protoclusters and a cosmological box of 49 cMpc/h per side. We compare predictions and observations of the galaxy properties, including colors of galaxies obtained with radiative transfer, to analyze UVJ diagrams. We showed that the DIANOGA simulations produce a galaxy stellar mass function in broad agreement with observations, with a higher fraction of high-mass galaxies (\\(M_{\\ast}>10^{10} \\ M_{\\odot}\\)) in massive halos in protoclusters, compared to the box. The same signal, with lower significance, is also observed in the wide-field protocluster structures, indicating an accelerated evolution of galaxies before their infall into massive halos. Our simulations underestimate SFRs of galaxies both in protoclusters and in the box, compared to observations, due to low gas reservoirs. We find a weak suppression of SFRs in protocluster galaxies (~0.05 dex), compared to the box, increasing up to ~0.25 dex in massive halos. The quenched galaxy fraction varies significantly across different protocluster halos, consistent with observations. The simulations show a strong dependence of quenched fractions on halo mass and an excess of quenched galaxies in the wide-field protocluster region, compared to the cosmological box. UVJ diagram analysis shows qualitative agreement with observed color distributions of star-forming and quenched galaxies, except for few massive galaxies with steeper reddening vectors than typically assumed in observations.

We implement a sub-resolution prescription for the unresolved dynamical friction onto black holes (BHs) in the OpenGadget3 code. We carry out cosmological simulations of a volume of 16 cMpc3 and zoom-ins of a galaxy group and of a galaxy cluster. The advantages of our new technique are assessed in comparison to commonly adopted methods to hamper spurious BH displacements, i.e. repositioning onto a local minimum of the gravitational potential and ad-hoc boosting of the BH particle dynamical mass. The newly-introduced dynamical friction correction provides centering of BHs on host halos which is at least comparable with the other techniques. It predicts half as many merger events with respect to the repositioning prescription, with the advantage of being less prone to leave sub-structures without any central BH. Simulations featuring our dynamical friction prescription produce a smaller (by up to 50% with respect to repositioning) population of wandering BHs and final BH masses in good agreement with observations. As for individual BH-BH interactions, our dynamical friction model captures the gradual inspiraling of orbits before the merger occurs. By contrast, the repositioning scheme, in its most classical renditions considered, describes extremely fast mergers, while the dynamical mass misrepresents the BHs' dynamics, introducing numerical scattering between the orbiting BHs. Given its performances in describing the centering of BHs within host galaxies and the orbiting of BH pair before their merging, our dynamical friction correction opens interesting applications for an accurate description of the evolution of BH demography within cosmological simulations of galaxy formation at different cosmic epochs and within different environments.