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Large-scale cosmological galaxy formation simulations typically prevent gas in the interstellar medium (ISM) from cooling below $\approx 10^4$ K. This has been motivated by the inability to resolve the Jeans mass in molecular gas (>>$10^5\,\mathrm{M}_{\odot}$) which would result in undesired artificial clumping. We show that the classical Jeans criteria derived for Newtonian gravity are not applicable in the simulated ISM if the spacing of resolution elements representing the dense ISM is below the gravitational force softening length and gravity is therefore softened and not Newtonian. We re-derive the Jeans criteria for softened gravity in Lagrangian codes and use them to analyse gravitational instabilities at and below the hydrodynamical resolution limit for simulations with adaptive and constant gravitational softening lengths. In addition, we define criteria for which a numerical runaway collapse of dense gas clumps can occur caused by over-smoothing of the hydrodynamical properties relative to the gravitational force resolution. This effect is illustrated using simulations of isolated disk galaxies with the smoothed particle hydrodynamics code Swift. We also demonstrate how to avoid the formation of artificial clumps in gas and stars by adjusting the gravitational and hydrodynamical force resolutions., Comment: 24 pages, 15 figures, accepted for publication in MNRAS, smaller updates to match published version

We use smoothed-particle hydrodynamics simulations of isolated Milky Way-mass disk galaxies that include cold, interstellar gas to test subgrid prescriptions for star formation (SF). Our fiducial model combines a Schmidt law with a gravitational instability criterion, but we also test density thresholds and temperature ceilings. While SF histories are insensitive to the prescription for SF, the Kennicutt-Schmidt (KS) relations between SF rate and gas surface density can discriminate between models. We show that our fiducial model, with an SF efficiency per free-fall time of 1 per cent, agrees with spatially-resolved and azimuthally-averaged observed KS relations for neutral, atomic and molecular gas. Density thresholds do not perform as well. While temperature ceilings selecting cold, molecular gas can match the data for galaxies with solar metallicity, they are unsuitable for very low-metallicity gas and hence for cosmological simulations. We argue that SF criteria should be applied at the resolution limit rather than at a fixed physical scale, which means that we should aim for numerical convergence of observables rather than of the properties of gas labelled as star-forming. Our fiducial model yields good convergence when the mass resolution is varied by nearly 4 orders of magnitude, with the exception of the spatially-resolved molecular KS relation at low surface densities. For the gravitational instability criterion, we quantify the impact on the KS relations of gravitational softening, the SF efficiency, and the strength of supernova feedback, as well as of observable parameters such as the inclusion of ionized gas, the averaging scale, and the metallicity., Comment: Submitted to MNRAS, 23 pages, 20 figures

Using the SWIFT simulation code we study different forms of active galactic nuclei (AGN) feedback in idealized galaxy groups and clusters. We first present a physically motivated model of black hole (BH) spin evolution and a numerical implementation of thermal isotropic feedback (representing the effects of energy-driven winds) and collimated kinetic jets that they launch at different accretion rates. We find that kinetic jet feedback is more efficient at quenching star formation in the brightest cluster galaxies (BCGs) than thermal isotropic feedback, while simultaneously yielding cooler cores in the intracluster medium (ICM). A hybrid model with both types of AGN feedback yields moderate star formation rates, while having the coolest cores. We then consider a simplified implementation of AGN feedback by fixing the feedback efficiencies and the jet direction, finding that the same general conclusions hold. We vary the feedback energetics (the kick velocity and the heating temperature), the fixed efficiencies and the type of energy (kinetic versus thermal) in both the isotropic and the jet case. The isotropic case is largely insensitive to these variations. In particular, we highlight that kinetic isotropic feedback (used e.g. in IllustrisTNG) is similar in its effects to its thermal counterpart (used e.g. in EAGLE). On the other hand, jet feedback must be kinetic in order to be efficient at quenching. We also find that it is much more sensitive to the choice of energy per feedback event (the jet velocity), as well as the efficiency. The former indicates that jet velocities need to be carefully chosen in cosmological simulations, while the latter motivates the use of BH spin evolution models., Comment: Accepted for publication in MNRAS

We present hydrodynamic simulations of the interstellar medium (ISM) within the circumnuclear disk (CND) of a typical AGN-dominated galaxy influenced by mechanical feedback from an active galactic nucleus(AGN). The simulations are coupled with the CHIMES non-equilibrium chemistry network to treat the radiative-cooling and AGN-heating. A focus is placed on the central 100 pc scale where AGN outflows are coupled to the ISM and constrained by observational Seyfert-2 galaxies. AGN-feedback models are implemented with different wind-velocity and mass-loading factors. We post-process the simulation snapshots with a radiative-transfer code to obtain the molecular emission lines. We find that the inclusion of an AGN promotes the formation of CO in clumpy and dense regions surrounding supermassive-blackholes (SMBH). The CO(1-0) intensity maps ($<$6 Myr) in the CND seem to match well with observations of NGC 1068 with a best match for a model with 5000 $\rm km/s$ wind-velocity and a high mass-loading factor. We attempt to discern between competing explanations for the apparent counter-rotating gas disk in the NGC 1068 through an analysis of kinematic maps of the CO line emission. We suggest that mechanical AGN-feedback could explain the alignment-stability of position-angle across the different CND radii around the SMBH through momentum and energy loading of the wind. It is the wind-velocity that drives the disk out of alignment on a 100 pc scale for a long period of time. The position-velocity diagrams are in broad agreement with the predicted Keplerian rotation-curve in the model without-AGN, but the AGN models exhibit a larger degree of scatter, in better agreement with NGC 1068 observations., Comment: 16 pages, 13 figures. Accepted for publication in MNRAS

To fully take advantage of the data provided by large-scale structure surveys, we need to quantify the potential impact of baryonic effects, such as feedback from active galactic nuclei (AGN) and star formation, on cosmological observables. In simulations, feedback processes originate on scales that remain unresolved. Therefore, they need to be sourced via subgrid models that contain free parameters. We use machine learning to calibrate the AGN and stellar feedback models for the FLAMINGO cosmological hydrodynamical simulations. Using Gaussian process emulators trained on Latin hypercubes of 32 smaller-volume simulations, we model how the galaxy stellar mass function and cluster gas fractions change as a function of the subgrid parameters. The emulators are then fit to observational data, allowing for the inclusion of potential observational biases. We apply our method to the three different FLAMINGO resolutions, spanning a factor of 64 in particle mass, recovering the observed relations within the respective resolved mass ranges. We also use the emulators, which link changes in subgrid parameters to changes in observables, to find models that skirt or exceed the observationally allowed range for cluster gas fractions and the stellar mass function. Our method enables us to define model variations in terms of the data that they are calibrated to rather than the values of specific subgrid parameters. This approach is useful, because subgrid parameters are typically not directly linked to particular observables, and predictions for a specific observable are influenced by multiple subgrid parameters., Comment: 24 pages, 10 figures (Including the appendix). Accepted for publication in MNRAS. Minor changes w.r.t. version 1. For visualisations, see the FLAMINGO website at https://flamingo.strw.leidenuniv.nl/

We introduce the Virgo Consortium's FLAMINGO suite of hydrodynamical simulations for cosmology and galaxy cluster physics. To ensure the simulations are sufficiently realistic for studies of large-scale structure, the subgrid prescriptions for stellar and AGN feedback are calibrated to the observed low-redshift galaxy stellar mass function and cluster gas fractions. The calibration is performed using machine learning, separately for three resolutions. This approach enables specification of the model by the observables to which they are calibrated. The calibration accounts for a number of potential observational biases and for random errors in the observed stellar masses. The two most demanding simulations have box sizes of 1.0 and 2.8 Gpc and baryonic particle masses of $1\times10^8$ and $1\times10^9 \text{M}_\odot$, respectively. For the latter resolution the suite includes 12 model variations in a 1 Gpc box. There are 8 variations at fixed cosmology, including shifts in the stellar mass function and/or the cluster gas fractions to which we calibrate, and two alternative implementations of AGN feedback (thermal or jets). The remaining 4 variations use the unmodified calibration data but different cosmologies, including different neutrino masses. The 2.8 Gpc simulation follows $3\times10^{11}$ particles, making it the largest ever hydrodynamical simulation run to $z=0$. Lightcone output is produced on-the-fly for up to 8 different observers. We investigate numerical convergence, show that the simulations reproduce the calibration data, and compare with a number of galaxy, cluster, and large-scale structure observations, finding very good agreement with the data for converged predictions. Finally, by comparing hydrodynamical and `dark-matter-only' simulations, we confirm that baryonic effects can suppress the halo mass function and the matter power spectrum by up to $\approx20$ per cent., Comment: 44 pages, 23 figures. Accepted for publication in MNRAS. V3 includes changes made in published version: jet simulations were redone to fix a bug, but the differences are nearly invisible. For visualizations, see the FLAMINGO website at https://flamingo.strw.leidenuniv.nl/

Numerical simulations have become one of the key tools used by theorists in all the fields of astrophysics and cosmology. The development of modern tools that target the largest existing computing systems and exploit state-of-the-art numerical methods and algorithms is thus crucial. In this paper, we introduce the fully open-source highly-parallel, versatile, and modular coupled hydrodynamics, gravity, cosmology, and galaxy-formation code SWIFT. The software package exploits hybrid shared- and distributed-memory task-based parallelism, asynchronous communications, and domain-decomposition algorithms based on balancing the workload, rather than the data, to efficiently exploit modern high-performance computing cluster architectures. Gravity is solved for using a fast-multipole-method, optionally coupled to a particle mesh solver in Fourier space to handle periodic volumes. For gas evolution, multiple modern flavours of Smoothed Particle Hydrodynamics are implemented. SWIFT also evolves neutrinos using a state-of-the-art particle-based method. Two complementary networks of sub-grid models for galaxy formation as well as extensions to simulate planetary physics are also released as part of the code. An extensive set of output options, including snapshots, light-cones, power spectra, and a coupling to structure finders are also included. We describe the overall code architecture, summarise the consistency and accuracy tests that were performed, and demonstrate the excellent weak-scaling performance of the code using a representative cosmological hydrodynamical problem with $\approx$$300$ billion particles. The code is released to the community alongside extensive documentation for both users and developers, a large selection of example test problems, and a suite of tools to aid in the analysis of large simulations run with SWIFT., Comment: 43 pages, 20 figures, accepted for publication in MNRAS. Code, documentation, and examples available at www.swiftsim.com

All modern galaxy formation models employ stochastic elements in their sub-grid prescriptions to discretise continuous equations across the time domain. In this paper, we investigate how the stochastic nature of these models, notably star formation, black hole accretion, and their associated feedback, that act on small ($<$ kpc) scales, can back-react on macroscopic galaxy properties (e.g. stellar mass and size) across long ($>$ Gyr) timescales. We find that the scatter in scaling relations predicted by the EAGLE model implemented in the SWIFT code can be significantly impacted by random variability between re-simulations of the same object, even when galaxies are resolved by tens of thousands of particles. We then illustrate how re-simulations of the same object can be used to better understand the underlying model, by showing how correlations between galaxy stellar mass and black hole mass disappear at the highest black hole masses ($M_{\rm BH} > 10^8$ M$_\odot$), indicating that the feedback cycle may be interrupted by external processes. We find that although properties that are collected cumulatively over many objects are relatively robust against random variability (e.g. the median of a scaling relation), the properties of individual galaxies (such as galaxy stellar mass) can vary by up to 25\%, even far into the well-resolved regime, driven by bursty physics (black hole feedback) and mergers between galaxies. We suggest that studies of individual objects within cosmological simulations be treated with caution, and that any studies aiming to closely investigate such objects must account for random variability within their results., Comment: Accepted for publication in MNRAS

We present a subgrid model for supernova feedback designed for cosmological simulations of galaxy formation that may include a cold interstellar medium (ISM). The model uses thermal and kinetic channels of energy injection, which are built upon the stochastic kinetic and thermal models for stellar feedback used in the OWLS and EAGLE simulations, respectively. In the thermal channel, the energy is distributed statistically isotropically and injected stochastically in large amounts per event, which minimizes spurious radiative energy losses. In the kinetic channel, we inject the energy in small portions by kicking gas particles in pairs in opposite directions. The implementation of kinetic feedback is designed to conserve energy, linear and angular momentum, and is statistically isotropic. To test the model, we run simulations of isolated Milky Way-mass and dwarf galaxies, in which the gas is allowed to cool down to 10 K. Using the thermal and kinetic channels together, we obtain smooth star formation histories and powerful galactic winds with realistic mass loading factors. Furthermore, the model produces spatially resolved star formation rates (SFRs) and velocity dispersions that are in agreement with observations. We vary the numerical resolution by several orders of magnitude and find excellent convergence of the global SFRs and wind mass loading. We show that large thermal-energy injections generate a hot phase of the ISM and modulate the star formation by ejecting gas from the disc, while the low-energy kicks increase the turbulent velocity dispersion in the neutral ISM, which in turn helps suppress star formation., Comment: 23 pages, 17 figures (including appendix); Accepted for publication in MNRAS

We implement a black hole spin evolution and jet feedback model into SWIFT, a smoothed particle hydrodynamics code. The jet power is determined self-consistently assuming Bondi accretion, using a realistic, spin-dependant efficiency. The jets are launched along the spin axis of the black hole, resulting in natural reorientation and precession. We apply the model to idealised simulations of galaxy groups and clusters, finding that jet feedback successfully quenches gas cooling and star formation in all systems. Our group-size halo ($M_\mathrm{200}=10^{13}$ $\mathrm{M}_\odot$) is quenched by a strong jet episode triggered by a cooling flow, and it is kept quenched by a low-power jet fed from hot halo accretion. In more massive systems ($M_\mathrm{200}\geq 10^{14}$ $\mathrm{M}_\odot$), hot halo accretion is insufficient to quench the galaxies, or to keep them quenched after the first cooling episode. These galaxies experience multiple episodes of gas cooling, star formation and jet feedback. In the most massive galaxy cluster that we simulate ($M_\mathrm{200}=10^{15}$ $\mathrm{M}_\odot$), we find peak cold gas masses of $10^{10}$ $\mathrm{M}_\odot$ and peak star formation rates of a few times $100$ $\mathrm{M}_\odot\mathrm{yr}^{-1}$. These values are achieved during strong cooling flows, which also trigger the strongest jets with peak powers of $10^{47}$ $\mathrm{erg}\hspace{0.3mm}\mathrm{s}^{-1}$. These jets subsequently shut off the cooling flows and any associated star formation. Jet-inflated bubbles draw out low-entropy gas that subsequently forms dense cooling filaments in their wakes, as seen in observations., Comment: Accepted for publication in MNRAS

Using high-resolution hydrodynamical simulations of galaxy clusters, we study the interaction between the brightest cluster galaxy, its supermassive black hole (BH) and the intracluster medium (ICM). We create initial conditions for which the ICM is in hydrostatic equilibrium within the gravitational potential from the galaxy and an NFW dark matter halo. Two free parameters associated with the thermodynamic profiles determine the cluster gas fraction and the central temperature, where the latter can be used to create cool-core or non-cool-core systems. Our simulations include radiative cooling, star formation, BH accretion, and stellar and active galactic nucleus (AGN) feedback. Even though the energy of AGN feedback is injected thermally and isotropically, it leads to anisotropic outflows and buoyantly rising bubbles. We find that the BH accretion rate (BHAR) is highly variable and only correlates strongly with the star formation rate (SFR) and the ICM when it is averaged over more than $1~\rm Myr$. We generally find good agreement with the theoretical precipitation framework. In $10^{13}~\rm M_\odot$ haloes, AGN feedback quenches the central galaxy and converts cool-core systems into non-cool-core systems. In contrast, higher-mass, cool-core clusters evolve cyclically. Episodes of high BHAR raise the entropy of the ICM out to the radius where the ratio of the cooling time and the local dynamical time $t_{\rm cool}/t_{\rm dyn} > 10$, thus suppressing condensation and, after a delay, the BHAR. The corresponding reduction in AGN feedback allows the ICM to cool and become unstable to precipitation, thus initiating a new episode of high SFR and BHAR., Comment: 22 pages, 15 figures (including appendix); submitted to MNRAS; Supplementary material is available on Youtube at https://youtu.be/HQhc_mytj0A and online on a single website page at https://home.strw.leidenuniv.nl/~nobels/supplementary_idealised_cluster_paper.php

Supernova (SN) feedback plays a crucial role in simulations of galaxy formation. Because blastwaves from individual SNe occur on scales that remain unresolved in modern cosmological simulations, SN feedback must be implemented as a subgrid model. Differences in the manner in which SN energy is coupled to the local interstellar medium and in which excessive radiative losses are prevented have resulted in a zoo of models used by different groups. However, the importance of the selection of resolution elements around young stellar particles for SN feedback has largely been overlooked. In this work, we examine various selection methods using the smoothed particle hydrodynamics code SWIFT. We run a suite of isolated disk galaxy simulations of a Milky Way-mass galaxy and small cosmological volumes, all with the thermal stochastic SN feedback model used in the EAGLE simulations. We complement the original mass-weighted neighbour selection with a novel algorithm guaranteeing that the SN energy distribution is as close to isotropic as possible. Additionally, we consider algorithms where the energy is injected into the closest, least dense, or most dense neighbour. We show that different neighbour-selection strategies cause significant variations in star formation rates, gas densities, wind mass loading factors, and galaxy morphology. The isotropic method results in more efficient feedback than the conventional mass-weighted selection. We conclude that the manner in which the feedback energy is distributed among the resolution elements surrounding a feedback event is as important as changing the amount of energy by factors of a few., Comment: 16 pages, 13 figures (including appendix); Accepted for publication in MNRAS