We present a robust method to constrain average galaxy star formation rates (SFRs), star formation histories (SFHs), and the intracluster light (ICL) as a function of halo mass. Our results are consistent with observed galaxy stellar mass functions, specific star formation rates (SSFRs), and cosmic star formation rates (CSFRs) from z = 0 to z = 8. We consider the effects of a wide range of uncertainties on our results, including those affecting stellar masses, SFRs, and the halo mass function at the heart of our analysis. As they are relevant to our method, we also present new calibrations of the dark matter halo mass function, halo mass accretion histories, and halo-subhalo merger rates out to z = 8. We also provide new compilations of CSFRs and SSFRs; more recent measurements are now consistent with the buildup of the cosmic stellar mass density at all redshifts. Implications of our work include: halos near 1012 M ☉ are the most efficient at forming stars at all redshifts, the baryon conversion efficiency of massive halos drops markedly after z ~ 2.5 (consistent with theories of cold-mode accretion), the ICL for massive galaxies is expected to be significant out to at least z ~ 1-1.5, and dwarf galaxies at low redshifts have higher stellar mass to halo mass ratios than previous expectations and form later than in most theoretical models. Finally, we provide new fitting formulae for SFHs that are more accurate than the standard declining tau model. Our approach places a wide variety of observations relating to the SFH of galaxies into a self-consistent framework based on the modern understanding of structure formation in ΛCDM. Constraints on the stellar mass-halo mass relationship and SFRs are available for download online.

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The Average Star Formation Histories of Galaxies in Dark Matter Halos from z = 0-8

We introduce the Illustris Project, a series of large-scale hydrodynamical simulations of galaxy formation. The highest resolution simulation, Illustris-1, covers a volume of (106.5 Mpc)^3, has a dark mass resolution of 6.26 × 10^6 M_⊙, and an initial baryonic matter mass resolution of 1.26 × 10^6 M_⊙. At z = 0 gravitational forces are softened on scales of 710 pc, and the smallest hydrodynamical gas cells have an extent of 48 pc. We follow the dynamical evolution of 2 × 1820^3 resolution elements and in addition passively evolve 1820^3 Monte Carlo tracer particles reaching a total particle count of more than 18 billion. The galaxy formation model includes: primordial and metal-line cooling with self-shielding corrections, stellar evolution, stellar feedback, gas recycling, chemical enrichment, supermassive black hole growth, and feedback from active galactic nuclei. Here we describe the simulation suite, and contrast basic predictions of our model for the present-day galaxy population with observations of the local universe. At z = 0 our simulation volume contains about 40 000 well-resolved galaxies covering a diverse range of morphologies and colours including early-type, late-type and irregular galaxies. The simulation reproduces reasonably well the cosmic star formation rate density, the galaxy luminosity function, and baryon conversion efficiency at z = 0. It also qualitatively captures the impact of galaxy environment on the red fractions of galaxies. The internal velocity structure of selected well-resolved disc galaxies obeys the stellar and baryonic Tully–Fisher relation together with flat circular velocity curves. In the well-resolved regime, the simulation reproduces the observed mix of early-type and late-type galaxies. Our model predicts a halo mass dependent impact of baryonic effects on the halo mass function and the masses of haloes caused by feedback from supernova and active galactic nuclei.

Introducing the Illustris Project: simulating the coevolution of dark and visible matter in the Universe

We present a series of high-resolution cosmological simulations of galaxy formation to z = 0, spanning halo masses ∼10^8–10^(13) M⊙, and stellar masses ∼10^4–10^(11) M⊙. Our simulations include fully explicit treatment of the multiphase interstellar medium and stellar feedback. The stellar feedback inputs (energy, momentum, mass, and metal fluxes) are taken directly from stellar population models. These sources of feedback, with zero adjusted parameters, reproduce the observed relation between stellar and halo mass up to M_(halo) ∼ 10^(12) M⊙. We predict weak redshift evolution in the M*–M_(halo) relation, consistent with current constraints to z > 6. We find that the M*–M_(halo) relation is insensitive to numerical details, but is sensitive to feedback physics. Simulations with only supernova feedback fail to reproduce observed stellar masses, particularly in dwarf and high-redshift galaxies: radiative feedback (photoheating and radiation pressure) is necessary to destroy giant molecular clouds and enable efficient coupling of later supernovae to the gas. Star formation rates (SFRs) agree well with the observed Kennicutt relation at all redshifts. The galaxy-averaged Kennicutt relation is very different from the numerically imposed law for converting gas into stars, and is determined by self-regulation via stellar feedback. Feedback reduces SFRs and produces reservoirs of gas that lead to rising late-time star formation histories, significantly different from halo accretion histories. Feedback also produces large short-time-scale variability in galactic SFRs, especially in dwarfs. These properties are not captured by common ‘sub-grid’ wind models.

Galaxies on FIRE (Feedback In Realistic Environments): stellar feedback explains cosmologically inefficient star formation

A reexamination is conducted of the formation of dwarf, diffuse, metal-poor galaxies due to supernova-driven winds, in view of data on the systematic properties of dwarfs in the Local Group and Virgo Cluster. The critical condition for global gas loss as a result of the first burst of star formation is that the virial velocity lie below an approximately 100 km/sec critical value. This leads, as observed, to two distinct classes of galaxies, encompassing the diffuse dwarfs, which primarily originate from typical density perturbations, and the normal, brighter galaxies, including compact dwarfs, which can originate only from the highest density peaks. This furnishes a statistical biasing mechanism for the preferential formation of bright galaxies in denser regions, enhancing high surface brightness galaxies' clustering relative to the diffusive dwarfs.

Dwarf galaxies, cold dark matter, and biased galaxy formation

Euclid is a European Space Agency medium-class mission selected for launch in 2020 within the cosmic vision 2015–2025 program. The main goal of Euclid is to understand the origin of the accelerated expansion of the universe. Euclid will explore the expansion history of the universe and the evolution of cosmic structures by measuring shapes and red-shifts of galaxies as well as the distribution of clusters of galaxies over a large fraction of the sky. Although the main driver for Euclid is the nature of dark energy, Euclid science covers a vast range of topics, from cosmology to galaxy evolution to planetary research. In this review we focus on cosmology and fundamental physics, with a strong emphasis on science beyond the current standard models. We discuss five broad topics: dark energy and modified gravity, dark matter, initial conditions, basic assumptions and questions of methodology in the data analysis. This review has been planned and carried out within Euclid’s Theory Working Group and is meant to provide a guide to the scientific themes that will underlie the activity of the group during the preparation of the Euclid mission.

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Cosmology and Fundamental Physics with the Euclid Satellite

Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be further improved with time-stepping schemes that use input from cosmological perturbation theory. Specifically, we introduce a class of time-stepping schemes derived by matching the particle trajectories in a single leapfrog/Verlet drift-kick-drift step to those predicted by Lagrangian perturbation theory (LPT). As a corollary, these schemes exactly yield the analytic Zel’dovich solution in 1D in the pre-shell-crossing regime (i.e. before particle trajectories cross). One representative of this class is the popular ‘FastPM’ scheme by Feng et al. 2016 [1], which we take as our baseline. We then construct more powerful LPT-inspired integrators and show that they outperform FastPM and standard integrators in fast simulations in two and three dimensions with O(1 − 100) timesteps, requiring less steps to accurately reproduce the power spectrum and bispectrum of the density field. Furthermore, we demonstrate analytically and numerically that, for any integrator, higher-order convergence cannot be achieved in the post-shell-crossing regime, owing to the lacking regularity of the acceleration field. Also, we study the impact of the timestep spacing and of a decaying mode present in the initial conditions. Importantly, we find that symplecticity of the integrator plays a minor role for fast approximate simulations with a small number of timesteps. © 2023 Elsevier Inc. All rights reserved.

Perturbation-theory informed integrators for cosmological simulations

Collisionless simulations of structure formation with significant local primordial non-Gaussianities at Mpc scales have shown that a non-Gaussian tail favouring underdensities, with a negative $f_{\rm NL}$ parameter, can significantly change the merging history of galaxy-sized dark matter halos, which then typically assemble later than in vanilla $\Lambda$CDM. Moreover, such a small-scale negative $f_{\rm NL}$ could have interesting consequences for the cosmological $S_8$ tension. Here, we complement our previous work on collisionless simulations with new hydrodynamical simulations of galaxy formation in boxes of 30 Mpc/$h$, using the {\sc RAMSES} code. In particular, we show that all feedback prescriptions being otherwise identical, simulations with a negative $f_{\rm NL} \sim -1000$ on small scales, hence forming galaxies a bit later than in vanilla $\Lambda$CDM, allow to form simulated galaxies with more disky kinematics than in the vanilla case. Therefore, such small-scale primordial non-Gaussianities could potentially help alleviate, simultaneously, tensions in cosmology and galaxy formation. These hydrodynamical simulations on small scales will need to be complemented with larger box simulations with scale-dependent non-Gaussianities, to statistically confirm these trends and explore their observational consequences in further detail.

Hydrodynamical simulations of galaxy formation with non-Gaussian initial conditions

Cosmological perturbation theory is known to converge poorly for predicting the spherical collapse and void evolution of collisionless matter. Using the exact parametric solution as a testing ground, we develop two asymptotic methods in spherical symmetry that resolve the gravitational evolution to much higher accuracy than Lagrangian perturbation theory (LPT), which is the current gold standard in the literature. One of the methods selects a stable ﬁxed-point solution of the renormalization-group ﬂow equation, thereby predicting already at the leading order the critical exponent of the phase transition to collapsed structures. The other method completes the truncated LPT series far into the ultra-violet (UV) regime, by adding a non-analytic term that captures the critical nature of the gravitational collapse. We ﬁnd that the UV method most accurately resolves the evolution of the non-linear density as well as its one-point probability distribution function. Similarly accurate predictions are achieved with the renormalization-group method, especially when paired with Pad´e approximants. Further, our results yield new, very accurate, formulae to relate linear and non-linear density contrasts. Finally, we chart possible ways on how to adapt our methods to the case of cosmological random ﬁeld initial conditions.

Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon


 We present the Rhapsody-C simulations that extend the Rhapsody-G suite of massive galaxy clusters at the Mvir ∼ 1015 M⊙ scale with cosmological magneto-hydrodynamic zoom-in simulations that include anisotropic thermal conduction, modified supermassive black hole (SMBH) feedback, new SMBH seeding and SMBH orbital decay model. These modelling improvements have a dramatic effect on the SMBH growth, star formation and gas depletion in the proto-clusters. We explore the parameter space of the models and report their effect on both star formation and the thermodynamics of the intra-cluster medium (ICM) as observed in X-ray and SZ observations. We report that the star formation in proto-clusters is strongly impacted by the choice of the SMBH seeding as well as the orbital decay of SMBHs. Feedback from AGNs is substantially boosted by the SMBH decay, its time evolution and impact range differ noticeably depending on the AGN energy injection scheme used. Compared to a mass-weighted injection whose energy remains confined close to the central SMBHs, a volume-weighted thermal energy deposition allows to heat the ICM out to large radii which severely quenches the star formation in proto-clusters. By flattening out temperature gradients in the ICM, anisotropic thermal conduction can reduce star formation early on but weakens and delays the AGN activity. Despite the dissimilarities found in the stellar and gaseous content of our haloes, the cluster scaling relations we report are surprisingly insensitive to the subresolution models used and are in good agreement with recent observational and numerical studies.

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Rhapsody-C simulations – anisotropic thermal conduction, black hole physics, and the robustness of massive galaxy cluster scaling relations


 Galaxy mergers are common processes in the Universe. As a large fraction of galaxies hosts at their centres a central supermassive black hole (SMBH), mergers can lead to the formation of a supermassive black hole binary (SMBHB). The formation of such a binary is more efficient when the SMBHs are embedded in a nuclear star cluster (NSC). NSCs are dense and massive stellar clusters present in the majority of the observed galaxies. Their central densities can reach up to 107 M⊙/pc3 and their masses can be as large as a few 107 M⊙. The direct detection of an SMBHB is observationally challenging. In this work, we illustrate how the large scale structural and dynamical properties of an NSC can help to identify nucleated galaxies that recently went through a merger that possibly led to the formation of a central SMBHB. Our models show that the merger can imprint signatures on the shape, density profile, rotation and velocity structure of the NSC. The strength of the signatures depends on the mass ratio between the SMBHs and on the orbital initial conditions of the merger. In addition, the number of hypervelocity stars produced in the mergers is linked to the SMBHB properties. The merger can also contribute to the formation of the nuclear stellar disc of the galaxy.

Oliver Hahn

Papers

Perturbation-theory informed integrators for cosmological simulations

Hydrodynamical simulations of galaxy formation with non-Gaussian initial conditions

Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Rhapsody-C simulations – anisotropic thermal conduction, black hole physics, and the robustness of massive galaxy cluster scaling relations

Searching for clues of past binary supermassive black hole mergers in nuclear star clusters