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 disk 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.

Previous simulations of the growth of cosmic structures have broadly reproduced the 'cosmic web' of galaxies that we see in the Universe, but failed to create a mixed population of elliptical and spiral galaxies, because of numerical inaccuracies and incomplete physical models. Moreover, they were unable to track the small-scale evolution of gas and stars to the present epoch within a representative portion of the Universe. Here we report a simulation that starts 12 million years after the Big Bang, and traces 13 billion years of cosmic evolution with 12 billion resolution elements in a cube of 106.5 megaparsecs a side. It yields a reasonable population of ellipticals and spirals, reproduces the observed distribution of galaxies in clusters and characteristics of hydrogen on large scales, and at the same time matches the 'metal' and hydrogen content of galaxies on small scales.

We present the full public release of all data from the Illustris simulation project. Illustris is a suite of large volume, cosmological hydrodynamical simulations run with the moving-mesh code Arepo and including a comprehensive set of physical models critical for following the formation and evolution of galaxies across cosmic time. Each simulates a volume of (106.5 Mpc) 3 and self-consistently evolves five different types of resolution elements from a starting redshift of z = 127 to the present day, z = 0. These components are: dark matter particles, gas cells, passive gas tracers, stars and stellar wind particles, and supermassive black holes. This data release includes the snapshots at all 136 available redshifts, halo and subhalo catalogs at each snapshot, and two distinct merger trees. Six primary realizations of the Illustris volume are released, including the flagship Illustris-1 run. These include three resolution levels with the fiducial "full" baryonic physics model, and a dark matter only analog for each. In addition, we provide four distinct, high time resolution, smaller volume "subboxes". The total data volume is ∼265 TB, including ∼800 full volume snapshots and ∼30,000 subbox snapshots. We describe the released data products as well as tools we have developed for their analysis. All data may be directly downloaded in its native HDF5 format. Additionally, we release a comprehensive, web-based API which allows programmatic access to search and data processing tasks. In both cases we provide example scripts and a getting-started guide in several languages: currently, IDL, Python, and Matlab. This paper addresses scientific issues relevant for the interpretation of the simulations, serves as a pointer to published and on-line documentation of the project, describes planned future additional data releases, and discusses technical aspects of the release.

Early-type galaxies provide unique tests for the predictions of the cold dark matter cosmology and the baryonic physics assumptions entering models for galaxy formation. In this work, we use the Illustris simulation to study correlations of three main properties of early-type galaxies, namely, the stellar orbital anisotropies, the central dark matter fractions and the central radial density slopes, as well as their redshift evolution since z = 1.0. We find that lower-mass galaxies or galaxies at higher redshift tend to be bluer in rest-frame colour, have higher central gas fractions, and feature more tangentially anisotropic orbits and steeper central density slopes than their higher-mass or lowerredshift counterparts, respectively. The projected central dark matter fraction within the effective radius shows a very mild mass dependence but positively correlates with galaxy effective radii due to the aperture effect. The central density slopes obtained by combining strong lensing measurements with single aperture kinematics are found to differ from the true density slopes. We identify systematic biases in this measurement to be due to two common modelling assumptions, isotropic stellar orbital distributions and power-law density profiles. We also compare the properties of early-type galaxies in Illustris to those from existing galaxy and strong lensing surveys, we find in general broad agreement but also some tension, which poses a potential challenge to the stellar formation and feedback models adopted by the simulation.

Discrepancies between the observed and model-predicted radio flux ratios are seen in a number of quadruply-lensed quasars. The most favoured interpretation of these anomalies is that CDM substructures present in lensing galaxies perturb the lens potentials and alter image magnifications and thus flux ratios. So far no consensus has emerged regarding whether or not the predicted CDM substructure abundance fully accounts for the lensing flux anomaly observations. Accurate modelling relies on a realistic lens sample in terms of both the lens environment and internal structures and substructures. In this paper we construct samples of generalised and specific lens potentials, to which we add (rescaled) subhalo populations from the galaxy-scale Aquarius and the cluster-scale Phoenix simulation suites. We further investigate the lensing effects from subhalos of masses several orders of magnitude below the simulation resolution limit. The resulting flux ratio distributions are compared to the currently best available sample of radio lenses. The observed anomalies in B0128+437, B0712+472 and B1555+375 are more likely to be caused by propagation effects or oversimplified/improper lens modelling, signs of which are already seen in the data. Among the quadruple systems that have closely located image triplets/pairs, the anomalous flux ratios of MG0414+0534 can be reproduced by adding CDM subhalos to its macroscopic lens potential, with a probability of 5% − 20%; for B0712+472, B1422+231, B1555+375 and B2045+265, these probabilities are only of a few percent. We hence find that CDM substructures are unlikely to be the whole reason for radio flux anomalies. We discuss other possible effects that might also be at work.

A power-law density model, i.e., ρ(r) ∝ r −γ ′ has been commonly employed in strong gravitational lensing studies, including the so-called time-delay technique used to infer the Hubble constant H 0 . However, since the radial scale at which strong lensing features are formed corresponds to the transition from the dominance of baryonic matter to dark matter, there is no known reason why galaxies should follow a power law in density. The assumption of a power law artificially breaks the mass-sheet degeneracy, a well-known invariance transformation in gravitational lensing which affects the product of Hubble constant and time delay and can therefore cause a bias in the determination of H 0 from the time-delay technique. In this paper, we use the Illustris hydrodynamical simulations to estimate the amplitude of this bias, and to understand how it is related to observational properties of galaxies. Investigating a large sample of Illustris galaxies that have velocity dispersion σ SIE 160 km s −1 at redshifts below z = 1, we find that the bias on H 0 introduced by the power-law assumption can reach 20% − 50%, with a scatter of 10% − 30% (rms). However, we find that by selecting galaxies with an inferred power-law model slope close to isothermal, it is possible to reduce the bias on H 0 to < ∼ 5%, and the scatter to < ∼ 10%. This could potentially be used to form less biased statistical samples for H 0 measurements in the upcoming large survey era.

We use the high-resolution Aquarius simulations of the formation of Milky Way-sized haloes in the cold dark matter cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with ∼10 8 particles (at a mass resolution m p ∼ 10 3 to 10 4 h −1 M ) within its virial radius. Subhaloes with masses m sub 10 5 h −1 M are well resolved, an improvement of at least two orders of magnitude over previous lensing studies. We incorporate a baryonic component modelled as a Hernquist profile and account for the response of the dark matter via adiabatic contraction. We focus on the 'anomalous' flux ratio problem, in particular on the violation of the cusp-caustic relation due to substructures. We find that subhaloes with masses less than ∼10 8 h −1 M play an important role in causing flux anomalies; such low-mass subhaloes have been unresolved in previous studies. There is large scatter in the predicted flux ratios between different haloes and between different projections of the same halo. In some cases, the frequency of predicted anomalous flux ratios is comparable to that observed for the radio lenses, although in most cases it is not. The probability for the simulations to reproduce the observed violations of the cusp lenses is ≈10 −3 . We therefore conclude that the amount of substructure in the central regions of the Aquarius haloes is insufficient to explain the observed frequency of violations of the cusp-caustic relation. These conclusions are based purely on our dark matter simulations which ignore the effect of baryons on subhalo survivability.

We assess the effectiveness of the Jeans-Anisotropic-MGE (JAM) technique with a state-of-the-art cosmological hydrodynamic simulation, the Illustris project. We perform JAM modelling on 1413 simulated galaxies with stellar mass M * > 10 10 M , and construct an axisymmetric dynamical model for each galaxy. Combined with a Markov Chain Monte Carlo (MCMC) simulation, we recover the projected root-mean-square velocity (V rms ) field of the stellar component, and investigate constraints on the stellar mass-to-light ratio, M * /L, and the fraction of dark matter f DM within 2.5 effective radii (R e ). We find that the enclosed total mass within 2.5 R e is well constrained to within 10%. However, there is a degeneracy between the dark matter and stellar components with correspondingly larger individual errors. The 1σ scatter in the recovered M * /L is 30 − 40% of the true value. The accuracy of the recovery of M * /L depends on the triaxial shape of a galaxy. There is no significant bias for oblate galaxies, while for prolate galaxies the JAM-recovered stellar mass is on average 18% higher than the input values. We also find that higher image resolutions alleviate the dark matter and stellar mass degeneracy and yield systematically better parameter recovery.