Joop Schaye

The EAGLE project: simulating the evolution and assembly of galaxies and their environments

We introduce the Virgo Consortiums EAGLE project, a suite of hydrodynamical simulations that follow the formation of galaxies and black holes in representative volumes. We discuss the limitations of such simulations in light of their finite resolution and poorly constrained subgrid physics, and how these affect their predictive power. One major improvement is our treatment of feedback from massive stars and AGN in which thermal energy is injected into the gas without the need to turn off cooling or hydrodynamical forces, allowing winds to develop without predetermined speed or mass loading factors. Because the feedback efficiencies cannot be predicted from first principles, we calibrate them to the z~0 galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy mass function is reproduced to ≲0.2 dex over the full mass range, 108<M∗/M⊙≲1011, a level of agreement close to that attained by semi-analytic models, and unprecedented for hydrodynamical simulations. We compare our results to a representative set of low-redshift observables not considered in the calibration, and find good agreement with the observed galaxy specific star formation rates, passive fractions, Tully-Fisher relation, total stellar luminosities of galaxy clusters, and column density distributions of intergalactic CIV and OVI. While the mass-metallicity relations for gas and stars are consistent with observations for M∗≳109M⊙, they are insufficiently steep at lower masses. The gas fractions and temperatures are too high for clusters of galaxies, but for groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. EAGLE constitutes a valuable new resource for studies of galaxy formation.

The physics driving the cosmic star formation history

We investigate the physics driving the cosmic star formation (SF) history using the more than 50 large, cosmological, hydrodynamical simulations that together comprise the OverWhelmingly Large Simulations project. We systematically vary the parameters of the model to determine which physical processes are dominant and which aspects of the model are robust. Generically, we find that SF is limited by the build-up of dark matter haloes at high redshift, reaches a broad maximum at intermediate redshift and then decreases as it is quenched by lower cooling rates in hotter and lower density gas, gas exhaustion and self-regulated feedback from stars and black holes. The higher redshift SF is therefore mostly determined by the cosmological parameters and to a lesser extent by photoheating from reionization. The location and height of the peak in the SF history, and the steepness of the decline towards the present, depend on the physics and implementation of stellar and black hole feedback. Mass loss from intermediate-mass stars and metal-line cooling both boost the SF rate at late times. Galaxies form stars in a self-regulated fashion at a rate controlled by the balance between, on the one hand, feedback from massive stars and black holes and, on the other hand, gas cooling and accretion. Paradoxically, the SF rate is highly insensitive to the assumed SF law. This can be understood in terms of self-regulation: if the SF efficiency is changed, then galaxies adjust their gas fractions so as to achieve the same rate of production of massive stars. Self-regulated feedback from accreting black holes is required to match the steep decline in the observed SF rate below redshift 2, although more extreme feedback from SF, for example in the form of a top-heavy initial stellar mass function at high gas pressures, can help.

Cosmological simulations of the growth of supermassive black holes and feedback from active galactic nuclei: method and tests

We present a method that self-consistently tracks the growth of supermassive black holes (BHs) and the feedback from active galactic nuclei (AGN) in cosmological, hydrodynamical simulations. Our model is a substantially modified version of the one introduced by Springel, Di Matteo & Hernquist implemented in a significantly expanded version of the gadget III code, which contains new prescriptions for star formation, supernova feedback, radiative cooling and chemodynamics. We simulate the growth of BHs from an initial seed state via Eddington-limited accretion of the surrounding gas, and via mergers with other BHs. Because cosmological simulations at present lack both the resolution and the physics to model the multiphase interstellar medium, they tend to strongly underestimate the Bondi–Hoyle accretion rate. To allow low-mass BHs to grow, it is therefore necessary to increase the predicted Bondi–Hoyle rates in star-forming gas by large factors, either by explicitly multiplying the accretion rate by a numerical correction factor or by using an unresolved, subgrid model for the gas close to the BH. We explore the physical regimes where the use of such multiplicative factors is reasonable, and through this introduce a new prescription for gas accretion by BHs. Feedback from AGN is modelled by coupling a fraction of the rest-mass energy of the accreted gas thermally into the surrounding medium. We describe the implementation as well as the limitations of the model in detail and motivate all the changes relative to previous work. We demonstrate how general physical considerations can be used to choose many of the parameters of the model and demonstrate that the fiducial model reproduces observational constraints. We employ a large suite of cosmological simulations, in which the parameters of the BH model are varied away from their fiducial values, to investigate the robustness of the predictions for the cosmic star formation history and the redshift zero cosmic BH density, BH scaling relations and galaxy-specific star formation rates. We find that the freedom introduced by the need to increase the predicted accretion rates by hand, the standard procedure in the literature, is the most significant source of uncertainty. Our simulations demonstrate that supermassive BHs are able to regulate their growth by releasing a fixed amount of energy for a given halo mass, independent of the assumed efficiency of AGN feedback, which sets the normalization of the BH scaling relations. Regardless of whether BH seeds are initially placed above or below the BH scaling relations, they grow on to the same scaling relations. AGN feedback efficiently suppresses star formation in high-mass galaxies.

The effect of photoionization on the cooling rates of enriched, astrophysical plasmas

A B ST R A C T Radiativecooling iscentralto a widerangeofastrophysicalproblem s.Despiteits im portance,cooling ratesaregenerally com puted using very restrictiveassum ptions, such as collisionalionization equilibrium and solar relative abundances.W e sim ul- taneously relax both assum ptions and investigate the eects ofphoto-ionization of heavy elem entsby them eta-galacticUV/X-ray background and ofvariationsin rela- tiveabundanceson thecoolingratesofopticallythin gasin ionization equilibrium .W e �nd thatphoto-ionization by them eta-galacticbackground radiation reducesthenet cooling ratesby up to an orderofm agnitudeforgasdensitiesand tem peraturestyp- icalofthe shock-heated intergalactic m edium and proto-galaxies(10 4 K< T < 10 6 K, �=hi < 100).In addition,photo-ionization changesthe relative contributionsofdif- ferentelem entstothecoolingrates.W econcludethatphoto-ionization by theionizing background and heavy elem entsboth need to be taken into accountin orderforthe cooling ratesto be correctto orderofm agnitude.M oreover,ifthe ratesneed to be known to better than a factor ofa few,then departures ofthe relative abundances from solar need to be taken into account.W e propose a m ethod to com pute cool- ing rateson an elem ent-by-elem entbasisby interpolating pre-com puted tables that take photo-ionization into account.W e provide such tables for a popular m odelof the evolving UV/X-ray background radiation,com puted using the photo-ionization package cloudy. K ey w ords: atom icprocesses| plasm as| coolingows| galaxies:form ation | intergalacticm edium

A Survey of z > 5.7 Quasars in the Sloan Digital Sky Survey. II. Discovery of Three Additional Quasars at z > 6*

We present the discovery of three new quasars at z > 6 in ~ 1300 deg2 of Sloan Digital Sky Survey imaging data, J114816.64+525150.3 (z = 6.43), J104845.05+463718.3 (z = 6.23), and J163033.90+401209.6 (z = 6.05). The first two objects have weak Lyα emission lines; their redshifts are determined from the positions of the Lyman break. They are only accurate to ~0.05 and could be affected by the presence of broad absorption line systems. The last object has a Lyα strength more typical of lower redshift quasars. Based on a sample of six quasars at z > 5.7 that cover 2870 deg2 presented in this paper and in Paper I, we estimate the comoving density of luminous quasars at z ~ 6 and M1450 5.7 quasars and high-resolution, ground-based images (seeing ~04) of three additional z > 5.7 quasars show that none of them is gravitationally lensed. The luminosity distribution of the high-redshift quasar sample suggests the bright-end slope of the quasar luminosity function at z ~ 6 is shallower than Ψ ∝ L-3.5 (2 σ), consistent with the absence of strongly lensed objects.

Star Formation Thresholds and Galaxy Edges: Why and Where

We study global star formation thresholds in the outer parts of galaxies by investigating the stability of disk galaxies embedded in dark halos. The disks are self-gravitating, contain metals and dust, and are exposed to UV radiation. We find that the critical surface density for the existence of a cold interstellar phase depends only weakly on the parameters of the model and coincides with the empirically derived surface density threshold for star formation. Furthermore, it is shown that the drop in the thermal velocity dispersion associated with the transition from the warm to the cold gas phase triggers gravitational instability on a wide range of scales. The presence of strong turbulence does not undermine this conclusion if the disk is self-gravitating. Models based on the hypothesis that the onset of thermal instability determines the star formation threshold in the outer parts of galaxies can reproduce many observations, including the threshold radii, the column densities, and the sizes of stellar disks as a function of disk scale length and mass. Finally, prescriptions are given for implementing star formation thresholds in (semi-)analytic models and three-dimensional hydrodynamical simulations of galaxy formation.

On the relation between the Schmidt and Kennicutt–Schmidt star formation laws and its implications for numerical simulations

When averaged over large scales, star formation in galaxies is observed to follow the empirical Kennicutt-Schmidt (KS) law for surface densities above a constant threshold. While the observed law involves surface densities, theoretical models and simulations generally work with volume density laws (i.e. Schmidt laws). We derive analytic relations between star formation laws expressed in terms of surface densities, volume densities, and pressures and we show how these relations depend on parameters such as the effective equation of state of the multiphase interstellar medium. Our analytic relations enable us to implement observed surface density laws into simulations. Because the parameters of our prescription for star formation are observables, we are not free to tune them to match the observations. We test our theoretical framework using high-resolution simulations of isolated disc galaxies that assume an effective equation of state for the multiphase interstellar medium. We are able to reproduce the star formation threshold and both the slope and the normalization of arbitrary input KS laws without tuning any parameters and with very little scatter, even for unstable galaxies and even if we use poor numerical resolution. Moreover, we can do so for arbitrary effective equations of state. Our prescription therefore enables simulations of galaxies to bypass our current inability to simulate the formation of stars. On the other hand, the fact that we can reproduce arbitrary input thresholds and KS laws, rather than just the particular ones picked out by nature, indicates that simulations that lack the physics and/or resolution to simulate the multiphase interstellar medium can only provide limited insight into the origin of the observed star formation laws.

The Aquila comparison project: the effects of feedback and numerical methods on simulations of galaxy formation

We compare the results of various cosmological gas-dynamical codes used to simulate the formation of a galaxy in the Λ cold dark matter structure formation paradigm. The various runs (13 in total) differ in their numerical hydrodynamical treatment [smoothed particle hydrodynamics (SPH), moving mesh and adaptive mesh refinement] but share the same initial conditions and adopt in each case their latest published model of gas cooling, star formation and feedback. Despite the common halo assembly history, we find large code-to-code variations in the stellar mass, size, morphology and gas content of the galaxy at z= 0, due mainly to the different implementations of star formation and feedback. Compared with observation, most codes tend to produce an overly massive galaxy, smaller and less gas rich than typical spirals, with a massive bulge and a declining rotation curve. A stellar disc is discernible in most simulations, although its prominence varies widely from code to code. There is a well-defined trend between the effects of feedback and the severity of the disagreement with observed spirals. In general, models that are more effective at limiting the baryonic mass of the galaxy come closer to matching observed galaxy scaling laws, but often to the detriment of the disc component. Although numerical convergence is not particularly good for any of the codes, our conclusions hold at two different numerical resolutions. Some differences can also be traced to the different numerical techniques; for example, more gas seems able to cool and become available for star formation in grid-based codes than in SPH. However, this effect is small compared to the variations induced by different feedback prescriptions. We conclude that state-of-the-art simulations cannot yet uniquely predict the properties of the baryonic component of a galaxy, even when the assembly history of its host halo is fully specified. Developing feedback algorithms that can effectively regulate the mass of a galaxy without hindering the formation of high angular momentum stellar discs remains a challenge.

Simulating galactic outflows with kinetic supernova feedback

Feedback from star formation is thought to play a key role in the formation and evolution of galaxies, but its implementation in cosmological simulations is currently hampered by a lack of numerical resolution. We present and test a subgrid recipe to model feedback from massive stars in cosmological smoothed particle hydrodynamics simulations. The energy is distributed in kinetic form among the gas particles surrounding recently formed stars. The impact of the feedback is studied using a suite of high-resolution simulations of isolated disc galaxies embedded in dark haloes with total mass 10 10 and 10 12 h -1 M ⊙ . We focus, in particular, on the effect of pressure forces on wind particles within the disc, which we turn off temporarily in some of our runs to mimic a recipe that has been widely used in the literature. We find that this popular recipe gives dramatically different results because (ram) pressure forces on expanding superbubbles determine both the structure of the disc and the development of large-scale outflows. Pressure forces exerted by expanding superbubbles puff up the disc, giving the dwarf galaxy an irregular morphology and creating a galactic fountain in the massive galaxy. Hydrodynamic drag within the disc results in a strong increase in the effective mass loading of the wind for the dwarf galaxy, but quenches much of the outflow in the case of the high-mass galaxy.

Metallicity of the Intergalactic Medium Using Pixel Statistics. II. The Distribution of Metals as Traced by C IV

We measure the distribution of carbon in the intergalactic medium as a function of redshift z and overdensity δ. Using a hydrodynamical simulation to link the H I absorption to the density and temperature of the absorbing gas, and a model for the UV background radiation, we convert ratios of C IV to H I pixel optical depths into carbon abundances. For the median metallicity this technique was described and tested in Paper I of this series. Here we generalize it to reconstruct the full probability distribution of the carbon abundance and apply it to 19 high-quality quasar absorption spectra. We find that the carbon abundance is spatially highly inhomogeneous and is well described by a lognormal distribution for fixed δ and z. Using data in the range log δ = -0.5-1.8 and z = 1.8-4.1, and a renormalized version of the 2001 Haardt & Madau model for the UV background radiation from galaxies and quasars, we measure a median metallicity of [C/H] = -3.47 + 0.08(z - 3) + 0.65(log δ - 0.5) and a lognormal scatter of σ([C/H]) = 0.76 + 0.02(z - 3) - 0.23(log δ - 0.5). Thus, we find significant trends with overdensity but no evidence for evolution. These measurements imply that gas in this density range accounts for a cosmic carbon abundance of [C/H] = -2.80 ± 0.13 (ΩC ≈ 2 × 10-7), with no evidence for evolution. The dominant source of systematic error is the spectral shape of the UV background, with harder spectra yielding higher carbon abundances. While the systematic errors due to uncertainties in the spectral hardness may exceed the quoted statistical errors for δ < 10, we stress that UV backgrounds that differ significantly from our fiducial model give unphysical results. The measured lognormal scatter is strictly independent of the spectral shape, provided the background radiation is uniform. We also present measurements of the C III/C IV ratio (which rule out temperatures high enough for collisional ionization to be important for the observed C IV) and of the evolution of the effective Lyα optical depth.