Claudio Dalla Vecchia

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.

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.

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.

Simulating galactic outflows with thermal supernova feedback

Cosmological simulations make use of sub-grid recipes for the implementation of galactic winds driven by massive stars because direct injection of supernova energy in thermal form leads to strong radiative losses, rendering the feedback inefficient. We argue that the main cause of the catastrophic cooling is a mismatch between the mass of the gas in which the energy is injected and the mass of the parent stellar population. Because too much mass is heated, the temperatures are too low and the cooling times too short. We use analytic arguments to estimate, as a function of the gas density and the numerical resolution, the minimum heating temperature that is required for the injected thermal energy to be efficiently converted into kinetic energy. We then propose and test a stochastic implementation of thermal feedback that uses this minimum temperature increase as an input parameter and that can be employed in both particle-based and grid-based codes. We use smoothed particle hydrodynamic simulations to test the method on models of isolated disc galaxies in dark matter haloes with total mass 1010 and 1012 h−1 M⊙. The thermal feedback strongly suppresses the star formation rate and can drive massive, large-scale outflows without the need to turn off radiative cooling temporarily. In accordance with expectations derived from analytic arguments, for sufficiently high resolution the results become insensitive to the imposed temperature jump and also agree with high-resolution simulations employing kinetic feedback.

Impact of baryon physics on dark matter structures: a detailed simulation study of halo density profiles

The back-reaction of baryons on the dark matter halo density profile is of great interest, not least because it is an important systematic uncertainty when attempting to detect the dark matter. Here, we draw on a large suite of high-resolution cosmological hydrodynamical simulations to systematically investigate this process and its dependence on the baryonic physics associated with galaxy formation. The effects of baryons on the dark matter distribution are typically not well described by adiabatic contraction models. In the inner 10 per cent of the virial radius the models are only successful if we allow their parameters to vary with baryonic physics, halo mass and redshift, thereby removing all predictive power. On larger scales the profiles from dark matter only simulations consistently provide better fits than adiabatic contraction models, even when we allow the parameters of the latter models to vary. The inclusion of baryons results in significantly more concentrated density profiles if radiative cooling is efficient and feedback is weak. The dark matter halo concentration can in that case increase by as much as 30 (10) per cent on galaxy (cluster) scales. The most significant effects occur in galaxies at high redshift, where there is a strong anticorrelation between the baryon fraction in the halo centre and the inner slope of both the total and the dark matter density profiles. If feedback is weak, isothermal inner profiles form, in agreement with observations of massive, early-type galaxies. However, we find that active galactic nuclei (AGN) feedback, or extremely efficient feedback from massive stars, is necessary to match observed stellar fractions in groups and clusters, as well as to keep the maximum circular velocity similar to the virial velocity as observed for disc galaxies. These strong feedback models reduce the baryon fraction in galaxies by a factor of 3 relative to the case with no feedback. The AGN is even capable of reducing the baryon fraction by a factor of 2 in the inner region of group and cluster haloes. This in turn results in inner density profiles which are typically shallower than isothermal and the halo concentrations tend to be lower than in the absence of baryons. We therefore conclude that the disagreement between the concentrations inferred from observations of groups of galaxies and predictions from simulations that was identified by Duffy et al. is not alleviated by the inclusion of baryons.

The effects of galaxy formation on the matter power spectrum: a challenge for precision cosmology

Upcoming weak lensing surveys, such as LSST, EUCLID and WFIRST, aim to measure the matter power spectrum with unprecedented accuracy. In order to fully exploit these observations, models are needed that, given a set of cosmological parameters, can predict the non-linear matter power spectrum at the level of 1 per cent or better for scales corresponding to comoving wavenumbers 0.1 k 10h Mpc −1 . We have employed the large suite of simulations from the OverWhelmingly Large Simulations (OWLS) project to investigate the effects of various baryonic processes on the matter power spectrum. In addition, we have examined the distribution of power over different mass components, the back-reaction of the baryons on the cold dark matter and the evolution of the dominant effects on the matter power spectrum. We find that single baryonic processes are capable of changing the power spectrum by up to several tens of per cent. Our simulation that includes AGN feedback, which we consider to be our most realistic simulation as, unlike those used in previous studies, it has been shown to solve the overcooling problem and to reproduce optical and X-ray observations of groups of galaxies, predicts a decrease in power relative to a dark matter only simulation ranging, at z = 0, from 1 per cent at k ≈ 0.3h Mpc −1 to 10 per cent at k ≈ 1h Mpc −1 and to 30 per cent at k ≈ 10h Mpc −1 . This contradicts the naive view that baryons raise the power through cooling, which is the dominant effect only for k 70h Mpc −1 . Therefore, baryons, and particularly AGN feedback, cannot be ignored in theoretical power spectra for k 0.3h Mpc −1 . It will thus be necessary to improve our understanding of feedback processes

The rates and modes of gas accretion on to galaxies and their gaseous haloes

We study the rate at which gas accretes on to galaxies and haloes and investigate whether the accreted gas was shocked to high temperatures before reaching a galaxy. For this purpose we use a suite of large cosmological, hydrodynamical simulations from the OWLS project. We improve on previous work by considering a wider range of halo masses and redshifts, by distinguishing accretion on to haloes and galaxies, by including important feedback processes, and by comparing simulations with different physics. Gas accretion is mostly smooth, with mergers only becoming important for groups and clusters. The specific rate of gas accretion on to haloes is, like that for dark matter, only weakly dependent on halo mass. For halo masses Mhalo � 10 11 Mit is relatively insensitive to feedback processes. In contrast, accretion rates on to galaxies are determined by radiative cooling and by outflows driven by supernovae and active galactic nuclei. Galactic winds increase the halo mass at which the central galaxies grow the fastest by about two orders of magnitude to Mhalo � 10 12 M� . Gas accretion is bimodal, with maximum past temperatures either of order the virial temperature or . 10 5 K. The fraction of gas accreted on to haloes in the hot mode is insensitive to feedback and metal-line cooling. It increases with redshift, but is mostly determined by halo mass, increasing gradually from less than 10% for � 10 11 Mto greater than 90% at � 10 13 M� . In contrast, for accretion on to galaxies the cold mode is always significant and the relative contributions of the two accretion modes are more sensitive to feedback and metal-line cooling. On average, the majority of stars present in any mass halo at any redshift were formed from gas accreted in the cold mode, although the hot mode contributes typically over 10% for Mhalo & 10 11 M� . Thus, while gas accretion on to haloes can be robustly predicted, the rate of accretion on to galaxies is sensitive to uncertain feedback processes. Nevertheless, it is clear that galaxies, but not their gaseous haloes, are predominantly fed by gas that did not experience an accretion shock when it entered the host halo.

Baryon effects on the internal structure of ΛCDM haloes in the EAGLE simulations

We investigate the internal structure and density profiles of haloes of mass 1010–1014 M⊙ in the Evolution and Assembly of Galaxies and their Environment (EAGLE) simulations. These follow the formation of galaxies in a Λ cold dark matter Universe and include a treatment of the baryon physics thought to be relevant. The EAGLE simulations reproduce the observed present-day galaxy stellar mass function, as well as many other properties of the galaxy population as a function of time. We find significant differences between the masses of haloes in the EAGLE simulations and in simulations that follow only the dark matter component. Nevertheless, haloes are well described by the Navarro–Frenk–White density profile at radii larger than ∼5 per cent of the virial radius but, closer to the centre, the presence of stars can produce cuspier profiles. Central enhancements in the total mass profile are most important in haloes of mass 1012–1013 M⊙, where the stellar fraction peaks. Over the radial range where they are well resolved, the resulting galaxy rotation curves are in very good agreement with observational data for galaxies with stellar mass M* < 5 × 1010 M⊙. We present an empirical fitting function that describes the total mass profiles and show that its parameters are strongly correlated with halo mass.

Ubiquitous seeding of supermassive black holes by direct collapse

We study for the first time the environment of massive black hole (BH) seeds (∼10 4−5 M� ) formed via the direct collapse of pristine gas clouds in massive haloes (≥10 7 M� )a tz > 6. Our model is based on the evolution of dark matter haloes within a cosmological N-body simulation, combined with prescriptions for the formation of BH along with both Population III (Pop III) and Population II (Pop II) stars. We calculate the spatially varying intensity of Lyman–Werner (LW) radiation from stars and identify the massive pristine haloes in which it is high enough to shut down molecular hydrogen cooling. In contrast to previous BH seeding models with a spatially constant LW background, we find that the intensity of LW radiation due to local sources, Jlocal, can be up to ∼10 6 times the spatially averaged background in the simulated volume and exceeds the critical value, Jcrit, for the complete suppression of molecular cooling, in some cases by four orders of magnitude. Even after accounting for possible metal pollution in a halo from previous episodes of star formation, we find a steady rise in the formation rate of direct collapse BHs (DCBHs) with decreasing redshift from 10 −3 Mpc −3 z −1 at z = 12 to 10 −2 Mpc −3 z −1 at z = 6. The onset of Pop II star formation at z ≈ 16 simultaneously marks the onset of the epoch of DCBH formation, as the increased level of LW radiation from Pop II stars is able to elevate the local levels of the LW intensity to Jlocal > Jcrit, while Pop III stars fail to do so at any time. The number density of DCBHs is sensitive to the number of LW photons and can vary by over an order of magnitude at z = 7 after accounting for reionization feedback. Haloes hosting DCBHs are more clustered than similar massive counterparts that do not host DCBHs, especially at redshifts z 10. Also, the DCBHs that form at z > 10 are found to reside in highly clustered regions, whereas the DCBHs formed around z ∼ 6a re more common. We also show that planned surveys with James Webb Space Telescope should be able to detect the supermassive stellar precursors of DCBHs.