Cosmological Smoothed Particle Hydrodynamics Simulations Research Articles

Numerical convergence of hydrodynamical simulations of galaxy formation: the abundance and internal structure of galaxies and their cold dark matter haloes

ABSTRACT We address the issue of numerical convergence in cosmological smoothed particle hydrodynamics simulations using a suite of runs drawn from the eagle project. Our simulations adopt subgrid models that produce realistic galaxy populations at a fiducial mass and force resolution, but systematically vary the latter in order to study their impact on galaxy properties. We provide several analytic criteria that help guide the selection of gravitational softening for hydrodynamical simulations, and present results from runs that both adhere to and deviate from them. Unlike dark matter-only simulations, hydrodynamical simulations exhibit a strong sensitivity to gravitational softening, and care must be taken when selecting numerical parameters. Our results – which focus mainly on star formation histories, galaxy stellar mass functions and sizes – illuminate three main considerations. First, softening imposes a minimum resolved escape speed, vϵ, due to the binding energy between gas particles. Runs that adopt such small softening lengths that $v_\epsilon \gtrsim 10\, {\rm km\, s^{-1}}$ (the sound speed in ionized ${\sim }10^4\, {\rm K}$ gas) suffer from reduced effects of photoheating. Secondly, feedback from stars or active galactic nuclei may suffer from numerical overcooling if the gravitational softening length is chosen below a critical value, ϵeFB. Thirdly, we note that small softening lengths exacerbate the segregation of stars and dark matter particles in halo centres, often leading to the counterintuitive result that galaxy sizes increase as softening is reduced. The structure of dark matter haloes in hydrodynamical runs respond to softening in a way that reflects the sensitivity of their galaxy populations to numerical parameters.

SImulator of GAlaxy Millimetre/submillimetre Emission (sígame): CO emission from massivez = 2 main-sequence galaxies

We present SIGAME (SImulator of GAlaxy Millimetre/submillimetre Emission), a new numerical code designed to simulate the 12CO rotational line emission spectrum of galaxies. Using sub-grid physics recipes to post-process the outputs of smoothed particle hydrodynamics (SPH) simulations, a molecular gas phase is condensed out of the hot and partly ionized SPH gas. The gas is subjected to far-UV radiation fields and cosmic ray ionization rates which are set to scale with the local star formation rate volume density. Level populations and radiative transport of the CO lines are solved with the 3-D radiative transfer code LIME. We have applied SIGAME to cosmological SPH simulations of three disc galaxies at z=2 with stellar masses in the range ~(0.5-2)x10^11 Msun and star formation rates ~40-140 Msun/yr. Global CO luminosities and line ratios are in agreement with observations of disc galaxies at z~2 up to and including J=3-2 but falling short of the few existing J=5-4 observations. The central 5 kpc regions of our galaxies have CO 3-2/1-0 and 7-6/1-0 brightness temperature ratios of ~0.55-0.65 and ~0.02-0.08, respectively, while further out in the disc the ratios drop to more quiescent values of ~0.5 and <0.01. Global CO-to-H2 conversion (alpha_CO) factors are ~=1.5 Msun*pc^2/(K km s/1), i.e. ~2-3 times below typically adopted values for disc galaxies, and alpha_CO increases with radius, in agreement with observations of nearby galaxies. Adopting a top-heavy Giant Molecular Cloud (GMC) mass spectrum does not significantly change the results. Steepening the GMC density profile leads to higher global line ratios for J_up>=3 and CO-to-H2 conversion factors [~=3.6 Msun*pc^2/(K km/s)].

Formation ofin situstellar haloes in Milky Way-mass galaxies

We study the formation of stellar haloes in three Milky Way-mass galaxies using cosmological smoothed particle hydrodynamics simulations, focusing on the subset of halo stars that form in situ, as opposed to those accreted from satellites. In situ stars in our simulations dominate the stellar halo out to 20 kpc and account for 30-40 per cent of its total mass. We separate in situ halo stars into three straightforward, physically distinct categories according to their origin: stars scattered from the disc of the main galaxy ('heated disc'), stars formed from gas smoothly accreted on to the halo ('smooth' gas) and stars formed in streams of gas stripped from infalling satellites ('stripped' gas). We find that most belong to the stripped gas category. Those originating in smooth gas outside the disc tend to form at the same time and place as the stripped-gas population, suggesting that their formation is associated with the same gas-rich accretion events. The scattered disc star contribution is negligible overall but significant in the Solar neighbourhood, where ~90 per cent of stars on eccentric orbits once belonged to the disc. However, the distinction between halo and thick disc in this region is highly ambiguous. The chemical and kinematic properties of the different components are very similar at the present day, but the global properties of the in situ halo differ substantially between the three galaxies in our study. In our simulations, the hierarchical buildup of structure is the driving force behind not only the accreted stellar halo, but also those halo stars formed in situ.

Submillimetre galaxies in cosmological hydrodynamic simulations: source number counts and the spatial clustering

We use large cosmological smoothed particle hydrodynamics simulations to study the formation and evolution of submillimetre galaxies (SMGs). In our previous work, we studied the statistical properties of ultraviolet-selected star-forming galaxies at high redshifts. We populate the same cosmological simulations with SMGs by calculating the reprocessing of stellar light by dust grains into far-infrared to millimetre wavebands in a self-consistent manner. We generate light-cone outputs to compare directly the statistical properties of the simulated SMGs with available observations. Our model reproduces the submillimetre source number counts and the clustering amplitude. We show that bright SMGs with flux S > 1 mJy reside in haloes with masses of ∼1013 M⊙ and have stellar masses greater than 1011 M⊙. The angular cross-correlation between the SMGs and Lyman α emitters is significantly weaker than that between the SMGs and Lyman-break galaxies. The cross-correlation is also weaker than the autocorrelation of the SMGs. The redshift distribution of the SMGs shows a broad peak at z ∼ 2, where bright SMGs contribute significantly to the global cosmic star formation rate density. Our model predicts that there are hundreds of SMGs with S > 0.1 mJy at z > 5 per 1 deg2 field. Such SMGs can be detected by ALMA.

Lyman α emitters in cosmological simulations - I. Lyman α escape fraction and statistical properties at z= 3.1

We use very large cosmological smoothed particle hydrodynamics simulations to study the properties of high-redshift Lyman α emitters (LAEs). We identify star-forming galaxies at z= 3.1 in a cosmological volume of 100 h−1 Mpc on a side. We develop a phenomenological model of absorption, scattering and escape of Lyman α photons on the assumption that the clumpiness of the interstellar medium in a galaxy is correlated with the larger scale substructure richness. The radiative transfer effect proposed by Neufeld allows a large fraction of Lyman α photons to escape from a clumpy galaxy even if it contains a substantial amount of dust. Our model reproduces, for the first time, all of the following observed properties of LAEs at z= 3.1: the angular correlation function, ultraviolet (UV) and Lyman α luminosity functions and the equivalent width distribution. A simple model that takes only dust absorption into account fails in reproducing LAEs that are also bright in UV, suggesting that the kind of effect we consider is needed. Our model predicts a bimodal age distribution for LAEs. Most of the galaxies with large Lyman α equivalent widths are young, whereas there are also old, massive and dusty LAEs, similar to recently found high-redshift LAEs. The large LAEs have escape fractions of Lyman α photons of fesc∼ 0.05–0.1.

On the inconsistency between the estimates of cosmic star formation rate and stellar mass density of high-redshift galaxies

There are mainly two different approaches to measure the cosmic star formation history: direct star formation rate density (SFRD) and stellar mass density rhostar as functions of redshift. Compilations of current observations seem to show a disparity in the two quantities, in the sense that the integral of SFRD is higher than the observed rhostar (after considering gas recycling). Using cosmological smoothed particle hydrodynamics simulations based on the concordance Lambda cold dark matter model, we show that the two quantities become more consistent with each other when we consider the observed galaxy mass limit. The comparison between simulations and (dust corrected) observed cosmic SFRD shows a good agreement, while the observed rhostar is significantly lower than the simulation results. This can be reconciled if the current high-$z$ galaxy surveys are missing faint low-mass galaxies due to their flux limit. Our simulated GSMFs have steep low-mass end slopes of alpha < -2 at z>3, and when these numerous low-mass galaxies are included, the total rhostar matches with the integral of SFRD.

Mechanisms of baryon loss for dark satellites in cosmological smoothed particle hydrodynamics simulations

We present a study of satellites in orbit around a high-resolution, smoothed particle hydrodynamics (SPH) galaxy simulated in a cosmological context. The simulated galaxy is approximately of the same mass as the Milky Way. The cumulative number of luminous satellites at z= 0 is similar to the observed system of satellites orbiting the Milky Way although an analysis of the satellite mass function reveals an order of magnitude more dark satellites than luminous satellites. Some of the dark subhaloes are more massive than some of the luminous subhaloes at z= 0. What separates luminous and dark subhaloes is not their mass at z= 0, but the maximum mass the subhaloes ever achieve. We study the effect of four mass-loss mechanisms on the subhaloes: ultraviolet (UV) ionizing radiation, ram-pressure stripping, tidal stripping and stellar feedback, and compare the impact of each of these four mechanisms on the satellites. In the lowest mass subhaloes, UV is responsible for the majority of the baryonic mass-loss. Ram-pressure stripping removes whatever mass remains from the low-mass satellites. More massive subhaloes have deeper potential wells and retain more mass during reionization. However, as satellites pass near the centre of the main halo, tidal forces cause significant mass-loss from satellites of all masses. Satellites that are tidally stripped from the outside can account for the luminous satellites that are of lower mass than some of the dark satellites. Stellar feedback has the greatest impact on medium-mass satellites that had formed stars, but lost all their gas by z= 0. Our results demonstrate that the missing-satellite problem is not an intractable issue with the cold dark matter cosmology, but is rather a manifestation of baryonic processes.

EFFECTS OF ULTRAVIOLET BACKGROUND AND LOCAL STELLAR RADIATION ON THE H I COLUMN DENSITY DISTRIBUTION

We study the impact of ultraviolet background (UVB) radiation field and the local stellar radiation on the H_I column density distribution f(N_HI) of damped Ly-alpha systems (DLAs) and sub-DLAs at z=3 using cosmological smoothed particle hydrodynamics simulations. We find that, in the previous simulations with an optically thin approximation, the UVB was sinking into the H_I cloud too deeply, and therefore we underestimated the f(N_HI) at 19 < log(N_HI) < 21.2 compared to the observations. If the UVB is shut off in the high-density regions with n_gas > 6 x 10^{-3} cm^{-3}, then we reproduce the observed f(N_HI) at z=3 very well. We also investigate the effect of local stellar radiation by post-processing our simulation with a radiative transfer code, and find that the local stellar radiation does not change the f(N_HI) very much. Our results show that the shape of f(N_HI) is determined primarily by the UVB with a much weaker effect by the local stellar radiation and that the optically thin approximation often used in cosmological simulation is inadequate to properly treat the ionization structure of neutral gas in and out of DLAs. Our result also indicates that the DLA gas is closely related to the transition region from optically-thick neutral gas to optically-thin ionized gas within dark matter halos.

The growth of central and satellite galaxies in cosmological smoothed particle hydrodynamics simulations

We examine the accretion and merger histories of central and satellite galaxies in a smoothed particle hydrodynamics (SPH) cosmological simulation that resolves galaxies down to 7 × 109 M⊙. Most friends-of-friends haloes in the simulation have a distinct central galaxy, typically 2–5 times more massive than the most massive satellite. As expected, satellites have systematically higher assembly redshifts than central galaxies of the same baryonic mass, and satellites in more massive haloes form earlier. However, contrary to the simplest expectations, satellite galaxies continue to accrete gas and convert it to stars; the gas accretion declines steadily over a period of 0.5–1 Gyr after the satellite halo merges with a larger parent halo. Satellites in a cluster mass halo eventually begin to lose baryonic mass. Typically, satellites in our simulation are 0.1–0.2 mag bluer than in models that assume no gas accretion on to satellites after a halo merger. Since z= 1, 27 per cent of central galaxies (above 3 × 1010 M⊙) and 22 per cent of present-day satellite galaxies have merged with a smaller system above a 1:4 mass ratio; about half of the satellite mergers occurred after the galaxy became a satellite and half before. In effect, satellite galaxies can remain ‘central’ objects of halo substructures, with continuing accretion and mergers, making the transition in assembly histories and physical properties a gradual one. Implementing such a gradual transformation in semi-analytic models would improve their agreement with observed colour distributions of satellite galaxies in groups and with the observed colour dependence of galaxy clustering.

Keeping the Universe ionized: photoheating and the clumping factor of the high-redshift intergalactic medium

The critical star formation rate (SFR) density required to keep the intergalactic hydro- gen ionized depends crucially on the average rate of recombinations in the intergalac- tic medium (IGM). This rate is proportional to the clumping factor C ≡� ρ 2� IGM/�ρ b� 2 , where ρb and �ρ bare the local and cosmic mean baryon density, respectively, and the brackets �� IGM indicate spatial averaging over the recombining gas in the IGM. We per- form a suite of cosmological smoothed particle hydrodynamic simulations that include ra- diative cooling to calculate the volume-weighted clumping factor of the IGM at redshifts z ≥ 6. We focus on the effect of photoionization heating by a uniform ultraviolet background and find that photoheating strongly reduces the clumping factor because the increased pressure support smoothes out small-scale density fluctuations. Photoionization heating is often said to provide a negative feedback on the re-ionization of the IGM because it suppresses the cosmic SFR by boiling the gas out of low-mass haloes. However, because of the reduction of the clumping factor it also makes it easier to keep the IGM ionized. Photoheating therefore also provides a positive feedback which, while known to exist, has received much less attention. We demonstrate that this positive feedback is in fact very strong. Using conservative assumptions, we find that if the IGM was reheated at z 9, the observed population of star-forming galaxies at z ≈ 6 may be sufficient to keep the IGM ionized, provided that the fraction of ionizing photons that escape the star-forming regions to ionize the IGM is larger than ∼0.2.

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 sub-grid 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 halos with total mass 10^{10} and 10^{12} Msol/h. 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 of 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.

Shape, Spin, and Baryon Fraction of Clusters in the MareNostrum Universe

The MareNostrum Universe is one of the largest cosmological smoothed particle hydrodynamics simulations done so far. It consists of 10243 dark and 10243 gas particles in a box of 500 h-1 Mpc on a side. Here we study the shapes and spins of the dark matter and gas components of the 10,000 most massive objects extracted from the simulation as well as the gas fraction in those objects. We find that the shapes of objects tend to be prolate both in the dark matter and gas. There is a clear dependence of shape on halo mass, the more massive ones being less spherical than the less massive objects. The gas distribution is nevertheless much more spherical than the dark matter, although the triaxiality parameters of gas and dark matter differ only by a few percent, and it increases with cluster mass. The spin parameters of gas and dark matter can be well fitted by a lognormal distribution function. On average, the spin of gas is 1.4 times larger than the spin of dark matter. We find a similar behavior for the spins at higher redshifts, with a slight decrease of the spin ratios to 1.16 at z = 1. The cosmic normalized baryon fraction in the entire cluster sample ranges from Yb = 0.94 at z = 1 to Yb = 0.92 at z = 0. At both redshifts we find a slight, but statistically significant, decrease of Yb with cluster mass.

Accretion, feedback and galaxy bimodality: a comparison of the GalICS semi-analytic model and cosmological SPH simulations

We compare the galaxy population of a smoothed particle hydrodynamics (SPH) simulation to those predicted by the GalICS (Galaxies In Cosmological Simulations) N-body + semi-analytic model and a stripped down version of GalICS that omits the effects of supernova and active galactic nucleus (AGN) feedback. The SPH simulation and the no-feedback GalICS model make similar predictions for the baryonic mass functions of galaxies and for the dependence of these mass functions on environment and redshift. The two methods also make similar predictions for the galaxy content of dark matter haloes as a function of halo mass and for the gas accretion history of galaxies. There is a fairly good correspondence between the 'cold' and 'hot' accretion modes of the SPH simulation and the rapid and slow cooling regimes of the GalICS calculation. Both the SPH and no-feedback GalICS models predict a bimodal galaxy population at z = 0. The 'red' sequence of gas poor, old galaxies is populated mainly by satellite systems, which are starved of fresh gas after they begin orbiting in larger haloes, while, contrary to observations, the central galaxies of massive haloes lie on the 'blue' star-forming sequence as a result of continuing hot gas accretion at late times. Furthermore, both models overpredict the observed baryonic mass function, especially at the high-mass end. In the full GalICS model, supernova-driven outflows reduce the masses of low and intermediate mass galaxies by about a factor of 2. AGN feedback suppresses gas cooling in large haloes, producing a sharp cut-off in the baryonic mass function and moving the central galaxies of these massive haloes to the red sequence. Our results imply that the observational failings of the SPH simulation and the no-feedback GalICS model are a consequence of missing input physics rather than computational inaccuracies. Truncating the accretion of gas in satellite galaxies automatically produces a bimodal distribution with a quenched population, but explaining the star formation shutdown in the most massive galaxies requires a mechanism like AGN feedback that suppresses the accretion of gas on to central galaxies in large haloes.

Detectability of [Cii] 158 μm Emission from High‐Redshift Galaxies: Predictions for ALMA andSPICA

We discuss the detectability of high-redshift galaxies via [C II] 158 μm line emission by coupling an analytic model with cosmological smoothed particle hydrodynamics (SPH) simulations that are based on the concordance Λ cold dark matter (CDM) model. Our analytic model describes a multiphase interstellar medium (ISM) irradiated by the far-ultraviolet (FUV) radiation from local star-forming regions, and it calculates thermal and ionization equilibrium between cooling and heating. The model allows us to predict the mass fraction of a cold neutral medium (CNM) embedded in a warm neutral medium (WNM). Our cosmological SPH simulations include a treatment of radiative cooling/heating, star formation, and feedback effects from supernovae and galactic winds. Using our method, we make predictions for the [C II] luminosity from high-redshift galaxies that can be directly compared with upcoming observations by the Atacama Large Millimeter Array (ALMA) and the Space Infrared Telescope for Cosmology and Astrophysics (SPICA). We find that the number density of high-redshift galaxies detectable by ALMA and SPICA via [C II] emission depends significantly on the amount of neutral gas, which is highly uncertain. Our calculations suggest that, in a CDM universe, most [C II] sources at z = 3 are faint objects with Sν < 0.01 mJy. Lyman break galaxies (LBGs) brighter than RAB = 23.5 mag are expected to have flux densities Sν = 1-3 mJy depending on the strength of galactic wind feedback. The recommended observing strategy for ALMA and SPICA is to aim at very bright LBGs or star-forming DRG/BzK galaxies.

Lyman break galaxies at z = 4–6 in cosmological smoothed particle hydrodynamics simulations

We perform a spectrophotometric analysis of galaxies at redshifts z= 4–6 in cosmological smoothed particle hydrodynamics simulations of a Λ cold dark matter universe. Our models include radiative cooling and heating by a uniform ultraviolet (UV) background, star formation, supernova feedback, and a phenomenological model for galactic winds. Analysing a series of simulations of varying box size and particle number allows us to isolate the impact of numerical resolution on our results. Specifically, we determine the luminosity functions in B, V, R, i′ and z′ filters, and compare the results with observational surveys of Lyman break galaxies (LBGs) performed with the Subaru telescope and the Hubble Space Telescope. We find that the simulated galaxies have UV colours consistent with observations and fall in the expected region of the colour—colour diagrams used by the Subaru group. The stellar masses of the most massive galaxies in our largest simulation increase their stellar mass from M★~ 1011 M⊙ at z= 6 to M★~ 1011.7 M⊙ at z= 3. Assuming a uniform extinction of E(B−V) = 0.15, we also find reasonable agreement between simulations and observations in the space density of UV bright galaxies at z= 3–6, down to the magnitude limit of each survey. For the same moderate extinction level of E(B−V) ~ 0.15, the simulated luminosity functions match observational data, but have a steep faint-end slope with α~−2.0. We discuss the implications of the steep faint-end slope found in the simulations. Our results confirm the generic conclusion from earlier numerical studies that UV bright LBGs at z≥ 3 are the most massive galaxies with E(B−V) ~ 0.15 at each epoch.

Detecting shock waves in cosmological smoothed particle hydrodynamics simulations

We develop a formalism for the identification and accurate estimation of the strength of structure formation shocks during cosmological smoothed particle hydrodynamics simulations. Shocks play a decisive role not only for the thermalization of gas in virializing structures but also for the acceleration of relativistic cosmic rays (CRs) through diffusive shock acceleration. Our formalism is applicable both to ordinary non-relativistic thermal gas, and to plasmas composed of CRs and thermal gas. To this end, we derive an analytic solution to the one-dimensional Riemann shock tube problem for a composite plasma of CRs and thermal gas. We apply our methods to study the properties of structure formation shocks in high-resolution hydrodynamic simulations of the Lambda cold dark matter (� CDM) model. We find that most of the energy is dissipated in weak internal shocks with Mach numbers M ∼ 2 which are predominantly central flow shocks or merger shock waves traversing halo centres. Collapsed cosmological structures are surrounded by external shocks with much higher Mach numbers up to M ∼ 1000, but they play only a minor role in the energy balance of thermalization. This is because of the higher pre-shock gas densities within non-linear structures, and the significant increase of the mean shock speed as the characteristic halo mass grows with cosmic time. We show that after the epoch of cosmic reionization the Mach number distribution is significantly modified by an efficient suppression of strong external shock waves due to the associated increase of the sound speed of the diffuse gas. Invoking a model for CR acceleration in shock waves, we find that the average strength of shock waves responsible for CR energy injection is higher than that for shocks that dominate the thermalization of the gas. This implies that the dynamical importance of shock-injected CRs is comparatively large in the low-density, peripheral halo infalling regions, but is less important for the weaker flow shocks occurring in central highdensity regions of haloes. When combined with radiative dissipation and star formation, our formalism can also be used to study CR injection by supernova shocks, or to construct models for shock-induced star formation in the interstellar medium.

Feedback and metal enrichment in cosmological smoothed particle hydrodynamics simulations — I. A model for chemical enrichment

We discuss a model for treating chemical enrichment by Type II and Type Ia supernova (SNII and SNIa) explosions in simulations of cosmological structure formation. Our model includes metal-dependent radiative cooling and star formation in dense collapsed gas clumps. Metals are returned into the diffuse interstellar medium by star particles using a local smoothed particle hydrodynamics (SPH) smoothing kernel. A variety of chemical abundance patterns in enriched gas arise in our treatment owing to the different yields and lifetimes of SNII and SNIa progenitor stars. In the case of SNII chemical production, we adopt metal-dependent yields. Because of the sensitive dependence of cooling rates on metallicity, enrichment of galactic haloes with metals can in principle significantly alter subsequent gas infall and the build-up of the stellar components. Indeed, in simulations of isolated galaxies we find that a consistent treatment of metal-dependent cooling produces 25 per cent more stars outside the central region than simulations with a primordial cooling function. In the highly enriched central regions, the evolution of baryons is however not affected by metal cooling, because here the gas is always dense enough to cool. A similar situation is found in cosmological simulations because we include no strong feedback processes which could spread metals over large distances and mix them into unenriched diffuse gas. We demonstrate this explicitly with test simulations which adopt suprasolar cooling functions leading to large changes both in the stellar mass and in the metal distributions. We also find that the impact of metallicity on the star formation histories of galaxies may depend on their particular evolutionary history. Our results hence emphasize the importance of feedback processes for interpreting the cosmic metal enrichment.

The cosmological simulation code gadget-2

We discuss the cosmological simulation code GADGET-2, a new massively parallel TreeSPH code, capable of following a collisionless fluid with the N-body method, and an ideal gas by means of smoothed particle hydrodynamics (SPH). Our implementation of SPH manifestly conserves energy and entropy in regions free of dissipation, while allowing for fully adaptive smoothing lengths. Gravitational forces are computed with a hierarchical multipole expansion, which can optionally be applied in the form of a TreePM algorithm, where only short-range forces are computed with the `tree'-method while long-range forces are determined with Fourier techniques. Time integration is based on a quasi-symplectic scheme where long-range and short-range forces can be integrated with different timesteps. Individual and adaptive short-range timesteps may also be employed. The domain decomposition used in the parallelisation algorithm is based on a space-filling curve, resulting in high flexibility and tree force errors that do not depend on the way the domains are cut. The code is efficient in terms of memory consumption and required communication bandwidth. It has been used to compute the first cosmological N-body simulation with more than 10^10 dark matter particles, reaching a homogeneous spatial dynamic range of 10^5 per dimension in a 3D box. It has also been used to carry out very large cosmological SPH simulations that account for radiative cooling and star formation, reaching total particle numbers of more than 250 million. We present the algorithms used by the code and discuss their accuracy and performance using a number of test problems. GADGET-2 is publicly released to the research community.

Damped Lyman-α Absorbers in Cosmological SPH Simulations: the “Metallicity Problem”

We study the distribution of star formation rate (SFR) and metallicity of damped Lyman-α absorbers (DLAs) using cosmological smoothed particle hydrodynamics (SPH) simulations of the Λ cold dark matter (CDM) model. Our simulations include a phenomenological model for feedback by galactic winds which allows us to examine the effect of galactic outflows on the distribution of SFR and metallicity of DLAs. For models with strong galactic winds, we obtain good agreement with recent observations with respect to total neutral hydrogen mass density, NHI column-density distribution, abundance of DLAs, and for the distribution of SFR in DLAs. However, we also find that the median metallicity of simulated DLAs is higher than the values typically observed by nearly an order of magnitude. This discrepancy with observations could be due to shortcomings in the treatment of the supernova feedback or the multiphase structure of the gas in our current simulations. Recent observations by Wolfe et al. (2003a,b) seem to point to the same problem; i.e. the observed DLA metallicities are much lower than those expected from the (either observed or simulated) DLA star formation rates, a puzzle that has been known as the “missing metals”-problem for the globally averaged quantities.

Thermal conduction in cosmological SPH simulations

Thermal conduction in the intracluster medium has been proposed as a possible heating mechanism for offsetting central cooling losses in rich clusters of galaxies. In this study, we introduce a new formalism to model conduction in a diffuse ionised plasma using smoothed particle hydrodynamics (SPH), and we implement it in the parallel TreePM/SPH-code GADGET-2. We consider only isotropic conduction and assume that magnetic suppression can be described in terms of an effective conductivity, taken as a fixed fraction of the temperature-dependent Spitzer rate. We also account for saturation effects in low-density gas. Our formulation manifestly conserves thermal energy even for individual and adaptive timesteps, and is stable in the presence of small-scale temperature noise. This allows us to evolve the thermal diffusion equation with an explicit time integration scheme along with the ordinary hydrodynamics. We use a series of simple test problems to demonstrate the robustness and accuracy of our method. We then apply our code to spherically symmetric realizations of clusters, constructed under the assumptions of hydrostatic equilibrium and a local balance between conduction and radiative cooling. While we confirm that conduction can efficiently suppress cooling flows for an extended period of time in these isolated systems, we do not find a similarly strong effect in a first set of clusters formed in self-consistent cosmological simulations. However, their temperature profiles are significantly altered by conduction, as is the X-ray luminosity.