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The Voids-within-Voids-within-Voids project used dark-matter-only (DMO) simulations to study the abundance and structure of dark matter (DM) haloes over the full mass range populated in the standard Lambda cold dark matter cosmology. Here, we explore how baryonic effects modify these results for |$z=0$| halo masses in the range |$10^4$| – |$10^7~\mathrm{M_\odot }$|⁠ , below the threshold for galaxy formation. Our main study focuses on three simulations from identical initial conditions at |$z=127$|⁠ , one following DMO, one including non-radiative gas, and one additionally including the baryonic physics relevant in this halo mass range (cooling and photoheating). In the non-radiative simulation, above |$10^{5.5}~\mathrm{M_\odot }$|⁠ , halo abundance and internal structure are very similar to the DMO simulation, and the baryon to DM ratio is everywhere close to the cosmic value. At lower mass, this ratio drops and haloes are less concentrated and less massive in the non-radiative case. Test simulations at higher resolution show this to be mainly a resolution effect; the expected drop in baryon content due to residual pressure effects only becomes substantial for |$z=0$| haloes below |${\sim}10^{2.7}~\mathrm{M_\odot }$|⁠. However, gas is heated by reionization at |$z=6$| in our 'full physics' run, and this results in almost complete expulsion of gas from all haloes in our simulated mass range. This suppresses the halo mass function by |${\sim}30{{\ \rm per\ cent}}$|⁠ , lowers halo concentration, and consequently weakens the DM annihilation signal by |${\sim}40{-}60{{\ \rm per\ cent}}$|⁠. [ABSTRACT FROM AUTHOR]

We present an extended suite of the Auriga cosmological gravo-magnetohydrodynamical 'zoom-in' simulations of 40 Milky Way-mass haloes and 26 dwarf galaxy–mass haloes run with the moving-mesh code arepo. Auriga adopts the Lambda cold dark matter cosmogony and includes a comprehensive galaxy formation physics model following the coupled cosmic evolution of dark matter, gas, stars, and supermassive black holes which has been shown to produce numerically well-converged galaxy properties for Milky Way-mass systems. We describe the first public data release of this augmented suite of Auriga simulations, which includes raw snapshots, group catalogues, merger trees, initial conditions, and supplementary data, as well as public analysis tools with worked examples of how to use the data. To demonstrate the value and robustness of the simulation predictions, we analyse a series of low-redshift global properties that compare well with many observed scaling relations, such as the Tully–Fisher relation, the star-forming (SF) main sequence, and H  i gas fraction/disc thickness. Finally, we show that SF gas discs appear to build rotation and velocity dispersion rapidly for |$z\gtrsim 3$| before they 'settle' into ever-increasing rotation-dispersion ratios (⁠|$V/\sigma$|⁠). This evolution appears to be in rough agreement with some kinematic measurements from H |$\alpha$| observations, and demonstrates an application of how to utilize the released data. [ABSTRACT FROM AUTHOR]

We use the voids-within-voids-within-voids (VVV) simulations, a suite of successive nested N -body simulations with extremely high resolution (denoted, from low to high resolution, by L0 to L7), to test the Press–Schechter (PS), Sheth–Tormen (ST), and extended Press–Schechter (EPS) formulae for the halo abundance over the entire mass range, from minihaloes of 10−6 M⊙, to cluster haloes of 1015 M⊙, at different redshifts, from z = 30 to the present. We find that at z = 0 and z = 2, ST best reproduces the results of L0, which has the mean cosmic density (overdensity δ = 0), at 1011−15 M⊙. The higher resolution levels (L1–L7) are biased underdense regions (δ < −0.6). The EPS formalism takes this into account since it gives the mass function of a region conditioned, in this case, on having a given underdensity. EPS provides good matches to these higher levels, with deviations ≲20 per cent, at 10−6−12.5 M⊙. At z ∼ 7−15, the ST predictions for L0 and the EPS for L1–L7 show somewhat larger deviations from the simulation results. However, at even higher redshifts, z ∼ 30, EPS fits the simulations well again. We confirm our results by picking more subvolumes from the L0 simulation, finding that our conclusions depend only weakly on the size and overdensity of the region. The good agreement of EPS with the higher level simulations implies that PS (or ST) gives an accurate description of the total halo mass function in representative regions of the universe. [ABSTRACT FROM AUTHOR]

We take advantage of the unprecedented dynamical range provided by the 'Cosmic-Zoom' project to study the mass accretion history (MAH) of present-day dark matter haloes over the entire mass range present in the Lambda cold dark matter paradigm when the dark matter is made of weakly interacting massive particles of mass 100 GeV. In particular, we complement previous studies by exploring the MAHs of haloes with mass from |$10^8\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$| down to Earth mass, |$10^{-6}\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$|⁠. The formation redshift of low-mass haloes anticorrelates weakly with mass, peaking at z = 3 for haloes of mass |$10^{-4}\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$|⁠. Even lower masses are affected by the free-streaming cut-off in the primordial spectrum of density fluctuations and form at lower redshift. We compare MAHs in our simulations with predictions from two analytical models based on the extended Press–Schechter theory (EPS), and three empirical models derived by fitting and extrapolating either results from cosmological N -body simulations or Monte Carlo realizations of halo growth. All models fit our simulations reasonably well over the mass range for which they were calibrated. While the empirical models match better for more massive haloes, |$M\gt 10^{10}\ h^{-1}\,\mathrm{{\rm M}_{\odot }}$|⁠ , the analytical models do better when extrapolated down to Earth mass. At the higher masses, we explore the correlation between local environment density and MAH, finding that biases are relatively weak, with typical MAHs for haloes in extremely low-density and in typical regions differing by less than 20 per cent at high redshift. If this result can be extrapolated to lower halo masses, we conclude that EPS theory predicts the hierarchical build up of dark matter haloes quite well over the entire halo mass range. [ABSTRACT FROM AUTHOR]

The discovery that neutrinos have mass has important consequences for cosmology. The main effect of massive neutrinos is to suppress the growth of cosmic structure on small scales. Such growth can be accurately modelled using cosmological N -body simulations, but doing so requires accurate initial conditions (ICs). There is a trade-off, especially with first-order ICs, between truncation errors for late starts and discreteness and relativistic errors for early starts. Errors can be minimized by starting simulations at late times using higher order ICs. In this paper, we show that neutrino effects can be absorbed into scale-independent coefficients in higher order Lagrangian perturbation theory (LPT). This clears the way for the use of higher order ICs for massive neutrino simulations. We demonstrate that going to higher order substantially improves the accuracy of simulations. To match the sensitivity of surveys like DESI and Euclid, errors in the matter power spectrum should be well below |$1{{\ \rm per\ cent}}$|⁠. However, we find that first-order Zel'dovich ICs lead to much larger errors, even when starting as early as z  = 127, exceeding |$1{{\ \rm per\ cent}}$| at z  = 0 for k > 0.5 Mpc−1 for the power spectrum and k > 0.1 Mpc−1 for the equilateral bispectrum in our simulations. Ratios of power spectra with different neutrino masses are more robust than absolute statistics, but still depend on the choice of ICs. For all statistics considered, we obtain |$1{{\ \rm per\ cent}}$| agreement between 2LPT and 3LPT at z  = 0. [ABSTRACT FROM AUTHOR]

We present sibelius-dark , a constrained realization simulation of the local volume to a distance of 200 Mpc from the Milky Way. sibelius-dark is the first study of the ' Simulations Beyond The Local Universe ' (sibelius) project, which has the goal of embedding a model Local Group-like system within the correct cosmic environment. The simulation is dark-matter-only, with the galaxy population calculated using the semi-analytic model of galaxy formation, galform. We demonstrate that the large-scale structure that emerges from the sibelius constrained initial conditions matches well the observational data. The inferred galaxy population of sibelius-dark also match well the observational data, both statistically for the whole volume and on an object-by-object basis for the most massive clusters. For example, the K -band number counts across the whole sky, and when divided between the northern and southern Galactic hemispheres, are well reproduced by sibelius-dark. We find that the local volume is somewhat unusual in the wider context of ΛCDM: it contains an abnormally high number of supermassive clusters, as well as an overall large-scale underdensity at the level of ≈5 per cent relative to the cosmic mean. However, whilst rare, the extent of these peculiarities does not significantly challenge the ΛCDM model. sibelius-dark is the most comprehensive constrained realization simulation of the local volume to date, and with this paper we publicly release the halo and galaxy catalogues at z  = 0, which we hope will be useful to the wider astronomy community. [ABSTRACT FROM AUTHOR]

The existence of hot, accreted gaseous coronae around massive galaxies is a long-standing central prediction of galaxy formation models in the ΛCDM cosmology. While observations now confirm that extraplanar hot gas is present around late-type galaxies, the origin of the gas is uncertain with suggestions that galactic feedback could be the dominant source of energy powering the emission. We investigate the origin and X-ray properties of the hot gas that surrounds galaxies of halo mass, |$(10^{11}\!-\!10^{14}) \, \mathrm{M}_\odot$|⁠ , in the cosmological hydrodynamical eagle simulations. We find that the central X-ray emission, ≤0.10 R vir, of haloes of mass |$\le 10^{13} \, \mathrm{M}_\odot$| originates from gas heated by supernovae (SNe). However, beyond this region, a quasi-hydrostatic, accreted atmosphere dominates the X-ray emission in haloes of mass |$\ge 10^{12} \, \mathrm{M}_\odot$|⁠. We predict that a dependence on halo mass of the hot gas to dark matter mass fraction can significantly change the slope of the L X– M vir relation (which is typically assumed to be 4/3 for clusters) and we derive the scaling law appropriate to this case. As the gas fraction in haloes increases with halo mass, we find a steeper slope for the L X– M vir in lower mass haloes, |$\le 10^{14} \, \mathrm{M}_\odot$|⁠. This varying gas fraction is driven by active galactic nuclei feedback. We also identify the physical origin of the so-called 'missing feedback' problem, the apparently low X-ray luminosities observed from high star-forming, low-mass galaxies. This is explained by the ejection of SNe-heated gas from the central regions of the halo. [ABSTRACT FROM AUTHOR]

We study structure formation in a set of cosmological simulations to uncover the scales in the initial density field that gave rise to the formation of present-day structures. Our simulations share a common primordial power spectrum (here Λ cold dark matter, ΛCDM), but the introduction of hierarchical variations of the phase information allows us to systematically study the scales that determine the formation of structure at later times. We consider the variance in z  = 0 statistics such as the matter power spectrum and halo mass function. We also define a criterion for the existence of individual haloes across simulations, and determine what scales in the initial density field contain sufficient information for the non-linear formation of unique haloes. We study how the characteristics of individual haloes such as the mass and concentration, as well as the position and velocity, are affected by variations on different scales, and give scaling relations for haloes of different mass. Finally, we use the example of a cluster-mass halo to show how our hierarchical parametrization of the initial density field can be used to create variants of particular objects. With properties such as mass, concentration, kinematics, and substructure of haloes set on distinct and well-determined scales, and its unique ability to introduce variations localized in real space, our method is a powerful tool to study structure formation in cosmological simulations. [ABSTRACT FROM AUTHOR]

N -body simulations make unambiguous predictions for the abundance of substructures within dark matter haloes. However, the inclusion of baryons in the simulations changes the picture because processes associated with the presence of a large galaxy in the halo can destroy subhaloes and substantially alter the mass function and velocity distribution of subhaloes. We compare the effect of galaxy formation on subhalo populations in two state-of-the-art sets of hydrodynamical Λcold dark matter (ΛCDM) simulations of Milky Way mass haloes, Apostle and Auriga. We introduce a new method for tracking the orbits of subhaloes between simulation snapshots that gives accurate results down to a few kiloparsecs from the centre of the halo. Relative to a dark matter-only simulation, the abundance of subhaloes in Apostle is reduced by 50 per cent near the centre and by 10 per cent within r 200. In Auriga , the corresponding numbers are 80 per cent and 40 per cent. The velocity distributions of subhaloes are also affected by the presence of the galaxy, much more so in Auriga than in Apostle. The differences on subhalo properties in the two simulations can be traced back to the mass of the central galaxies, which in Auriga are typically twice as massive as those in Apostle. We show that some of the results from previous studies are inaccurate due to systematic errors in the modelling of subhalo orbits near the centre of haloes. [ABSTRACT FROM AUTHOR]

The total number and luminosity function of the population of dwarf galaxies of the Milky Way (MW) provide important constraints on the nature of the dark matter and on the astrophysics of galaxy formation at low masses. However, only a partial census of this population exists because of the flux limits and restricted sky coverage of existing Galactic surveys. We combine the sample of satellites recently discovered by the Dark Energy Survey (DES) with the satellites found in Sloan Digital Sky Survey (SDSS) Data Release 9 (together these surveys cover nearly half the sky) to estimate the total luminosity function of satellites down to M V = 0. We apply a new Bayesian inference method in which we assume that the radial distribution of satellites independently of absolute magnitude follows that of subhaloes selected according to their peak maximum circular velocity. We find that there should be at least $$124^{+40}_{-27}$$ (68 per cent CL, statistical error) satellites brighter than M V = 0 within 300 kpc of the Sun. As a result of our use of new data and better simulations, and a more robust statistical method, we infer a much smaller population of satellites than reported in previous studies using earlier SDSS data only; we also address an underestimation of the uncertainties in earlier work by accounting for stochastic effects. We find that the inferred number of faint satellites depends only weakly on the assumed mass of the MW halo and we provide scaling relations to extend our results to different assumed halo masses and outer radii. We predict that half of our estimated total satellite population of the MW should be detected by the Large Synoptic Survey Telescope. The code implementing our estimation method is available online. 1 [ABSTRACT FROM AUTHOR]

The Milky Way's (MW) satellite population is a powerful probe of warm dark matter (WDM) models as the abundance of small substructures is very sensitive to the properties of the WDM particle. However, only a partial census of the MW's complement of satellite galaxies exists because surveys of the MW's close environs are incomplete both in depth and in sky coverage. We present a new Bayesian analysis that combines the sample of satellites recently discovered by the Dark Energy Survey (DES) with those found in the Sloan Digital Sky Survey (SDSS) to estimate the total satellite galaxy luminosity function down to M v = 0. We find that there should be at least $124_{ - 27}^{ + 40}$ (68% CL, statistical error) satellites as bright or brighter than M v = 0 within 300 kpc of the Sun, with only a weak dependence on MW halo mass. When it comes online the Large Synoptic Survey Telescope should detect approximately half of this population. We also show that WDM models infer the same number of satellites as in ΛCDM, which will allow us to rule out those models that produce insufficient substructure to be viable. [ABSTRACT FROM AUTHOR]

The observed stellar kinematics of dispersion-supported galaxies are often used to measure dynamical masses. Recently, several analytical relationships between the stellar line-of-sight velocity dispersion, the projected (2D) or deprojected (3D) half-light radius and the total mass enclosed within the half-light radius, relying on the spherical Jeans equation, have been proposed. Here, we use the APOSTLE cosmological hydrodynamical simulations of the Local Group to test the validity and accuracy of such mass estimators for both dispersion and rotationsupported galaxies, for field and satellite galaxies, and for galaxies of varying masses, shapes and velocity dispersion anisotropies.We find that themass estimators ofWalker et al. andWolf et al. are able to recover themasses of dispersion-dominated systems with little systematic bias, but with a 1σscatter of 25 and 23 per cent, respectively. The error on the estimated mass is dominated by the impact of the 3D shape of the stellar mass distribution, which is difficult toconstrain observationally. This intrinsic scatter becomes the dominant source of uncertainty in the masses estimated for galaxies like the dwarf spheroidal (dSph) satellites of the Milky Way, where the observational errors in their sizes and velocity dispersions are small. Such scatter may also affect the inner density slopes of dSphs derived from multiple stellar populations, relaxing the significance with which Navarro-Frenk-White profiles may be excluded, depending on the degree to which the relevant propertiesof the different stellar populations are correlated. Finally, we derive a new optimal mass estimator that removes the residual biases and achieves a statistically significant reduction in the scatter to 20 per cent overall for dispersion-dominated galaxies, allowing more precise and accurate mass estimates. [ABSTRACT FROM AUTHOR]

We use the Copernicus Complexio (COCO) high-resolution N-body simulations to investigate differences in the properties of small-scale structures in the standard cold dark matter (CDM) model and in a model with a cutoff in the initial power spectrum of density fluctuations consistent with both a thermally produced warm dark matter (WDM) particle with a rest mass of 3.3 keV and a sterile neutrino with mass 7 keV and leptogenesis parameter L6 = 8.7. The latter corresponds to the 'coldest' model with this sterile neutrino mass compatible with the identification of the recently detected 3.5 keV X-ray line as resulting from particle decay. CDM and WDM predict very different number densities of subhaloes with mass ≲ 109 h-1Mʘ although they predict similar, nearly universal, normalized subhalo radial density distributions. Haloes and subhaloes in both models have cuspy Navarro-Frenk-White profiles, but WDM subhaloes below the cut-off scale in the power spectrum (corresponding to maximum circular velocities Vz=0max ≤ 50 kms-1) are less concentrated than their CDM counterparts. We make predictions for observable properties using the GALFORM semi-analytic model of Galaxy formation. Both models predict Milky Way satellite luminosity functions consistent with observations, although the WDM model predicts fewer very faint satellites. This model, however, predicts slightly more UV bright galaxies at redshift z > 7 than CDM, but both are consistent with observations. Gravitational lensing offers the best prospect of distinguishing between the models. [ABSTRACT FROM AUTHOR]

We introduce Copernicus Complexio (coco), a high-resolution cosmological N-body simulation of structure formation in the ΛCDM model. coco follows an approximately spherical region of radius ~17.4 h−1 Mpc embedded in a much larger periodic cube that is followed at lower resolution. The high-resolution volume has a particle mass of 1.135 × 105 h−1 M⊙ (60 times higher than the Millennium-II simulation). coco gives the dark matter halo mass function over eight orders of magnitude in halo mass; it forms ~60 haloes of galactic size, each resolved with about 10 million particles. We confirm the power-law character of the subhalo mass function, .... (>μ)∝μ−s down to a reduced subhalo mass Msub/M200 ≡ μ = 10−6, with a best-fitting power-law index, s = 0.94, for hosts of mass 〈M200〉 = 1012 h−1 M⊙. The concentration-mass relation of coco haloes deviates from a single power law for masses M200 < afew × 108 h−1 M⊙, where it flattens, in agreement with results by Sanchez-Conde et al. The host mass invariance of the reduced maximum circular velocity function of subhaloes, ν ≡ Vmax/V200, hinted at in previous simulations, is clearly demonstrated over five orders of magnitude in host mass. Similarly, we find that the average, normalized radial distribution of subhaloes is approximately universal (i.e. independent of subhalo mass), as previously suggested by the Aquarius simulations of individual haloes. Finally, we find that at fixed physical subhalo size, subhaloes in lower mass hosts typically have lower central densities than those in higher mass hosts. [ABSTRACT FROM AUTHOR]

We use a large sample of isolated dark matter halo pairs drawn from cosmological N-body simulations to identify candidate systems whose kinematics match that of the Local Group (LG) of galaxies. We find, in agreement with the 'timing argument' and earlier work, that the separation and approach velocity of the Milky Way (MW) and Andromeda (M31) galaxies favour a total mass for the pair of ~5 × 1012M☉. A mass this large, however, is difficult to reconcile with the small relative tangential velocity of the pair, as well as with the small deceleration from the Hubble flow observed for the most distant LG members. Halo pairs that match these three criteria have average masses a factor of ~2 times smaller than suggested by the timing argument, but with large dispersion. Guided by these results, we have selected 12 halo pairs with total mass in the range 1.6-3.6 × 1012M☉ for the APOSTLE project (A Project Of Simulating The Local Environment), a suite of hydrodynamical resimulations at various numerical resolution levels (reaching up to ~104 M☉ per gas particle) that use the subgrid physics developed for the EAGLE project. These simulations reproduce, by construction, the main kinematics of the MW-M31 pair, and produce satellite populations whose overall number, luminosities, and kinematics are in good agreement with observations of theMWand M31 companions. The APOSTLE candidate systems thus provide an excellent testbed to confront directly many of the predictions of the A cold dark matter cosmology with observations of our local Universe. [ABSTRACT FROM AUTHOR]

Since reionization prevents star formation in most haloes less massive than 3 × 109M⊙, dwarf galaxies only populate a fraction of existing dark matter haloes. We use hydrodynamic cosmological simulations of the Local Group to study the discriminating factors for galaxy formation in the early Universe and connect them to the present-day properties of galaxies and haloes. A combination of selection effects related to reionization, and the subsequent evolution of haloes in different environments, introduces strong biases between the population of haloes that host dwarf galaxies, and the total halo population. Haloes that host galaxies formed earlier and are more concentrated. In addition, haloes more affected by tidal stripping are more likely to host a galaxy for a given mass or maximum circular velocity, vmax, today. Consequently, satellite haloes are populated more frequently than field haloes, and satellite haloes of 108-109M⊙ or νmax of 12-20 km s-1, compatible with stellar kinematics of Local Group dwarf spheroidals, have experienced a greater than average reduction in both mass and νmax after infall. They are on closer, more radial orbits with higher infall velocities and earlier infall times. Together, these effects make dwarf galaxies highly biased tracers of the underlying dark matter distribution. [ABSTRACT FROM AUTHOR]

The recent detection of a 3.5 keV X-ray line from the centres of galaxies and clusters by Bulbul et al. and Boyarsky et al. has been interpreted as emission from the decay of 7 keV sterile neutrinos which could make up the (warm) dark matter (WDM). As part of the Copernicus Complexio (COCO) programme, we investigate the properties of dark matter haloes formed in a high-resolution cosmological N-body simulation from initial conditions similar to those expected in a universe in which the dark matter consists of 7 keV sterile neutrinos. This simulation and its cold dark matter (CDM) counterpart have ~13.4 bn particles, each of mass ~105 h-1M☉, providing detailed information about halo structure and evolution down to dwarf galaxy mass scales. Non-linear structure formation on small scales (M200 ≲2 × 109 h-1M☉) begins slightly later in COCO-WARM than in COCO-COLD. The halo mass function at the present day in the WDM model begins to drop below its CDM counterpart at a mass ~2 × 109 h-1M☉ and declines very rapidly towards lower masses so that there are five times fewer haloes of mass M200 = 108 h-1M☉ in COCO-WARM than in COCO-COLD. Halo concentrations on dwarf galaxy scales are correspondingly smaller in COCO-WARM, and we provide a simple functional form that describes its evolution with redshift. The shapes of haloes are similar in the two cases, but the smallest haloes in COCO-WARM rotate slightly more slowly than their CDM counterparts. [ABSTRACT FROM AUTHOR]

The relation between galaxies and dark matter haloes is of vital importance for evaluating theoretical predictions of structure formation and galaxy formation physics. We use hydrodynamic cosmological simulations of the Local Group to show that the widely used method of abundance matching based on dark matter only simulations fails at the low-mass end because two of its underlying assumptions are broken: only a small fraction of low-mass (<109.5 M⊙) haloes host a visible galaxy, and baryon effects lower their growth rate. In this regime, reliance on dark matter only simulations for abundance matching is inappropriate and can lead to incorrect results. We find that the reported discrepancy between observational estimates of the halo masses of dwarf galaxies and the values predicted by abundance matching does not point to a failure of Λ cold dark matter, but simply to a failure to account for baryonic effects. Our results also imply that the Local Group contains only a few hundred observable galaxies in contrast with the thousands of faint dwarfs that abundance matching would suggest. We show how relations derived from abundance matching can be corrected, so that they can be used self-consistently to calibrate models of galaxy formation. [ABSTRACT FROM AUTHOR]

We introduce the Virgo Consortium's Evolution and Assembly of GaLaxies and their Environments (EAGLE) project, a suite of hydrodynamical simulations that follow the formation of galaxies and supermassive black holes in cosmologically representative volumes of a standard Λ cold dark matter universe. 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 active galactic nuclei (AGN) in which thermal energy is injected into the gas without the need to turn off cooling or decouple 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 present-day galaxy stellar mass function and the amplitude of the galaxy-central black hole mass relation, also taking galaxy sizes into account. The observed galaxy stellar mass function is reproduced to ≲ 0.2 dex over the full resolved 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 C iv and O vi. While the mass–metallicity relations for gas and stars are consistent with observations for M* ≳ 109 M⊙ (M* ≳ 1010 M⊙ at intermediate resolution), they are insufficiently steep at lower masses. For the reference model, the gas fractions and temperatures are too high for clusters of galaxies, but for galaxy groups these discrepancies can be resolved by adopting a higher heating temperature in the subgrid prescription for AGN feedback. The EAGLE simulation suite, which also includes physics variations and higher resolution zoomed-in volumes described elsewhere, constitutes a valuable new resource for studies of galaxy formation. [ABSTRACT FROM AUTHOR]

We present the first cosmological simulations of dwarf galaxies, which include dark matter self-interactions and baryons. We study two dwarf galaxies within cold dark matter, and four different elastic self-interacting scenarios with constant and velocity-dependent cross-sections, motivated by a new force in the hidden dark matter sector. Our highest resolution simulation has a baryonic mass resolution of 1.8 × 102 M⊙ and a gravitational softening length of 34 pc at z = 0. In this first study we focus on the regime of mostly isolated dwarf galaxies with halo masses ∼ 1010 M⊙ where dark matter dynamically dominates even at sub-kpc scales. We find that while the global properties of galaxies of this scale are minimally affected by allowed self-interactions, their internal structures change significantly if the cross-section is large enough within the inner sub-kpc region. In these dark-matter-dominated systems, self-scattering ties the shape of the stellar distribution to that of the dark matter distribution. In particular, we find that the stellar core radius is closely related to the dark matter core radius generated by self-interactions. Dark matter collisions lead to dwarf galaxies with larger stellar cores and smaller stellar central densities compared to the cold dark matter case. The central metallicity within 1 kpc is also larger by up to ∼15 per cent in the former case. We conclude that the mass distribution and characteristics of the central stars in dwarf galaxies can potentially be used to probe the self-interacting nature of dark matter. [ABSTRACT FROM AUTHOR]

We study the effect of baryons on the abundance of structures and substructures in a Λ cold dark matter (CDM) cosmology, using a pair of high-resolution cosmological simulations from the Galaxies-Intergalactic Medium Interaction Calculation project. Both simulations use identical initial conditions, but while one contains only dark matter, the other also includes baryons. We find that gas pressure, reionization, supernova feedback, stripping and truncated accretion systematically reduce the total mass and the abundance of structures below ∼1012 M⊙ compared to the pure dark matter simulation. Taking this into account and adopting an appropriate detection threshold lower the abundance of observed galaxies with maximum circular velocities vmax < 100 km s−1, significantly reducing the reported discrepancy between ΛCDM and the measured H i velocity function of the Arecibo Legacy Fast ALFA survey. We also show that the stellar-to-total mass ratios of galaxies with stellar masses of ∼105–107 M⊙ inferred from abundance matching of the (sub)halo mass function to the observed galaxy mass function increase by a factor of ∼2. In addition, we find that an important fraction of low-mass subhaloes are completely devoid of stars. Accounting for the presence of dark subhaloes below 1010 M⊙ further reduces the abundance of observable objects and leads to an additional increase in the inferred stellar-to-total mass ratio by factors of 2–10 for galaxies in haloes of 109–1010 M⊙. This largely reconciles the abundance matching results with the kinematics of individual dwarf galaxies in ΛCDM. We propose approximate corrections to the masses of objects derived from pure dark matter calculations to account for baryonic effects. [ABSTRACT FROM AUTHOR]

We describe a methodology to accurately compute halo mass functions, progenitor mass functions, merger rates and merger trees in non-cold dark matter universes using a self-consistent treatment of the generalized extended Press–Schechter formalism. Our approach permits rapid exploration of the subhalo population of galactic haloes in dark matter models with a variety of different particle properties or universes with rolling, truncated or more complicated power spectra. We make detailed comparisons of analytically derived mass functions and merger histories with recent warm dark matter cosmological N-body simulations, and find excellent agreement. We show that once the accretion of smoothly distributed matter is accounted for, coarse-grained statistics such as the mass accretion history of haloes can be almost indistinguishable between cold and warm dark matter cases. However, the halo mass function and progenitor mass functions differ significantly, with the warm dark matter cases being strongly suppressed below the free-streaming scale of the dark matter. We demonstrate the importance of using the correct solution for the excursion set barrier first-crossing distribution in warm dark matter – if the solution for a flat barrier is used instead, the truncation of the halo mass function is much slower, leading to an overestimate of the number of low-mass haloes. [ABSTRACT FROM PUBLISHER]

ABSTRACT We apply a basis function expansion method to create a time-evolving density/potential approximation of the late growth of simulated N-body dark matter haloes. We demonstrate how the potential of a halo from the Aquarius Project can be accurately represented by a small number of basis functions, and show that the halo expansion (HEX) method provides a way to replay simulations. We explore the level of accuracy of the technique as well as some of its limitations. We find that the number of terms included in the expansion must be large enough to resolve the large-scale distribution and shape of the halo but, beyond this, additional terms result in little further improvement. Particle and subhalo orbits can be integrated in this realistic, time-varying halo potential approximation, at much lower cost than the original simulation, with high fidelity for many individual orbits, and a good match to the distributions of orbital energy and angular momentum. Statistically, the evolution of structural subhalo properties, such as mass, half-mass radius and characteristic circular velocity, are very well reproduced in the HEX approximation over several Gyr. We demonstrate an application of the technique by following the evolution of an orbiting subhalo at much higher resolution than can be achieved in the original simulation. Our method represents a significant improvement over commonly used techniques based on static analytical descriptions of the halo potential. [ABSTRACT FROM AUTHOR]

ABSTRACT Cosmological N-body simulations indicate that the spherically averaged density profiles of cold dark matter (CDM) haloes are accurately described by Einasto profiles, where the logarithmic slope is a power law of adjustable exponent, γ≡ d ln ρ/d ln r∝ rα. The pseudo-phase-space density (PPSD) profiles of CDM haloes also show remarkable regularity, and are well approximated by simple power laws, Q( r) ≡ρ/σ3∝ r−χ. As reported in earlier work, this is because Jeans' equations imply, for values of α typical of CDM haloes, that the PPSD profiles of Einasto haloes should resemble power laws over a wide radial range. Significant deviations from a power-law Q profile are nevertheless expected near the centre of Einasto haloes. Conversely, density profiles must deviate from a simple Einasto form if a power-law Q( r) profile holds at all radii. We use an ensemble of haloes drawn from the Millennium-II Simulation to study which of these two descriptions describes best the mass profile of CDM haloes. Our analysis indicates that, at the resolution of the best available simulations, both Einasto and power-law PPSD profiles (with adjustable exponents α and χ, respectively) provide equally acceptable fits to the simulations. Although we are unable to discriminate between these two models, our results confirm the need for a 'shape' parameter, like α or χ, to specify fully the mass profile of a CDM halo. Understanding what determines this shape parameter in the case of individual haloes would help us gain insight into what drives departures from self-similarity in CDM halo structure and how they correlate with evolutionary history, environment or initial conditions. [ABSTRACT FROM AUTHOR]

We calculate the orbital angular momentum of dark matter subhaloes in the Aquarius simulations of cold dark matter (CDM) galactic haloes. We calculate the orientation of their angular momentum relative to that of the spin vector of their host halo and find a variety of different configurations. All six Aquarius haloes contain statistically significant populations of subhalo orbits that are aligned with the main halo spin. All haloes possess a population of subhaloes that rotates in the same direction as the main halo and three of them possess, in addition, a population that rotates in the opposite direction. These configurations arise from the filamentary accretion of subhaloes. Quasi-planar distributions of coherently rotating satellites, such as those inferred in the Milky Way and other galaxies, arise naturally in simulations of a ΛCDM universe. [ABSTRACT FROM AUTHOR]

ABSTRACT We present cosmological hydrodynamical simulations of the formation of dwarf galaxies in a representative sample of haloes extracted from the Millennium-II Simulation. Our six haloes have a z= 0 mass of ∼1010 M⊙ and show different mass assembly histories which are reflected in different star formation histories. We find final stellar masses in the range 5 × 107- 108 M⊙, consistent with other published simulations of galaxy formation in similar mass haloes. Our final objects have structures and stellar populations consistent with observed dwarf galaxies. However, in a Λ cold dark matter universe, 1010 M⊙ haloes must typically contain galaxies with much lower stellar mass than our simulated objects if they are to match observed galaxy abundances. The dwarf galaxies formed in our own and all other current hydrodynamical simulations are more than an order of magnitude more luminous than expected for haloes of this mass. We discuss the significance and possible implications of this result. [ABSTRACT FROM AUTHOR]

We use N-body simulations to investigate the radial dependence of the density, ρ, and velocity dispersion, σ, in cold dark matter (CDM) haloes. In particular, we explore how closely , a surrogate measure of the phase-space density, follows a power law in radius. Our study extends earlier work by considering, in addition to spherically averaged profiles, local Q estimates for individual particles, ; profiles based on the ellipsoidal radius dictated by the triaxial structure of the halo, ; and by carefully removing substructures in order to focus on the profile of the smooth halo, . The resulting profiles follow closely a power law near the centre, but show a clear upturn from this trend near the virial radius, r200. The location and magnitude of the deviations are in excellent agreement with the predictions from Bertschinger's spherical secondary-infall similarity solution. In this model, in the inner, virialized regions, but departures from a power-law occur near r200 because of the proximity of this radius to the location of the first shell crossing – the shock radius in the case of a collisional fluid. Particles there have not yet fully virialized, and so Q departs from the inner power-law profile. Our results imply that the power-law nature of Q profiles only applies to the inner regions and cannot be used to predict accurately the structure of CDM haloes beyond their characteristic scale radius. [ABSTRACT FROM AUTHOR]

We investigate the properties of satellite galaxies in cosmological N-body/smooth particle hydrodynamics simulations of galaxy formation in Milky Way-sized haloes. Because of their shallow potential wells, satellite galaxies are very sensitive to heating processes which affect their gas content. Their properties can therefore be used to constrain the nature of feedback processes that regulate galaxy formation. In our simulations, we assume that all the energy produced by supernovae is used as kinetic energy to drive galactic winds. Several of our simulations produce bright, disc-dominated galaxies. We find that wind models in which the wind speed, , is proportional to the local velocity dispersion of the dark matter, (and thus the wind mass-loading, ), make star formation in satellites sporadic, reproduce the observed satellite luminosity function reasonably well (down to ) and match the luminosity–metallicity relation observed in the Local Group satellites. By contrast, models that assume a constant wind speed overproduce faint satellites and predict an incorrect luminosity–metallicity relation. Our simulations therefore suggest that the feedback processes that operate on the scale of satellite galaxies should generate galactic outflows whose mass-loading varies inversely with the depth of the potential. [ABSTRACT FROM AUTHOR]

We investigate the magnitude and internal alignment of the angular momentum of cold dark matter haloes in simulations with and without baryons. We analyse the cumulative angular momentum profiles of hundreds of thousands of well-resolved haloes in the Millennium Simulation of Springel et al. and in a smaller, but higher resolution, simulation, in total spanning 5 orders of magnitude in mass. For haloes of a given mass, the median specific angular momentum increases with radius as . The direction of the vector varies considerably with radius: the median angle between the inner and total angular momentum vectors is about . To investigate how baryons affect halo spin, we use another high-resolution simulation, which includes gas cooling, star formation and feedback. This simulation produces a sample of galaxies with a realistic distribution of disc-to-total ratios, D/ T: two-thirds of the galaxies have in the B band. The formation of the galaxy spins up the dark matter within such that the specific halo angular momentum increases by ≈50 per cent in the median. The dark matter angular momentum becomes better aligned, but there remains a broad distribution of (mis-)alignments between the halo and the central galaxy, with a median angle between their angular momenta of . Galaxies have a range of orientations relative to the shape of the halo: half of them have their minor axes misaligned by more than , although only about 10 per cent of the galaxies lie within of the plane perpendicular to the major axis of their halo. Finally, we align a sample of haloes according to the orientation of their galaxies and stack the projected mass distributions. Although the individual haloes are significantly aspherical, galaxy–halo misalignments produce a stacked mass distribution that cannot be distinguished from circular. If the lack of alignment found in our simulations is realistic, it will be extremely difficult for weak lensing studies to measure the ellipticity of cold dark matter haloes using this technique. [ABSTRACT FROM AUTHOR]

We describe and test a new method for creating initial conditions for cosmological N-body dark matter simulations based on second-order Lagrangian perturbation theory (2lpt). The method can be applied to multimass particle distributions making it suitable for creating resimulation, or ‘zoom’ initial conditions. By testing against an analytic solution, we show that the method works well for a spherically symmetric perturbation with radial features ranging over more than three orders of magnitude in linear scale and 11 orders of magnitude in particle mass. We apply the method and repeat resimulations of the rapid formation of a high-mass halo at redshift ∼50 and the formation of a Milky Way mass dark matter halo at redshift zero. In both cases, we find that many properties of the final halo show a much smaller sensitivity to the start redshift with the 2lpt initial conditions than simulations started from Zel'dovich initial conditions. For spherical overdense regions, structure formation is erroneously delayed in simulations starting from Zel'dovich initial conditions, and we demonstrate for the case of the formation of the high-redshift halo that this delay can be accounted for using the spherical collapse model. In addition to being more accurate, 2lpt initial conditions allow simulations to start later, saving computer time. [ABSTRACT FROM AUTHOR]

The highly flattened distribution of satellite galaxies in the Milky Way (MW) presents a number of puzzles. First, its polar alignment stands out from the planar alignments commonly found in other galaxies. Secondly, recent proper-motion measurements reveal that the orbital angular momentum of at least three, and possibly as many as eight, of the MW's satellites points (within ) along the axis of their flattened configuration, suggesting some form of coherent motion. In this paper, we use a high-resolution cosmological simulation to investigate whether this pattern conflicts with the expectations of the cold dark matter model of structure formation. We find that this seemingly unlikely setup occurs often: approximately 35 per cent of the time, we find systems in which the angular momentum of three individual satellites points along, or close to, the short axis of the satellite distribution. In addition, in 30 per cent of the systems we find that the net angular momentum of the six best-aligned satellites lies within of the short axis of the satellite distribution, as observed for the MW. [ABSTRACT FROM AUTHOR]

We use the high-resolution Aquarius simulations of the formation of Milky Way-sized haloes in the Λ cold dark matter cosmology to study the effects of dark matter substructures on gravitational lensing. Each halo is resolved with particles (at a mass resolution to ) within its virial radius. Subhaloes with masses 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 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 . 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. [ABSTRACT FROM AUTHOR]

We present the Millennium-II Simulation (MS-II), a very large N-body simulation of dark matter evolution in the concordance Λ cold dark matter (ΛCDM) cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size with five times better spatial resolution (a Plummer equivalent softening of ) and with 125 times better mass resolution (a particle mass of ). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and non-linear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from haloes similar to those hosting Local Group dwarf spheroidal galaxies to haloes corresponding to the richest galaxy clusters. The ‘Milky Way’ haloes of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass haloes. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogues and assembly trees for the MS-II in the same format within the same archive as those already released for the MS. [ABSTRACT FROM AUTHOR]

In a universe with a cosmological constant, the large-scale gravitational potential varies in time and this is, in principle, observable. Using an N-body simulation of a Λ cold dark matter universe, we show that linear theory is not sufficiently accurate to predict the power spectrum of the time derivative, , needed to compute the imprint of large-scale structure on the cosmic microwave background (CMB). The linear part of the power spectrum [the integrated Sachs–Wolfe effect (ISW)] drops quickly as the relative importance of diminishes at high redshift, while the non-linear part [the Rees–Sciama effect (RS)] evolves more slowly with redshift. Therefore, the deviation of the total power spectrum from linear theory occurs at larger scales at higher redshifts. The deviation occurs at at . The cross-correlation power spectrum of the density δ with behaves differently from the power spectrum of . First, the deviation from linear theory occurs at smaller scales ( at ). Secondly, the correlation becomes negative when the non-linear effect dominates. For the cross-correlation power spectrum of galaxy samples with the CMB, the non-linear effect becomes significant at and rapidly makes the cross-power spectrum negative. For high-redshift samples, the cross-correlation is expected to be suppressed by 5–10 per cent on arcminute scales. The RS effect makes a negligible contribution to the large-scale ISW cross-correlation measurement. However, on arcminute scales it will contaminate the expected cross-correlation signal induced by the Sunyaev–Zel'dovich effect. [ABSTRACT FROM AUTHOR]

We describe a method for constructing mock galaxy catalogues which are well suited for use in conjunction with large photometric surveys. We use the semi-analytic galaxy formation model of Bower et al. implemented in the Millennium N-body simulation of the evolution of dark matter clustering in a Λ cold dark matter cosmology. We apply our method to the specific case of the surveys soon to commence with PS1, the first of four telescopes planned for the Pan-STARRS. PS1 has five photometric bands, and y and will carry out an all-sky ‘3π’ survey and a medium deep survey (MDS) over 84 deg2. We calculate the expected magnitude limits for extended sources in the two surveys. We find that, after 3 year, the 3π survey will have detected over 108 galaxies in all five bands, 10 million of which will lie at redshift , while the MDS will have detected over 107 galaxies with 0.5 million lying at . These numbers at least double if the detection in the shallowest band, y, is not required. We then evaluate the accuracy of photometric redshifts estimated using an off-the-shelf photo- z code. With the grizy bands alone, it is possible to achieve an accuracy in the 3π survey of in the range , which could be reduced by about 15 per cent using near-infrared photometry from the Infrared Deep Sky Survey (UKIDDS) survey, but would increase by about 25 per cent for the deeper sample without the y-band photometry. For the MDS, an accuracy of is achievable for using grizy. A dramatic improvement in accuracy is possible by selecting only red galaxies. In this case, is achievable for ∼100 million galaxies at in the 3π survey and for 30 million galaxies in the MDS at . We investigate the effect of using photometric redshifts in the estimate of the baryonic acoustic oscillation scale. We find that PS1 will achieve a similar accuracy in this estimate as a spectroscopic survey of 20 million galaxies. [ABSTRACT FROM AUTHOR]

We study predictions for dark matter (DM) phase-space structure near the Sun based on high-resolution simulations of six galaxy haloes taken from the Aquarius project. The local DM density distribution is predicted to be remarkably smooth; the density at the Sun differs from the mean over a best-fitting ellipsoidal equidensity contour by less than 15 per cent at the 99.9 per cent confidence level. The local velocity distribution is also very smooth, but it differs systematically from a (multivariate) Gaussian distribution. This is not due to the presence of individual clumps or streams, but to broad features in the velocity modulus and energy distributions that are stable in both space and time and reflect the detailed assembly history of each halo. These features have a significant impact on the signals predicted for weakly interacting massive particle and axion searches. For example, weakly interacting massive particles recoil rates can deviate by ∼10 per cent from those expected from the best-fitting multivariate Gaussian models. The axion spectra in our simulations typically peak at lower frequencies than in the case of multivariate Gaussian velocity distributions. Also in this case, the spectra show significant imprints of the formation of the halo. This implies that once direct DM detection has become routine, features in the detector signal will allow us to study the DM assembly history of the Milky Way. A new field, ‘DM astronomy’, will then emerge. [ABSTRACT FROM AUTHOR]

We explore the clustering properties of high-redshift dark matter haloes, focusing on haloes massive enough to host early generations of stars or galaxies at redshift 10 and greater. Haloes are extracted from an array of dark matter simulations able to resolve down to the ‘mini-halo’ mass scale at redshifts as high as 30, thus encompassing the expected full mass range of haloes capable of hosting luminous objects and sources of reionization. Halo clustering on large-scales agrees with the Sheth, Mo & Tormen halo bias relation within all our simulations, greatly extending the regime where large-scale clustering is confirmed to be ‘universal’ at the 10–20 per cent level (which means, e.g., that 3σ haloes of cluster mass at have the same large-scale bias with respect to the mass distribution as 3σ haloes of galaxy mass at ). However, on small-scales, the clustering of our massive haloes at these high redshifts is stronger than expected from comparisons with small-scale halo clustering extrapolated from lower redshifts. This implies ‘non-universality’ in the scale-dependence of halo clustering, at least for the commonly used parametrizations of the scale-dependence of bias that we consider. We provide a fit for the scale-dependence of bias in our results. This study provides a basis for using extraordinarily high-redshift galaxies (redshift ∼10) as a probe of cosmology and galaxy formation at its earliest stages. We show also that mass and halo kinematics are strongly affected by finite simulation volumes. This suggests the potential for adverse affects on gas dynamics in hydrodynamic simulations of limited volumes, such as is typical in simulations of the formation of the ‘first stars’, though further study is warranted. [ABSTRACT FROM AUTHOR]

We use two very large cosmological simulations to study how the density profiles of relaxed Λ cold dark matter dark haloes depend on redshift and on halo mass. We confirm that these profiles deviate slightly but systematically from the NFW form and are better approximated by the empirical formula, , first used by Einasto to fit star counts in the Milky Way. The best-fitting value of the additional shape parameter, α, increases gradually with mass, from for present-day galaxy haloes to for the rarest and most massive clusters. Halo concentrations depend only weakly on mass at , and this dependence weakens further at earlier times. At the average concentration of relaxed haloes does not vary appreciably over the mass range accessible to our simulations . Furthermore, in our biggest simulation, the average concentration of the most massive, relaxed haloes is constant at for . These results agree well with those of Zhao et al. and support the idea that halo densities reflect the density of the universe at the time they formed, as proposed by Navarro, Frenk & White. With their original parameters, the NFW prescription overpredicts halo concentrations at high redshift. This shortcoming can be reduced by modifying the definition of halo formation time, although the evolution of the concentrations of Milky Way mass haloes is still not reproduced well. In contrast, the much-used revisions of the NFW prescription by Bullock et al. and Eke, Navarro & Steinmetz predict a steeper drop in concentration at the highest masses and stronger evolution with redshift than are compatible with our numerical data. Modifying the parameters of these models can reduce the discrepancy at high masses, but the overly rapid redshift evolution remains. These results have important implications for currently planned surveys of distant clusters. [ABSTRACT FROM AUTHOR]

We generate mock galaxy catalogues for a grid of different cosmologies, using rescaled N-body simulations in tandem with a semi-analytic model run using consistent parameters. Because we predict the galaxy bias, rather than fitting it as a nuisance parameter, we obtain an almost pure constraint on σ8 by comparing the projected two-point correlation function we obtain to that from the Sloan Digital Sky Survey (SDSS). A systematic error arises because different semi-analytic modelling assumptions allow us to fit the r-band luminosity function equally well. Combining our estimate of the error from this source with the statistical error, we find . We obtain consistent results if we use galaxy samples with a different magnitude threshold, or if we select galaxies by bJ-band rather than r-band luminosity and compare to data from the 2dF Galaxy Redshift Survey (2dFGRS). Our estimate for σ8 is higher than that obtained for other analyses of galaxy data alone, and we attempt to find the source of this difference. We note that in any case, galaxy clustering data provide a very stringent constraint on galaxy formation models. [ABSTRACT FROM AUTHOR]

We use the Millennium Simulation (MS) to study the statistics of Λ cold dark matter (ΛCDM) halo concentrations at . Our results confirm that the average halo concentration declines monotonically with mass; the concentration–mass relation is well fitted by a power law over three decades in mass, up to the most massive objects that form in a ΛCDM universe . This is in clear disagreement with the predictions of the model proposed by Bullock et al. for these rare objects, and agrees better with the original predictions of Navarro, Frenk & White. The large volume surveyed, together with the unprecedented numerical resolution of the MS, allows us to estimate with confidence the distribution of concentrations and, consequently, the abundance of systems with unusual properties. About one in a hundred cluster haloes have concentrations exceeding , a result that may be useful in interpreting the likelihood of unusually strong massive gravitational lenses, such as Abell 1689, in the ΛCDM cosmogony. A similar fraction of about 1 per cent of galaxy-sized haloes have and this could be relevant to models that attempt to reconcile the ΛCDM cosmology with rotation curves of low surface brightness galaxies by appealing to haloes of unexpectedly low concentration. We find that halo concentrations are independent of spin once haloes manifestly out of equilibrium have been removed from the sample. Compared to their relaxed brethren, the concentrations of out-of-equilibrium haloes tend to be lower and have more scatter, while their spins tend to be higher. A number of previously noted trends within the halo population are induced primarily by these properties of unrelaxed systems. Finally, we compare the result of predicting halo concentrations using the mass assembly history of the main progenitor with predictions based on simple arguments regarding the assembly time of all progenitors. The latter are typically as good or better than the former, suggesting that halo concentration depends not only on the evolutionary path of a halo's main progenitor, but on how and when all of its constituents collapsed to form non-linear objects. [ABSTRACT FROM AUTHOR]

We address the question of how well the density profile of galaxy clusters can be determined by combining strong lensing and velocity dispersion data. We use cosmological dark matter simulations of clusters to test the reliability of the method, producing mock catalogues of tangential and radial gravitational arcs and simulating the radial velocity dispersion profile of the cluster brightest central galaxy. The density profiles of the simulated clusters closely follow the Navarro, Frenk & White (NFW) form, but we find that the recovered values of the inner slope are systematically underestimated, by about 0.4 in the mean, if the lens is assumed to be axially symmetric. However, if the ellipticity and orientation of the isocontours of the cluster lensing potential are taken into account, then the inner slopes can be recovered quite accurately for a significant subset of the clusters whose central surface density profiles appear the most regular. These have lensing potentials with ellipticities in the range 0.15–0.4. Further simulations projecting one cluster along many random lines of sight show that, even for lower ellipticities, the central slopes are underestimated by ∼10–35 per cent. These simulations closely mimic past observations, suggesting that existing estimates of the central slopes may be biased towards low values. For the remaining clusters, where the lensing potential is strongly perturbed by active merging or by substructure, the correct determination of the inner slope requires a more accurate model for the lens. When the halo profile is modelled by a generalized NFW profile, we find that the inferred scale radius and characteristic density, unlike the inner slope, are generally poorly constrained, since there is a strong degeneracy between these two parameters. [ABSTRACT FROM AUTHOR]

We investigate the baryon fraction in dark matter haloes formed in non-radiative gas-dynamical simulations of the Λ cold dark matter (CDM) cosmogony. By combining a realization of the Millennium Simulation with a simulation of a smaller volume focusing on dwarf haloes, our study spans five decades in halo mass, from 1010 to 1015 h−1 M⊙. We find that the baryon fraction within the halo virial radius is typically 90 per cent of the cosmic mean, with a rms scatter of 6 per cent, independently of redshift and of halo mass down to the smallest resolved haloes. Our results show that, contrary to the proposal of Mo et al., pre-virialization gravitational heating is unable to prevent the collapse of gas within galactic and protogalactic haloes, and confirm the need for non-gravitational feedback in order to reduce the efficiency of gas cooling and star formation in dwarf galaxy haloes. Simulations including a simple photoheating model (where a gas temperature floor of is imposed from z= 11) confirm earlier suggestions that photoheating can only prevent the collapse of baryons in systems with virial temperatures T200≲ 2.2 Tfloor≈ 4.4 × 104 K (corresponding to a virial mass of M200∼ 1010 h−1 M⊙ and a circular velocity of V200∼ 35 km s−1). Photoheating may thus help regulate the formation of dwarf spheroidals and other galaxies at the extreme faint end of the luminosity function, but it cannot, on its own, reconcile the abundance of sub- L★ galaxies with the vast number of dwarf haloes expected in the ΛCDM cosmogony. The lack of evolution or mass dependence seen in the baryon fraction augurs well for X-ray cluster studies that assume a universal and non-evolving baryon fraction to place constraints on cosmological parameters. [ABSTRACT FROM AUTHOR]

We investigate the spins and shapes of over a million dark matter haloes identified at in the Millennium simulation. Our sample spans halo masses ranging from dwarf galaxies to rich galaxy clusters. The very large dynamic range of this Λ cold dark matter cosmological simulation enables the distribution of spins and shapes and their variation with halo mass and environment to be characterized with unprecedented precision. We compare results for haloes identified using three different algorithms, and investigate (and remove) biases in the estimate of angular momentum introduced both by the algorithm itself and by numerical effects. We introduce a novel halo definition called the TREE halo, based on the branches of the halo merger trees, which is more appropriate for comparison with real astronomical objects than the traditional ‘friends-of-friends’ and ‘spherical overdensity’ (SO) algorithms. We find that for this many objects, the traditional lognormal function is no longer an adequate description of the distribution, , of the dimensionless spin parameter λ, and we provide a different function that gives a better fit forTREE andSO haloes. The variation in spin with halo mass is weak but detectable, although the trend depends strongly on the halo definition used. For the entire population of haloes, we find median values of , depending on the definition of a halo. The haloes exhibit a range of shapes, with a preference for prolateness over oblateness. More-massive haloes tend to be less spherical and more prolate. We find that the more-spherical haloes have less coherent rotation in the median, and those closest to being spherical have a spin independent of mass . The most-massive haloes have a spin independent of shape . The majority of haloes have their angular momentum vector aligned with their minor axis and perpendicular to their major axis. We find a general trend for higher spin haloes to be more clustered, with a stronger effect for more-massive haloes. For galaxy cluster haloes, this can be larger than a factor of ∼2. [ABSTRACT FROM AUTHOR]

We use an array of high-resolution N-body simulations to determine the mass function of dark matter haloes at redshifts 10–30. We develop a new method for compensating for the effects of finite simulation volume that allows us to find an approximation to the true ‘global’ mass function. By simulating a wide range of volumes at different mass resolution, we calculate the abundance of haloes of mass 105−12 h−1 M⊙. This enables us to predict accurately the abundance of the haloes that host the sources that reionize the Universe. In particular, we focus on the small mass haloes (≳105.5−6 h−1 M⊙) likely to harbour Population III stars where gas cools by molecular hydrogen emission, early galaxies in which baryons cool by atomic hydrogen emission at a virial temperature of ∼104K (∼107.5−8 h−1 M⊙), and massive galaxies that may be observable at redshift ∼10. When we combine our data with simulations that include high-mass haloes at low redshift, we find that the best fit to the halo mass function depends not only on the linear overdensity, as is commonly assumed in analytic models, but also on the slope of the linear power spectrum at the scale of the halo mass. The Press–Schechter model gives a poor fit to the halo mass function in the simulations at all epochs; the Sheth-Tormen model gives a better match, but still overpredicts the abundance of rare objects at all times by up to 50 per cent. Finally, we consider the consequences of the recently released WMAP 3-yr cosmological parameters. These lead to much less structure at high redshift, reducing the number of ‘mini-haloes’ by more than a factor of two and the number of galaxy hosts by nearly four orders of magnitude. Code to generate our best-fitting halo mass function may be downloaded from . [ABSTRACT FROM AUTHOR]

We study the environmental dependence of the formation epoch of dark matter haloes in the Millennium Simulation: a ten billion particle N-body simulation of standard Lambda cold dark matter cosmology. A sensitive test of this dependence – the marked correlation function – reveals highly significant evidence that haloes of a given mass form earlier in denser regions. We define a marked cross-correlation function, which helps quantify how this effect depends upon the choice of the halo population used to define the environment. The mean halo formation redshift as a function of the local overdensity in dark matter is also well determined, and we see an especially clear dependence for galaxy-sized haloes. This contradicts one of the basic predictions of the excursion set model of structure formation, even though we see that this theory predicts other features of the distribution of halo formation epochs rather well. It also invalidates an assumption usually employed in the popular halo, or halo occupation distribution, models of galaxy clustering, namely that the distribution of halo properties is a function of halo mass but not of halo environment. [ABSTRACT FROM AUTHOR]

We have performed hydrodynamic simulations of galaxy formation in a cold dark matter (ΛCDM) universe. We have followed galaxy formation in a dark matter halo, chosen to have a relatively quiet recent merger history, using different models for star formation and feedback. In all cases, we have adopted a multiphase description of the interstellar medium and modelled star formation in quiescent and burst modes. We have explored two triggers for starbursts – strong shocks and high gas density – allowing for the possibility that stars in the burst may form with a top-heavy initial mass function. We find that the final morphology of the galaxy is extremely sensitive to the modelling of star formation and feedback. Starting from identical initial conditions, galaxies spanning the entire range of Hubble types, with B-band disc-to-total luminosity ratios ranging from 0.2 to 0.9, can form in the same dark matter halo. Models in which starbursts are induced by high gas density (qualitatively similar to models in which feedback is produced by active galactic nuclei) generate energetic winds and result in galaxies with an early-type morphology. Models in which the starbursts are induced by strong shocks lead to extended discs. In this case, the feedback associated with the bursts suppresses the collapse of baryons in small haloes, helping to create a reservoir of hot gas that is available for cooling after , following the bulk of the dynamical activity that builds up the halo. This gas then cools to form an extended, young stellar disc. [ABSTRACT FROM AUTHOR]