Lambda Cold Dark Matter ( Delta *LCDM) is now the standard theory of structure formation in the universe. We present the first results from the new Bolshoi dissipationless cosmological Delta *LCDM ...simulation that uses cosmological parameters favored by current observations. The Bolshoi simulation was run in a volume 250 h --1 Mpc on a side using ~8 billion particles with mass and force resolution adequate to follow subhalos down to the completeness limit of V circ = 50 km s--1 maximum circular velocity. Using merger trees derived from analysis of 180 stored time steps we find the circular velocities of satellites before they fall into their host halos. Using excellent statistics of halos and subhalos (~10 million at every moment and ~50 million over the whole history) we present accurate approximations for statistics such as the halo mass function, the concentrations for distinct halos and subhalos, the abundance of halos as a function of their circular velocity, and the abundance and the spatial distribution of subhalos. We find that at high redshifts the concentration falls to a minimum value of about 4.0 and then rises for higher values of halo mass--a new result. We present approximations for the velocity and mass functions of distinct halos as a function of redshift. We find that while the Sheth-Tormen (ST) approximation for the mass function of halos found by spherical overdensity is quite accurate at low redshifts, the ST formula overpredicts the abundance of halos by nearly an order of magnitude by z = 10. We find that the number of subhalos scales with the circular velocity of the host halo as V 1/2 host, and that subhalos have nearly the same radial distribution as dark matter particles at radii 0.3-2 times the host halo virial radius. The subhalo velocity function N(> V sub) scales as V --3 circ. Combining the results of Bolshoi and Via Lactea-II simulations, we find that inside the virial radius of halos with the number of satellites is N(> V sub) = (V sub/58 km s--1)--3 for satellite circular velocities in the range 4 km s--1 < V sub < 150 km s--1.
Although supernova (SN) explosions and stellar winds happen at very small scales, they affect the interstellar medium (ISM) at galactic scales and regulate the formation of a whole galaxy. Previous ...attempts of mimicking these effects in simulations of galaxy formation use very simplified assumptions. We develop a much more realistic prescription for modeling the feedback, which minimizes any ad hoc subgrid physics. We start with developing high-resolution models of the ISM and formulate the conditions required for its realistic functionality: formation of multiphase medium with hot chimneys, superbubbles, cold molecular phase, and very slow consumption of gas. We find that this can be achieved only by doing what the real universe does: formation of dense (>10 H atoms cm-3), cold (T 100 K) molecular phase, where the star formation happens, and which young stars disrup. Another important ingredient is the effect of runaway stars: massive binary stars ejected from molecular clouds when one of the companions becomes an SN. Those stars can move to 10-100 pc away from molecular clouds before exploding themselves as SNe. This greatly facilitates the feedback. Once those effects are implemented into cosmological simulations, galaxy formation proceeds more realistically. For example, we do not have the overcooling problem. The angular momentum problem (resulting in a too massive bulge) is also reduced substantially: the rotation curves are nearly flat. The galaxy formation also becomes more violent. Just as often observed in quasar absorption lines, there are substantial outflows from forming and active galaxies. At high redshifts we routinely find gas with few hundred km s-1 and occasionally 1000-2000 km s-1. The gas has high metallicity, which may exceed the solar metallicity. The temperature of the gas in the outflows and in chimneys can be very high: T = 107-108 K. The density profile of dark matter is still consistent with a cuspy profile. The simulations reproduce this picture only if the resolution is very high: better than 50 pc, which is 10 times better than the typical resolution in previous cosmological simulations. Our simulations of galaxy formation reach the resolution of 35 pc.
ABSTRACT
We introduce the Uchuu suite of large high-resolution cosmological N-body simulations. The largest simulation, named Uchuu, consists of 2.1 trillion (12 8003) dark matter particles in a box ...of side-length 2.0 $\, h^{-1} \, \rm Gpc$, with particle mass of 3.27 × 108$\, h^{-1}\, \rm M_{\odot }$. The highest resolution simulation, Shin-Uchuu, consists of 262 billion (64003) particles in a box of side-length 140 $\, h^{-1} \, \rm Mpc$, with particle mass of 8.97 × 105$\, h^{-1}\, \rm M_{\odot }$. Combining these simulations, we can follow the evolution of dark matter haloes and subhaloes spanning those hosting dwarf galaxies to massive galaxy clusters across an unprecedented volume. In this first paper, we present basic statistics, dark matter power spectra, and the halo and subhalo mass functions, which demonstrate the wide dynamic range and superb statistics of the Uchuu suite. From an analysis of the evolution of the power spectra, we conclude that our simulations remain accurate from the baryon acoustic oscillation scale down to the very small. We also provide parameters of a mass–concentration model, which describes the evolution of halo concentration and reproduces our simulation data to within 5 per cent for haloes with masses spanning nearly eight orders of magnitude at redshift 0 ≤ z ≤ 14. There is an upturn in the mass–concentration relation for the population of all haloes and of relaxed haloes at z ≳ 0.5, whereas no upturn is detected at z < 0.5. We make publicly available various N-body products as part of Uchuu Data Release 1 on the Skies & Universes site.1 Future releases will include gravitational lensing maps and mock galaxy, X-ray cluster, and active galactic nucleus catalogues.
Predicting structural properties of dark matter haloes is one of the fundamental goals of modern cosmology. We use the suite of MultiDark cosmological simulations to study the evolution of dark ...matter halo density profiles, concentrations, and velocity anisotropies. We find that in order to understand the structure of dark matter haloes and to make 1–2 per cent accurate predictions for density profiles, one needs to realize that halo concentration is more complex than the ratio of the virial radius to the core radius in the Navarro–Frenk–White (NFW) profile. For massive haloes, the average density profile is far from the NFW shape and the concentration is defined by both the core radius and the shape parameter α in the Einasto approximation. We show that haloes progress through three stages of evolution. They start as rare density peaks and experience fast and nearly radial infall that brings mass closer to the centre, producing a highly concentrated halo. Here, the halo concentration increases with increasing halo mass and the concentration is defined by the α parameter with a nearly constant core radius. Later haloes slide into the plateau regime where the accretion becomes less radial, but frequent mergers still affect even the central region. At this stage, the concentration does not depend on halo mass. Once the rate of accretion and merging slows down, haloes move into the domain of declining concentration–mass relation because new accretion piles up mass close to the virial radius while the core radius is staying constant. Accurate analytical fits are provided.
We study the concentration of dark matter haloes and its evolution in N-body simulations of the standard Λ cold dark matter (ΛCDM) cosmology. The results presented in this paper are based on four ...large N-body simulations with ∼10 billion particles each: the Millennium-I and -II, Bolshoi and MultiDark simulations. The MultiDark (or BigBolshoi) simulation is introduced in this paper. This suite of simulations with high mass resolution over a large volume allows us to compute with unprecedented accuracy the concentration over a large range of scales (about six orders of magnitude in mass), which constitutes the state of the art of our current knowledge on this basic property of dark matter haloes in the ΛCDM cosmology. We find that there is consistency among the different simulation data sets, despite the different codes, numerical algorithms and halo/subhalo finders used in our analysis. We confirm a novel feature for halo concentrations at high redshifts: a flattening and upturn with increasing mass. The concentration c(M, z) as a function of mass and the redshift and for different cosmological parameters shows a remarkably complex pattern. However, when expressed in terms of the linear rms fluctuation of the density field σ(M, z), the halo concentration c(σ) shows a nearly universal simple U-shaped behaviour with a minimum at a well-defined scale at σ∼ 0.71. Yet, some small dependences with redshift and cosmology still remain. At the high-mass end (σ < 1), the median halo kinematic profiles show large signatures of infall and highly radial orbits. This c-σ(M, z) relation can be accurately parametrized and provides an analytical model for the dependence of concentration on halo mass. When applied to galaxy clusters, our estimates of concentrations are substantially larger - by a factor up to 1.5 - than previous results from smaller simulations, and are in much better agreement with results of observations.
We study the concentration of dark matter haloes and its evolution in N-body simulations of the standard Λ cold dark matter (ΛCDM) cosmology. The results presented in this paper are based on four ...large N-body simulations with 10 billion particles each: the Millennium-I and -II, Bolshoi and MultiDark simulations. The MultiDark (or BigBolshoi) simulation is introduced in this paper. This suite of simulations with high mass resolution over a large volume allows us to compute with unprecedented accuracy the concentration over a large range of scales (about six orders of magnitude in mass), which constitutes the state of the art of our current knowledge on this basic property of dark matter haloes in the ΛCDM cosmology. We find that there is consistency among the different simulation data sets, despite the different codes, numerical algorithms and halo/subhalo finders used in our analysis. We confirm a novel feature for halo concentrations at high redshifts: a flattening and upturn with increasing mass. The concentration c(M, z) as a function of mass and the redshift and for different cosmological parameters shows a remarkably complex pattern. However, when expressed in terms of the linear rms fluctuation of the density field σ(M, z), the halo concentration c(σ) shows a nearly universal simple U-shaped behaviour with a minimum at a well-defined scale at σ 0.71. Yet, some small dependences with redshift and cosmology still remain. At the high-mass end (σ < 1), the median halo kinematic profiles show large signatures of infall and highly radial orbits. This c-σ(M, z) relation can be accurately parametrized and provides an analytical model for the dependence of concentration on halo mass. When applied to galaxy clusters, our estimates of concentrations are substantially larger - by a factor up to 1.5 - than previous results from smaller simulations, and are in much better agreement with results of observations. PUBLICATION ABSTRACT
We present a new algorithm for generating merger trees and halo catalogs which explicitly ensures consistency of halo properties (mass, position, and velocity) across time steps. Our algorithm has ...demonstrated the ability to improve both the completeness (through detecting and inserting otherwise missing halos) and purity (through detecting and removing spurious objects) of both merger trees and halo catalogs. In addition, our method is able to robustly measure the self-consistency of halo finders; it is the first to directly measure the uncertainties in halo positions, halo velocities, and the halo mass function for a given halo finder based on consistency between snapshots in cosmological simulations. We use this algorithm to generate merger trees for two large simulations (Bolshoi and Consuelo) and evaluate two halo finders (ROCKSTAR and BDM). We find that both the ROCKSTAR and BDM halo finders track halos extremely well; in both, the number of halos which do not have physically consistent progenitors is at the 1%-2% level across all halo masses. Our code is publicly available at http://code.google.com/p/consistent-trees. Our trees and catalogs are publicly available at http://hipacc.ucsc.edu/Bolshoi/.
Any successful model of galaxy formation needs to explain the low rate of star formation in the small progenitors of today's galaxies. This inefficiency is necessary for reproducing the low ...stellar-to-virial mass fractions, suggested by current abundance matching models. A possible driver of this low efficiency is the radiation pressure exerted by ionizing photons from massive stars. The effect of radiation pressure in cosmological, zoom-in galaxy formation simulations is modelled as a non-thermal pressure that acts only in dense and optically thick star-forming regions. We also include photoionization and photoheating by massive stars. The full photoionization of hydrogen reduces the radiative cooling in the 104-4.5 K regime. The main effect of radiation pressure is to regulate and limit the high values of gas density and the amount of gas available for star formation. This maintains a low star formation rate of ∼1 M⊙ yr−1 in haloes with masses about 1011 M⊙ at z ≃ 3. Infrared trapping and photoionization/photoheating processes are secondary effects in this mass range. The galaxies residing in these low-mass haloes contain only ∼0.6 per cent of the total virial mass in stars, roughly consistent with abundance matching. Radiative feedback maintains an extended galaxy with a rising circular velocity profile.
Using three-dimensional (3D) spectroscopy with a scanning Fabry–Perot interferometer, we study the kinematics of ionized gas in 59 nearby dwarf galaxies. Combining our results with data from the ...literature, we provide a global relation between the gas velocity dispersion σ and the star formation rate (SFR) and Hα luminosity for galaxies with a very broad range of star formation rates: SFR = 0.001–300 M⊙ yr−1. We find that the SFR–σ relation for the combined sample of dwarf galaxies, star-forming, local luminous and ultraluminous infrared galaxies can be fitted in the form σ ∝ SFR5.3 ± 0.2. This implies that the slope of the L–σ relation inferred from a sample of rotation-supported disc galaxies (including mergers) is similar to the L–σ relation of individual giant H ii regions. We present arguments that the velocity dispersion of the ionized gas does not reflect virial motions in the gravitational potential of dwarf galaxies and instead is determined mainly by the energy injected into the interstellar medium by ongoing star formation.
The cooling of gas in the centers of dark matter halos is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually ...calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. In contrast, halos in the hierarchical structure formation scenarios grow via multiple violent mergers and accretion along filaments, and particle orbits in the halos are highly eccentric. We study the effects of the cooling of gas in the inner regions of halos using high-resolution cosmological simulations that include gas dynamics, radiative cooling, and star formation. We find that the dissipation of gas indeed increases the density of dark matter and steepens its radial profile in the inner regions of halos compared to the case without cooling. For the first time, we test the adiabatic contraction model in cosmological simulations and find that the standard model systematically overpredicts the increase of dark matter density in the inner 5% of the virial radius. We show that the model can be improved by a simple modification of the assumed invariant from M(r)r to M(r) r, where r and r are the current and orbit-averaged particle positions. This modification approximately accounts for orbital eccentricities of particles and reproduces simulation profiles to within 10%-20%. We present analytical fitting functions that accurately describe the transformation of the dark matter profile in the modified model and can be used for interpretation of observations.
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