We present two large cosmological N -body simulations, called Horizon Run 2 (HR2) and Horizon Run 3 (HR3), made using 6000 3 = 216 billions and 7210 3 = 374 billion particles, spanning a volume of (7.200 h −1 Gpc) 3 and (10.815 h −1 Gpc) 3 , respectively. These simulations improve on our previous Horizon Run 1 (HR1) up to a factor of 4.4 in volume, and range from 2600 to over 8800 times the volume of the Millennium Run. In addition, they achieve a considerably finer mass resolution, down to 1.25 × 10 11 h −1 M ⊙ , allowing to resolve galaxy-size halos with mean particle separations of 1.2h −1 Mpc and 1.5h −1 Mpc, respectively. We have measured the power spectrum, correlation function, mass function and basic halo properties with percent level accuracy, and verified that they correctly reproduce the ΛCDM theoretical expectations, in excellent agreement with linear perturbation theory. Our unprecedentedly large-volume N -body simulations can be used for a variety of studies in cosmology and astrophysics, ranging from large-scale structure topology, baryon acoustic oscillations, dark energy and the characterization of the expansion history of the Universe, till galaxy formation science -in connection with the new SDSS-III. To this end, we made a total of 35 all-sky mock surveys along the past light cone out to z = 0.7 (8 from the HR2 and 27 from the HR3), to simulate the BOSS geometry. The simulations and mock surveys are already publicly available at http://astro.kias.re.kr/Horizon-Run23/.

Large galaxy redshift surveys have long been used to constrain cosmological models and structure formation scenarios. In particular, the largest structures discovered observationally are thought to carry critical information on the amplitude of large-scale density fluctuations or homogeneity of the universe, and have often challenged the standard cosmological framework. The Sloan Great Wall (SGW) recently found in the Sloan Digital Sky Survey (SDSS) region casts doubt on the concordance cosmological model with a cosmological constant (i.e. the flat ΛCDM model). Here we show that the existence of the SGW is perfectly consistent with the ΛCDM model, a result that only our very large cosmological N -body simulation (the Horizon Run 2, HR2) could supply. In addition, we report on the discovery of a void complex in the SDSS much larger than the SGW, and show that such size of the largest void is also predicted in the ΛCDM paradigm. Our results demonstrate that an initially homogeneous isotropic universe with primordial Gaussian random phase density fluctuations growing in accordance with the General Relativity, can explain the richness and size of the observed large-scale structures in the SDSS. Using the HR2 simulation we predict that a future galaxy redshift survey about four times deeper or with 3 magnitude fainter limit than the SDSS should reveal a largest structure of bright galaxies about twice as big as the SGW.

In support of the new Sloan III survey, which will measure the baryon oscillation scale using the luminous red galaxies (LRGs), we have run the largest N-body simulation to date using 4120 3 = 69.9 billion particles, and covering a volume of (6.592 h −1 Gpc) 3 . This is over 2000 times the volume of the Millennium Run, and corner-to-corner stretches all the way to the horizon of the visible universe. LRG galaxies are selected by finding the most massive gravitationally bound, cold dark matter subhalos, not subject to tidal disruption, a technique that correctly reproduces the 3D topology of the LRG galaxies in the Sloan Survey. We have measured the covariance function, power spectrum, and the 3D topology of the LRG galaxy distribution in our simulation and made 32 mock surveys along the past light cone to simulate the Sloan III survey. Our large N-body simulation is used to accurately measure the non-linear systematic effects such as gravitational evolution, redshift space distortion, past light cone space gradient, and galaxy biasing, and to calibrate the baryon oscillation scale and the genus topology. For example, we predict from our mock surveys that the baryon acoustic oscillation peak scale can be measured with the cosmic variance-dominated uncertainty of about 5% when the SDSS-III sample is divided into three equal volume shells, or about 2.6% when a thicker shell with 0.4 < z < 0.6 is used. We find that one needs to correct the scale for the systematic effects amounting up to 5.2% to use it to constrain the linear theories. And the uncertainty in the amplitude of the genus curve is expected to be about 1% at 15 h −1 Mpc scale. We are making the simulation and mock surveys publicly available.

Abstract:The Horizon Run 4 is a cosmological N -body simulation designed for the study of coupled evolution between galaxies and large-scale structures of the Universe, and for the test of galaxy formation models. Using 6300 3 gravitating particles in a cubic box of L box = 3150 h −1 Mpc, we build a dense forest of halo merger trees to trace the halo merger history with a halo mass resolution scale down to M s = 2.7 × 10 11 h −1 M ⊙ . We build a set of particle and halo data, which can serve as testbeds for comparison of cosmological models and gravitational theories with observations. We find that the FoF halo mass function shows a substantial deviation from the universal form with tangible redshift evolution of amplitude and shape. At higher redshifts, the amplitude of the mass function is lower, and the functional form is shifted toward larger values of ln(1/σ). We also find that the baryonic acoustic oscillation feature in the two-point correlation function of mock galaxies becomes broader with a peak position moving to smaller scales and the peak amplitude decreasing for increasing directional cosine µ compared to the linear predictions. From the halo merger trees built from halo data at 75 redshifts, we measure the half-mass epoch of halos and find that less massive halos tend to reach half of their current mass at higher redshifts. Simulation outputs including snapshot data, past lightcone space data, and halo merger data are available at http://sdss.kias.re.kr/astro/Horizon-Run4 .