Hideki Yahagi

Clustering of Lyman Break Galaxies at z = 4 and 5 in the Subaru Deep Field: Luminosity Dependence of the Correlation Function Slope

We explored the clustering properties of Lyman break galaxies at z = 4 and 5 with an angular two-point correlation function on the basis of the very deep and wide Subaru Deep Field data. We confirmed the previous result that the clustering strength of LBGs depends on the UV luminosity in the sense that brighter LBGs are more strongly clustered. In addition, we found an apparent dependence of the correlation function slope on UV luminosity for LBGs at both z = 4 and 5. More luminous LBGs have a steeper correlation function. The bias parameter was found to be a scale-dependent function for bright LBGs, whereas it appears to be almost scale-independent for faint LBGs. Luminous LBGs have a higher bias at smaller angular scales, which decreases as the scale increases. To compare these observational results, we constructed numerical mock LBG catalogs based on a semianalytic model of hierarchical clustering combined with high-resolution N-body simulation, carefully mimicking the observational selection effects. The luminosity functions and the overall correlation functions for LBGs at z = 4 and 5 predicted by this mock catalog were found to be almost consistent with the observation. The observed dependence of the clustering on UV luminosity was not reproduced by the model, unless subsamples of distinct halo mass were considered. That is, LBGs belonging to more massive dark halos had steeper and larger amplitude correlation functions. With this model, we found that LBG multiplicity in massive dark halos amplifies the clustering strength at small scales, which steepens the correlation function. The hierarchical clustering model could therefore be reconciled with the observed luminosity dependence of the correlation function if there is a tight correlation between UV luminosity and halo mass. Our finding that the slope of the correlation function depends on luminosity could be an indication that massive dark halos hosted multiple bright LBGs.

The origin of globular cluster systems from cosmological simulations

We investigate the structural, kinematical and chemical properties of globular cluster systems (GCSs) in galaxies of different Hubble types in a self-consistent manner based on high-resolution cosmological N-body simulations combined with semi-analytic models of galaxy and globular cluster (GC) formation. We focus on correlations between the physical properties of GCSs and those of their host galaxies for ∼10 5 simulated galaxies located at the centres of dark matter haloes (i.e. we do not consider satellite galaxies in subhaloes). Our principal results, which can be tested against observations, are as follows. The majority (∼90 per cent) of GCs currently in haloes are formed in low-mass galaxies at redshifts greater than 3 with mean formation redshifts of z = 5.7 (12.7Gyr ago) and 4.3 (12.3Gyr ago) for metal-poor GCs (MPCs) and metal-rich GCs (MRCs), respectively. About 52 per cent of galaxies with GCs show clear bimodality in their metallicity distribution functions, though less luminous galaxies with M B fainter than -17 are much less likely to show bimodality owing to little or no MRCs. The number fraction of MRCs does not depend on Hubble type but is generally smaller for less luminous galaxies. The specific frequencies (S N ) of GCSs are typically higher in ellipticals (S N ∼ 4.0) than in spirals (S N ∼ 1.8), and higher again (S N ∼ 5.0) for galaxies located at the centres of clusters of galaxies. The total number of GCs per unit halo mass does not depend strongly on M B or Hubble type of the host galaxy. The mean metallicities of MPCs and MRCs depend on M B such that they are higher in more luminous galaxies, though the dependence is significantly weaker for MPCs. The spatial distributions of MRCs are more compact than those of MPCs and we find that the half-number radii of MPCs (r e,mpc ) correlate with the halo masses (M h ) such that r e,mpc oc M h 0.18 . There is no significant difference in velocity dispersions between MPCs and MRCs. We qualitatively compare our results to observational data where possible. Finally, we discuss these results in the wider context of galaxy formation and evolution.

MASS FUNCTION OF LOW-MASS DARK HALOS

The mass function of dark halos in a Λ-dominated cold dark matter universe is investigated. We analyze 529 output files from five runs of N-body simulations using the friends-of-friends cluster finding algorithm. All the runs use 5123 particles in the box size of 35-140 h-1 Mpc. Mass of particles for 35 h-1 Mpc runs is 2.67 × 107 h-1 M☉. Because of the high-mass resolution of our simulations, the multiplicity function in the low-mass range, where the mass is well below the characteristic mass and ν = δc/σ 1.0, is evaluated in the present work, and it is well fitted by the functional form (ST) proposed by Sheth & Tormen. However, the maximum value of the multiplicity function from our simulations at ν ~ 1 is smaller, and its low-mass tail is shallower when compared with the ST multiplicity function.

N-Body Code with Adaptive Mesh Refinement

We have developed a simulation code with the techniques that enhance both spatial and time resolution of the particle-mesh (PM) method, for which the spatial resolution is restricted by the spacing of structured mesh. The adaptive-mesh refinement (AMR) technique subdivides the cells that satisfy the refinement criterion recursively. The hierarchical meshes are maintained by the special data structure and are modified in accordance with the change of particle distribution. In general, as the resolution of the simulation increases, its time step must be shortened and more computational time is required to complete the simulation. Since the AMR enhances the spatial resolution locally, we reduce the time step locally also, instead of shortening it globally. For this purpose, we used a technique of hierarchical time steps (HTS), which changes the time step, from particle to particle, depending on the size of the cell in which particles reside. Some test calculations show that our implementation of AMR and HTS is successful. We have performed cosmological simulation runs based on our code and found that many of halo objects have density profiles that are well fitted to the universal profile proposed in 1996 by Navarro, Frenk, & White over the entire range of their radius.

Formation of intracluster globular clusters

We first present the results of numerical simulations on formation processes and physical properties of old globular clusters (GCs) located within clusters of galaxies (‘intracluster GCs’) and in between clusters of galaxies (‘intercluster GCs’). Our high-resolution cosmological simulations with models of GC formation at high redshifts (z > 6) show that about 30 per cent of all GCs in a rich cluster can be regarded as intracluster GCs that can freely drift, being trapped by gravitational potential of the cluster rather than by the cluster member galaxies. The radial surface density profiles of the simulated intracluster GCs are highly likely to be flatter than those of GCs within cluster member galaxies. We also find that about 1 per cent of all GCs formed before z > 6 are not located within any virialized haloes and can be regarded as ‘intercluster’ (or ‘intergalactic’) GCs. We discuss the dependencies of the physical properties of intracluster and intercluster GCs on the initial density profiles of GCs within low-mass dark matter haloes at high redshifts (z > 6).

Panoramic Views of Cluster-Scale Assemblies Explored by Subaru Wide-Field Imaging

We have started PISCES project; a panoramic imaging and spectroscopic survey of distant clusters on Subaru. It exploits the unique wide-field imaging capability of Suprime-Cam, which provides a 34 � × 27 � field of view corresponding to a physical area of 16 ×13Mpc 2 at z ∼ 1. We plan to target 15 clusters at 0.4 z 1.3. We report on our first results concerning the inner structures and large-scale structures of two distant clusters at z = 0.55 and 0.83 together with the earlier results on a z =0 .41 cluster. The photometric redshift technique has been applied to multi-color data in order to remove most of the foreground/background galaxies so as to isolate the cluster member candidates. We have found large-scale filamentary structures around the clusters, extending out to > 5Mpc from the cores, as well as complex inner structures. The galaxy distributions in the inner regions of the clusters look similar to the X-ray intensity maps, suggesting that most of the optical structures trace physically bound systems. We also compared the structures of the three clusters with those of model clusters in a numerical simulation (N-body + semi-analytic model) by parameterising the shapes of the iso-density contours of galaxies, and found a broad agreement. Our results that cluster-scale assembly takes place along filaments during hierarchical clustering need to be confirmed spectroscopically in the near future.

The radial alignment of dark matter subhaloes: from simulations to observations

We explore the radial alignment of subhalos in 2-dimensional projections of cosmological simulations. While most other recent studies focussed on quantifying the signal utilizing the full 3-dimensional spatial information any comparison to observational data has to be done in projection along random lines-of-sight. We have a suite of well resolved host dark matter halos at our disposal ranging from 6× 10 14 h −1 M⊙ down to 6× 10 13 h −1 M⊙. For these host systems we do observe that the major axis of the projected 2D mass distribution of subhalos aligns with its (projected) distance vector to the host’s centre. The signal is actually stronger than the observed alignment. However, when considering only the innermost 10-20% of the subhalo’s particles for the 2D shape measurement we recover the observed correlation. We further acknowledge that this signal is independent of subhalo mass.

The Forest Method as a New Parallel Tree Method with the Sectional Voronoi Tessellation

We have developed a new parallel tree method which will be called the forest method hereafter. This new method uses the sectional Voronoi tessellation (SVT) for the domain decomposition. The SVT decomposes a whole space into polyhedra and allows their flat borders to move by assigning different weights. The forest method determines these weights based on the load balancing among processors by means of the overload diffusion (OLD). Moreover, since all the borders are flat, before receiving the data from other processors, each processor can collect enough data to calculate the gravity force with precision. Both the SVT and the OLD are coded in a highly vectorizable manner to accommodate on vector parallel processors. The parallel code based on the forest method with the Message Passing Interface is run on various platforms so that a wide portability is guaranteed. Extensive calculations with 15 processors of Fujitsu VPP300/16R indicate that the code can calculate the gravity force exerted on 105 particles in each second for some ideal dark halo. This code is found to enable an N-body simulation with 107 or more particles for a wide dynamic range and is therefore a very powerful tool for the study of galaxy formation and large-scale structure in the universe.

The U-shaped distribution of globular cluster-specific frequencies in a biased globular cluster formation scenario

Using high-resolution numerical simulations, we investigate mass- and luminosity-normalized specific frequencies (TN and SN, respectively) of globular cluster systems (GCSs) in order to understand the origin of the observed U-shaped relation between SN and the V-band magnitude (MV) of their host galaxies. We adopt a biased GC formation scenario in which GC formation is truncated in galaxy halos that are virialized at a later redshift, ztrun. TN is derived for galaxies with present-day GCs and converted into SN for reasonable galaxy mass-to-light ratios (M/L). We find that TN depends on halo mass (Mh) in the sense that TN can be larger in more massive halos with Mh > 109 M☉, if ztrun is as high as 15. However, we find that the dependence is too weak to explain the observed SN-MV relation and the wide range of SN in low-mass early-type galaxies with -20.5 mag < MV < -16.0 mag for a reasonable constant M/L. The MV dependence of SN for the low-mass galaxies can be well reproduced, if the mass-to-light ratio Mh/LV ∝ M, where α is as steep as -1. Based on these results, we propose that the origin of the observed U-shaped SN-MV relation of GCSs can be understood in terms of the bimodality in the dependence of Mh/LV on Mh of their host galaxies. We also suggest that the observed large dispersion in SN in low-mass galaxies is due partly to the large dispersion in TN.

Vectorization and Parallelization of the Adaptive Mesh Refinement N-Body Code

We describe our vectorized and parallelized adaptive mesh refinement (AMR) N-body code with shared time steps, and report its performance on a Fujitsu VPP5000 vector-parallel supercomputer. Our AMR N-body code puts hierarchical meshes recursively where higher resolution is required and the time step of all particles are the same. The parts that are the most difficult to vectorize are loops that access the mesh data and particle data. We vectorized such parts by changing the loop structure, so that the innermost loop steps through the cells instead of the particles in each cell, in other words, by changing the loop order from the depth-first order to the breadth-first order. We also parallelized our code for distributed memory machines. The important part of parallelization is data decomposition. We sorted the hierarchical mesh data by the Morton order, or the recursive N-shaped order, level by level and split and allocated the mesh data to the processors. Particles are allocated to the processor to which the finest refined cells including the particles are also assigned. Our timing analysis using Λ-dominated cold dark matter simulations shows that our parallel code speeds up almost ideally up to 32 processors, the largest number of processors in our test.