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Register a new userGenus statistics using the Delaunay tessellation field estimation method: (I) tests with the Millennium Simulation and the SDSS DR7
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We study the topology of cosmic large-scale structure through the genus statistics, using galaxy catalogues generated from the Millennium Simulation and observational data from the latest Sloan Digital Sky Survey Data Release (SDSS DR7). We introduce a new method for constructing galaxy density fields and for measuring the genus statistics of its isodensity surfaces. It is based on a Delaunay tessellation field estimation (DTFE) technique that allows the definition of a piece-wise continuous density field and the exact computation of the topology of its polygonal isodensity contours, without introducing any free numerical parameter. Besides this new approach, we also employ the traditional approaches of smoothing the galaxy distribution with a Gaussian of fixed width, or by adaptively smoothing with a kernel that encloses a constant number of neighboring galaxies. Our results show that the Delaunay-based method extracts the largest amount of topological information. Unlike the traditional approach for genus statistics, it is able to discriminate between the different theoretical galaxy catalogues analyzed here, both in real space and in redshift space, even though they are based on the same underlying simulation model. In particular, the DTFE approach detects with high confidence a discrepancy of one of the semi-analytic models studied here compared with the SDSS data, while the other models are found to be consistent.
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The Millennium N-body simulation and the Sloan Digital Sky Survey seventh data release (SDSS DR7) galaxy and galaxy group catalogues are compared to study the properties of galaxy groups and the distribution of galaxies in groups. We construct mock galaxy group catalogues for a Millennium semi-analytical galaxy catalogue by using the same friends-of-friends method, which was used by Tago et al to analyse the SDSS data. We analyse in detail the group luminosities, group richnesses, virial radii, sizes of groups and their rms velocities for four volume-limited samples from observations and simulations. Our results show that the spatial densities of groups agree within one order of magnitude in all samples with a rather good agreement between the mock catalogues and observations. All group property distributions have similar shapes and amplitudes for richer groups. For galaxy pairs and small groups, the group properties for observations and simulations are clearly different. In addition, the spatial distribution of galaxies in small groups is different: at the outskirts of the groups the galaxy number distributions do not agree, although the agreement is relatively good in the inner regions. Differences in the distributions are mainly due to the observational limitations in the SDSS sample and to the problems in the semi-analytical methods that produce too compact and luminous groups.
Based on galaxies from the Sloan Digital Sky Survey (SDSS) and subhalos in the corresponding reconstructed region from the constrained simulation of ELUCID, we study the alignment of central galaxies relative to their host groups in the group catalog, as well as the alignment relative to the corresponding subhalos in the ELUCID simulation. Galaxies in observation are matched to dark matter subhalos in the ELUCID simulation using a novel neighborhood abundance matching method. In observation, the major axes of galaxies are found to be preferentially aligned to the major axes of their host groups. There is a color dependence of galaxy-group alignment that red centrals have a stronger alignment along the major axes of their host groups than blue centrals. Combining galaxies in observation and subhalos in the ELUCID simulation, we also find that central galaxies have their major axes to be aligned to the major axes of their corresponding subhalos in the ELUCID simulation. We find that the galaxy-group and galaxy-subhalo alignment signals are stronger for galaxies in more massive halos. We find that the alignments between main subhalos and the SDSS matched subhalo systems in simulation are slightly stronger than the galaxy-group alignments in observation.
Using a sample of spiral galaxies selected from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7) and Galaxy Zoo 2 (GZ2), we investigate the alignment of spin axes of spiral galaxies with their surrounding large scale structure, which is characterized by the large-scale tidal field reconstructed from the data using galaxy groups above a certain mass threshold. We find that the spin axes of only have weak tendency to be aligned with (or perpendicular to) the intermediate (or minor) axis of the local tidal tensor. The signal is the strongest in a cluster environment where all the three eigenvalues of the local tidal tensor are positive. Compared to the alignments between halo spins and local tidal field obtained in N-body simulations, the above observational results are in best agreement with those for the spins of inner regions of halos, suggesting that the disk material traces the angular momentum of dark matter halos in the inner regions.
We present validation tests of emulator-based halo model method for cosmological parameter inference, assuming hypothetical measurements of the projected correlation function of galaxies, $w_{rm p}(R)$, and the galaxy-galaxy weak lensing, $Delta!Sigma(R)$, from the spectroscopic SDSS galaxies and the Hyper Suprime-Cam Year1 (HSC-Y1) galaxies. To do this, we use textsc{Dark Emulator} developed in Nishimichi et al. based on an ensemble of $N$-body simulations, which is an emulation package enabling a fast, accurate computation of halo clustering quantities for flat-geometry $w$CDM cosmologies. Adopting the halo occupation distribution, the emulator allows us to obtain model predictions of $Delta!Sigma$ and $w_{rm p}$ for the SDSS-like galaxies at a few CPU seconds for an input set of parameters. We present performance and validation of the method by carrying out Markov Chain Monte Carlo analyses of the mock signals measured from a variety of mock catalogs that mimic the SDSS and HSC-Y1 galaxies. We show that the halo model method can recover the underlying true cosmological parameters to within the 68% credible interval, except for the mocks including the assembly bias effect (although we consider the unrealistically-large amplitude of assembly bias effect). Even for the assembly bias mock, we demonstrate that the cosmological parameters can be recovered {it if} the analysis is restricted to scales $Rgtrsim 10~h^{-1}{rm Mpc}$. We also show that, by using a single population of source galaxies to infer the relative strengths of $Delta!Sigma$ for multiple lens samples at different redshifts, the joint probes method allows for self-calibration of photometric redshift errors and multiplicative shear bias. Thus we conclude that the emulator-based halo model method can be safely applied to the HSC-Y1 dataset, achieving a precision of $sigma(S_8)simeq 0.04$.
There have been a number of studies dedicated to identification of fossil galaxy groups, arguably groups with a relatively old formation epoch. Most of such studies identify fossil groups, primarily based on a large luminosity gap, which is the magnitude gap between the two most luminous galaxies in the group. Studies of these types of groups in the millennium cosmological simulations show that, although they have accumulated a significant fraction of their mass, relatively earlier than groups with a small luminosity gap, this parameter alone is not highly efficient in fully discriminating between the old and young galaxy groups, a label assigned based on halo mass accumulation history. We study galaxies drawn from the semi-analytic models of Guo et al. (2011), based on the Millennium Simulation. We establish a set of four observationally measurable parameters which can be used in combination, to identify a subset of galaxy groups which are old, with a very high probability. We thus argue that a sample of fossil groups selected based on luminosity gap will result in a contaminated sample of old galaxy groups. By adding constraints on the luminosity of the brightest galaxy, and its offset from the group luminosity centroid, we can considerably improve the age-dating.
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