Intrinsic correlation of halo ellipticity and its implications for large-scale weak lensing surveys

We use a large set of state-of-the-art cosmological N-body simulations [512^3 particles] to study the intrinsic ellipticity correlation functions of halos. With the simulations of different resolutions, we find that the ellipticity correlations converge once the halos have more than 160 members. For halos with fewer members, the correlations are underestimated, and the underestimation amounts to a factor of 2 when the halos have only 20 particles. After correcting for the resolution effects, we show that the ellipticity correlations of halos in the bigger box (L=300 mpc) agree very well with those obtained in the smaller box (L=100 mpc). Combining these results from the different simulation boxes, we present accurate fitting formulae for the ellipticity correlation function c_{11}(r) and for the projected correlation functions Sigma_{11}(r_p) and Sigma_{22}(r_p) over three orders of magnitude in halo mass. The latter two functions are useful for predicting the contribution of the intrinsic correlations to deep lensing surveys. With reasonable assumptions for the redshift distribution of galaxies and for the mass of galaxies, we find that the intrinsic ellipticity correlation can contribute significantly not only to shallow surveys but also to deep surveys. Our results indicate that previous similar studies significantly underestimated this contribution for their limited simulation resolutions.Comment: 5 pages with 3 figures; minor revisions, accepted for publication in MNRAS (Letters

The density profile of equilibrium and non-equilibrium dark matter halos

We study the diversity of the density profiles of dark matter halos based on a large set of high-resolution cosmological simulations of 256^3 particles. The cosmological models include four scale-free models and three representative cold dark matter models. The simulations have good force resolution, and there are about 400 massive halos with more than 10^4 particles within the virial radius in each cosmological model. Our unbiased selection of all massive halos enables to quantify how well the bulk of dark matter halos can be described by the Navarro, Frenk & White (NFW) profile which was established for equilibrium halos. We find that about seventy percent of the halos can be fitted by the NFW profile with a fitting residual dvi_{max} less than 30% in Omega_0=1 universes. This percentage is higher in lower density cosmological models. The rest of the halos exhibits larger deviations from the NFW profile for more significant internal substructures. There is a considerable amount of variation in the density profile even for the halos which can be fitted by the NFW profile (i.e. dvi_{max}<0.30). The distribution of the profile parameter, the concentration $c$, can be well described by a lognormal function with the mean value \bar c slightly smaller (15%) than the NFW result and the dispersion \sigma_c in \ln c about 0.25. The more virialized halos with dvi_{max}<0.15 have the mean value \bar c in good agreement with the NFW result and a slightly smaller dispersion \sigma_c (about 0.2). Our results can alleviate some of the conflicts found recently between the theoretical NFW profile and observational results. Implications for theoretical and observational studies of galaxy formation are discussed.Comment: The final version accepted for publication in ApJ; one figure and one paragraph added to demonstrate that all the conclusions of the first version are solid to the resoltuion effects; 19 pages with 6 figure

Determine the galaxy bias factors on large scales using bispectrum method

We study whether the bias factors of galaxies can be unbiasedly recovered from their power spectra and bispectra. We use a set of numerical N-body simulations and construct large mock galaxy catalogs based upon the semi-analytical model of Croton et al. (2006). We measure the reduced bispectra for galaxies of different luminosity, and determine the linear and first nonlinear bias factors from their bispectra. We find that on large scales down to that of the wavenumber k=0.1h/Mpc, the bias factors b1 and b2 are nearly constant, and b1 obtained with the bispectrum method agrees very well with the expected value. The nonlinear bias factor b2 is negative, except for the most luminous galaxies with M<-23 which have a positive b2. The behavior of b2 of galaxies is consistent with the b2 mass dependence of their host halos. We show that it is essential to have an accurate estimation of the dark matter bispectrum in order to have an unbiased measurement of b1 and b2. We also test the analytical approach of incorporating halo occupation distribution to model the galaxy power spectrum and bispectrum. The halo model predictions do not fit the simulation results well on the precision requirement of current cosmological studies.Comment: 9 pages, 8 figures, accepted for publication in Ap

Modelling galaxy stellar mass evolution from z~0.8 to today

We apply the empirical method built for z=0 in the previous work of Wang et al. to a higher redshift, to link galaxy stellar mass directly with its hosting dark matter halo mass at z~0.8. The relation of the galaxy stellar mass and the host halo mass M_infall is constrained by fitting both the stellar mass function and the correlation functions at different stellar mass intervals of the VVDS observation, where M_infall is the mass of the hosting halo at the time when the galaxy was last the central galaxy. We find that for low mass haloes, their residing central galaxies are less massive at high redshift than those at low redshift. For high mass haloes, central galaxies in these haloes at high redshift are a bit more massive than the galaxies at low redshift. Satellite galaxies are less massive at earlier times, for any given mass of hosting haloes. Fitting both the SDSS and VVDS observations simultaneously, we also propose a unified model of the M_stars-M_infall relation, which describes the evolution of central galaxy mass as a function of time. The stellar mass of a satellite galaxy is determined by the same M_stars-M_infall relation of central galaxies at the time when the galaxy is accreted. With these models, we study the amount of galaxy stellar mass increased from z~0.8 to the present day through galaxy mergers and star formation. Low mass galaxies gain their stellar masses from z~0.8 to z=0 mainly through star formation. For galaxies of higher mass, the increase of stellar mass solely through mergers from z=0.8 can make the massive galaxies a factor ~2 larger than observed at z=0. We can also predict stellar mass functions of redshifts up to z~3, and the results are consistent with the latest observations.Comment: 12 pages, 10 figures, accepted for publication in MNRA

The Scaling of the Redshift Power Spectrum: Observations from the Las Campanas Redshift Survey

In a recent paper we have studied the redshift power spectrum $P^S(k,\mu)$ in three CDM models with the help of high resolution simulations. Here we apply the method to the largest available redshift survey, the Las Campanas Redshift Survey (LCRS). The basic model is to express $P^S(k,\mu)$ as a product of three factors P^S(k,\mu)=P^R(k)(1+\beta\mu^2)^2 D(k,\mu). Here $\mu$ is the cosine of the angle between the wave vector and the line of sight. The damping function $D$ for the range of scales accessible to an accurate analysis of the LCRS is well approximated by the Lorentz factor D=[1+{1\over 2}(k\mu\sigma_{12})^2]^{-1}. We have investigated different values for $\beta$ ($\beta=0.4$, 0.5, 0.6), and measured $P^R(k)$ and $\sigma_{12}(k)$ from $P^S(k,\mu)$ for different values of $\mu$. The velocity dispersion $\sigma_{12}(k)$ is nearly a constant from $k=0.5$ to 3 \mpci. The average value for this range is 510\pm 70 \kms. The power spectrum $P^R(k)$ decreases with $k$ approximately with $k^{-1.7}$ for $k$ between 0.1 and 4 \mpci. The statistical significance of the results, and the error bars, are found with the help of mock samples constructed from a large set of high resolution simulations. A flat, low-density ($\Omega_0=0.2$) CDM model can give a good fit to the data, if a scale-dependent special bias scheme is used which we have called the cluster-under-weighted bias (Jing et al.).Comment: accepted for publication in MNRAS, 20 pages with 7 figure