Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userBispectrum and Nonlinear Biasing of Galaxies: Perturbation Analysis, Numerical Simulation and SDSS Galaxy Clustering
128
0
0.0
(
0
)
Added by
Takahiro Nishimichi
Publication date
2006
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
We consider nonlinear biasing models of galaxies with particular attention to a correlation between linear and quadratic biasing coefficients, b_1 and b_2. We first derive perturbative expressions for b_1 and b_2 in halo and peak biasing models. Then we compute power spectra and bispectra of dark matter particles and halos using N-body simulation data and of volume-limited subsamples of Sloan Digital Sky Survey (SDSS) galaxies, and determine their b_1 and b_2. We find that the values of those coefficients at linear regimes (k<0.2h/Mpc) are fairly insensitive to the redshift-space distortion and the survey volume shape. The resulting normalized amplitudes of bispectra, Q, for equilateral triangles, are insensitive to the values of b_1 implying that b_2 indeed correlates with b_1. The present results explain the previous finding of Kayo et al. (2004) for the hierarchical relation of three-point correlation functions of SDSS galaxies. While the relations between b_1 and b_2 are quantitatively different for specific biasing models, their approximately similar correlations indicate a fairly generic outcome of the biasing due to the gravity in primordial Gaussian density fields.
rate research
Read More
We propose a general formalism for galaxy biasing and apply it to methods for measuring cosmological parameters, such as regression of light versus mass, the analysis of redshift distortions, measures involving skewness and the cosmic virial theorem. The common linear and deterministic relation g=b*d between the density fluctuation fields of galaxies g and mass d is replaced by the conditional distribution P(g|d) of these random fields, smoothed at a given scale at a given time. The nonlinearity is characterized by the conditional mean <g|d>=b(d)*d, while the local scatter is represented by the conditional variance s_b^2(d) and higher moments. The scatter arises from hidden factors affecting galaxy formation and from shot noise unless it has been properly removed. For applications involving second-order local moments, the biasing is defined by three natural parameters: the slope b_h of the regression of g on d, a nonlinearity b_t, and a scatter s_b. The ratio of variances b_v^2 and the correlation coefficient r mix these parameters. The nonlinearity and the scatter lead to underestimates of order b_t^2/b_h^2 and s_b^2/b_h^2 in the different estimators of beta (=Omega^0.6/b_h). The nonlinear effects are typically smaller. Local stochasticity affects the redshift-distortion analysis only by limiting the useful range of scales, especially for power spectra. In this range, for linear stochastic biasing, the analysis reduces to Kaisers formula for b_h (not b_v), independent of the scatter. The distortion analysis is affected by nonlinear properties of biasing but in a weak way. Estimates of the nontrivial features of the biasing scheme are made based on simulations and toy models, and strategies for measuring them are discussed. They may partly explain the range of estimates for beta.
Differences in clustering properties between galaxy subpopulations complicate the cosmological interpretation of the galaxy power spectrum, but can also provide insights about the physics underlying galaxy formation. To study the nature of this relative clustering, we perform a counts-in-cells analysis of galaxies in the Sloan Digital Sky Survey (SDSS) in which we measure the relative bias between pairs of galaxy subsamples of different luminosities and colours. We use a generalized chi-squared test to determine if the relative bias between each pair of subsamples is consistent with the simplest deterministic linear bias model, and we also use a maximum likelihood technique to further understand the nature of the relative bias between each pair. We find that the simple, deterministic model is a good fit for the luminosity-dependent bias on scales above ~2 Mpc/h, which is good news for using magnitude-limited surveys for cosmology. However, the colour-dependent bias shows evidence for stochasticity and/or non-linearity which increases in strength toward smaller scales, in agreement with previous studies of stochastic bias. Also, confirming hints seen in earlier work, the luminosity-dependent bias for red galaxies is significantly different from that of blue galaxies: both luminous and dim red galaxies have higher bias than moderately bright red galaxies, whereas the biasing of blue galaxies is not strongly luminosity-dependent. These results can be used to constrain galaxy formation models and also to quantify how the colour and luminosity selection of a galaxy survey can impact measurements of the cosmological matter power spectrum.
We perform an extensive analysis of nonlinear and stochastic biasing of galaxies and dark halos in spatially flat low-density CDM universe using cosmological hydrodynamic simulations. We compare their biasing properties with the predictions of an analytic halo biasing model. Dark halos in our simulations exhibit reasonable agreement with the predictions only on scales larger than 10h^{-1}Mpc, and on smaller scales the volume exclusion effect of halos due to their finite size becomes substantial. Interestingly the biasing properties of galaxies are better described by extrapolating the halo biasing model predictions. We also find the clear dependence of galaxy biasing on their formation epoch; the distribution of old populations of galaxies tightly correlates with the underlying mass density field, while that of young populations is slightly more stochastic and anti-biased relative to dark matter. The amplitude of two-point correlation function of old populations is about 3 times larger than that of the young populations. Furthermore, the old population of galaxies reside within massive dark halos while the young galaxies are preferentially formed in smaller dark halos. Assuming that the observed early and late-type galaxies correspond to the simulated old and young populations of galaxies, respectively, all of these segregations of galaxies are consistent with observational ones for the early and late-type of galaxies such as the morphology--density relation of galaxies.
We formulate the concept of non-linear and stochastic galaxy biasing in the framework of halo occupation statistics. Using two-point statistics in projection, we define the galaxy bias function, b_g(r_p), and the galaxy-dark matter cross-correlation function, R_{gm}(r_p), where r_p is the projected distance. We use the analytical halo model to predict how the scale dependence of b_g and R_{gm}, over the range 0.1 Mpc/h < r_p < 30 Mpc/h, depends on the non-linearity and stochasticity in halo occupation models. In particular we quantify the effect due to the presence of central galaxies, the assumption for the radial distribution of satellite galaxies, the richness of the halo, and the Poisson character of the probability to have a certain number of satellite galaxies in a halo of a certain mass. Overall, brighter galaxies reveal a stronger scale dependence, and out to a larger radius. In real-space, we find that galaxy bias becomes scale independent, with R_{gm} = 1, for radii r > 1 - 5 Mpc/h, depending on luminosity. However, galaxy bias is scale-dependent out to much larger radii when one uses the projected quantities defined in this paper. These projected bias functions have the advantage that they are more easily accessible observationally and that their scale dependence carries a wealth of information regarding the properties of galaxy biasing. To observationally constrain the parameters of the halo occupation statistics and to unveil the origin of galaxy biasing we propose the use of the bias function Gamma_{gm}(r_p)=b_g(r_p)/R_{gm}(r_p). This function is obtained via a combination of weak gravitational lensing and galaxy clustering, and it can be measured using existing and forthcoming imaging and spectroscopic galaxy surveys.
The apparent anisotropies of the galaxy clustering in observable redshift space provide a unique opportunity to simultaneously probe cosmic expansion and gravity on cosmological scales via the Alcock--Paczynski effect and redshift-space distortions. While the improved theoretical models have been proposed and developed to describe the apparent anisotropic clustering at weakly non-linear scales, the applicability of these models is still limited in the presence of the non--perturbative smearing effect caused by the randomness of the relative velocities. Although the cosmological constraint from the anisotropic clustering will be certainly improved with a more elaborate theoretical model, we here consider an alternative way by using the statistical power of both the power spectrum and bispectrum at large scales. Based on the Fisher matrix analysis, we estimate the benefit of combining the power spectra and bispectra, finding that the constraints on the cosmic expansion and growth of structure will be improved by a factor of two. This compensates for the loss of constraining power using the power spectrum alone due to the randomness of the relative velocities.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
