arXiv subjects

Li-Zhi Fang

Publications and source records attributed to Li-Zhi Fang.

At least 73 records · Page 4Linked to original sources

arXiv2000

Measuring the galaxy power spectrum and scale-scale correlations with multiresolution-decomposed covariance -- I. method

We present a method of measuring galaxy power spectrum based on the multiresolution analysis of the discrete wavelet transformation (DWT). Since the DWT representation has strong capability of suppressing the off-diagonal components of the covariance for selfsimilar clustering, the DWT covariance for popular models of the cold dark matter cosmogony generally is diagonal, or $j$(scale)-diagonal in the scale range, in which the second scale-scale correlations are weak. In this range, the DWT covariance gives a lossless estimation of the power spectrum, which is equal to the corresponding Fourier power spectrum banded with a logarithmical scaling. In the scale range, in which the scale-scale correlation is significant, the accuracy of a power spectrum detection depends on the scale-scale or band-band correlations. This is, for a precision measurements of the power spectrum, a measurement of the scale-scale or band-band correlations is needed. We show that the DWT covariance can be employed to measuring both the band-power spectrum and second order scale-scale correlation. We also present the DWT algorithm of the binning and Poisson sampling with real observational data. We show that the alias effect appeared in usual binning schemes can exactly be eliminated by the DWT binning. Since Poisson process possesses diagonal covariance in the DWT representation, the Poisson sampling and selection effects on the power spectrum and second order scale-scale correlation detection are suppressed into minimum. Moreover, the effect of the non-Gaussian features of the Poisson sampling can be calculated in this frame.

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arXiv2000

Non-Gaussianity and the recovery of the mass power spectrum from the Ly$α$ forest

We investigate the effect of non-Gaussianity on the reconstruction of the initial mass field from the Ly$α$ forest. We show that the transmitted flux of QSO absorption spectra are highly non-Gaussian in terms of the statistics, the kurtosis spectrum and scale-scale correlation. These non-Gaussianities can not be completely removed by the conventional algorithm of Gaussianization, and the scale-scale correlations are largely retained in the mass field recovered by the Gaussian mapping. Therefore, the mass power spectrum recovered by the conventional algorithm is systematically lower than the initial mass spectrum on scales at which the local scale-scale correlation is substantial. To reduce the non-Gaussian contamination, we present two methods. The first is to perform the Gaussianization scale-by-scale using the discrete wavelet transform (DWT) decomposition. We show that the non-Gaussian features of the Ly$α$ forest basically will no longer exist in the scale-by-scale Gaussianized mass field. The second method is to choose a proper orthonormal basis (representation) to suppress the effect of the non-Gaussian correlations. In the quasilinear regime of cosmic structure formation, the DWT power spectrum is efficient for suppressing the non-Gaussian contamination. These two methods significantly improve the recovery of the mass power spectrum from the Ly$α$ forest.

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arXiv1999

The origin of scale-scale correlations of the density perturbations during inflation

We show that scale-scale correlations are a generic feature of slow-roll inflation theories. These correlations result from the long-time tails characteristic of the time dependent correlations because the long wavelength density perturbation modes are diffusion-like. A relationship between the scale-scale correlations and time-correlations is established providing a way to reveal the time correlations of the perturbations during inflation. This mechanism provides for a testable prediction that the scale-scale correlations at two different spatial points will vanish.

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arXiv1999

Virialization of Galaxy Clusters and Beyond

Using samples of structures identified by a multi-scale decomposition from numerical simulation, we analyze the scale-dependence of the virialization of clusters. We find that beyond the scale of full virialization there exists a radius range over which clusters are quasi-virialized, i.e. while the internal structure of an {\it individual} cluster is at substantial departure from dynamical relaxation, some {\it statistical} properties of the multi-scale identified clusters are approximately the same as those for the virialized systems. The dynamical reason of the existence of quasi-virialization is that some of the scaling properties of dynamically relaxed systems of cosmic gravitational clustering approximately hold beyond the full virialization regime. The "individual-statistical" duality of the quasi-virialization provides an explanation of the observed puzzle that the total masses of clusters derived from virial theorem are statistically the same as the gravitational lensing determined masses, in spite of the presence of irregular configuration and substructures in individual clusters. It also explains the tight correlation between the velocity dispersion of optical galaxies and the temperature of X-ray emitting gas. Consequently, the virial mass estimators based on the assumptions of isothermal and hydrostatic model are statistically applicable to scales on which the clusters are quasi-virialized. In the quasi-virialization regime, the temperature functions of clusters also show scaling. This feature is a useful discriminator among cosmological models.

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arXiv1999

Breaking Degeneracy of Dark Matter Models by the Scale-Scale Correlations of Galaxies

Recently, scale-scale correlations have been detected in the distributions of quasar's Ly$α$ absorption lines and the maps of cosmic temperature fluctuations. In this paper, we investigate the scale-scale correlations in galaxy distributions. Using samples of mass field given by N-body simulation, we first show that the scale-scale correlation of 2-D and 3-D mass distributions at present day is capable of breaking the degeneracy between the SCDM (standard cold dark matter model) and OCDM (open CDM model) or LCDM (flat CDM model), and even show the difference between the OCDM and LCDM. Using biased galaxy samples produced in an appropriate bias model, we show that the scale-scale correlation of galaxy distribution at zero redshift is still a powerful tool to break the degeneracy in the parameter space, including both cosmological and biasing parameters. We analyze the scale-scale correlations of the APM bright galaxy catalog, and compare it with the mock catalog in the SCDM, OCDM and LCDM models. We find that all the spectra of local and non-local scale-scale correlations predicted by the OCDM model are in excellent agreement with those of the APM-BGC sample, while the SCDM and LCDM mock catalog appear to have somewhat weaker scale-scale correlations than the observation.

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arXiv1999

The Flatness of Mass-to-Light Ratio on Large Scales

It has been suggested that the mass-to-light ($M/L$) ratio of gravitationally clustering objects is scale-independent on scales beyond galaxy clusters, and may also be independent of the mass of the objects. In this paper, we show that the scale behavior of $M/L$ ratio is closely related to the scaling of cosmic structures larger than clusters. The scale dependence of the $M/L$ ratio can be determined by comparing the observed scaling of richness function (RF) of multi-scale identified objects with the model-predicted scaling of mass function (MF) of large scale structures. Using the multi-scale identified clusters from IRAS 1.2 Jy galaxy survey, we have made comparisons of the observed RF scaling of IRAS $r_{cl}$-clusters with the MF scalings given by simulations of three popular models SCDM, LCDM and OCDM. We find that, the M/L ratio basically is scale-independent from the Abell radius up to about 24 $h^{-1}$Mpc, while it seems to show a slight, but systematical, increase over this scale range. This result is weakly dependent on the cosmological parameters.

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arXiv1999

Abundances and Correlations of Structures Beyond Galaxy Clusters

We investigated the structures on scales beyond the typical clusters of galaxies. These structures are crucial to understand the cosmic gravitational clustering in the pre-virialized stage, or quasilinear règime. Based on the multi-resolution analysis of the discrete wavelet transformation, we got statistical available ensembles of $r_{cl}$-clusters, i.e. the structures on scale $r_{cl}$, in the range $1 \leq r_{cl} \leq 24 h^{-1}$ Mpc for both N-body simulation and the IRAS 1.2 Jy galaxy survey samples. If the mass-to-light ratio on scales larger than clusters asymptotically reaches a constant, we found that the abundances and correlations of these IRAS $r_{cl}$-clusters to be basically consistent with the predictions of the flat low-density CDM model (LCDM) and the open CDM model (OCDM), except the model-predicted abundance of $r_{cl} = 24 h^{-1}$ Mpc clusters seems to be higher than IRAS data. The standard CDM (SCDM) gives too much power, and too weak correlations on all the scales. For a given $r_{cl}$, the amplitude of two-point correlation function of $r_{cl}$-clusters is increasing with their richness. However, for a given richness (defined by the mean separation of neighbor objects), the clustering strengths of both simulation and observation sample are found to be declining with $r_{cl}$ when $r_{cl}$ is larger than 3 - 4 $h^{-1}$ Mpc. Therefore, the ``universal'' increase of the correlation amplitude with the scale of objects from galaxies, groups, to poor, rich clusters is broken down for structures of $r_{cl} > 3 - 4 h^{-1}$ Mpc. Supercluster should not be a member of the ``universal'' increase family.

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arXiv1999

Cosmological Constraints on the Host Halos of GRBs

The recently observed bright optical transients(OT) of high redshift GRBs indicate that they are in a violent dynamical state. We think it is reasonable to assume that the GRBs form in the environment of gravitationally collapsed halos of the cosmic matter field, and we investigate the basic parameters of the halos which are favored to host GRBs. If the harboring coefficient $f$ of GRBs per halo is weakly dependent on the mass of the halo, the redshift data of GRB OTs can yield significant constraints on the massive halos hosting GRBs. We show that, in the framework of popular cold dark matter (CDM) models, the GRB-favored environments are newly collapsed halos (i.e. their ages less than about $2 \times 10^9$ yr) with masses around $10^9$ $h^{-1}$ M$_{\odot}$. In this scenario, low redshift GRBs, if they exist, could not have the same cosmic origin as the high redshift ones. To fit with the observed rate of GRBs, we conclude that each GRB halo can host probably no more than one GRB event on average. This result implies that GRBs may be related to the merging of the halos.

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arXiv1999

The Lx-T and Lx-sigma Relationships for Galaxy Clusters Revisited

The relationships between the X-ray determined bolometric luminosity Lx, the temperature T of the intracluster gas, and the optical measured velocity dispersion sigma of the cluster galaxies are updated for galaxy clusters using the largest sample of 256 clusters drawn from literature. The newly established relationships, based on the doubly weighted orthogonal distance regression (ODR) method, are justified by both their self-consistency and co-consistency, which can then be used to test the theoretical models of cluster formation and evolution. The observationally determined Lx-T and Lx-sigma relationships, $L_x\propto T^{2.72\pm0.05}\propto σ^{5.24\pm0.29}$, are marginally consistent with those predicted in the scenario that both intracluster gas and galaxies are in isothermal and hydrostatic equilibrium with the underlying gravitational potential of clusters. A comparison between these observed and predicted Lx-T relationships also suggests that the mean cluster baryon fraction fb remains approximately constant among different clusters, $f_b\approx0.17$, which gives rise to a low-mass density universe of $Ω_m\approx0.3$.

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arXiv1999

Mass Density Perturbations from Inflation with Thermal Dissipation

We study the power spectrum of the mass density perturbations in an inflation scenario that includes thermal dissipation. We show that the condition on which the thermal fluctuations dominate the primordial density perturbations can easily be realized even for weak dissipation, i.e., the rate of dissipation is less than the Hubble expansion. We find that our spectrum of primordial density perturbations follows a power law behavior, and exhibits a ``thermodynamical'' feature -- the amplitude and power index of the spectrum depend mainly on the thermodynamical variable $M$, the inflation energy scale. Comparing this result with the observed temperature fluctuations of the cosmic microwave background, we find that both amplitude and index of the power spectrum can be fairly well fitted if $M \sim 10^{15}-10^{16}$ GeV.

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arXiv1998

Evidence for Scale-Scale Correlations in the Cosmic Microwave Background Radiation

We perform a discrete wavelet analysis of the COBE-DMR 4yr sky maps and find a significant scale-scale correlation on angular scales from about 11 to 22 degrees, only in the DMR face centered on the North Galactic Pole. This non-Gaussian signature does not arise either from the known foregrounds or the correlated noise maps, nor is it consistent with upper limits on the residual systematic errors in the DMR maps. Either the scale-scale correlations are caused by an unknown foreground contaminate or systematic errors on angular scales as large as 22 degrees, or the standard inflation plus cold dark matter paradigm is ruled out at the $> 99%$ confidence level.

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arXiv1998

Detecting the non-Gaussian Spectrum of QSO's Ly$α$ Absorption Line Distribution

We present an analysis of the non-Gaussianity in the distribution of Ly$α$ forest lines in the QSO absorption spectra. Statistical tests performed on this data indicate that there may be large scale structure even though the power spectrum of the Ly$α$ line distribution on large scales is found to be flat. It is apparent that higher (than two) order statistics are crucial in quantifying the clustering behavior of Ly$α$ clouds. Using the discrete wavelet on three independent data sets of Ly$α$ forests, we find that the distribution of Ly$α$ forests does show non-Gaussian behavior on scales from 5 to 10 h$^{-1}$ Mpc with confidence level larger than 95%. Two data sets available on large scales are found to be non-Gaussian on even larger scales. These techniques are effective in discriminating among models of the Ly$α$ forest formation, which are degenerate at second and lower order statistics (abridged).

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arXiv1998

Updating the $σ$-$T$ relationship for galaxy clusters

The relationship between the X-ray determined temperature $T$ of the intracluster gas and the optical measured velocity dispersion $σ$ of the cluster galaxies is often believed to be not only a straightforward but also robust test for the dynamical properties of galaxy clusters. Here, we present the $σ$-$T$ relationship using the 94 clusters drawn from the largest sample of 149 clusters in literature, for which both $σ$ and $T$ are observationally determined. Employment of the doubly weighted orthogonal distance regression to our sample yields $σ=10^{2.47\pm0.06}T^{0.67\pm0.09}$, indicating an apparent deviation of dynamical state from that predicted by the isothermal and hydrostatic equilibrium model for galaxy clusters, though the average ratio $β_{spec}$ of specific energy in galaxies to that in gas is found to be in excellent agreement with unity. It shows that a nonisothermal gas distribution with a mean polytropic index of $γ=1.3$ can account for the reported $σ$-$T$ relationship, while overall clusters can still be regarded as dynamically-relaxed systems.

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arXiv1998

A comparison of different cluster mass estimates: consistency or discrepancy ?

Rich and massive clusters of galaxies at intermediate redshift are capable of magnifying and distorting the images of background galaxies. A comparison of different mass estimators among these clusters can provide useful information about the distribution and composition of cluster matter and their dynamical evolution. Using a hitherto largest sample of lensing clusters drawn from literature, we compare the gravitating masses of clusters derived from the strong/weak gravitational lensing phenomena, from the X-ray measurements based on the assumption of hydrostatic equilibrium, and from the conventional isothermal sphere model for the dark matter profile characterized by the velocity dispersion and core radius of galaxy distributions in clusters. While there is an excellent agreement between the weak lensing, X-ray and isothermal sphere model determined cluster masses, these methods are likely to underestimate the gravitating masses enclosed within the central cores of clusters by a factor of 2--4 as compared with the strong lensing results. Such a mass discrepancy has probably arisen from the inappropriate applications of the weak lensing technique and the hydrostatic equilibrium hypothesis to the central regions of clusters as well as an unreasonably large core radius for both luminous and dark matter profiles. Nevertheless, it is pointed out that these cluster mass estimators may be safely applied on scales greater than the core sizes. Namely, the overall clusters of galaxies at intermediate redshift can still be regarded as the dynamically relaxed systems, in which the velocity dispersion of galaxies and the temperature of X-ray emitting gas are good indicators of the underlying gravitational potentials of clusters.

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arXiv1998

Scale Invariance of Rich Cluster Abundance: A Possible Test for Models of Structure Formation

We investigate the dependence of cluster abundance $n(>M,r_{cl})$, i.e., the number density of clusters with mass larger than $M$ within radius $r_{cl}$, on scale parameter $r_{cl}$. Using numerical simulations of clusters in the CDM cosmogonic theories, we notice that the abundance of rich clusters shows a simple scale invariance such that $n[>(r_{cl}/r_0)^αM, r_{cl}]= n(>M,r_0)$, in which the scaling index $α$ remains constant in a scale range where halo clustering is fully developed. The abundances of scale $r_{cl}$ clusters identified from IRAS are found basically to follow this scaling, and yield $α\sim 0.5$ in the range $1.5 < r_{cl} < 4 h^{-1}$Mpc. The scaling gains further supports from independent measurements of the index $α$ using samples of X-ray and gravitational lensing mass estimates. We find that all the results agree within error limit as: $α\sim 0.5 - 0.7$ in the range of $1.5 < r_{cl} < 4 h^{-1}$Mpc. These numbers are in good consistency with the predictions of OCDM ($Ω_M=0.3$) and LCDM ($Ω_M+Ω_Λ =1$), while the standard CDM model has different behavior. The current result seems to favor models with a low mass density.

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arXiv1998

Detecting Scale-Dependence of Bias from APM-BGC Galaxies

We present an investigation of the scale-dependence of bias described by the linear model: $(δρ({\bf x})/\barρ)_{g} = b (δρ(x)/\barρ)_{m}$, $b$ being the bias parameter, and $ρ({\bf x})_{g}$ and $ρ({\bf x})_{m}$ are the galaxy number density and mass density, respectively. Using a discrete wavelet decomposition, we show that the behavior of bias scale-dependence cannot be described by one parameter $b$. In the linear bias model the scale-dependence should be measured by the $j$-spectra of wavelet-coefficient-represented bias parameters $\tilde{b}^{(n)}_j$ and $b_j^{(n)}$, $n$ being positive integers. Because $\tilde{b}^{(n)}_j$ with different $n$ are independent from each other, a systematic analysis of the $j$-spectra of $\tilde{b}^{(n)}_j$ and $b_j^{(n)}$ is necessary. We performed a $j$-spectrum analysis for samples of elliptical and lenticular (EL), and spiral (SP) galaxies listed in the APM bright galaxy catalog. We found that, for statistics of two-point correlation functions or DWT power spectrum, the scale-independence holds within 1 $σ$. However, the bias scale-dependence becomes substantial when phase-sensitive statistics (e.g. $\tilde{b}^{(n)}_j$ with $n>2$ or $b_j^{(n)}$) are applied. These results indicate that the bias scale-dependence has the same origin as the non-Gaussianity of galaxy distributions. This is generally consistent with the explanation that the bias scale-dependence originated from non-linear and non-local relationship between galaxy formation and their environment.

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arXiv1998

Ly-alpha/H-alpha Ratio of Singly Ionized Helium in Quasars

He II Ly-alpha 304/H-alpha 1640 emission lines are mainly produced by recombination, and their canonical ratio of about 10 may be a sensitive reddening indicator. We obtain the high S/N optical spectra of two quasars and combine them with the far-UV spectra that show the He II 304 emission. For HS 1700+64, the He II 1640 emission is not detected, and an upper limit to it sets the ratio greater than 20. For Q0302-003, the ratio is very low, on the order of unity. The most plausible cause for such a low ratio is extinction in the EUV band by very fine grains of dust. Q0302-003 has a prominent narrow component of FWHM ~ 2000 km/s in its major emission lines, and it appears that reddening is associated only with the line-emitting region. We suggest that the geometry of the line-emitting region in high-z quasars resembles that in the low-luminosity active galaxies, with the presence of dust mostly in the outer part.

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arXiv1998

A Possible Bias Model for Quasars

We propose that the majority of quasars at redshift $z\sim 1 - 5$ formed in the environment of new born collapsed halos with 1-D velocity dispersion $σ_v^{1d} \sim 400 \kms$. The harboring coefficient $f$ of quasars per halo and the lifetime of quasars depend only on local process, not modulated by the density inhomogeneities on scales larger than the size of the halos. Thus, the bias of quasars on scale larger than the size of these halos is mainly determined by the parameter $σ_v$ used for quasar environment identification. With this model, the popular structure formation models, like SCDM and LCDM, can be fairly well reconciled with the data of quasars, including a. observed feature of the environment for quasars; b. redshift evolution of quasar abundance; c. the two-point correlation functions of quasars. This bias model predicts that the correlation function of quasars doesn't significantly evolve, or only slightly increases with redshift.

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