arXiv subjects

Li-Zhi Fang

Publications and source records attributed to Li-Zhi Fang.

At least 37 records · Page 2Linked to original sources

arXiv2006

A WENO Algorithm of the Temperature and Ionization Profiles around a Point Source

We develop a numerical solver for radiative transfer problems based on the weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive flux corrections, in order to solve the temperature and ionization profiles around a point source of photons in the reionization epoch. Algorithms for such simulation must be able to handle the following two features: 1. the sharp profiles of ionization and temperature at the ionizing front (I-front) and the heating front (T-front), and 2. the fraction of neutral hydrogen within the ionized sphere is extremely small due to the stiffness of the rate equations of atom processes. The WENO scheme can properly handle these two features, as it has been shown to have high order of accuracy and good convergence in capturing discontinuities and complicated structures in fluid as well as to be significantly superior over piecewise smooth solutions containing discontinuities. With this algorithm, we show the time-dependence of the preheated shell around a UV photon source. In the first stage the I-front and T-front are coincident, and propagate with almost the speed of light. In later stage, when the frequency spectrum of UV photons is hardened, the speeds of propagation of the ionizing and heating fronts are both significantly less than the speed of light, and the heating front is always beyond the ionizing front. In the spherical shell between the I- and T-fronts, the IGM is heated, while atoms keep almost neutral. The time scale of the preheated shell evolution is dependent on the intensity of the photon source. We also find that the details of the pre-heated shell and the distribution of neutral hydrogen remained in the ionized sphere are actually sensitive to the parameters used. The WENO algorithm can provide stable and robust solutions to study these details.

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arXiv2006

The DWT Power Spectrum of the two-degree Field Galaxy Redshift Survey

The power spectrum of the two-degree Field Galaxy Redshift Survey (2dFGRS) sample is estimated with the discrete wavelet transform (DWT) method. The DWT power spectra within $0.04 <k< 2.3 h$Mpc$^{-1}$ are measured for three volume-limited samples defined in connective absolute magnitude bins $-19 \sim -18$, $-20 \sim -19$ and $-21 \sim -20$. We show that the DWT power spectrum can effectively distinguish $Λ$CDM models of $σ_8=0.84$ and $σ_8=0.74$. We adopt maximum likelihood method to perform three-parameter fitting with bias parameter $b$, pairwise velocity dispersion $σ_{pv}$ and redshift distortion parameter $β=Ω_m^{0.6}/b$ to the measured DWT power spectrum. Fitting results denotes that in a $σ_8=0.84$ universe the best fitted $Ω_m$ given by the three samples are consistent in the range $0.28 \sim 0.36$, and the best fitted $σ_{pv}$ are $398^{+35}_{-27}$, $475^{+37}_{-29}$ and $550 \pm 20$km/s for the three samples, respectively. However in the model of $σ_8=0.74$, our three samples give very different values of $Ω_m$. We repeat the fitting by using empirical formula of redshift distortion. The result of the model of low $σ_8$ is still poor, especially, one of the best value $σ_{pv}$ is as large as $10^3$km/s. The power spectrum of 2dFGRS seems in disfavor of models with low amplitude of density fluctuations.

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arXiv2006

Is the cosmic UV background fluctuating at redshift z ~ 6 ?

We study the Gunn-Peterson effect of the photo-ionized intergalactic medium(IGM) in the redshift range 5< z <6.4 using semi-analytic simulations based on the lognormal model. Assuming a rapidly evolved and spatially uniform ionizing background, the simulation can produce all the observed abnormal statistical features near redshift z ~ 6. They include: 1) rapidly increase of absorption depths; 2) large scatter in the optical depths; 3) long-tailed distributions of transmitted flux and 4) long dark gaps in spectra. These abnormal features are mainly due to rare events, which correspond to the long-tailed probability distribution of the IGM density field, and therefore, they may not imply significantly spatial fluctuations in the UV ionizing background at z ~ 6.

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arXiv2006

X-ray Emission of Baryonic Gas in the Universe: Luminosity-Temperature Relationship and Soft-Band Background

We study the X-ray emission of baryon fluid in the universe using the WIGEON cosmological hydrodynamic simulations. It has been revealed that cosmic baryon fluid in the nonlinear regime behaves like Burgers turbulence, i.e. the fluid field consists of shocks. Like turbulence in incompressible fluid, the Burgers turbulence plays an important role in converting the kinetic energy of the fluid to thermal energy and heats the gas. We show that the simulation sample of the $Λ$CDM model without adding extra heating sources can fit well the observed distributions of X-ray luminosity versus temperature ($L_{\rm x}$ vs. $T$) of galaxy groups and is also consistent with the distributions of X-ray luminosity versus velocity dispersion ($L_{\rm x}$ vs. $σ$). Because the baryonic gas is multiphase, the $L_{\rm x}-T$ and $L_{\rm x}-σ$ distributions are significantly scattered. If we describe the relationships by power laws $L_{\rm x}\propto T^{α_{LT}}$ and $L_{\rm x}\propto σ^{α_{LV}}$, we find $α_{LT}>2.5$ and $α_{LV}>2.1$. The X-ray background in the soft $0.5-2$ keV band emitted by the baryonic gas in the temperature range $10^5 50\barρ_{\rm dm}$ is generally clustered and discretely distributed. Therefore, almost all of the soft X-ray background comes from clustered sources, and the contribution from truly diffuse gas is probably negligible. This point agrees with current X-ray observations.

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arXiv2006

A WENO Algorithm for the Radiative Transfer and Ionized Sphere at Reionization

We show that the algorithm based on the weighted essentially nonoscillatory (WENO) scheme with anti-diffusive flux corrections can be used as a solver of the radiative transfer equations. This algorithm is highly stable and robust for solving problems with both discontinuities and smooth solution structures. We test this code with the ionized sphere around point sources. It shows that the WENO scheme can reveal the discontinuity of the radiative or ionizing fronts as well as the evolution of photon frequency spectrum with high accuracy on coarse meshes and for a very wide parameter space. This method would be useful to study the details of the ionized patch given by individual source in the epoch of reionization. We demonstrate this method by calculating the evolution of the ionized sphere around point sources in physical and frequency spaces. It shows that the profile of the fraction of neutral hydrogen and the ionized radius are sensitively dependent on the intensity of the source.

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arXiv2006

A Unified Fitting of HI and HeII LyαTransmitted Flux of QSO HE2347 with LCDM Hydrodynamic Simulations

Using cosmological hydrodynamic simulations of the LCDM model, we present a comparison between the simulation sample and real data sample of HI and HeII Lyαtransmitted flux in the absorption spectra of the QSO HE2347-4342. The LCDM model is successful in simultaneously explaining the statistical features of both HI and HeII Lyαtransmitted flux. It includes: 1.) the power spectra of the transmitted flux of HI and HeII can be well fitted on all scales > 0.28h^{-1} Mpc for H, and > 1.1h^{-1} Mpc for He; 2.) the Doppler parameters of absorption features of HeII and HI are found to be turbulent-broadening; 3.) the ratio of HeII to HI optical depths are substantially scattered, due to the significant effect of noise. A large part of the η-scatter is due to the noise in the HeII flux. However, the real data contain more low-ηevents than simulation sample. This discrepancy may indicate that the mechanism leading extra fluctuations upon the simulation data, such as a fluctuating UV radiation background, is needed. Yet, models of these extra fluctuations should satisfy the constraints: 1.) if the fluctuations are Gaussian, they should be limited by the power spectra of observed HI and HeII flux; 2.) if the fluctuations are non-Gaussian, they should be limited by the observed non-Gaussian features of the HI and HeII flux.

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arXiv2006

Cross-correlation between WMAP and 2MASS: non-Gaussianity induced by SZ effect

We study the SZ-effect-induced non-Gaussianity in the cosmic microwave background (CMB) fluctuation maps. If a CMB map is contaminated by the SZ effect of galaxies or galaxy clusters, the CMB maps should have similar non-Gaussian features as the galaxy and cluster fields. Using the WMAP data and 2MASS galaxy catalog we show that the non-Gaussianity of the 2MASS galaxies is imprinted on WMAP maps. The signature of non-Gaussianity can be seen with the 4^{th} order cross correlation between the wavelet variables of the WMAP maps and 2MASS clusters. The intensity of the 4^{th} order non-Gaussian features is found to be consistent with the contamination of the SZ effect of 2MASS galaxies. We also show that this non-Gaussianity can not be seen by the high order auto-correlation of the WMAP. This is because the SZ signals in the auto-correlations of the WMAP data generally is weaker than the WMAP-2MASS cross correlations by a factor f^2, which is the ratio between the powers of SZ effect map and the CMB fluctuations on the scale considered. Therefore, the ratio of high order auto-correlations of CMB maps to cross-correlations of the CMB maps and galaxy field would be effective to constrain the powers of SZ effect on various scales.

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arXiv2006

Low-Redshift Cosmic Baryon Fluid on Large Scales and She-Leveque Universal Scaling

We investigate the statistical properties of cosmic baryon fluid in the nonlinear regime, which is crucial for understanding the large-scale structure formation of the universe. With the hydrodynamic simulation sample of the Universe in the cold dark matter model with a cosmological constant, we show that the intermittency of the velocity field of cosmic baryon fluid at redshift z=0 in the scale range from the Jeans length to about 16 Mpc/h can be extremely well described by She-Leveque's universal scaling formula. The baryon fluid also possesses the following features: (1) for volume weight statistics, the dissipative structures are dominated by sheets, and (2) the relation between the intensities of fluctuations is hierarchical. These results imply that the evolution of highly evolved cosmic baryon fluid is similar to a fully developed turbulence.

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arXiv2005

The velocity field of baryonic gas in the universe

The dynamic evolution of the baryonic intergalactic medium (IGM) caused by the underlying dark matter gravity is governed by the Navier-Stokes equations in which many cooling and heating processes are involved. However, it has long been recognized that the growth mode dynamics of cosmic matter clustering can be sketched by a random force driven Burgers' equation if cooling and heating are ignored. Just how well the dynamics of the IGM can be described as a Burgers fluid has not been fully investigated probably because cooling and heating are essential for a detailed understanding of the IGM. Using IGM samples produced by a cosmological hydrodynamic simulation in which heating and cooling processes are properly accounted for, we show that the IGM velocity field in the nonlinear regime shows the features of a Burgers fluid, that is, when the Reynolds number is high, the velocity field consists of an ensemble of shocks. Consequently, (1) the IGM velocity $v$ is generally smaller than that of dark matter; (2) for the smoothed field, the IGM velocity shows tight correlation with dark matter given by $v \simeq s v_{dm}$, with $s<1$, such that the lower the redshift, the smaller $s$; (3) the velocity PDFs are asymmetric between acceleration and deceleration events; (4) the PDF of velocity difference $Δv=v(x+r)-v(x)$ satisfies the scaling relation for a Burgers fluid, i.e., $P(Δv)=(1 r^y)F(Δv/r^y)$. We find the scaling function and parameters for the IGM which are applicable to the entire scale range of the samples (0.26 - 8 h$^{-1}$ Mpc). These properties show that the similarity mapping between the IGM and dark matter is violated on scales much larger than the Jeans length of the IGM.

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arXiv2005

Power Spectrum and Intermittency of Ly$α$ Transmitted Flux of QSO He2347-4342

We have studied the power spectrum and the intermittent behavior of the fluctuations in the transmitted flux of HE2347-4342 ${\rm Ly}α$ absorption in order to investigate if there is any discrepancy between the LCDM model with parameters given by the WMAP and observations on small scales. If the non-Gaussianity of cosmic mass field is assumed to come only from halos with an universal mass profile of the LCDM model, the non-Gaussian behavior of mass field would be effectively measured by its intermittency, because intermittency is a basic statistical feature of the cuspy structures. We have shown that the Ly$α$ transmitted flux field of HE2347-4342 is significantly intermittent on small scales. With the hydrodynamic simulation, we demonstrate that the LCDM model is successful in explaining the power spectrum and intermittency of ${\rm Ly}α$ transmitted flux. Using statistics ranging from the second to eighth order, we find no discrepancy between the LCDM model and the observed transmitted flux field, and no evidence to support the necessity of reducing the power of density perturbations relative to the standard LCDM model up to comoving scales as small as about $0.08 {\rm h}^{-1} {\rm Mpc}$. Moreover, our simulation samples show that the intermittent exponent of the Ly$α$ transmitted flux field is probably scale-dependent. This result is different from the prediction of universal mass profile with a constant index of the central cusp. The scale-dependence of the intermittent exponent indicates that the distribution of baryonic gas is decoupled from the underlying dark matter.

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arXiv2005

A Parameter-free Statistical Measurement of Halos with Power Spectra

We show that, in the halo model of large-scale structure formation, the difference between the Fourier and the DWT (discrete wavelet transform) power spectra provides a statistical measurement of the halos. This statistical quantity is free from parameters related to the shape of the mass profile and the identification scheme of halos. That is, the statistical measurement is invariant in the sense that models with reasonably defined and selected parameters of the halo models should yield the same difference of the Fourier and DWT spectra. This feature is useful to extract ensemble averaged properties of halos, which cannot be obtained with the identification of individual halo. To demonstrate this point, we show with WIGEON hydrodynamical simulation samples that the spectrum difference provides a quantitative measurement of the discrepancy of the distribution of baryonic gas from that of the underlying dark matter field within halos. We also show that the mass density profile of halos in physical space can be reconstructed with this statistical measurement. This profile essentially is the average over an ensemble of halos, including well virialized halos as well as halos with significant internal substructures. Moreover, this reconstruction is sensitive to the tail of the mass density profile. We showed that the profile with $1/r^3$ tail gives very different result from that of $1/r^2$. Other possible applications of this method are discussed as well.

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arXiv2005

Distributions of the Baryon Fraction on Large Scales in the Universe

(Abridged) The nonlinear evolution of a system consisting of baryons and dark matter is generally characterized by strong shocks and discontinuities. The baryons slow down significantly at postshock areas of gravitational strong shocks, which can occur in high overdense as well as low overdense regions. Consequently, the baryon fraction would be nonuniform on large scales. We studied these phenomena with simulation samples produced by the WENO hybrid cosmological hydrodynamic/N-body code. We find that the baryon fraction in high mass density regions is lower on average than the cosmic baryon fraction, and many baryons accumulate in the regions with moderate mass density to form a high baryon fraction phase (HBFP). In dense regions with rho>100, which are the possible hosts for galaxy clusters, the baryon fraction can be lower than the cosmic baryon fraction by about 10%--20% at z ~ 0. Our simulation samples show that about 3% of the cosmic baryon budget was hidden in the HBFP at redshift z=3, while this percentage increases to about 14% at the present day. The gas in the HBFP cannot be detected either by Ly-alpha forests of QSO absorption spectra or by soft X-ray background. That is, the HBFP would be missed in the baryon budget given by current observations.

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arXiv2004

Statistical features of 21-cm emission from the epoch between reionization and Gunn-Peterson transparency

We investigate the 21 cm emission from the epoch between reionization z_r and Gunn-Peterson transparency z_{gp}. According to the lognormal model of the thermal history around reionization, hydrogen clouds in z_r > z > z_{gp} are hot and a predominant part of baryonic gas is ionized, but still opaque to Ly-alpha photons. Therefore, 21 cm emission is a distinctive characteristic of this epoch. We show that the 21 cm emission comes from both uncollapsed and collapsing hydrogen clouds. The spatial distribution of the brightness temperature excess $δT_b$ is highly non-Gaussian. It consists of spikes with high $δT_b$ and a low $δT_b$ area between the spikes. The field has the following statistical features: (1) the one-point distributions of $δT_b$ are described approximately by power-law tailed probability distribution functions; (2) the nth-order moment of $δT_b$ is increasing much faster with n than that of a Gaussian field, but slower than that of a lognormal field; (3) the scale-scale correlation of the $δT_b$ field is significant for all scales larger than the Jeans length of the gas. These features would be useful for distinguishing the 21 cm emission of the early clustering from the noise of foreground contamination.

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arXiv2004

Temperature and Entropy Fields of Baryonic Gas in the Universe

(Abridged)The temperature (T) and entropy (S) fields of baryonic gas/IGM are analyzed using simulation samples by a cosmological hydro/N-body code. We show that in the nonlinear regime the dynamical similarity between the IGM and dark matter will be broken by strong shocks. The heating and entropy production by the shocks breaks the IGM into multiple phases. The mean entropy, or the cosmological entropy floor, is found to be more than 100 h^(-1/3) keV cm^2 in all regions when z < 1. At redshift z ~ 2 - 3, high-entropy gas (S > 50 h^(-1/3) keV cm^2) mostly resides in areas on scales larger than 1 h^(-1) Mpc and with density $ρ_{dm}>10^2$. Therefore, gravitational shocks are an effective preheating mechanism of the IGM, and probably enough to provide the entropy excess of clusters and groups if the epoch of the gas falling in cluster cores is not earlier than z ~ 2 - 3. On the other hand, at redshifts z < 4, there is always a more than 90% volume of the low dark matter mass density regions filled by the IGM with T < 10^4.5 K. Therefore, the multiphased character and non-Gaussianity of the IGM field would explain the high-temperature and high-entropy gas observed in groups and clusters.

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arXiv2004

The Statistical Discrepancy between the IGM and Dark Matter Fields: One-Point Statistics

We investigate the relationship between the mass and velocity fields of the intergalactic medium (IGM) and dark matter. Although the evolution of the IGM is dynamically governed by the gravity of the underlying dark matter field, some statistical properties of the IGM inevitably decouple from those of the dark matter once the nonlinearity of the dynamical equations and the stochastic nature of the field is considered. With simulation samples produced by a hybrid cosmological hydrodynamic/N-body code, which is effective in capturing shocks and complicated structures with high precision, we find that the one-point distributions of the IGM field are systematically different from that of dark matter as follows: 1.) the one-point distribution of the IGM peculiar velocity field is exponential at least at redshifts less than 2, while the dark matter velocity field is close to a Gaussian field; 2.) although the one-point distributions of the IGM and dark matter are similar, the point-by-point correlation between the IGM and dark matter density fields significantly differs on all scales and redshifts analyzed; 3.) the one-point density distributions of the difference between IGM and dark matter fields are highly non-Gaussian and long tailed. These discrepancies violate the similarity between the IGM and dark matter and cannot be explained simply as Jeans smoothing of the IGM. However, these statistical discrepancies are consistent with the fluids described by stochastic-force driven nonlinear dynamics.

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arXiv2004

Spatial Locality of Galaxy Correlation Function in Phase Space: Samples from the 2MASS Extended Source Catalog

We analyze the statistical properties and dynamical implications of galaxy distributions in phase space for samples selected from the 2MASS Extended Source Catalog. The galaxy distribution is decomposed into modes $δ({\bf k, x})$ which describe the number density perturbations of galaxies in phase space cell given by scale band $\bf k$ to ${\bf k}+Δ{\bf k}$ and spatial range $\bf x$ to ${\bf x}+Δ{\bf x}$. In the nonlinear regime, $δ({\bf k, x})$ is highly non-Gaussian. We find, however, that the correlations between $δ({\bf k, x})$ and $δ({\bf k', x'})$ are always very weak if the spatial ranges (${\bf x}$, ${\bf x}+Δ{\bf x}$) and (${\bf x'}$, ${\bf x'}+Δ{\bf x'}$) don't overlap. This feature is due to the fact that the spatial locality of the initial perturbations is memorized during hierarchical clustering. The highly spatial locality of the 2MASS galaxy correlations is a strong evidence for the initial perturbations of the cosmic mass field being spatially localized, and therefore, consistent with a Gaussian initial perturbations on scales as small as about 0.1 h$^{-1}$ Mpc. Moreover, the 2MASS galaxy spatial locality indicates that the relationship between density perturbations of galaxies and the underlying dark matter should be localized in phase space. That is, for a structure consisting of perturbations on scales from $k$ to $ k+Δ{k}$, the nonlocal range in the relation between galaxies and dark matter should {\it not} be larger than $|{Δ{\bf x}}|=2π/|Δ{\bf k}|$. The stochasticity and nonlocality of the bias relation between galaxies and dark matter fields should be no more than the allowed range given by the uncertainty relation $|{Δ{\bf x}|| Δ{\bf k}}|=2π$.

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arXiv2004

Off-equilibrium dynamics of the primordial perturbations in the inflationary universe: the O(N) model

Using the O(N) model as an example, we investigate the self-interaction effects of inflaton on the dynamics of the primordial perturbations. When taking interactions into account, it is essential to employ a self-consistent off-equilibrium formalism to study the evolution of the inflationary background field and its fluctuations with the back-reaction effects. Within the Hartree factorization scheme, we show that the O(N) model has at least two observable remains left behind the off-equilibrium processes: the running spectral index of primordial density perturbations and the correlations between perturbation modes in phase space. We find that the running of the spectral index is fully determined by the rate of the energy transfer from the inflationary background field to its fluctuations via particle creation processes as well as the dynamics of the background field itself. Furthermore, the amplitude of the field fluctuations turns out to be scale-dependent due to the off-equilibrium evolution. As a consequence, the scale-dependence of fluctuations yields a correlation between the phase space modes of energy density perturbations, while the one-point function of the fluctuations in each Hartree mode is still Gaussian. More importantly, the mode-mode correlation of the primordial perturbations depends upon the dynamics of the self-interaction {\it as well as} the initial conditions of the inflation. Hence, we propose that the running spectral index and the correlation between phase-space modes would be two observable fossils to probe the epoch of inflation, even beyond.

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arXiv2004

Running spectral index and mode-mode correlation of inflationary perturbations from off-equilibrium effects

We study the off-equilibrium effects of inflaton on the dynamics of primordial perturbations in the O(N) model. A self-consistent off-equilibrium formalism is employed to investigate the evolution of the inflationary background field and its fluctuations with the back-reaction effects. We find two observable remains left behind the off-equilibrium processes: the running spectral index of primordial density perturbations and the correlations between perturbation modes in phase space, which would serve as the imprints to probe the epoch of inflation, even beyond.

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