arXiv subjects

Li-Zhi Fang

Publications and source records attributed to Li-Zhi Fang.

At least 91 records · Page 5Linked to original sources

arXiv1997

The Collapse of Neutron Stars in High-Mass Binaries as the Energy Source for the Gamma-Ray Bursts

The energy source has remained to be the great mystery in understanding of the gamma-ray bursts (GRBs) if the events are placed at cosmological distances as indicated by a number of recent observations. The currently popular models include (1)the merger of two neutron stars or a neutron star and a black hole binary and (2)the hypernova scenario of the collapse of a massive member in a close binary. Since a neutron star will inevitably collapse into a black hole if its mass exceeds the limit $M_{max}\approx3M_{\odot}$, releasing a total binding gravitational energy of $\sim10^{54}$ erg, we explore semi-empirically the possibility of attributing the energy source of GRB to the accretion- induced collapse of a neutron star (AICNS) in a massive X-ray binary system consisting of a neutron star and a type O/B companion. This happens because a significant mass flow of $\sim10^{-3}$--$10^{-4}M_{\odot}$ yr$^{-1}$ may be transferred onto the neutron star through the Roche-lobe overflow and primarily during the spiral-in phase when it plunges into the envelope of the companion, which may eventually lead to the AICNS before the neutron star merges with the core of the companion. In this scenario, a ``dirty'' fireball with a moderate amount of beaming is naturally expected because of the nonuniformity of the stellar matter surrounding the explosion inside the companion, and a small fraction ($\sim0.1%$) of the energy is sufficient to create the observed GRBs. In addition, the bulk of the ejecting matter of the companion star with a relatively slow expansion rate may act as the afterglow. Assuming a non-evolutionary model for galaxies, we estimate that the birthrate of the AICNS events is about 2 per day within a volume to redshift $z=1$ for an $Ω_0=1$ universe, consistent with the reported GRB rate.

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arXiv1997

Quasar-galaxy associations from gravitational lensing: revisited

The theoretically expected amplitude of the associations of background quasars with foreground galaxies as a result of gravitational lensing has been updated in this paper. Since the galactic matter alone yields an amplitude of quasar overdensity smaller than that observed, a special attention has been paid to the examination or re-examination of the uncertainties in the estimate of the quasar enhancement factor arising from the cosmic evolution of galaxies, the core radius and velocity bias of galactic matter distributions, the clusters of galaxies, the obstruction effect by galactic disks, the non-zero cosmological constant, etc. Unfortunately, none of these factors has been shown to be able to significantly improve the situation, although a combination of some effects may provide a result that marginally agrees with observations. It is concluded that the quasar-galaxy association still remains to be an unsolved puzzle in today's astronomy, if the reported quasar-galaxy associations are not due to the statistical variations and/or the observed quasar number counts as a whole have not been seriously contaminated by gravitational lensing.

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arXiv1997

An Attempt to Determine the Largest Scale of Primordial Density Perturbations in the Universe

Inflationary cosmology predicts that the particle horizon should be generically much bigger than the present-day Hubble radius, $1/H_0$. This implies a special regime of super-Hubble scale energy density fluctuations imprinted on the cosmic microwave background radiation (CMBR), which from present theory could only be explained by inflation Causality constraints are used to determine models for the power spectrum that accommodate a suppression scale. A three parameter likelihood analysis is performed of the COBE-DMR 4-year data with respect to the amplitude, spectral index, and suppression scale. It is found that all suppression length scales larger than $1/H_0$ are consistent with the data, but that scales of order $1/H_0$ are slightly preferred, at roughly the one-sigma level. Many non-inflation models would be consistent with a small suppression length scale, whereas for standard inflation models, the duration of the inflation epoch would have to be bounded by a fairly small upper limit. Suppression scales smaller than $1/H_0$ are strongly excluded by the anisotrophy data.

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arXiv1997

Density Perturbations of Thermal Origin During Inflation

We study thermally induced density perturbations during inflation. This scenario is characterized by two thermodynamical conditions: (1) The primordial perturbations originate in the epoch when the inflationary universe contains a thermalized heat bath. (2) The perturbations of the inflationary scalar field are given by the fluctuation-dissipation relation. We show that the spectrum of the primordial perturbations is of power law, but tilted, and there is a relation between the amplitude and the index of the power spectrum. Aside from the mass scale of the inflation, the amplitude-index relation does not depend on other parameters like $g$-factor. These results are found to be well consistent with observations of the temperature fluctuations of cosmic microwave background if the mass scale of the inflation is about $10^{15}$ GeV. Instead of the purely adiabatic case, the consequent density perturbation is an admixture of adiabatic and isocurvature one. Therefore, the detection of super-Hubble suppression of the spectrum would be effective for further discrimination between the thermally originated models and others.

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arXiv1997

Environmental Effect on the Associations of Background Quasars with Foreground Objects: II. Numerical Simulations

Using numerical simulations of cluster formation in the standard CDM model (SCDM) and in a low-density, flat CDM model with a cosmological constant (LCDM), we investigate the gravitational lensing explanation for the reported associations between background quasars and foreground clusters. Under the thin-lens approximation and the unaffected background hypothesis , we show that the recently detected quasar overdensity around clusters of galaxies on scales of $\sim10$ arcminutes cannot be interpreted as a result of the gravitational lensing by cluster matter and/or by their environmental and projected matter along the line of sight, which is consistent with the analytical result based on the observed cluster and galaxy correlations (Wu, et al. 1996). It appears very unlikely that uncertainties in the modeling of the gravitational lensing can account for the disagreement between the theoretical predictions and the observations. We conclude that either the detected signal of the quasar-cluster associations is a statistical fluke or the associations are are generated by mechanisms other than the magnification bias.

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arXiv1997

Abundance and Clustering of QSOs in Cosmic Structure Formation Models

Combining the observations of spatial abundance and two-point correlation function of QSOs, we can effectively set constraints on models of cosmic structure formation. Both the abundance of gravitationally confined halos and their two-point correlation functions can be calculated in the conventional Press-Schechter formalism. We apply this method to examine the properties of possible host halos of QSOs in three popular models: the standard cold dark matter (SCDM) model, the low density flat cold dark matter (LCDM) model and the cold-plus-hot dark matter (CHDM) model. The LCDM and CHDM models are normalized to the COBE-DMR observations, and the SCDM is normalized to $σ= 0.58$. We find that the SCDM and LCDM models can pass the abundance-plus-correlation test for QSOs. However, the CHDM are difficult to produce host halos to fit with the number density of high redshift QSOs and their clustering on large scales (10 h^{-1} Mpc) simultaneously. We studied various mechanisms, originated both gravitationally and non-gravitationally, which may lead to a biasing of the halo clustering. We conclude that these effects are too weak in order to release the trouble of the CHDM models.

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arXiv1997

Large-scale Structures revealed by Wavelet Decomposition

We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical discription of LSS. Among the topics studied are the the DWT estimation of the probability distribution function; the reconstruction of the power spectrum; the regularization of complex geometry in observational samples; cluster identification; extraction and identification of coherent structures; scale-decomposition of non-Gaussianity, such as spectra of skewnes and kurtosis and scale-scale correlations. These methods are applied to both observational and simulated samples of the QSO Lyman-alpha forests. It is clearly demonstrated that the statistical measures developed using the DWT are needed to distinguish between competing models of structure formation. The DWT also reveals physical features in these distributions not detected before. We conclude with a look towards the future of the use of the DWT in LSS.

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arXiv1997

A Statistical Comparison of Cluster Mass Estimates from Optical/X-ray Observations and Gravitational Lensing

We present a statistical comparison of three different estimates of cluster mass, namely, the dynamical masses obtained from the velocity dispersion of optical galaxies, the X-ray masses measured from the temperature of X-ray emitting gas under the assumption of isothermal hydrostatic equilibrium, and the gravitational lensing masses derived from the strong/weak distortions of background galaxy images. Using a sample of 29 lensing clusters available in literature, we have shown that the dynamical masses are in agreement with the gravitational lensing masses, while the X-ray method has systematically underestimated cluster masses by a factor 2-3 as compared with the others. These results imply that galaxies indeed trace the gravitational potential of their clusters, and there is no bias between the velocities of the dark matter particles and the galaxies in clusters. The X-ray cluster mass discrepancy is probably from the simplification in the models for the X-ray gas distribution and dynamical evolution.

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arXiv1996

Comparisons of Cluster Mass Determinations by X-ray Observations and Gravitational Lensing

Gravitational lensing by clusters of galaxies has been detected on scales ranging from $\sim10^{-1}$ Mpc to $\sim10$ Mpc, namely, arcs/arclets, weak lensing and quasar-cluster associations. This allows us to derive an overall radius matter distribution of clusters of galaxies. While the dynamical analysis of the X-ray observations has yielded a great number of data for the virial cluster masses, it becomes possible to statistically compare the cluster mass determinations by these two independent methods. In this letter we show that as compared with gravitational lensing, the dynamical analysis under the assumption of isothermal and hydrostatic equilibrium has systematically underestimated the cluster masses inside the Abell radius by a factor of $\sim2$ with scatter between $0.7$ and $5$. Because the same correction factor should be applicable to the gas baryon fraction of clusters of galaxies obtained from the X-ray data, it is probably too premature to claim a baryon crisis in today's cosmology.

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arXiv1996

Wavelet Space-Scale Decomposition Analysis of QSO's Lyman-Alpha Lines: Spectrum of non-Gaussianity

Using a discrete wavelet based space-scale decomposition (SSD), the spectrum of the skewness and kurtosis is developed to describe the non-Gaussian signatures in cosmologically interesting samples. Because the basis of the discrete wavelet is compactly supported, the one-point distribution of the father function coefficients (FFCs) taken from one realization is a good estimate of the probability distribution function of the density if the ``fair sample hypothesis" holds. These FFC one-point distributions can also avoid the constraints of the central limit theorem on the detection of non-Gaussianity. Thus the FFC one-point distributions are effective in detecting non-Gaussian behavior in samples such as non-Gaussian clumps embedded in a Gaussain background, regardless of the number or density of the clumps. We demonstrate that the non-Gaussianity can reveal not only the magnitudes but also the scales of non-Gaussianity. Also calculated are the FFC one-point distributions, skewness and kurtosis spectra for real data and linearly simulated samples of QSO Ly$α$ forests. When considering only second and lower order of statistics, such as the number density and two-point correlation functions, the simulated data show the same features as the real data. However, the the kurtosis spectra of samples given by different models are found to be different. On the other hand, the spectra of skewness and kurtosis for independent observational data sets are found to be the same. Moreover, the real data are significantly different from the non-Gaussianity spectrum of various posssible random samples. Therefore the non-Gaussain spectrum is necessary and valuable for model discrimination.

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arXiv1996

Environmental Effect on the Associations of Background Quasars with Foreground Objects: I. Analytic Investigation

The associations of the angular positions of background quasars with foreground galaxies, clusters of galaxies and quasars are often attributed to the statistical lensing by gravitational potentials of the matter along the lines of sight, although it has been known that none of the individual objects (galaxies, clusters or quasars) are able to fully explain the reported amplitudes of the quasar number enhancements. This probably arises from the fact that the gravitational lensing effect by the environmental matter surrounding these objects has been ignored. In this paper we conduct an extensive study of the influence of the environmental matter on the prediction of quasar enhancement factor by employing the spatial two-point correlation function. Assuming a singular isothermal sphere for mass density profile in galaxy and cluster of galaxies, we estimate the average surface mass density $\overlineΣ$ around galaxies, clusters and quasars from the galaxy-galaxy, cluster-cluster, cluster-galaxy and quasar-galaxy correlations. Our results show that the $\overlineΣ$ induced quasar number enhancement in the scenario of gravitational magnification depends critically on the mass density parameters of galaxies ($Ω_g$) and clusters of galaxies ($Ω_c$) in the universe. For a flat cosmological model of $Ω_0=1$ the environmental matter can indeed play an important role in the lensing origin of the quasar-quasar and quasar-galaxy associations if $Ω_g\simΩ_c\simΩ_0$, while it is unlikely that $\overlineΣ$ is sufficient to account for the reported quasar overdensity behind quasars/galaxies if galaxies and clusters of galaxies contribute no more than $25\%$ to the matter of the universe. Nonetheless, the

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arXiv1996

Deep Wide-Field Spectrophotometry of the Open Cluster M67

We present nine color CCD intermediate-band spectrophotometry of a two square degree field centered on the old open cluster M67, from 3890$\rm Å$ to nearly 1$μ$. These observations are taken as a part of the BATC (Beijing-Arizona-Taipei-Connecticut) Color Survey of the Sky, for both scientific and calibration reasons. With these data we show that the BATC survey can reach its goal of obtaining spectrophotometry to a zero point accuracy of 0.01 mag, and down to V = 21 with 0.3 mag random error. We fit the color-magnitude diagrams (CMDs) with Worthey's theoretical models. The net result is the excellent fit of the 4.0 Gyr, [Fe/H] = $-0.10$ model to our data, including a good fit to the main sequence (MS) turn-off. Our data are consistent with a toy model with 50\% of the stars in M67 being binaries and a random distribution of binary mass-ratios, although other models with different mass-ratio distributions cannot be ruled out. The spatial distribution and mass function (MF) of stars in M67 show marked effects of dynamical evolution and evaporation of stars from the cluster. Blue stragglers and binary stars are the most condensed within the cluster, with degree of condensation depending on mass.We find M67 to have an elongated shape, oriented at an angle of $15^{\circ}$ relative to the galactic plane. Within its tidal radius, the observed MF of M67 between 1.2 $\rm M_\odot$ and $\rm 0.8 M_\odot$ has a Salpeter slope $\rm η= -1.93 \pm 0.66$. For stars of mass below 0.8 $\rm M_\odot$, $\rm η\sim 0$. It is plausible that the leveling-off of the MF at lower masses is a result of evaporation of lower mass stars in this mass range at a rate of one every $\sim 10^7$ years. If so, it is plausible that the IMF of M67 has the canonical field value of $\rm η= -2.0$.

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arXiv1996

On the Possible Variations of the Hubble Constant with Distance

Current measurements of the Hubble constant $H_0$ on scale less than $\sim100$ Mpc appear to be controversial, while the observations made at high redshift seem to provide a relatively low value. On the other hand, the Hubble expansion is driven by the matter content of the universe. The dynamical analysis on scale of a few $\sim10$ Mpc indicates that the matter density $Ω_0$ is only $\sim0.2$--$0.3$, which is significantly smaller than $Ω_0=1$ predicted in the standard inflation model. This might support the tendency of a decreasing Hubble constant towards distance. In this paper, we discuss the influence of a possible variant Hubble constant on two fundamental relations in astronomy: the magnitude-redshift ($m$--$z$) and the number-magnitude relations. Using a distant type Ia supernova at $z=0.458$, we show that the deceleration parameter $q_0$ or $Ω_0$ cannot be determined from the $m$--$z$ relation at moderate/high redshift unless the variation of the Hubble constant is {\it a priori} measured. It is further demonstrated that the number density of distant sources would be underestimated when their local calibration is employed, which may partially account for the number excess of the faint blue galaxies observed at moderate/high redshift.

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arXiv1996

Quasar-Cluster Associations and Gravitational Lensing by Large-Scale Matter Clumps

Motivated by the significant overdensity of background bright quasars recently detected behind the foreground clusters of galaxies on scale of $10$ arcminutes, we have investigated the possibility of attributing the quasar-cluster associations to gravitational lensing by large-scale matter inhomogeneities. Based on the conventional lensing models, we have shown that the reported quasar overdensity is unlikely to be generated by cluster matter alone. The situation does not change even if all the clusters of galaxies which follow their spatial two-point correlation function are taken into account, while matter clumps on scale of $>20$ Mpc are also found to be unable to provide the required mass surface density since their density contrast is strictly limited by the anisotropy measurements of the cosmic background radiation. Moreover, we have pointed out that the influence of a nonzero cosmological constant on the quasar-cluster associations is very minor. We conclude that either the observed quasar number counts have been seriously contaminated by the magnification bias of matter inhomogeneities of the universe or there should exists some intercluster matter on scale of less than $\sim20$ Mpc, e.g. from cluster-galaxy correlation, whose mean cosmic density is about an order of magnitude higher than that of clusters of galaxies.

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arXiv1996

Phase Randomization and Doppler Peaks in the CMB Angular Power Spectrum

Using the Boltzmann equation with a Langevin-like term describing the stochastic force in a baryon-photon plasma, we investigate the influence of the incoherent electron-photon scattering on the subhorizon evolution of the cosmic microwave radiation. The stochastic fluctuation caused by each collision on average is found to be small. Nevertheless, it leads to a significant Brownian drifting of the phase in the acoustic oscillation, and the coherent oscillations cannot be maintained during their dynamical evolution. As a consequence, the proposed Doppler peaks probably do not exist.

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arXiv1995

Wavelet Space-Scale-Decomposition Analysis of QSO's Ly$α$ Absorption Lines: Spectrum of Density Perturbations

A method for measuring the spectrum of a density field by a discrete wavelet space-scale decomposition (SSD) has been studied. We show how the power spectrum can effectively be described by the father function coefficients (FFC) of the wavelet SSD. We demonstrate that the features of the spectrum, such as the magnitude, the index of a power law, and the typical scales, can be determined with high precision by the FFC reconstructed spectrum. This method does not require the mean density, which normally is poorly determined. The problem of the complex geometry of observed samples can also be easily solved because the basis are always orthogonal, regardless the geometry of the samples. Using this method, we examine the spectra inferred from Ly$α$ forests of both simulated and real samples. We find that 1.) the magnitude of the 1-D spectra is significantly dfferent froma Poisson process; 2) the 1-d spectra are flat on scales less than 5 h$^{-1}$ Mpc, and increase slowly at larger ranges; 3.) the reconstructed 3-D spectra have about the same power as the COBE normalized linear spectrum of the SCDM model on scales less than 40 h$^{-1}$ Mpc, but is larger than the SCDM model on scales larger than 40 h$^{-1}$ Mpc; 4) the magnitudes of high redshift ($z>2.51$) spectra generally are larger than those of low redshift ($z<2.51$).

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arXiv1995

A Wavelet Space-Scale-Decomposition Analysis of Structure and Evolution fo QSO's Ly$α$ Absorption Lines

A wavelet space-scale decomposition (SSD) analysis of large scale structures in the universe has been developed. The SSD method of identifying and measuring structures in the spatial distribution of objects has been demonstrated. The position and strength (richness) of the identified clusters can be described by the corresponding coefficient of the wavelet transform. Using this technique, we systematically detected the clustering and its evolution of QSO's Ly$α$ forest lines in real data and simulated samples. We showed that the clusters of Ly$α$ absorbers do exist on scales as large as at least 20 h$^{-1}$ Mpc at significance levels of 2-4 $σ$. Independent data sets show about the same strength distribution of the decomposed clusters. The number densities of the clusters on scales of 10 - 20 h$^{-1}$ Mpc are found to evolve in an opposite sense as that of the lines themselves, i.e. they decrease with redshift. We also showed that the number density and the strength distribution of clusters can play an important role in testing or discriminating models, i.e. it can distinguish real data and simulated samples, which cannot be discriminated by traditional ways. We used Daubechies 4 and Mallat wavelets as the bases of the SSD. All above-mentioned conclusions do not depend on either wavelet basis.

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arXiv1995

Thermally Induced Density Perturbations in the Inflation Era

The possibility of thermally induced initial density perturbations in inflationary cosmology is examined. The fluctuation dynamics of a scalar field plus thermal bath system during slow roll is described by a Langevin-like equation. Fluctuation-dissipation arguments show that for a wide parameter range within the standard inflation model, the thermal fluctuations of the scalar field can dominate its quantum fluctuations. The initial amplitude of density perturbations is found to lie in a range which is consistent with the recent observations of cosmic temperature fluctuations.

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