arXiv subjects

Xiang-Ping Wu

Publications and source records attributed to Xiang-Ping Wu.

At least 73 records · Page 4Linked to original sources

arXiv1999

On the Matter Distribution of Galaxy Cluster Containing a Compact Core

Increasing evidences provided primarily by the cluster lensing and numerical simulations of cluster formation indicate that galaxy clusters may contain compact cores that are substantially smaller than the cores revealed by the X-ray observations of hot intracluster gas. In this paper we present a model that describes how two distinct cores can grow simultaneously as a result of infall from the background dark matter. This model needs a pre-existing localized large fluctuation, which can be the non-Gaussian density peak of the primordial fluctuations, to seed the individual growing cluster. On the other hand, numerous recent observations also show that no strong evolution is detected for galaxy clusters within the redshift up to $z\sim 0.8$. We therefore present a comparison of observations with the saturated cluster configuration resulting from our infall model. In the saturated state, the predicted compact core mass is about few$\times 10^{11} M_\odot$ and the core size about 1 kpc for a cluster mass $\sim$ several $\times 10^{15} M_\odot$ within a radius of 3 Mpc. We have successfully reproduced the dark matter distribution revealed by the gravitational lensing, and the observed radial distributions of cluster galaxies, intracluster gas (i.e., the conventional $β$ model) and baryon fractions in a consistent way. This model, when combined with the observed X-ray surface brightness profiles of clusters, predicts that the overall temperature of intracluster gas has a tendency of radial decline with a mean polytropic index $γ\approx1.2$. Finally, the so-called $β$ discrepancy finds a natural explanation for such a polytropic gas in our model.

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arXiv1999

Correlation Between the Halo Concentration (c) and the Virial Mass (Mvir) Determined from X-ray Clusters

Numerical simulations of structure formation have suggested that there exists a good correlation between the halo concentration c (or the characteristic density delta_c) and the virial mass Mvir for any virialized dark halo described by the Navarro, Frenk & White (1995) density profile. In this Letter, we present an observational determination of the c-Mvir (or delta_c-Mvir) relation in the mass range of 10^14< Mvir <10^16 (solar mass) using a sample of 63 X-ray luminous clusters. The best-fit power law relation, which is roughly independent of the values of Omega_M and Lambda, is c propto Mvir^(-0.5) or delta_c propto Mvir^(-1.2), indicating n=-0.7 for a scale-free power spectrum of the primordial density fluctuations. We discuss the possible reasons for the conflict with the predictions by typical CDM models such as SCDM, LCDM and OCDM.

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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

Constraints on the Asymptotic Baryon Fractions of Galaxy Clusters at Large Radii

While X-ray measurements have so far revealed an increase in the volume-averaged baryon fractions $f_b(r)$ of galaxy clusters with cluster radii $r$, $f_b(r)$ should asymptotically reach a universal value $f_b(\infty)=f_b$, provided that clusters are representative of the Universe. In the framework of hydrostatic equilibrium for intracluster gas, we have derived the necessary conditions for $f_b(\infty)=f_b$: The X-ray surface brightness profile described by the $β$ model and the temperature profile approximated by the polytropic model should satisfy $γ\approx2(1-1/3β)$ and $γ\approx1+1/3β$ for $β<1$ and $β>1$, respectively, which sets a stringent limit to the polytropic index: $γ<4/3$. In particular, a mildly increasing temperature with radius is required if the observationally fitted $β$ parameter is in the range $1/3<β<2/3$. It is likely that a reliable determination of the universal baryon fraction can be achieved in the small $β$ clusters because the disagreement between the exact and asymptotic baryon fractions for clusters with $β>2/3$ breaks down at rather large radii ($\ga30r_c$) where hydrostatic equilibrium has probably become inapplicable. We further explore how to obtain the asymptotic value $f_b(\infty)$ of baryon fraction from the X-ray measurement made primarily over the finite central region of a cluster. We demonstrate our method using a sample of 19 strong lensing clusters, which enables us to place a useful constraint on $f_b(\infty)$: $0.094\pm0.035 \leq f_b(\infty) \leq 0.41\pm0.18$. An optimal estimate of $f_b(\infty)$ based on three cooling flow clusters with $β<1/2$ in our lensing cluster sample yields $ = 0.142\pm0.007$ or $Ω_M = 0.35\pm0.09$.

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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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arXiv1998

Baryon Fractions and Cluster Mass Estimates

I report the current status on the determinations of the baryon fractions and dynamical/lensing masses of galaxy clusters as well as the $σ$ - $T$ relationship, making use of all the published data in literature which include 304 measurements for baryon fractions, 320/21 data points for masses of intracluster gas/cluster galaxies, (152+228)/72 data points for cluster masses derived from X-ray emitting gas/optical galaxies based on the hydrostatic equilibrium hypothesis, 46/33 measurements for the projected cluster masses obtained from strong/weak lensing. A straightforward statistical analysis reveals the following features: (1)The cluster baryon fraction indeed shows an increasing tendency towards a value of $\sim30%$ at large cluster radius; (2)The dynamical cluster masses are in fairly good agreement with the masses determined by weak lensing technique; (3)The cluster masses provided by strong lensing and other methods are essentially consistent within a factor of $\sim2$. (4)The cluster $σ-T$ relationship is in concordance with the scenario that overall galaxy clusters are the well relaxed dynamical systems. These results are strongly suggestive of a low-mass density universe ($Ω_m<0.3$), in which the fraction of baryonic matter ($\sim30%$) is not very small !

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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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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

On the Consistency between the Outer Rotation Curve of the Galaxy and the Microlensing Rate towards the Large Magellanic Cloud

Recent determination of the outer rotation curve of the Galaxy suggests that the total Galactic mass is likely to concentrate into a region of radius $\sim2R_0$. If this finding is correct, the previously estimated optical depth of microlensing events towards the Large Magellanic Cloud (LMC) should be correspondingly reduced. It appears that a truncated Galactic halo model instead of the standard isothermal one extending to LMC accounts naturally for the reported microlensing rate by the MACHO collaboration. Such an explanation is indeed obvious yet has been overlooked in the past.

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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

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

Do the lensing cross-sections of faint galaxies cover the whole sky ?

Very deep galaxy surveys have revealed a considerably large population of faint galaxies, which leads to the speculation that all distant objects are moderately magnified by the gravitational lensing effects of galaxies (Fried 1997). In this letter, we present a simple estimate of the lensing amplitudes by all galaxies up to redshift $z=2$ in terms of galaxy merging and answer the question whether the sky is fully covered by the lensing cross-sections of galaxies. It is shown that, as a result of the combination of the increase of galaxy number density and the decrease of galaxy velocity dispersion with lookback time, less than $\sim1/10$ of the sky to $z=2$ can be moderately affected by galaxies acting as lenses with magnification $μ>1.1$. This conclusion is independent of the galaxy limiting magnitude. In other words, no matter how high the surface number density of faint galaxies becomes, it is unlikely that their lensing cross-sections of $μ>1.1$ can cover the whole sky.

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arXiv1997

A remark on the inversion of the magnification bias in the quasar-galaxy associations

We present an alternative but intuitive method of obtaining the true or intrinsic quasar luminosity function through the observed one in the framework of gravitational lensing. Such a so-called inversion of the magnification bias can be straightforwardly performed by means of the Mellin transformation instead of other complex methods. Application of our approach to the well-known form of the observed quasar luminosity function identifies the previous results in literature.

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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

Self-Microlensing in Compact Binary Systems

The signature of the self-microlensing in compact binaries (white dwarfs, neutron stars and black holes) is a flare with the characteristic time of typically a few minutes. The probability of detecting these microlensing events can be as high as $1/50$ for a flux sensitivity of $Δm=0.01$ in magnitude. The discovery of the self-microlensing by binaries would furnish an additional way to find the masses of the lens and the companion and will be promising for the searches of black holes.

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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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