Solving the Conundrum of Dark Matter and Dark Energy in Galaxy Clusters

This paper develops the Dark Matter by Quantum Gravitation theory, DMbQG theory hereafter, in clusters of galaxies in the cosmologic model ΛCDM of the Universe. Originally this theory was developed by the author for galaxies, especially using MW and M31 rotation curves. An important result got by the DMbQG theory is that the total mass associated to a galactic halo depend on the square root of radius, being its dominion unbounded. Apparently, this result would be absurd because of divergence of the total mass. As the DE is negligible at galactic scale, it is needed to extend the theory to clusters in order to study the capacity of DE to counterbalance to DM. Thanks this property, the DMbQG theory finds unexpected theoretical results. In this work, it is defined, the total mass as baryonic matter plus DM and the gravitating mass as the addition of the total mass plus the negative mass associated to dark energy. In clusters it is defined the zero gravity radius (RZG hereafter) as the radius needed by the dark energy to counterbalance the total mass. It has been found that the ratio RZG/RVIRIAL ≈ 7.3 and its Total mass associated at RZG is ≈2.7 MVIRIAL. In addition, it has been calculated that the sphere with the extended halo radius RE = 1.85 RZG has a ratio DM density versus DE density equal to 3/7 and its total mass associated at RE is ≈3.6 MVIRIAL. This works postulates that the factor 3.6 may equilibrate perfectly the strong imbalance between the Local mater density parameter (0.08) versus the current Global matter density one (0.3). Currently, this fact is a big conundrum in cosmology, see chapter 7. Also it has been found that the zero velocity radius, RZV hereafter, i.e. the cluster border because of the Hubble flow, is ≈0.6 RZG and its gravitating mass is ≈ 1.5 MVIR. By derivation of gravitating mass function, it is calculated that at 0.49 RZG, this function reaches its maximum whose value is ≈1.57 MVIR. Throughout the paper, some of these results have been validated with recent data published for the Virgo cluster. As Virgo is the nearest big cluster, it is the perfect benchmark to validate any new theory about DM and DE. These new theoretical findings offer to scientific community a wide number of tests to validate or reject the theory. The validation of DMbQG theory would mean to know the nature of DM that at the present, it is an important challenge for the astrophysics science.

Study of 26 Galactic Open Clusters with Extended Main-sequence Turnoffs

Recent studies indicate that some Galactic open clusters(OCs)exhibit extended main-sequence turnoff(eMSTO)in their color–magnitude diagrams(CMDs).However,the number of Galactic OCs with eMSTO structures detected so far is limited,and the reasons for their formation are still unclear.This work identifies 26 Galactic OCs with undiscovered eMSTOs and investigates the causes of these features.Stellar population types and fundamental parameters of cluster samples are acquired using CMD fitting methods.Among them,the results of 11 OCs are reliable as the observed CMDs are well-reproduced.We propose the crucial role of stellar binarity and confirm the importance of stellar rotation in reproducing eMSTO morphologies.The results also show that the impact of age spread is important,as it can adequately explain the structure of young OCs and fit the observed CMDs of intermediate-age OCs better.

Weak Merging Scenario of CLASH Cluster A209

We study the structural and dynamical properties of A209 based on Chandra and XMM-Newton observations.We obtain detailed temperature,pressure,and entropy maps with the contour binning method,and find a hot region in the NW direction.The X-ray brightness residual map and corresponding temperature profiles reveal a possible shock front in the NW direction and a cold front feature in the SE direction.Combined with the galaxy luminosity density map we propose a weak merger scenario.A young sub-cluster passing from the SE to NW direction could explain the optical subpeak,the intracluster medium temperature map,the X-ray surface brightness excess,and the X-ray peak offset together.

A Possible X-ray Quasi-periodic Oscillation in the Narrow-line Seyfert 1 Galaxy Mrk 142

A possible quasi-periodic oscillation(QPO) at frequency 7.045 × 10^(-5) Hz is found in the narrow-line Seyfert 1galaxy Mrk 142 in the data of XMM-Newton collected on 2020 April 11.We find that the QPO signal is statistically significantly larger than the 5σ level and highly coherent with quality factor Q > 5 at the 0.3–10 keV band by using the method of the Lomb–Scargle Periodogram,the Weighted Wavelet Z-transform and the REDFIT.We analyze the data in 0.3–0.6 keV,0.6–1 keV,1–3 keV and 3–10 keV energy bands,and find obvious QPO signals at 0.3–0.6 keV and 1–3 keV bands.We then analyze the time-average spectra and time variability at the QPO frequency of 7.045 × 10^(-5) Hz,and use a model to fit them.We find that the QPO signal mainly comes from the X-ray hot corona.

Variable Stars in the 50BiN Open Cluster Survey.Ⅲ.NGC 884

Open clusters are the basic building blocks that serve as a laboratory for the study of young stellar populations in the Milky Way.Variable stars in open clusters provide a unique way to accurately probe the internal structure,temporal and dynamical evolutionary stages of individual stars and the host cluster.The most powerful tool for such studies is time-domain photometric observations.This paper follows the route of our previous work,concentrating on a photometric search for variable stars in NGC 884.The target cluster is the companion of NGC869,forming the well-known double cluster system that is gravitationally bound.From the observation run in 2016 November,a total of 9247 B-band CCD images and 8218Ⅴ-band CCD images were obtained.We detected a total of 15 stars with variability in visual brightness,including five Be stars,three eclipsing binaries,and seven of unknown types.Two new variable stars were discovered in this work.We also compared the variable star content of NGC 884 with its companion NGC 869.

Isochrone Fitting of Galactic Globular Clusters—Ⅵ.High-latitude Clusters NGC 5024 (M53),NGC 5053,NGC 5272 (M3),NGC 5466,and NGC7099 (M30)

We fit various color–magnitude diagrams(CMDs) of the high-latitude Galactic globular clusters NGC 5024(M53),NGC 5053,NGC 5272(M3),NGC 5466,and NGC 7099(M30) by isochrones from the Dartmouth Stellar Evolution Database and Bag of Stellar Tracks and Isochrones for α–enrichment [α/Fe] = +0.4.For the CMDs,we use data sets from Hubble Space Telescope,Gaia,and other sources utilizing,at least,25 photometric filters for each cluster.We obtain the following characteristics with their statistical uncertainties for NGC 5024,NGC 5053,NGC 5272,NGC 5466,and NGC 7099,respectively:metallicities [Fe/H] =-1.93 ± 0.02,-2.08 ± 0.03,-1.60 ± 0.02,-1.95 ± 0.02,and-2.07 ± 0.04 dex with their systematic uncertainty 0.1 dex;ages 13.00 ± 0.11,12.70 ± 0.11,11.63 ± 0.07,12.15 ± 0.11,and 12.80 ± 0.17 Gyr with their systematic uncertainty 0.8 Gyr;distances(systematic uncertainty added) 18.22 ± 0.06 ± 0.60,16.99 ± 0.06 ± 0.56,10.08 ± 0.04 ± 0.33,15.59 ±0.03 ± 0.51,and 8.29 ± 0.03 ± 0.27 kpc;reddenings E(B-V) = 0.023 ± 0.004,0.017 ± 0.004,0.023 ± 0.004,0.023 ± 0.003,and 0.045 ± 0.002 mag with their systematic uncertainty 0.01 mag;extinctions AV= 0.08 ± 0.01,0.06 ± 0.01,0.08 ± 0.01,0.08 ± 0.01,and 0.16 ± 0.01 mag with their systematic uncertainty 0.03 mag,which suggest the total Galactic extinction AV= 0.08 across the whole Galactic dust to extragalactic objects at the North Galactic Pole.The horizontal branch morphology difference of these clusters is explained by their different metallicity,age,mass-loss efficiency,and loss of low-mass members in the evolution of the core-collapse cluster NGC 7099 and loose clusters NGC 5053 and NGC 5466.

BSEC Method for Unveiling Open Clusters and its Application to Gaia DR3:83 New Clusters

Open clusters(OCs) are common in the Milky Way, but most of them remain undiscovered. There are numerous techniques, including some machine-learning algorithms, available for the exploration of OCs. However, each method has its limitations and therefore, different approaches to discovering OCs hold significant values. We develop a comprehensive approach method to automatically explore the data space and identify potential OC candidates with relatively reliable membership determination. This approach combines the techniques of Hierarchical Density-Based Spatial Clustering of Applications with Noise, Gaussian mixture model, and a novel cluster member identification technique, color excess constraint. The new method exhibits efficiency in detecting OCs while ensuring precise determination of cluster memberships. Because the main feature of this technique is to add an extra constraint(EC) for the members of cluster candidates using the homogeneity of color excess,compared to typical blind search codes, it is called Blind Search-Extra Constraint(BSEC) method. It is successfully applied to the Gaia Data Release 3, and 83 new OCs are found, whose color–magnitude diagrams(CMDs) are fitted well to the isochrones. In addition, this study reports 621 new OC candidates with discernible main sequence or red giant branch. It is shown that BSEC technique can discard some false negatives of previous works, which takes about three percentage of known clusters. It shows that as an EC, the color excess(or twocolor) constraint is useful for removing fake cluster member stars from the clusters that are identified from the positions and proper motions of stars, and getting more precise CMDs, when differential reddening of member stars of a cluster is not large(e.g., ΔE(G_(BP)-G_(RP)) < 0.5 mag). It makes the CMDs of 15% clusters clearer(in particular for the region near turnoff) and therefore is helpful for CMD and stellar population studies. Our result suggests that the color excess constraint is more appropriate for clusters with small differential reddening, such as globular clusters or older OCs, and clusters that the distances of member stars cannot be determined accurately.

A Fermi-LAT Study of Globular Cluster Dynamical Evolution in the Milky Way:Millisecond Pulsars as the Probe

Using archival Fermi-LAT data with a time span of~12 yr,we study the population of Millisecond Pulsars(MSPs)in Globular Clusters(GlCs)and investigate their dependence on cluster dynamical evolution in the Milky Way.We show that theγ-ray luminosity(L_(γ))and emissivity(i.e.,ε_(γ)=L_(γ)/M,with M the cluster mass)are good indicators of the population and abundance of MSPs in GlCs,and they are highly dependent on the dynamical evolution history of the host clusters.Specifically speaking,the dynamically older GlCs with more compact structures are more likely to have larger L_(γ)andε_(γ),and these trends can be summarized as strong correlations with cluster stellar encounter rateΓand the specific encounter rate(Λ=Γ/M),with L_(γ)∝Γ^(0.7±0.11)andε_(γ)∝Λ^(0.73±0.13)for dynamically normal GlCs.However,as GlCs evolve into deep core collapse,these trends are found to be reversed,implying that strong encounters may have lead to the disruption of Low-Mass X-ray Binaries and ejection of MSPs from core-collapsed systems.Besides,the GlCs are found to exhibit largerε_(γ)with increasing stellar mass function slope(ε_(γ)∝10^((0.52±0.1)α)),decreasing tidal radius(ε_(γ)∝R_(t)^(-10±0.22))and distances from the Galactic Center(GC,ε_(γ)∝R_(gc)^(-1.13±0.21)).These correlations indicate that,as GlCs losing kinetic energy and spiral in toward the GC,tidal stripping and mass segregation have a preference in leading to the loss of normal stars from GlCs,while MSPs are more likely to concentrate to cluster center and be deposited into the GC.Moreover,we gaugeε_(γ)of GlCs is~10-1000 times larger than the Galactic bulge,the latter is thought to reside thousands of unresolved MSPs and may be responsible for the GC 7-ray excess,which supports that GlCs are generous contributors to the population of MSPs in the GC.

Cluster Analysis of the Roma-BZCAT Blazars

Based on the collected multiwavelength data, namely in the radio(NVSS, FIRST, RATAN-600), IR(WISE),optical(Pan-STARRS), UV(GALEX), and X-ray(ROSAT, Swift-XRT) ranges, we have performed a cluster analysis for the blazars of the Roma-BZCAT catalog. Using two machine learning methods, namely a combination of PCA with k-means clustering and Kohonen's self-organizing maps(SOMs), we have constructed an independent classification of the blazars(five classes) and compared the classes with the known Roma-BZCAT classification(FSRQs, BL Lacs, galaxy-dominated BL Lacs, and blazars of an uncertain type) as well as with the high synchrotron peaked(HSP) blazars from the 3HSP catalog and blazars from the TeVCat catalog. The obtained groups demonstrate concordance with the BL Lac/FSRQ classification along with a continuous character of the change in the properties. The group of HSP blazars stands out against the overall distribution. We examine the characteristics of the five groups and demonstrate distinctions in their spectral energy distribution shapes. The effectiveness of the clustering technique for objective analysis of multiparametric arrays of experimental data is demonstrated.

A Dark Matter Theory by Quantum Gravitation for Galaxies and Clusters

This paper develops an original theory of dark matter in the current ΛCDM framework, whose main hypothesis is that DM is generated by the own gravitational field, according to an unknown quantum gravitational phenomenon. This work is the best version of the theory, which I have been developing and publishing since 2014. The hypothesis of DM by quantum gravitation, DMbQG hereafter, has two main consequences: the first one is that the law of DM generation has to be the same, in the halo region, for all the galaxies and the second one is that the haloes are unbounded, so the total DM goes up without limit as the gravitational field is unbounded as well. The first one consequence is backed by the fact that M31 and MW has a fitted function with the same power exponent for the rotation curve at the halo region and both giant galaxies are the only ones whose rotation curves at the halo region may be studied with accuracy. This paper is firstly developed all the theory with M31 rotation curve data up to Chapter 9. The most important formula of the theory is the called Direct mass, which calculates the total mass at a specific radius into the halo region. Chapter 10 is dedicated to apply the theory to Milky Way, it is calculated its total mass at different radius into the halo and such results have been validated successfully using the data of masses at different radius published by two researcher teams. In Chapter 11, it is calculated the direct mass for the Local Group, and it is shown how the DMbQG theory is able to calculate the total mass at 770 kpc, that the dynamical methods estimate to be 5×1012MΘ. In Chapter 12, it is shown a method to estimate the Direct mass formula for a cluster of galaxies, using only its virial mass and virial radius. By this method, it is estimated the parameter a2 of the Local Group, which match with the one calculated in previous chapter by a different method. Also are calculated the parameters a2 associated to Virgo and Coma clusters. In Chapter 13, it is demonstrated how the DE is able to counterbalance the DM at cluster scale, as the Direct mass grows up with the square root of radius whereas the DE grows up with the cubic power. The chapter is an introduction to the DMbQG theory for cluster of galaxies, which has been developed fully by the author in other works. This theory aims to be a powerful method to study DM in the halo region of galaxies and cluster of galaxies and conversely the measures in galaxies and clusters offer the possibility to validate the theory.

A Possible γ-Ray Pulsation from PSR J1740-5340B in the Globular Cluster NGC 6397

Recently, a new radio millisecond pulsar(MSP) J1740-5340B, hosted in the globular cluster(GC) NGC 6397,was reported with a 5.78 ms spin period in an eclipsing binary system with a 1.97 days orbital period. Based on a modified radio ephemeris updated by tool tempo2, we analyze the ~15 yr γ-ray data obtained from the Large Area Telescope on board the Fermi Gamma-ray Space Telescope and detect PSR J1740-5340B's γ-ray pulsation at a confidence level of ~4σ with a weighted H-test value of ~26. By performing a phase-resolved analysis, the γ-ray luminosity in on-pulse interval of PSR J1740-5340B is L_(γ)~ 3.8 × 10^(33) erg s^(-1) using NGC 6397's distance of 2.48 kpc. And γ-rays from the on-pulse part of PSR J1740-5340B contribute ~90% of the total observed γ-ray emissions from NGC 6397. No significant γ-ray pulsation of another MSP J1740-5340A in the GC is detected.Considering that the previous four cases of MSPs in GCs, more data in γ-ray, X-ray, and radio are encouraged to finally confirm the γ-ray emissions from MSP J1740-5340B, especially starving for a precise ephemeris.

A Simulation of the Dependence of Tidal Interaction on Galaxy Type in Compact Groups

We have investigated the role that different galaxy types have in galaxy-galaxy interactions in compact groups. N-body simulations of 6 galaxies consisting of a differing mixture of galaxy types were run to compare the relative importance of galaxy population demographic on evolution. Three different groups with differing galaxy content were tested: all spiral, a single elliptical and 50% elliptical. Tidal interaction strength and duration were recorded to assess the importance of an interaction. A group with an equal number of spiral and elliptical galaxies has some of the longest and strongest interactions with elliptical-elliptical interactions being most significant. These elliptical-elliptical interactions are not dominated by a single large event but consist of multiple interactions. Elliptical galaxies tidally interacting with spiral galaxies, have the next strongest interaction events. For the case when a group only has a single elliptical, the largest magnitude tidal interaction is an elliptical on a spiral. Spirals interact with each other through many small interactions. For a spiral only group, the interactions are the weakest compared to the other group types. These spiral interactions are not dominated by any singular event that might be expected to lead to a merger but are more of an ongoing harassment. These results suggest that within a compact group, early type galaxies will not form via merger out of an assemblage of spiral galaxies but rather that compact groups, in effect form around an early type galaxy.

Internal Defects Detection Method of the Railway Track Based on Generalization Features Cluster Under Ultrasonic Images

There may be several internal defects in railway track work that have different shapes and distribution rules,and these defects affect the safety of high-speed trains.Establishing reliable detection models and methods for these internal defects remains a challenging task.To address this challenge,in this study,an intelligent detection method based on a generalization feature cluster is proposed for internal defects of railway tracks.First,the defects are classified and counted according to their shape and location features.Then,generalized features of the internal defects are extracted and formulated based on the maximum difference between different types of defects and the maximum tolerance among same defects’types.Finally,the extracted generalized features are expressed by function constraints,and formulated as generalization feature clusters to classify and identify internal defects in the railway track.Furthermore,to improve the detection reliability and speed,a reduced-dimension method of the generalization feature clusters is presented in this paper.Based on this reduced-dimension feature and strongly constrained generalized features,the K-means clustering algorithm is developed for defect clustering,and good clustering results are achieved.Regarding the defects in the rail head region,the clustering accuracy is over 95%,and the Davies-Bouldin index(DBI)index is negligible,which indicates the validation of the proposed generalization features with strong constraints.Experimental results prove that the accuracy of the proposed method based on generalization feature clusters is up to 97.55%,and the average detection time is 0.12 s/frame,which indicates that it performs well in adaptability,high accuracy,and detection speed under complex working environments.The proposed algorithm can effectively detect internal defects in railway tracks using an established generalization feature cluster model.

Combining optical and X-ray observations of galaxy clusters to constrain cosmological parameters

Galaxy clusters present unique advantages for cosmological study.Here we collect a new sample of 10 lensing galaxy clusters with X-ray observations to constrain cosmological parameters.The redshifts of the lensing clusters lie between 0.1 and 0.6,and the redshift range of their arcs is from 0.4 to 4.9.These clusters are selected carefully from strong gravitational lensing systems which have both X-ray satellite observations and optical giant luminous arcs with known redshifts.Giant arcs usually appear in the central region of clusters,where mass can be traced with luminosity quite well.Based on gravitational lensing theory and a cluster mass distribution model,we can derive a ratio using two angular diameter distances.One is the distance between lensing sources and the other is that between the deflector and the source. Since angular diameter distance relies heavily on cosmological geometry,we can use these ratios to constrain cosmological models.Moreover,X-ray gas fractions of galaxy clusters can also be a cosmological probe.Because there are a dozen parameters to be fitted,we introduce a new analytic algorithm,Powell＇s UOBYQA（Unconstrained Optimization By Quadratic Approximation） ,to accelerate our calculation.Our result demonstrates that this algorithm is an effective fitting method for such a continuous multi-parameter constraint.We find an interesting fact that these two approaches are separately sensitive toΩΛandΩM.By combining them,we can get reasonable fitting values of basic cosmological parameters：ΩM=0.26 ＋0.04 -0.04,andΩΛ=0.82 ＋0.14 -0.16.

Biases in hydrostatic mass profiles introduced by hot gas substructures:Chandra study of four galaxy clusters

By analyzing the azimuthal variations of total gravitating mass profiles in the central 300 h^-1 71 kpc regions of four galaxy clusters with Chandra data, we find that the azimuthally-averaged mass profiles may have been systematically underestimated by 16^＋9 -8% at lσ significance in the 50-100 h^-1 71 kpc regions, probably due to the prevailing existence of 2-D hot gas substructures in 100-300h^-1 71 kpc. The mass biases become negligible（-7＋11 _9＋ %） at 〉 150 h^-1 71 kpc. We confirm the results that the gas temperature maps can be used to probe the departure from hydrostatic equilibrium and help quantify the systematic biases in X-ray mass measurements in the central regions of clusters.

Central gas entropy excess as direct evidence for AGN feedback in galaxy groups and clusters

By analyzing Chandra X-ray data of a sample of 21 galaxy groups and 19 galaxy clusters, we find that in 31 sample systems there exists a significant central （R ≤ 10 h^-171 kpc） gas entropy excess （AK0）, which corresponds to = 0.1 - 0.5 keV per gas particle, beyond the power-law model that best fits the radial entropy profile of the outer regions. We also find a distinct correlation between the central entropy excess △K0 and K-band luminosity LK of the central dominating galaxies （CDGs）, which is scaled as △K0 ∝ L K 1.6±04, where LK is tightly associated with the mass of the supermassive black hole hosted in the CDG. In fact, if an effective mass-to-energy conversionefficiency of 0.02 is assumed for the accretion process, the cumulative AGN feedback E AGN feedack=ηMBHc2 yields an extra heating of = 0.5 - 17.0keV per particle, which feedback is sufficient to explain the central entropy excess. In most cases, the AGN contribution can compensate the radiative loss of the X-ray gas within the cooling radius （= 0.002 - 2.2 keV per particle）, and apparently exceeds the energy required to cause the scaling relations to deviate from the self-similar predictions （=0.2 - 1.0 keV per particle）. In contrast to the AGN feedback, the extra heating provided by supernova explosions accounts for = 0.01 - 0.08 keV per particle in groups and is almost negligible in clusters. Therefore, the observed correlation between △K0 and Lx can be considered as direct evidence for AGN feedback in galaxy groups and clusters.

Not enough evidence to support the correlation between gamma-ray bursts and foreground galaxy clusters in the Swift Era

The correlation between distant Gamma-Ray Bursts （GRBs） and foreground galaxy clusters is re-examined by using the well localized （with an accuracy down to a few arcsec） Swift/XRT GRBs. The galaxy clusters are compiled from both the X-ray selected ROSAT brightest cluster sample （BCS） and the BCS extension by requiring δ ≥ 0° and b ≥ 20°. The Swift/XRT GRBs fulfilling the above selection criteria are cross-correlated with the clusters. Both Nearest-Neighbor analysis and the angular two-point cross-correlation function show that there is not enough evidence supporting the correlation between the GRBs and foreground clusters. We suggest that the non-correlation is probably related to the GRB number-flux relation slope.

Multicolor photometry of the galaxy cluster A98: substructures and star formation properties

An optical photometric observation with the Beijing-Arizona-Taiwan- Connecticut （BATC） multicolor system is carried out for A98 （z =0.104）, a galaxy cluster with two large enhancements in X-ray surface brightness. Spectral energy distributions （SEDs） covering 15 intermediate bands are obtained for all sources detected down to V - 20 mag in a field of 58′× 58′. After star-galaxy separation with colorcolor diagrams, a photometric redshift technique is applied to the galaxy sample for further membership determination. The color-magnitude relation is taken as a further restriction of the early-type cluster galaxies. As a result, a list of 198 faint member galaxies is achieved. Based on the newly generated sample of member galaxies, the dynamical substructures, A98N, A98S, and A98W, are investigated in detail. A separate galaxy group, A98X, is also found to the south of the main concentration of A98, which is gravitationally unbound to A98. For 74 spectroscopically confirmed member galaxies, the environmental effect on the star formation history is investigated. The bright galaxies in the core region are found to have shorter time scales of star formation, longer mean stellar ages, and higher interstellar medium metallicities, which can be interpreted in the context of the hierarchical cosmological scenario.

The Origin of Cosmic Structures Part 3 — Supermassive Black Holes and Galaxy Cluster Evolution

In Part 1 of this work, we showed that our new model of cosmology can account for the origin of all cosmic structures ranging in size from stars up to superclusters. In this model, at the time of nucleosynthesis, an imprint embedded in the vacuum regulated the creation of the protons (and electrons) that later made up the structures. Immediately after nucleosynthesis and for a considerable period afterward, the evolution was completely determined by the expansion of the universe. Gradually, however, gravitational influences became more important until finally, the expansion of the structures-to-be ceased at their zero velocity points. Stars, galaxies, and galaxy clusters all reached their zero velocity points more or less simultaneously at the usually accepted time of the beginning of galaxy formation. From that point onward, the evolution gravitation came to dominate the evolution although the expansion still exerted its influence. In this paper, we examine the subsequent cluster evolution in some detail. We establish the conditions required to prevent a free-fall collapse of the clusters and then show that galaxies with quasar-like active nuclei located within the cluster were the sources of the necessary radiation. We also show that the required galactic supermassive black holes were a consequence of the initial free-fall collapse of all galaxies.

Reconstruction of Gas Temperature and Density Profiles of the Galaxy Cluster RX J1347.5–1145

We use observations of Sunyaev-Zel＇dovich effect and X-ray surface brightness to reconstruct the radial profiles of gas temperature and density under the assumption of a spherically symmetric distribution of the gas. The method of reconstruction, first raised by Silk ＆ White, depends directly on the observations of the Sunyaev-Zel＇dovich effect and the X-ray surface brightness, without involving additional assumptions such as the equation of state of the gas or the conditions of hydrostatic equilibrium. We applied this method to the cluster RX J1347.5-1145, which has both the Sunyaev-Zel＇dovich effect and X-ray observa- tions with relative high precision. It is shown that it will be an effective method to obtain the gas distribution in galaxy clusters. Statistical errors of the derived temperature and density profiles of gas were estimated according to the observational uncertainties.