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Study of the Structure of the Coma Cluster Based on a Hierarchical Force Clustering Method
Six subclusters in the Coma cluster have been selected on the basis of ahierarchical clustering method that takes the gravitational interactionamong galaxies into account. Of these, 3 central subclusters around thegalaxies NGC 4889, NGC 4874, and NGC 4839 have been singled out. We haveused the objective statistical criterion applied by Vennik and Anosovain studies of close groups of galaxies to evaluate each member includedin a subcluster with a high probability. Galaxies with a significantdeficit of hydrogen HI, including objects from the Bravo-Alfaro list,have been identified with members of the subclusters, with the greatestnumber of them in the subclusters around NGC 4874 and NGC 4839. Aquantitative estimate of the hydrogen deficit using the HI index in theRCG3 catalog reveals a statistically significant excess value for thosegalaxies that are members of the subclusters compared to galaxies with ahydrogen deficit in the overall Coma cluster field. A substantial numberof the spiral galaxies with a hydrogen deficit in the subclusters turnedout to be radio galaxies as well.
| The H I Line Width/Linear Diameter Relationship as an Independent Test of the Hubble Constant
The relationship between corrected H I line widths and linear diameters(LW/LD) for spiral galaxies is used as an independent check on the valueof the Hubble constant. After calibrating the Tully-Fisher (TF) relationin both the B and I bands, the B-band relation is used for galaxies ofmorphological/luminosity types Sc I, Sc I.2, Sc I.3, Sab, Sb, Sb I-II,and Sb II to derive the LW/LD relation. We find that for this sample thescatter in the LW/LD is smallest with a Hubble constant of 90-95 kms-1 Mpc-1. Lower values of the Hubble constantproduce a separation in the LW/LD relation that is a function ofmorphological type. Since a Hubble constant of 90-95 is significantlylarger than the final Key Project value of 72 km s-1Mpc-1, a comparison of TF, surface brightness fluctuation(SBF), and fundamental plane (FP) is made. This comparison indicatesthat the Key Project TF distances to 21 clusters may be too large. For asample of 11 clusters, the Key Project TF distances provide anunweighted mean Hubble constant of 77 km s-1Mpc-1, while a combination of the FP, SBF, and our TFdistances for the same 11 clusters gives H0=91 kms-1 Mpc-1. A more subtle result in our data is amorphological dichotomy in the Hubble constant. The data suggest that ScI galaxies follow a Hubble constant of 90-95 while Sb galaxies follow aHubble constant closer to 75 km s-1 Mpc-1.Possible explanations for this result are considered, but it is shownthat this Sb/Sc I Hubble flow discrepancy is also present in the VirgoCluster and is consistent with previous investigations that indicatethat some galaxies carry a component of age-related intrinsic redshift.
| Distances to Galaxies from the Correlation between Luminosities and Line Widths. III. Cluster Template and Global Measurement of H0
The correlation between the luminosities and rotation velocities ofgalaxies can be used to estimate distances to late-type galaxies. It isan appropriate moment to reevaluate this method given the great deal ofnew information available. The major improvements described hereinclude: (1) the template relations can now be defined by large,complete samples, (2) the samples are drawn from a wide range ofenvironments, (3) the relations are defined by photometric informationat the B, R, I, and K' bands, (4) the multiband information clarifiesproblems associated with internal reddening, (5) the template zeropoints are defined by 24 galaxies with accurately known distances, and(6) the relations are applied to 12 clusters scattered across the skyand out to velocities of 8000 km s-1. The biggest change fromearlier calibrations are associated with point 5. Roughly a 15% increasein the distance scale has come about with the fivefold increase in thenumber of zero-point calibrators. The overall increase in the distancescale from the luminosity-line width methodology is about 10% afterconsideration of all factors. Modulo an assumed distance to the LargeMagellanic Cloud of 50 kpc and no metallicity corrections to the Cepheidcalibration, the resulting value of the Hubble constant isH0=77+/-8 km s-1 Mpc-1, where the erroris the 95% probable statistical error. Cumulative systematic errorsinternal to this analysis should not exceed 10%. Uncertainties in thedistance scale ladder external to this analysis are estimated at ~10%.If the Cepheid calibration is shifted from the LMC to NGC 4258 with adistance established by observations of circumnuclear masers, thenH0 is larger by 12%.
| Luminosity versus Phase-Space-Density Relation of Galaxies Revisited
We reexamined the correlation between the BTmagnitude and the phase-space-density parameterw=(D225vc)-1 of galaxies forthe Virgo, the Coma, the Fornax, and the Perseus clusters in an effortto better understand the physical underpinning of the fundamental plane.A tight correlation (BT=alog w+b) common to differentmorphological types of galaxies (E, S0, S) was found for the Virgo andthe Coma clusters, with a=1.87+/-0.10 and 1.33+/-0.11, respectively. Aninvestigation using only E galaxies was made for the four clusters. Theresults indicated that the empirical linear relation might be commonamong the Coma, the Fornax, and the Perseus clusters, with the VirgoCluster showing deviation. This relation, which is another way toproject the fundamental plane, has an expression insensitive to themorphology and may be suitable for treating galaxies of differentmorphological types collectively.
| 1.65 μm (H-band) surface photometry of galaxies. III. observations of 558 galaxies with the TIRGO 1.5 m telescope
We present near-infrared H-band (1.65 μm ) surface photometry of 558galaxies in the Coma Supercluster and in the Virgo cluster. This dataset, obtained with the Arcetri NICMOS3 camera ARNICA mounted on theGornergrat Infrared Telescope, is aimed at complementing, withobservations of mostly early-type objects, our NIR survey of spiralgalaxies in these regions, presented in previous papers of this series.Magnitudes at the optical radius, total magnitudes, isophotal radii andlight concentration indices are derived. We confirm the existence of apositive correlation between the near-infrared concentration index andthe galaxy H-band luminosity Based on observations taken at TIRGO(Gornergrat, Switzerland). TIRGO is operated by CAISMI-CNR, Arcetri,Firenze, Italy. Tables 1 and 2 are only available in electronic form atthe CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html
| 1.65 μm (H-band) surface photometry of galaxies. V. Profile decomposition of 1157 galaxies
We present near-infrared H-band (1.65 μm) surface brightness profiledecomposition for 1157 galaxies in five nearby clusters of galaxies:Coma, A1367, Virgo, A262 and Cancer, and in the bridge between Coma andA1367 in the ``Great Wall". The optically selected (mpg≤16.0) sample is representative of all Hubble types, from E to Irr+BCD,except dE and of significantly different environments, spanning fromisolated regions to rich clusters of galaxies. We model the surfacebrightness profiles with a de Vaucouleurs r1/4 law (dV), withan exponential disk law (E), or with a combination of the two (B+D).From the fitted quantities we derive the H band effective surfacebrightness (μe) and radius (re) of each component, theasymptotic magnitude HT and the light concentration indexC31. We find that: i) Less than 50% of the Ellipticalgalaxies have pure dV profiles. The majority of E to Sb galaxies is bestrepresented by a B+D profile. All Scd to BCD galaxies have pureexponential profiles. ii) The type of decomposition is a strong functionof the total H band luminosity (mass), independent of the Hubbleclassification: the fraction of pure exponential decompositionsdecreases with increasing luminosity, that of B+D increases withluminosity. Pure dV profiles are absent in the low luminosity rangeLH<1010 L\odot and become dominantabove 1011 L\odot . Based on observations taken atTIRGO, Gornergrat, Switzerland (operated by CAISMI-CNR, Arcetri,Firenze, Italy) and at the Calar Alto Observatory (operated by theMax-Planck-Institut für Astronomie (Heidelberg) jointly with theSpanish National Commission for Astronomy). Table 2 and Figs. 2, 3, 4are available in their entirety only in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/Abstract.html
| Arcsecond Positions of UGC Galaxies
We present accurate B1950 and J2000 positions for all confirmed galaxiesin the Uppsala General Catalog (UGC). The positions were measuredvisually from Digitized Sky Survey images with rms uncertaintiesσ<=[(1.2")2+(θ/100)2]1/2,where θ is the major-axis diameter. We compared each galaxymeasured with the original UGC description to ensure high reliability.The full position list is available in the electronic version only.
| Total magnitude, radius, colour indices, colour gradients and photometric type of galaxies
We present a catalogue of aperture photometry of galaxies, in UBVRI,assembled from three different origins: (i) an update of the catalogueof Buta et al. (1995) (ii) published photometric profiles and (iii)aperture photometry performed on CCD images. We explored different setsof growth curves to fit these data: (i) The Sersic law, (ii) The net ofgrowth curves used for the preparation of the RC3 and (iii) A linearinterpolation between the de Vaucouleurs (r(1/4) ) and exponential laws.Finally we adopted the latter solution. Fitting these growth curves, wederive (1) the total magnitude, (2) the effective radius, (3) the colourindices and (4) gradients and (5) the photometric type of 5169 galaxies.The photometric type is defined to statistically match the revisedmorphologic type and parametrizes the shape of the growth curve. It iscoded from -9, for very concentrated galaxies, to +10, for diffusegalaxies. Based in part on observations collected at the Haute-ProvenceObservatory.
| Tests of the Tully-Fisher Relation.II.Scatter Using Optical Rotation Curves
We investigate the amount of scatter in the Tully-Fisher relation (TFR)when using optical long-slit \ha\ rotation curves to determine thevelocity widths of spiral galaxies. We study a sample of 25 galaxies inthe Coma region of the sky which were shown in Bernstein et al.\markcite{B1} (1994) to exhibit an extraordinarily low scatter of 0.10mag RMS in the I magnitude vs 21-cm width TFR. Using the same Imagnitudes with new widths derived from high-quality \ha\ rotationcurves, we measure an RMS scatter of 0.14 mag in the TFR. This suggeststhat measurement errors and ``astrophysical errors'' (such asnon-circular gas motion) on the \ha\ velocity widths are below 6%, andoptical widths are nearly as good for TFR studies as 21-cm widths. Thescatter and form of the TFR are found to be robust under choice ofvelocity width-extraction algorithm, as long as the central portions ofthe optical rotation curve are ignored and low-S/N points are notweighted too heavily. In this small sample there is no evidence thatrotation curve shapes vary systematically with rotation velocity, northat rotation curve shape can be used to reduce the scatter in the TFR.
| The I band Tully-Fisher relation for cluster galaxies: data presentation.
Observational parameters which can be used for redshift-independentdistance determination using the Tully-Fisher (TF) technique are givenfor \ntot spiral galaxies in the fields of 24 clusters or groups. I bandphotometry for the full sample was either obtained by us or compiledfrom published literature. Rotational velocities are derived either from21 cm spectra or optical emission line long-slit spectra, and convertedto a homogeneous scale. In addition to presenting the data, a discussionof the various sources of error on TF parameters is introduced, and thecriteria for the assignment of membership to each cluster are given.
| An image database. II. Catalogue between δ=-30deg and δ=70deg.
A preliminary list of 68.040 galaxies was built from extraction of35.841 digitized images of the Palomar Sky Survey (Paper I). For eachgalaxy, the basic parameters are obtained: coordinates, diameter, axisratio, total magnitude, position angle. On this preliminary list, weapply severe selection rules to get a catalog of 28.000 galaxies, wellidentified and well documented. For each parameter, a comparison is madewith standard measurements. The accuracy of the raw photometricparameters is quite good despite of the simplicity of the method.Without any local correction, the standard error on the total magnitudeis about 0.5 magnitude up to a total magnitude of B_T_=17. Significantsecondary effects are detected concerning the magnitudes: distance toplate center effect and air-mass effect.
| Automated surface photometry for the Coma Cluster galaxies: The catalog
A homogeneous photometry catalog is presented for 450 galaxies withB25.5 less than or equal to 16 mag located in the 9.8 deg x9.8 deg region centered on the Coma Cluster. The catalog is based onphotographic photometry using an automated surface photometry softwarefor data reduction applied to B-band Schmidt plates. The catalogprovides accurate positions, isophotal and total magnitudes, major andminor axes, and a few other photometric parameters including rudimentarymorphology (early of late type).
| Colors, luminosities, and masses of disk galaxies. 2: Environmental dependenceis
The B-band and near-infrared (H) luminosity functions of spiral galaxiesare derived for the Coma and A1367 clusters and for a referencepopulation of 'field' galaxies in the Coma supercluster. They areconsistent at the bright end, but they differ significantly at the faintend, indicating an overdensity of spirals with blue color (B-H less than3.0) and faint H luminosity (H greater than -21.5) in clusters withrespect to the field. These objects have disturbed morphology andpeculiar velocities significantly larger than the rest of the clustersample. We discuss these results in the framework of a possibleenvironmental dependence of galaxy evolution, and we conclude thatenhanced current star formation in cluster spiral galaxies might occurdue to molecular gas collapse stimulated by the ram-pressure mechanism.
| Galaxy Properties at the North Galactic Pole. I. Photometric Properties on Large Spatial Scales
A two-color study of the galaxies detected on POSS-I in a 289 squaredegree region centered on the North Galactic Pole is presented. We use avariety of mapping techniques to characterize the large-scale spatialdistribution of galaxies. The depth and sample size of this new surveyallows, for the first time, the isolation of large photometricsubsamples of galaxies in high- and low-density environments on thescale of superclusters. Our principal finding is a statisticallysignificant difference between the mean photometric properties of thesesubsamples in the sense that galaxies in the high-density Coma andfilament environments have redder colors and larger concentrationindices than galaxies drawn from low-density interfilament regions.These results are in accord with the known morphology-density relation.Thus, appropriately chosen photometric and morphological parameters, inconcert with a galaxy surface density map, can be used to selectstructures from the projected galaxy distribution which correspond toregions of high density. An illustration of this point is our discoveryof a concentration of blue galaxies identified in our maps near the coreof the Coma cluster. This feature is comprised of early-type galaxieswhich exhibit signs of current or recent star formation. These resultsare predicated on relations between morphological type and photometricparameters derived from APS scans of POSS-I. We therefore discuss theimage calibration procedures used to compile our catalog of physicallysignificant photometric parameters. We demonstrate the morphologicaltype dependence among quantities such as mean color and imageconcentration index, and the lack of such a dependence for mean surfacebrightness.
| Tests of the Tully-Fisher relation. 1: Scatter in infrared magnitude versus 21 CM width
We examine the precision of the Tully-Fisher relation (TFR) using asample of galaxies in the Coma region of the sky, and find that it isgood to 5% or better in measuring relative distances. Total magnitudesand disk axis ratios are derived from H and I band surface photometry,and Arecibo 21 cm profiles define the rotation speeds of the galaxies.Using 25 galaxies for which the disk inclination and 21 cm width arewell defined, we find an rms deviation of 0.10 mag from a linear TFRwith dI/d(log Wc) = -5.6. Each galaxy is assumed to be at adistance proportional to its redshift, and an extinction correction of1.4(1-b/a) mag is applied to the total I magnitude. The measured scatteris less than 0.15 mag using milder extinction laws from the literature.The I band TFR scatter is consistent with measurement error, and the 95%CL limits on the intrinsic scatter are 0-0.10 mag. The rms scatter usingH band magnitudes is 0.20 mag (N = 17). The low width galaxies havescatter in H significantly in excess of known measurement error, but thehigher width half of the galaxies have scatter consistent withmeasurement error. The H band TFR slope may be as steep as the I bandslope. As the first applications of this tight correlation, we note thefollowing: (1) the data for the particular spirals commonly used todefine the TFR distance to the Coma cluster are inconsistent with beingat a common distance and are in fact in free Hubble expansion, with anupper limit of 300 km/s on the rms peculiar line-of-sight velocity ofthese gas-rich spirals; and (2) the gravitational potential in the disksof these galaxies has typical ellipticity less than 5%. The publisheddata for three nearby spiral galaxies with Cepheid distancedeterminations are inconsistent with our Coma TFR, suggesting that theselocal calibrators are either ill-measured or peculiar relative to theComa Supercluster spirals, or that the TFR has a varying form indifferent locales.
| Tully-Fisher distances to M31-like galaxies in the Coma cluster
Newly observed H I 21 cm linewidths for eight galaxies and morphologicaltypes for 33 galaxies are combined with data in the literature toconstruct a homogeneous magnitude-limited sample of spiral galaxies inthe Coma cluster. From this sample, we identify the seven Coma M31-likegalaxies, i.e. the spiral members with inclinations larger than -44 degand deprojected linewidths larger than -440 km/s. The distance moduli ofthese seven galaxies obtained by application of a blue-band Tully-Fisher(TF) relation are used to measure the distance to the Coma cluster. Ourresult, which is free of 'Malmquist' bias at the 3 sigma level, is adistance modulus of micron(0) = 34.4 +/- 0.2, which corresponds to aHubble constant H(0) of about 90 km/s Mpc. The observed rms dispersionof blue-band TF distance moduli for the seven Coma M31-like galaxies is0.14 mag, which is consistent with observational uncertainties alone,i.e. no intrinsic dispersion of the blue-band TF relation has beendetected above the observational rms noise level of 0.14 mag. This smallscatter is a specific result of our strict selection criteria adopted atthe onset of the analysis.
| A revised catalog of CfA1 galaxy groups in the Virgo/Great Attractor flow field
A new identification of groups and clusters in the CfA1 Catalog ofHuchra et al. is presented, using a percolation algorithm to identifydensity enhancements. It is shown that in the resulting catalog,contamination by interlopers is significantly reduced. The Schechterluminosity function is redetermined, including the Malmquist bias.
| The distance to the Coma cluster using the B-band Tully-Fisher relation
The present estimate of the distance to the Coma cluster on the basis ofthe B-band Tully-Fisher (T-F) relation has conducted photographicsurface photometry on all galaxies for which H I line width data in acircle of 4-deg radius centered on the Coma cluster. A detailed estimateis made of the cluster population incompleteness bias for the distanceestimation. While the correction for sample incompleteness, inconjunction with the T-F relation, increases the distance modulus, theresult cannot be as large as the value indicated by Kraan-Kortweg et al.(1988).
| Groups of galaxies in the Center for Astrophysics redshift survey
By applying the Huchra and Geller (1982) objective group identificationalgorithm to the Center for Astrophysics' redshift survey, a catalog of128 groups with three or more members is extracted, and 92 of these areused as a statistical sample. A comparison of the distribution of groupcenters with the distribution of all galaxies in the survey indicatesqualitatively that groups trace the large-scale structure of the region.The physical properties of groups may be related to the details oflarge-scale structure, and it is concluded that differences among groupcatalogs may be due to the properties of large-scale structures andtheir location relative to the survey limits.
| Near-infrared observations of galaxies in the Coma supercluster
Near-IR magnitudes have been obtained for 136 galaxies in the Coma/A1367supercluster region, and near-IR colors (J-H) and (H-K) for 90 and 87objects, respectively. The near-IR colors are contained in a small rangeand do not depend on morphological types, galaxy inclination, orenvironment. Optical-to-IR colors depend strongly on a galaxy'smorphological type and inclination. There is a dependence of therelative excess of radio, and to a lesser degree, of far-IR emission onrecent star formation activity. The magnitude-line width relation forgalaxies in Coma and A1367 obtained with these data has a larger spreadthan previously found with smaller samples. The data suggest a distancemodulus to Coma of about 35, regardless of the choice of primarycalibrators.
| 21 centimeter study of spiral galaxies in the Coma supercluster
High-sensitivity, 21 cm line observations of 130 galaxies in theComa/A1367 Supercluster region are presented and used to study thelarge-scale distribution of galaxies in the direction of the ComaSupercluster and the H I content in spiral galaxies as a function of thelocal galaxy density. Groups of galaxies are found to form aquasi-continuous structure that connects the Local Supercluster to theComa Supercluster. This structure is composed of real filaments only inthe vicinity of the Coma Cluster. Spiral galaxies in the surveyed groupsand multiple systems have H I content not dissimilar from that ofisolated galaxies. Galaxies within about 1 Abell radius from the ComaCluster contain about three times less hydrogen on average than isolatedgalaxies. There is a strong tendency for galaxies that are more severelyH I-depleted to be redder and of earlier Hubble type. In the ComaCluster a considerable fraction of late-type, blue galaxies have largedeficiency parameters.
| Taxonomical analysis of superclusters. II - The A1367/Coma supercluster
The nonhierarchical taxonomical method has been applied to a sample of185 galaxies, complete to m not greater than 15, in the A1367/Comaregion. Once the fore- and background galaxies have been identified, theanalysis of the A1367 cluster shows it composed by two gravitationallybound clumps at essentially the same redshift, 6396 km/s and 6562 km/s,respectively. Central Coma is traced by three different groups whosegravitational binding does not appear clearly. However, accepting theunique dynamical entity of Central Coma, some other neighboring groupswould be part of the cluster. In that case, the average radial velocityand dispersion of the Coma cluster would be 7013 and 423 km/s,respectively. The M/L ratios for the groups evidenced by the taxonomyrange from 13 to 170. The missing mass problem only appears when all thegalaxies in the sample are considered as members of a unique dynamicalstructure. The relationship found in other systems between the redshift,the morphological type and the radioemissivity is also present in thesample.
| Radio continuum survey of the Coma/A1367 supercluster. II - 1.5 GHz observations of 396 CGCG galaxies
1.5 GHz VLA radio continuum observations of 396 relatively isolated CGCGgalaxies in the Coma/A1367 supercluster yielded the detection of 95objects. These observations, added to the ones presented in previouspapers, form a complete sample of optically selected objects with m(p)equal to or less than 15.3. Two wide-angle-tailed sources have beenfound in smaller groups within the supercluster.
| Radio emission of isolated single and double galaxies
The catalogs of Karachentsev (1972) and Karachentseva (1973) are used tocompare the properties of isolated single and double galaxies, andquantitative results are obtained. It is shown that spiral galaxieswhich are members of pairs have a radio luminosity exceeding that ofsingle galaxies by 2.5 times on the average. In addition, it is foundthat members of interacting pairs are more powerful emitters in theradio range and that spiral galaxies which are members of triplets haveradio luminosities on a par with those of pair members.
| Gas deficiency in cluster galaxies - A comparison of nine clusters
The available 21 cm line data in the literature for galaxies in nineclusters is combined with new high-sensitivity observations of 51galaxies in five of the nine clusters in order to test fordiscriminating circumstances between those clusters which show H Ideficiency among their spiral population and those which do not. An H Ideficiency for the complete cluster sample is derived employing acomparison sample of galaxies chosen from the Catalog of IsolatedGalaxies. The deficiency and its radial dependence is summarized foreach cluster and a composite. A comparison of the environments indifferent clusters leads to the conclusion that the occurrence of H Ideficiency is correlated with the presence of a hot X-ray intraclustermedium, and that an ongoing interaction process is active through thecores of X-ray clusters.
| A 21 centimeter line survey of a complete sample of interacting and isolated galaxies
The paper presents 21 cm line observations of a complete sample ofinteracting and isolated galaxies made with the National Radio AstronomyObservatory 91 and 43 m telescopes and the Arecibo 3035 m telescope. The21 cm line data are combined with a homogeneous set of optical data onangular diameters, axial ratios, magnitudes, and colors, and integralproperties are calculated for the galaxies in both samples. In thispaper, the sample selection procedures, the method of observation, thedata reduction, and the observational errors are described. Thedetection percentages are presented for both samples.
| A survey of galaxy redshifts. IV - The data
The complete list of the best available radial velocities for the 2401galaxies in the merged Zwicky-Nilson catalog brighter than 14.5mz and with b (II) above +40 deg or below -30 deg ispresented. Almost 60 percent of the redshifts are from the CfA surveyand are accurate to typically 35 km/s.
| Pairs of spiral galaxies with magnitude differences greater than one
For isolated physical pairs of spiral galaxies in Karachentsev's (1972)catalog, we show that where the difference in brightness is greater thanone magnitude, the fainter galaxy has a significantly higher redshift onthe average. This result confirms, in an independent sample ofmorphologically similar galaxies, the result which has come from everyother test of companion galaxies - that they are systematically higherin redshift than the brighter galaxy.
| Double galaxy investigations. I - Observations
Redshift information from 240 A/mm spectrograms is presented for 370double arcsec galaxy systems from the Karachentsev (1972) catalog,including all pairs in that catalog with separation less than 80 arcsec.An extensive error discussion utilizing internal and external (21 cm)comparisons provides calibration of systematic error and determines theuncertainty for a typical high weight optical redshift to be plus orminus 65 km/sec. Internal differential redshifts within single spectrausing common lines achieve accuracies of 18-30 km/sec, depending uponseparation, and are available for about 200 pairs. Extensive informationon emission and other properties is also provided.
| The dynamics of rich clusters of galaxies. I - The Coma cluster
Self-consistent analytical dynamical models are used to study theendpoint of cluster formation, concentrating on the Coma cluster.Particular attention is paid to the effects of anisotropy in thevelocity dispersion and variations in the energy-distribution functionon the cluster structure, the effect on the core structure of a massivecentral object, the dynamical consequences of morphological segregation,cosmological infall and the edge of a cluster, the distribution of darkmatter in a cluster, and the implications of X-ray observations for thedistribution of gravitating material in a cluster. Radial velocity datais displayed, and new and repeated redshifts are reported for a numberof galaxies in the central regions of the cluster. Cluster membership isdetermined and a velocity-dispersion profile is derived. A compositesurface-density profile is derived, and amazing examples are shown ofmodels with virtually identical surface-density profiles but otherwisecompletely different internal dynamics.
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