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NASA NTRS1986

Ultraviolet extinction toward five open clusters, and the accuracy of IUE extinction measurements

The UV extinction curves of 33 main-sequence B stars in five open clusters are presented and analyzed. An analytic fitting function is introduced which represents the observed curves and codifies the structure of the 2175 A extinction bump. A set of extinction parameters are also defined which describe the shape of the far-UV extinction. These data are first used to determine whether the extinction toward any of the clusters is uniform, i.e., whether it can be represented by a single curve for the cluster. This is accomplished by comparing the observed scatter of the far-UV extinction measurements toward a given cluster with that predicted by an error model. The extinction toward four of the five clusters is found to be uniform. The extinction data for those clusters with uniform extinction are then used to determine the observational uncertainties in other extinction parameters for which a priori error estimates cannot be made. With one exception, all of the parameters which describe the shapes of UV extinction curves differ significantly from cluster to cluster. The exception is the central position of the UV extinction bump, which has the same value for all of the cluster extinction curves. Applications and interpretation of the results are given elsewhere.

Massa, D.↗

NASA NTRS1990

Optical emission from cooling flows in distant x ray clusters of galaxies

Although the Einstein satellite detected cooling flows in the x ray emission from clusters of galaxies 10 years ago, the understanding of these flows remains incomplete. The x ray emitting gas in the centers of these clusters is so dense that its cooling time is shorter than a Hubble time. Thus gas may cool and flow into the center of the cluster. This cooling gas is thermally unstable and should quickly become inhomogeneous. Optical filamentation (1-100 kpc scales) often appears near the centers of nearby clusters containing cooling flows, usually within the central galaxies accreting the gas. Indeed, only clusters with well-developed cooling flows seem to possess highly luminous, emission-line nebulae. Researchers present here some results of preliminary observational and theoretical studies of this class of emission-line objects. Researchers observed a complete, x ray selected sample of 25 distant clusters of galaxies extracted from the Einstein Extended Medium Sensitivity Survey. They discovered luminous extended H alpha emission in 10 of these clusters. Thus at least 40 percent of the clusters in the sample contain cool gas. If we crudely compare the sample to that of Arnaud (1988), in which approx. 40 percent of his 104 x ray clusters have cooling flows, the result implies that cooling flows may actually be a more common phenomenon in the past than in the present. The connection between the cooling flow and the H alpha emission is a mystery. The straightforward calculation of 1 (photoionization) to 3 (shocks) recombinations per H atom in the cooling flow gives mass infall rates 3 to 100 times greater than M derived from x ray observations. Researchers have made some preliminary theoretical calculations in an attempt to resolve this problem.

Donahue, Megan↗

NASA NTRS1990

IPC two-color analysis of x ray galaxy clusters

The mass distributions were determined of several clusters of galaxies by using X ray surface brightness data from the Einstein Observatory Imaging Proportional Counter (IPC). Determining cluster mass distributions is important for constraining the nature of the dark matter which dominates the mass of galaxies, galaxy clusters, and the Universe. Galaxy clusters are permeated with hot gas in hydrostatic equilibrium with the gravitational potentials of the clusters. Cluster mass distributions can be determined from x ray observations of cluster gas by using the equation of hydrostatic equilibrium and knowledge of the density and temperature structure of the gas. The x ray surface brightness at some distance from the cluster is the result of the volume x ray emissivity being integrated along the line of sight in the cluster.

White, Raymond E., III↗

NASA NTRS1991

Measurement of the spectral signature of small carbon clusters at near and far infrared wavelengths

A significant percentage of the carbon inventory of the circumstellar and interstellar media may be in the form of large refractory molecules (or small grains) referred to as carbon clusters. At the small end, uneven numbers of carbon atoms seem to be preferred, whereas above 12 atoms, clusters containing an even number of carbon atoms appear to be preferred in laboratory chemistry. In the lab, the cluster C-60 appears to be a particularly stable form and has been nicknamed Bucky Balls because of its resemblance to a soccer ball and to geodesic domes designed by Buckminster Fuller. In order to investigate the prevalence of these clusters, and their relationship to the polycyclic aromatic hydrocarbons (PAHs) that have become the newest focus of IR astronomy, it is necessary to determine the spectroscopic characteristics of these clusters at near and far infrared wavelengths. Described here is the construction of a near to far IR laser magnetic resonance spectrometer that has been built at the University of California Berkeley in order to detect and characterize these spectra. The equipment produces carbon clusters by laser evaporation of a graphitic target. The clusters are then cooled in a supersonic expansion beam in order to simulate conditions in the interstellar medium (ISM). The expansion beam feeds into the spectrometer chamber and permits concentrations of clusters sufficiently high as to permit ultra-high resolution spectroscopy at near and far IR wavelengths. The first successful demonstration of this apparatus occurred last year when the laboratory studies permitted the observational detection of C-5 in the stellar outflow surrounding IRC+10216 in the near-IR. Current efforts focus on reducing the temperature of the supersonic expansion beam that transport the C clusters evaporated from a graphite target into the spectrometer down to temperatures as low as 1 K.

Tarter, J.↗

NASA NTRS1992

Possibilistic clustering for shape recognition

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, we cast the clustering problem into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. We constructed an appropriate objective function whose minimum will characterize a good possibilistic partition of the data, and we derived the membership and prototype update equations from necessary conditions for minimization of our criterion function. In this paper, we show the ability of this approach to detect linear and quartic curves in the presence of considerable noise.

Keller, James M.↗

NASA NTRS1993

Possibilistic clustering for shape recognition

Clustering methods have been used extensively in computer vision and pattern recognition. Fuzzy clustering has been shown to be advantageous over crisp (or traditional) clustering in that total commitment of a vector to a given class is not required at each iteration. Recently fuzzy clustering methods have shown spectacular ability to detect not only hypervolume clusters, but also clusters which are actually 'thin shells', i.e., curves and surfaces. Most analytic fuzzy clustering approaches are derived from Bezdek's Fuzzy C-Means (FCM) algorithm. The FCM uses the probabilistic constraint that the memberships of a data point across classes sum to one. This constraint was used to generate the membership update equations for an iterative algorithm. Unfortunately, the memberships resulting from FCM and its derivatives do not correspond to the intuitive concept of degree of belonging, and moreover, the algorithms have considerable trouble in noisy environments. Recently, the clustering problem was cast into the framework of possibility theory. Our approach was radically different from the existing clustering methods in that the resulting partition of the data can be interpreted as a possibilistic partition, and the membership values may be interpreted as degrees of possibility of the points belonging to the classes. An appropriate objective function whose minimum will characterize a good possibilistic partition of the data was constructed, and the membership and prototype update equations from necessary conditions for minimization of our criterion function were derived. The ability of this approach to detect linear and quartic curves in the presence of considerable noise is shown.

Keller, James M.↗

NASA NTRS1993

Optical and near infrared photometry of Butcher-Oemler clusters

Rich clusters of galaxies at moderate redshifts (z approx. .3) have a larger proportion of optically blue galaxies than their low redshift counterparts. Spectroscopic examination of the blue galaxies by various authors has shown that the blue galaxies are generally Seyferts, show evidence for recent star formation, or are foreground objects. Unfortunately, spectroscopy is too time consuming to be used on large samples. Thus, we have looked for a way to separate Seyferts, starbursts, ellipticals and nonmembers using photometry alone. Five moderate redshift clusters, Abell numbers 777, 963, 1758, 1961 and 2218, have been observed in the V, R and K bands. We model the spectral energy distributions of various kinds of galaxies found in clusters and derive observed colors. We have modeled the spectral energy distributions (SED) of several kinds of galaxies and compute their colors as a function of redshift. We expect to see ellipticals, spirals, starbursts, post-starburst and Seyfert galaxies. The SED of elliptical and Sbc galaxies was observed by Rieke and Rieke. The SEDs for the starburst galaxies was created by adding a reddened 10(exp 8) year old burst to a spiral galaxy SED. The post-starburst (E+A) galaxy SEDs are composed of a slightly reddened 10(exp 9) year old burst and elliptical galaxy SED. SEDs for the Seyferts were created by adding a v(exp -1.1) power law, and a hot dust thermal spectrum to the Sbc. From the SEDs the colors of galaxies at various redshifts with assorted filters were computed. Lilly & Gunn (1985) have optical and infrared photometry for a sample of galaxies in CL0024+1654 observed spectroscopically by Dressler, Gunn and Schneider (1985). We have used this data to choose the most appropriate SEDs for our starburst and post-starburst models. The most likely explanation for the optically blue colors in most cluster galaxies is star formation. Very few galaxies lie in the Seyfert locus. Abel 1758 has more Seyfert candidates than the other clusters, we observed. It seems possible to roughly sort types of galaxies in clusters by color alone. The cluster population seems to vary considerably between clusters, but our K selected sample has few Seyferts in any cluster.

Shier, Lisa M.↗

NASA NTRS1993

A new giant luminous arc gravitational lens associated with a z = 0.62 galaxy cluster, and the environments of distant radio galaxies

In the course of a survey investigating the cluster environments of distant 3CR radio galaxies, I have identified a previously unknown 'giant luminous arc' gravitational lens. The lensing cluster is associated with the radio galaxy 3C 220.1 at z = 0.62 and is the most distant cluster now known to produce such arcs. I present imaging and spectroscopic observations of the cluster and the arc, and discuss the implications for the cluster mass. At z greater than 0.6 the cluster velocity dispersions implied by such giant arcs may provide an interesting constraint on theories of large scale structure formation. The parent investigation in which this arc was identified concerns galaxy clusters and radio galaxy environments at 0.35 less than z less than 0.8. At the present epoch, powerful FR 2 radio galaxies tend to be found in environments of poor or average galaxy density. In contrast, at the higher redshifts investigated here, richer group and cluster environments are common. I present additional data on other clusters from this survey, and discuss its extension to z greater than 1 through a program of near-infrared and optical imaging.

Dickinson, Mark↗

NASA NTRS1993

What determines the stellar mass functions in globular clusters?

We analyze the dependence of stellar mass function slopes for a sample of 17 globular clusters on a variety of cluster parameters. The principal novelty of our approach is the use of appropriate multivariate statistical methods to disentangle the complex situation which is present in this problem: the slopes depend simultaneously on more than one variable, and many cluster parameters are mutually correlated. We find that the mass function slopes in the range M/M(solar) = 0.5-0.8 are largely determined by the position in the Galaxy and to a lesser extent by the cluster metallicity. Clusters closer to the Galactic center or plane have shallower mass function slopes. At a given distance to the Galactic center, clusters closer to the Galactic plane have shallower mass function slopes. At a given R(GC) and/or Z(GP), more metal-rich clusters have shallower mass function slopes. Thus, the monovariate correlations with the position or metallicity are both correct, but only partial, and in terms of slopes, biased descriptions of the situation. We present trivariate least-squares solutions where the mass function slopes can be predicted within the measurement accuracy. This relation can serve as a powerful observational constraint for theories of globular cluster formation and evolution, and it is one of the tightest correlations between globular cluster properties now known.

Djorgovski, S.↗

NASA NTRS1994

Nonpolytropic model for the Coma Cluster

In this article we demonstrate, for the first time, how a physically motivated static model for both the gas and galaxies in the Coma Cluster of galaxies can jointly fit all available X-ray and optical imaging and spectroscopic data. The principal assumption of this nonpolytropic model (Cavaliere & Fusco-Femiano 1981, hereafter CFF), is that the intracluster gas temperature is proportional to the square of the galaxy velocity dispersion everywhere throughout the cluster; no other assumption about the gas temperature distribution is required. After demonstrating that the CFF nonpolytropic model is an adequate representation of the gas and galaxy distributions, the radial velocity dispersion profile, and the gas temperature distribution, we derive the following information about the Coma Cluster: 1. The central temperature is about 9 keV and the central density is 2.8 x 10(exp -3)/cm(exp 3) for the X-ray emitting plasma; 2. The binding mass of the cluster is approximately 2 x 10(exp 15) solar mass within 5 Mpc for (H(sub 0) = 50 km/sec/Mpc), with a mass-to-light ratio of approximately 160 solar mass/solar luminosity; 3. The contribution of the gas to the total virial mass increases with distance from the cluster center, and we estimate that this ratio is no greater than approximately 50% within 5 Mpc. The ability of the CFF nonpolytropic model to describe the current X-ray and optical data for the Coma Cluster suggests that a significant fraction of the thermal energy contained in the hot gas in this as well as other rich galaxy clusters may have come from the interaction between the galaxies and the ambient cluster medium. interaction between the galaxies and the ambient cluster medium.

Fusco-Femiano, R.↗

NASA NTRS1994

Probing the large-scale velocity field with clusters of galaxies

What is the role of clusters of galaxies in probing the large-scale velocity field of the universe? We investigate the distribution of peculiar velocities of clusters of galaxies in the popular low-density (omega = 0.3) flat cold dark matter (CDM) cosmological model, which best fits many large-scale structure observations. An omega = 1 CDM model is also studied for comparison. We find that clusters of galaxies are efficient tracers of the large-scale velocity field. The clusters exhibit a Maxwellian distribution of peculiar velocities, as expected from Gaussian initial density fluctuations. The cluster three-dimensional velocity distribution for the omega = 0.3 model peaks at nu approximately greater than 400 km/s and extends to high velocities of nu approximately 1200 km/s. The rms peculiar velocity of the clusters is 440 km/s. Approximately 10% of all model clusters move with high peculiar velocities nu greater or equal to 700 km/s. The observed velocity distribution of clusters of galaxies is compared with the predictions from cosmological models. The observed data exhibit a larger velocity tail than seen in the model simulations; however, due to the large observational uncertainties, the data are consistent at approximately equal to 3 sigma level with the odel predictions, and with a Gaussian initial density field. The large peculiar velocities reported for some clusters of galaxies (nu approximately greater than 3000 km/s) are likely to be overestimated, if the current model is viable.

Bahcall, Neta A.↗

NASA NTRS1994

Statistical association of QSO's with foreground galaxy clusters

We report a statistically significant overdensity of high redshift quasi-stellar objects (QSO's) in the directions of foreground galaxy clusters. QSO's are taken from the Large Bright QSO Survey (LBQS) between 1.4 less than or equal z less than or equal 2.2 with a limiting magnitude of m(sub B) = 18.5. Foreground clusters are regions within 6 Zwicky radii of small Zwicky clusters at a characteristic redshift of about z approximately = 0.2, covering about 40% of the total area surveyed (304 sq. deg). The overdensity, defined as the ratio of the number density of QSO's in the directions of clusters ('association QSO's) to that in the remainder of the fields ('background QSO's), is equal to 1.7, and formally differs from unity at 4.7 sigma significance. The observed overdensity probably is not due to statistical variation in QSO density, intrinsic QSO-QSO and/or cluster-cluster autocorrelations, or patchy Galactic obscuration. We thus interpret this observation as being due to statistical gravitational lensing of background QSO's by galaxy clusters. However, this amplitude of overdensity behind clusters cannot be accounted for in any cluster lensing model if the background QSO number-magnitude counts are similar to the intrinsic (unlensed) counts, and is implausible in any conventional model of cosmic mass distribution.

Rodrigues-Williams, Liliya L.↗

NASA NTRS1994

Baryonic dark clusters in galactic halos and their observable consequences

We consider the possibility that approximately 10% of the mass of a typical galaxy halo is in the form of massive (approximately 10(exp 7) solar masses), compact (escape speeds approximately 100 km/s) baryonic clusters made of neutron stars (approximately 10% by mass), black holes (less than or approximately equal to 1%) and brown dwarfs, asteroids, and other low-mass debris (approximately 90%). These general properties are consistent with several different observational and phenomenological constraints on cluster properties subject to the condition that neutron stars comprise approximately 1% of the total halo mass. Such compact, dark clusters could be the sites of a variety of collisional phenomena involving neutron stars. We find that integrated out to the Hubble distance approximately one neutron star-neutron star or neutron star-black hole collision occurs daily. Of order 0.1-1 asteroid-neutron star collisions may also happen daily in the halo of the Milky Way if there is roughly equal cluster mass per logarithmic particle mass interval between asteroids and brown dwarfs. These event rates are comparable to the frequency of gamma-ray burst detections by the Burst and Transient Source Experiment (BATSE) on the Compton Observatory, implying that if dark halo clusters are the sites of most gamma-ray bursts, perhaps approximately 90% of all bursts are extragalactic, but approximately 10% are galactic. It is possible that dark clusters of the kind discussed here could be detected directly by the Infrared Space Observatory (ISO) or Space Infrared Telescope Facility (SIRTF). If the clusters considered in this paper exist, they should produce spatially correlated gravitational microlensing of stars in the Large Magellanic Cloud (LMC). If 10% of the halo is in the form of dark baryonic clusters, and the remaining 90% is in brown dwarfs and other dark objects which are either unclustered or collected into low-mass clusters, then we expect that two events within approximately 1 min of one another are likely to be seen after a total of order 20-30 microlenses have been detected.

Wasserman, Ira↗

NASA NTRS1995

Spectroscopy of candidate young globular clusters in NGC 1275

We present spectra of the brightest member of the population of compact blue objects discovered in the peculiar galaxy NGC 1275 by Holtzman et al. (1992) using Hubble Space Telescope images. These spectra show strong Balmer absorption lines like those observed in A-type stars, as expected if the object is a young globular cluster. The age estimated from the strength of the Balmer lines is about 0.5 Gyr, although ages ranging from 0.1 Gyr to 0.9 Gyr cannot be confidently excluded given current models of stellar populations. If these estimated ages are adopted for the young cluster population of NGC 1275 as a whole, the fading predicted by stellar populations models gives a luminosity function which is consistent with that of the Galactic globular cluster system convolved with the observational selection function for the NGC 1275 system. We also use the equivalent widths of the Mg b and Fe 5270 features to constrain the metallicity of the young cluster. Combining these absorption-line widths with the age estimates from the Balmer lines and stellar population models, we find a metallicity of roughly solar, based on the Mg b index, and somewhat higher for the Fe 5270 index. The radial velocity of the absorption lines of the cluster spectrum is offset from the emission lines of the galaxy spectrum at the same position by - 130 km/s, providing further evidence for the identification of the object as a global cluster and opening up the future possibility of studying the kinematics of young cluster systems. The discovery of objects with the characteristics of young globular clusters in NGC 1275, which shows evidence of a recent interaction or merger, supports the hypothesis that galaxy interactions and mergers are favorable sites for the formation of globular clusters.

Zepf, Stephen E.↗

NASA NTRS1995

Map-based trigonometric parallaxes of open clusters: Coma

This is the fourth study in a series to determine the direct trigonometric parallaxes of four of the nearest open star clusters, the Hyades, the Pleiades, the Praesepe, and the nearby cluster in Coma (Gatewood et al. 1990; Gatewood et al. 1992); Gatewood & Kiewiet de Jonge 1994). The results for the open star cluster in Coma are compared with those of the other three clusters, and the members are found to be significantly subluminous. The trigonometric parallax of the cluster is estimated from that of three members studied with the Multichannel Astrometric Photometer (MAP) at the Thaw Refractor of the University of Pittsburgh's Allegheny Observatory. The weighted mean parallax of the cluster is +13.53 +/- 0.54 mass (0.00054 min), corresponding to a distance modulus of 4.34 +/- 0.09 mag. The U-B excess of the Coma cluster members may be used to adjust the observed absolute magnitudes and the B-V measurements as suggested by Sandage & Eggen (1959). The agreement obtained in this manner suggests that, like subdwarf stars, the stars of the Coma cluster appear subluminous because of line blanketing. One of the three members observed in this study was recognized as a member by its parallax and is the faintest known member of the cluster.

Gatewood, George↗

NASA NTRS1995

A serach for 'failed clusters' of galaxies

We describe a search for a new type of object - large clouds of hot gas with no visible galaxies - which we call failed clusters of galaxies. We calculate the expected X-ray luminosity, temperature, and angular diameter of such objects as a function of total cloud mass and convert the results to expected X-ray fluxes from failed clusters at different redshifts. Using the Einstein Imaging Proportional Counter (IPC) database, we establish a strategy to search for candidate failed clusters. From this initial screening of 1435 IPC fields, 17 candidates are selected for more detailed analysis, which indicates that 10 of these are very probably extended X-ray sources. Optical follow-up on the 10 prime candidates finds eight clusters of galaxies (including six reproted for the first time in this paper), one stellar identification, and one without an obvious optical counterpart (the candidate with the weakest evidence for X-ray extent). Investigation of several candidates with less evidence for X-ray extent yields two additional new clusters of galaxies. A conservative comparison of our results with the Einstein Extended Medium Sensitivity Survey demonstrates that failed clusters are a relatively unimportant contributor to the mass density of the universe. Our inability to find failed clusters is consistent with the hierarchical clustering scenario for the formation of galaxies and clusters.

Tucker, W. H.↗

NASA NTRS2000

The Distance and Mass of the Galaxy Cluster Abell 1995 Derived from Sunyaev-Zeldovich Effect and X-Ray Measurements

We present multiwavelength observations of the Abell 1995 galaxy cluster. From an analysis of X-ray spectroscopy and imaging data, we derive the electron temperature, cluster core radius, and central electron number density. Using optical spectroscopy of 15 cluster members, we derive an accurate cluster redshift and velocity dispersion. Finally, the interferometric imaging of the Sunyaev-Zeldovich effect toward Abell 1995 at 28.5 GHz provides a measure of the integrated pressure through the cluster. The X-ray and Sunyaev-Zeldovich effect observations are combined to determine the angular diameter distance to the cluster of D(sub A) = 1294(sup +294 +438, sub -283 -458) Mpc (Statistical followed by systematic uncertainty), implying a Hubble constant of H(sub 0) = 52.2(sup +11.4 +18.5, sub -11.9 -17.7) km/s.Mpc for Omega(sub M) = 0.3 and Omega(sub lambda) = 0.7. We find a best-fit H(sub 0) of 46 km/s.Mpc for the Omega(sub M) = 1 and Omega(sub lambda) = 0 cosmology, and 48 km/s.Mpc for Omega(sub M) = 0.3 and Omega(sub lambda) = 0.0. The X-ray data are also used to derive a total cluster mass of M(sup HSE, sub tot)(r(sub 500)) = 5.18(sup +0.62, sub -0.48) x 10(exp 14)/h solar mass; the optical velocity dispersion yields an independent and consistent estimate of M(sup virial, sub tot)(r(sub 500)) = 6.35(sup +1.51, sub -1.19) X 10(exp 14) /h solar mass. Both of the total mass estimates are evaluated at a fiducial radius, r(sub 500) = 830 /h kpc, where the overdensity is 500 times the critical density. The total cluster mass is then combined with gas mass measurements to determine a cluster gas mass fraction of F(sub g) = 0.056(sup +0.010, sub -0.013) /h(sup 3/2) in combination with recent baryon density constraints, the measured gas mass fraction yields an upper limit on the mass density parameter of Omega(sub M) h(sup 1/2) <= 0.34(sup +/0.06, sub 0.05.

Patel, Sandeep K.↗

NASA NTRS2003

Constraints on the Energy Content of the Universe from a Combination of Galaxy Cluster Observables

We demonstrate that constraints on cosmological parameters from the distribution of clusters as a function of redshift (dN/dz) are complementary to accurate angular diameter distance (D(sub A)) measurements to clusters, and their combination significantly tightens constraints on the energy density content of the Universe. The number counts can be obtained from X-ray and/or SZ (Sunyaev-Ze'dovich effect) surveys, and the angular diameter distances can be determined from deep observations of the intra-cluster gas using their thermal bremsstrahlung X-ray emission and the SZ effect. We combine constraints from simulated cluster number counts expected from a 12 deg(sup 2) SZ cluster survey and constraints from simulated angular diameter distance measurements based on the X-ray/SZ method assuming a statistical accuracy of 10% in the angular diameter distance determination of 100 clusters with redshifts less than 1.5. We find that Omega(sub m), can be determined within about 25%, Omega(sub lambda) within 20% and w within 16%. We show that combined dN/dz+(sub lambda) constraints can be used to constrain the different energy densities in the Universe even in the presence of a few percent redshift dependent systematic error in D(sub lambda). We also address the question of how best to select clusters of galaxies for accurate diameter distance determinations. We show that the joint dN/dz+ D(lambda) constraints on cosmological parameters for a fixed target accuracy in the energy density parameters are optimized by selecting clusters with redshift upper cut-offs in the range 0.55 approx. less than 1. Subject headings: cosmological parameters - cosmology: theory - galaxies:clusters: general

Molnar, Sandor M.↗