Search NASA⌕ Search

SEARCH · Search NASA

Results for “cluster approximation”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Measuring the Mass Distribution in Z is Approximately 0.2 Cluster Lenses with XMM, HST and CFHT

Being the most massive gravitationally bound objects in the Universe, clusters of galaxies are prime targets for studies of structure formation and evolution. Specifically the comoving space density of virialized clusters of a given mass (or X-ray temperature), but also the frequency and degree of substructure, as well as the shape of the cluster mass profile are quantities whose current values and evolution as a function of lookback time can provide important constraints on the cosmological and physical parameters of structure formation theories. The project funded by NASA grant NAG 5-10041 intended to take such studies to a new level by combining observations of a well-selected cluster sample by three state-of-the-art telescopes: HST, to accurately measure the mass distribution in the cluster core (approx. 0.5 h(sup -1)(sub 50) Mpc) via strong gravitational lensing; CFHT, to measure the large scale mass distribution out to approx. 3 Mpc via weak lensing; and XMM, to measure the gas density and temperature distribution accurately on intermediate scales < 1.5 Mpc. XMM plays a pivotal role in this context as the calibration of X-ray mass measurements through accurate, spatially resolved X-ray temperature measurements (particularly in the cosmologically most sensitive range of kT> 5 keV) is central to the questions outlined above. This set of observations promised to yield the best cluster mass measurements obtained so far for a representative sample, thus allowing us to: 1) Measure the high-mass end of the local cluster mass function; 2) Test predictions of a universal cluster mass profile; 3) calibrate the mass-temperature and temperature-luminosity relations for clusters and the scatter around these relations, which is vital for studies of cluster evolution using the X-ray temperature and X-ray luminosity functions.

Source record↗
NASA NTRS2008

Spectroscopic Confirmation of Two Massive Red-sequence-selected Galaxy Clusters at Z ~ Approximately Equal to 1.2 in the Sparcs-North Cluster Survey

The Spitzer Adaptation of the Red-sequence Cluster Survey (SpARCS) is a deep z -band imaging survey covering the Spitzer SWIRE Legacy fields designed to create the first large homogeneously-selected sample of massive clusters at z > 1 using an infrared adaptation of the cluster red-sequence method. We present an overview of the northern component of the survey which has been observed with CFHT/MegaCam and covers 28.3 deg(sup 2). The southern component of the survey was observed with CTIO/MOSAICII, covers 13.6 deg(sup 2), and is summarized in a companion paper by Wilson et al. (2008). We also present spectroscopic confirmation of two rich cluster candidates at z approx. 1.2. Based on Nod-and- Shuffle spectroscopy from GMOS-N on Gemini there are 17 and 28 confirmed cluster members in SpARCS J163435+402151 and SpARCS J163852+403843 which have spectroscopic redshifts of 1.1798 and 1.1963, respectively. The clusters have velocity dispersions of 490 +/- 140 km/s and 650 +/- 160 km/s, respectively which imply masses (M(sub 200)) of (1.0 +/- 0.9) x 10(exp 14) Stellar Mass and (2.4 +/- 1.8) x 10(exp 14) Stellar Mass. Confirmation of these candidates as bonafide massive clusters demonstrates that two-filter imaging is an effective, yet observationally efficient, method for selecting clusters at z > 1.

Muzzin, Adam↗
NASA NTRS1973

Thermal-bremsstrahlung interpretation of cluster X-ray sources.

Analysis of the X-ray data for the extended sources in Coma, Perseus, and Virgo in terms of an isothermal gas-sphere model emitting thermal-bremsstrahlung radiation. It is found that the gas distribution is somewhat less centrally condensed than the galaxies, and that the gas mass is generally a small fraction of the binding mass of each cluster. In the case of the Coma cluster, approximately one-eighth of the binding mass (with an uncertainty of about 50%) may be in the form of hot gas at 100,000,000 K if H sub zero = 50 km/sec/Mpc.

Lea, S. M.↗
NASA NTRS1987

The Einstein survey of the young stars in the Orion Nebula

The Orion Nebula is the best studied site of recent star formation in the Galaxy. The complete Einstein Observatory survey of the Orion Nebula covering a 2 deg x 2 deg region centered on the Trapezium is reported. An X-ray mosaic is presented for the Nebula along with a complete X-ray catalogue for this very young cluster. Approximately 150 distinct sources were found in this 4 sq deg region; spectral types and colors were obtained for about 1/2 of the optical counterparts of these sources. Comparison of the variability of the Orion X-ray sources with those found in the Rho Ophiuchi cloud leads to the conclusion that the Orion sources' variability is also likely to result from continual flaring activities. Eleven new late B stars associated with X-ray emission far exceeding that expected from early type stars were discovered. The X-rays may originate from pre-main sequence companions to these stars; a T-Tauri star of the same age would have the correct L sub x. Comparison of the solar type stars in Orion with those in the Pleiades, the Hyades, and the field suggests that the decay of activity with age is most appropriately described by an exponential, rather than a power law fit.

Zoonematkermani, S.↗
NASA NTRS1993

A test of the adhesion approximation for gravitational clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully non-linear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel-dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel-dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate than that from ZA or TZA, (b) the error in the phase angle of Fourier components is worse than that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.↗
NASA NTRS1994

A test of the adhesion approximation for gravitational clustering

We quantitatively compare a particle implementation of the adhesion approximation to fully nonlinear, numerical 'N-body' simulations. Our primary tool, cross-correlation of N-body simulations with the adhesion approximation, indicates good agreement, better than that found by the same test performed with the Zel'dovich approximation (hereafter ZA). However, the cross-correlation is not as good as that of the truncated Zel'dovich approximation (TZA), obtained by applying the Zel'dovich approximation after smoothing the initial density field with a Gaussian filter. We confirm that the adhesion approximation produces an excessively filamentary distribution. Relative to the N-body results, we also find that: (a) the power spectrum obtained from the adhesion approximation is more accurate that that from ZA to TZA, (b) the error in the phase angle of Fourier components is worse that that from TZA, and (c) the mass distribution function is more accurate than that from ZA or TZA. It appears that adhesion performs well statistically, but that TZA is more accurate dynamically, in the sense of moving mass to the right place.

Melott, Adrian L.↗
NASA NTRS1994

Coupled-Cluster Theory Employing Approximate Integrals: An Approach to Avoid the Input/Output and Storage Bottlenecks

By representing orbital products in an expansion basis, certain classes of two-electron integrals are approximated for use in CCSD(T) calculations (singles and doubles coupled-cluster plus a perturbational estimate of the effects of connected triple excitations). This leads to a very large reduction in disk storage and input/output requirements, with usually only a modest increase in computational effort. The new procedure will allow very large CCSD(T) calculations to be undertaken, limited only by available processor time. Using the molecular basis as the expansion basis, explicit numerical comparisons of equilibrium geometries, harmonic frequencies, and energy differences indicate that the error due to the use of approximate integrals is less than the error associated with truncation of the molecular basis set.

Rendell, Alistair P.↗
NASA NTRS1985

Are galactic bulge X-ray burst sources leftovers of distupted globular clusters

Since approximately 1979, it is known that galactic bulge X-ray sources are low-mass binary systems, and that the X-ray bursters are a subset of the bulge sources. Grindlay and Hertz (1983) reported on the close proximity (in four of twelve cases) of an X-ray burst source and a normal star. The two authors believe that these alignments are not coincidental. They suggest that the normal star is surviving giant in a disrupted globular cluster core, of which the X-ray source would also be a member. The present investigation has the objective to show that Grindlay and Hertz made an error in their statistical analysis of a factor of approximately 10. It is, thus, believed that there is insufficient evidence for the conclusion reported by Grindlay and Hertz. On the basis of the present investigation, it is concluded that there exists at present no statistically significant observational evidence that X-ray bursters, presently located outside globular clusters, were formed in globular clusters.

Van Paradijs, J.↗
NASA NTRS1994

Comparison of dynamical approximation schemes for nonlinear gravitaional clustering

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.

Melott, Adrian L.↗
NASA NTRS1993

Testing approximations for non-linear gravitational clustering

The accuracy of various analytic approximations for following the evolution of cosmological density fluctuations into the nonlinear regime is investigated. The Zel'dovich approximation is found to be consistently the best approximation scheme. It is extremely accurate for power spectra characterized by n = -1 or less; when the approximation is 'enhanced' by truncating highly nonlinear Fourier modes the approximation is excellent even for n = +1. The performance of linear theory is less spectrum-dependent, but this approximation is less accurate than the Zel'dovich one for all cases because of the failure to treat dynamics. The lognormal approximation generally provides a very poor fit to the spatial pattern.

Coles, Peter↗
NASA NTRS1983

X-ray emission from clusters of galaxies

Some X-ray spectral observations of approximately 30 clusters of galaxies from HEAO-1 are summarized. There exists strong correlations between X-ray luminosity, L(x), and temperature kT in the form L(x)alphaT to the 2.3 power. This result combined with the L(x) central galaxy density relation and the virial theorem indicates that the core dadius of the gas should be roughly independent of L(x) or KT and that more luminous clusters have a greater fraction of their virial mass in gas. The poor correlation of KT and optical velocity dispersion seems to indicate that clusters have a variety of equations of state. There is poor agreement between X-ray imaging observations and optical and X-ray spectral measures of the polytropic index. Most clusters show Fe emission lines with a strong indication that they all have roughly 1/2 solar abundance. The evidence for cooling in the cores of several clusters is discussed based on spectral observations with the Einstein solid state spectrometer.

Mushotzky, R. F.↗
NASA NTRS1984

X-ray emission from clusters of galaxies

Some X-ray spectral observations of approximately 30 clusters of galaxies from HEAO-1 are summarized. There exists strong correlation betwen X-ray luminosity, L(x), and temperature kT in the form L(x)alphaT to the 2.3 power. This result combined with the L(x) central galaxy density relation and the virial theorem indicates that the core dadius of the gas should be roughly independent of L(x) or Kt and that more luminous clusters have a greater fraction of their virial mass in gas. The poor correlation of KT and optical velocity dispersion seems to indicate that clusters have a variety of equations of state. There is poor agreement between X-ray imaging observations and optical and X-ray spectral measures of the polytropic index. Most clusters show Fe emission lines with a strong indication that they all have roughly 1/2 solar abundance. The evidence for cooling in the cores several clusters is discussed based on spectral observations with the Einstein solid state spectrometer.

Mushotzky, R. F.↗
NASA NTRS1973

The formation of planetesimals.

Four stages in the accretion of planetesimals are described. The initial stage is the condensation of dust particles from the gaseous solar nebula as it cools. These dust particles settle into a thin disk which is gravitationally unstable. A first generation of planetesimals, whose radii range up to about 0.1 km, form from the dust disk by direct gravitational collapse to solid densities on a time scale of the order of 1 year. The resulting disk, composed of first-generation planetesimals, is still gravitationally unstable, and the planetesimals are grouped into clusters containing approximately 10,000 members. The contraction of these clusters is controlled by the rate at which gas drag damps their internal rotational and random kinetic energies. On a time scale of a few thousand years, the clusters contract to form a second generation of planetesimals having radii of the order of 5 km. Further coalescence of planetesimals proceeds by direct collisions which seem capable of producing growth at a rate of the order of 15 cm per year at 1 AU.

Goldreich, P.↗
NASA NTRS1974

Cluster analysis based on dimensional information with applications to feature selection and classification

A new clustering algorithm is presented that is based on dimensional information. The algorithm includes an inherent feature selection criterion, which is discussed. Further, a heuristic method for choosing the proper number of intervals for a frequency distribution histogram, a feature necessary for the algorithm, is presented. The algorithm, although usable as a stand-alone clustering technique, is then utilized as a global approximator. Local clustering techniques and configuration of a global-local scheme are discussed, and finally the complete global-local and feature selector configuration is shown in application to a real-time adaptive classification scheme for the analysis of remote sensed multispectral scanner data.

Eigen, D. J.↗
NASA NTRS1993

Deep, wide-field, multi-band imaging of z approximately equal to 0.4 clusters and their environs

The existence of an excess population of blue galaxies in the cores of distant, rich clusters of galaxies, commonly referred to as the 'Butcher-Oemler' effect is now well established. Spectroscopy of clusters at z = 0.2-0.4 has confirmed that the luminous blue populations comprise as much as 20 percent of these clusters. This fraction is much higher that the 2 percent blue fraction found for nearby rich clusters, such as Coma, indicating that rapid galaxy evolution has occurred on a relatively short time scale. Spectroscopy has also shown that the 'blue' galaxies can basically be divided into three classes: 'starburst' galaxies with large (O II) equivalent widths, 'post-starburst' E+A galaxies (i.e. galaxies with strong Balmer lines shortward of 4000A but elliptical-like colors, and normal spiral/irregulars. Unfortunately, it is difficult to obtain enough spectra of individual galaxies in these intermediate redshift clusters to say anything statistically meaningful. Thus, limited information is available about the relative numbers of these three classes of 'blue' galaxies and the associated E/SO population in these intermediate redshift clusters. More statistically meaningful results can be derived from deep imaging of these clusters. However, the best published data to date (e.g. MacLaren et al. 1988; Dressler & Gunn 1992) are limited to the cluster cores and do not sample the galaxy luminosity functions very deeply at the bluest wavelengths. Furthermore, only limited spectro-energy distribution data is available below 4000A in the observed cluster rest frame providing limited sensitivity to 'recent' star formation activity. To improve this situation, we are currently obtaining deep, wide-field UBRI images of all known rich clusters at z approx. equals 0.4. Our main objective is to obtain the necessary color information to distinguish between the E+SO, 'E+A', and spiral/irregular galaxy populations throughout the cluster/supercluster complex. At this redshift, UBRI correspond to rest-frame 2500A/UVR bandpasses. The rest-frame UVR system provides a powerful 'blue' galaxy discriminate given the expected color distribution. Moreover, since 'hot' stars peak near 2500A, that bandpass is a powerful probe of recent star formation activity in all classes of galaxies. In particular, it is sensitive to ellipticals with 'UV excess' populations (MacLaren et al. 1988).

Silva, David R.↗
NASA NTRS1994

Hot gas in the cold dark matter scenario: X-ray clusters from a high-resolution numerical simulation

A new, three-dimensional, shock-capturing hydrodynamic code is utilized to determine the distribution of hot gas in a standard cold dark matter (CDM) model of the universe. Periodic boundary conditions are assumed: a box with size 85 h(exp -1) Mpc having cell size 0.31 h(exp -1) Mpc is followed in a simulation with 270(exp 3) = 10(exp 7.3) cells. Adopting standard parameters determined from COBE and light-element nucleosynthesis, sigma(sub 8) = 1.05, omega(sub b) = 0.06, and assuming h = 0.5, we find the X-ray-emitting clusters and compute the luminosity function at several wavelengths, the temperature distribution, and estimated sizes, as well as the evolution of these quantities with redshift. We find that most of the total X-ray emissivity in our box originates in a relatively small number of identifiable clusters which occupy approximately 10(exp -3) of the box volume. This standard CDM model, normalized to COBE, produces approximately 5 times too much emission from clusters having L(sub x) is greater than 10(exp 43) ergs/s, a not-unexpected result. If all other parameters were unchanged, we would expect adequate agreement for sigma(sub 8) = 0.6. This provides a new and independent argument for lower small-scale power than standard CDM at the 8 h(exp -1) Mpc scale. The background radiation field at 1 keV due to clusters in this model is approximately one-third of the observed background, which, after correction for numerical effects, again indicates approximately 5 times too much emission and the appropriateness of sigma(sub 8) = 0.6. If we have used the observed ratio of gas to total mass in clusters, rather than basing the mean density on light-element nucleosynthesis, then the computed luminosity of each cluster would have increased still further, by a factor of approximately 10. The number density of clusters increases to z approximately 1, but the luminosity per typical cluster decreases, with the result that evolution in the number density of bright clusters is moderate in this redshift range, showing a broad peak near z = 0.7, and then a rapid decline above redshift z = 3. Detailed computations of the luminosity functions in the range L(sub x) = 10(exp 40) - 10(exp 44) ergs/s in various energy bands are presented for both cluster central regions and total luminosities to be used in comparison with ROSAT and other observational data sets. The quantitative results found disagree significantly with those found by other investigators using semianalytic techniques. We find little dependence of core radius on cluster luminosity and a dependence of temperature on luminosity given by log kT(sub x) = A + B log L(sub x), which is slightly steeper (B = 0.38) than is indicated by observations. Computed temperatures are somewhat higher than observed, as expected, in that COBE-normalized CDM has too much power on the relevant scales. A modest average temperature gradient is found, with temperatures dropping to 90% of central values at 0.4 h(exp -1) Mpc and 70% of central values at 0.9 h(exp -1) Mpc. Examining the ratio of gas to total mass in the clusters normalized to Omega(sub B) h(exp 2) = 0.015, and comparing with observations, we conclude, in agreement with White (1991), that the cluster observations argue for an open universe.

Kang, Hyesung↗
NASA NTRS1994

Comparison of dynamical approximation schemes for non-linear gravitational clustering

We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.

Melott, Adrian L.↗