Engineering topics

Park, Changbom

Publications and source records attributed to Park, Changbom.

At least 19 records

NASA NTRS1994

The power spectrum of galaxies in the nearby universe

We compute the power spectrum of galaxy density fluctuations in a recently completed Southern Sky Redshift Survey of optically selected galaxies (SSRS2). The amplitude and shape of the SSRS2 power spectrum are consistent with results of the Center for Astrophysics redshift survey of the northern hemisphere (CfA2), including the abrupt change of slope on a scale of 30-50/h Mpc; these results are reproducible for independent volumes of space, and variations are consistent with the errors estimated from mock surveys. Taken together, the SSRS2 and the CfA2 form a complete sample of 14,383 galaxies which covers one-third of the sky. The power spectrum of this larger sample continues to rise on scales up to approximately 200/h Mpc, with weak evidence for flattening on the largest scales. The SSRS2 + CfA2 power spectrum and the power spectrum constraints implied by COBE are well matched by an Omega(h) is approximately 0.2, Omega + lambda(sub 0) = 1 cold dark matter model with minimal biasing of optically selected galaxies.

Da Costa, L. Nicolaci↗

NASA NTRS1994

Voids and constraints on nonlinear clustering of galaxies

Void statistics of the galaxy distribution in the Center for Astrophysics Redshift Survey provide strong constraints on galaxy clustering in the nonlinear regime, i.e., on scales R equal to or less than 10/h Mpc. Computation of high-order moments of the galaxy distribution requires a sample that (1) densely traces the large-scale structure and (2) covers sufficient volume to obtain good statistics. The CfA redshift survey densely samples structure on scales equal to or less than 10/h Mpc and has sufficient depth and angular coverage to approach a fair sample on these scales. In the nonlinear regime, the void probability function (VPF) for CfA samples exhibits apparent agreement with hierarchical scaling (such scaling implies that the N-point correlation functions for N greater than 2 depend only on pairwise products of the two-point function xi(r)) However, simulations of cosmological models show that this scaling in redshift space does not necessarily imply such scaling in real space, even in the nonlinear regime; peculiar velocities cause distortions which can yield erroneous agreement with hierarchical scaling. The underdensity probability measures the frequency of 'voids' with density rho less than 0.2 -/rho. This statistic reveals a paucity of very bright galaxies (L greater than L asterisk) in the 'voids.' Underdensities are equal to or greater than 2 sigma more frequent in bright galaxy samples than in samples that include fainter galaxies. Comparison of void statistics of CfA samples with simulations of a range of cosmological models favors models with Gaussian primordial fluctuations and Cold Dark Matter (CDM)-like initial power spectra. Biased models tend to produce voids that are too empty. We also compare these data with three specific models of the Cold Dark Matter cosmogony: an unbiased, open universe CDM model (omega = 0.4, h = 0.5) provides a good match to the VPF of the CfA samples. Biasing of the galaxy distribution in the 'standard' CDM model (omega = 1, b = 1.5; see below for definitions) and nonzero cosmological constant CDM model (omega = 0.4, h = 0.6 lambda(sub 0) = 0.6, b = 1.3) produce voids that are too empty. All three simulations match the observed VPF and underdensity probability for samples of very bright (M less than M asterisk = -19.2) galaxies, but produce voids that are too empty when compared with samples that include fainter galaxies.

Vogeley, Michael S.↗

NASA NTRS1994

Power spectrum, correlation function, and tests for luminosity bias in the CfA redshift survey

We describe and apply a method for directly computing the power spectrum for the galaxy distribution in the extension of the Center for Astrophysics Redshift Survey. Tests show that our technique accurately reproduces the true power spectrum for k greater than 0.03 h Mpc(exp -1). The dense sampling and large spatial coverage of this survey allow accurate measurement of the redshift-space power spectrum on scales from 5 to approximately 200 h(exp -1) Mpc. The power spectrum has slope n approximately equal -2.1 on small scales (lambda less than or equal 25 h(exp -1) Mpc) and n approximately -1.1 on scales 30 less than lambda less than 120 h(exp -1) Mpc. On larger scales the power spectrum flattens somewhat, but we do not detect a turnover. Comparison with N-body simulations of cosmological models shows that an unbiased, open universe CDM model (OMEGA h = 0.2) and a nonzero cosmological constant (CDM) model (OMEGA h = 0.24, lambda(sub zero) = 0.6, b = 1.3) match the CfA power spectrum over the wavelength range we explore. The standard biased CDM model (OMEGA h = 0.5, b = 1.5) fails (99% significance level) because it has insufficient power on scales lambda greater than 30 h(exp -1) Mpc. Biased CDM with a normalization that matches the Cosmic Microwave Background (CMB) anisotropy (OMEGA h = 0.5, b = 1.4, sigma(sub 8) (mass) = 1) has too much power on small scales to match the observed galaxy power spectrum. This model with b = 1 matches both Cosmic Background Explorer Satellite (COBE) and the small-scale power spect rum but has insufficient power on scales lambda approximately 100 h(exp -1) Mpc. We derive a formula for the effect of small-scale peculiar velocities on the power spectrum and combine this formula with the linear-regime amplification described by Kaiser to compute an estimate of the real-space power spectrum. Two tests reveal luminosity bias in the galaxy distribution: First, the amplitude of the pwer spectrum is approximately 40% larger for the brightest 50% of galaxies in volume-limited samples that have M(sub lim) greater than M*. This bias in the power spectrum is independent of scale, consistent with the peaks-bias paradigm for galaxy formation. Second, the distribution of local density around galaxies shows that regions of moderate and high density contain both very bright (M less than M* = -19.2 + 5 log h) and fainter galaxies, but that voids preferentially harbor fainter galaxies (approximately 2 sigma significance level).

Park, Changbom↗

NASA NTRS1994

Topological analysis of the CfA redshift survey

We study the topology of large-scale structure in the Center for Astrophysics Redshift Survey, which now includes approximately 12,000 galaxies with limiting magnitude m(sub B) is less than or equal to 15.5. The dense sampling and large volume of this survey allow us to compute the topology on smoothing scales from 6 to 20/h Mpc; we thus examine the topology of structure in both 'nonlinear' and 'linear' regimes. On smoothing scales less than or equal to 10/h Mpc this sample has 3 times the number of resolution elements of samples examined in previous studies. Isodensity surface of the smoothed galaxy density field demonstrate that coherent high-density structures and large voids dominate the galaxy distribution. We compute the genus-threshold density relation for isodensity surfaces of the CfA survey. To quantify phase correlation in these data, we compare the CfA genus with the genus of realizations of Gaussian random fields with the power spectrum measured for the CfA survey. On scales less than or equal to 10/h Mpc the observed genus amplitude is smaller than random phase (96% confidence level). This decrement reflects the degree of phase coherence in the observed galaxy distribution. In other words the genus amplitude on these scales is not good measure of the power spectrum slope. On scales greater than 10/h Mpc, where the galaxy distribution is rougly in the 'linear' regime, the genus ampitude is consistent with the random phase amplitude. The shape of the genus curve reflects the strong coherence in the observed structure; the observed genus curve appears broader than random phase (94% confidence level for smoothing scales less than or equal to 10/h Mpc) because the topolgoy is spongelike over a very large range of density threshold. This departre from random phase consistent with a distribution like a filamentary net of 'walls with holes.' On smoothing scales approaching approximately 20/h Mpc the shape of the CfA genus curve is consistent with random phase. There is very weak evidence for a shift of the genus toward a 'bubble-like' topology. To test cosmological models, we compute the genus for mock CfA surveys drawn from large (L greater than or approximately 400/h Mpc) N-body simulations of three variants of the cold dark matter (CDM) cosmogony. The genus amplitude of the 'standard' CDM model (omega h = 0.5, b = 1.5) differs from the observations (96% confidence level) on smoothing scales is less than or approximately 10/h Mpc. An open CDM model (omega h = 0.2) and a CDM model with nonzero cosmological constant (omega h = 0.24, lambda (sub 0) = 0.6) are consistent with the observed genus amplitude over the full range of smoothing scales. All of these models fail (97% confidence level) to match the broadness of the observed genus curve on smoothing scales is less than or equal to 10/h Mpc.

Vogeley, Michael S.↗

NASA NTRS1992

The formation of cosmic structure in a texture-seeded cold dark matter cosmogony

The growth of density fluctuations induced by global texture in an Omega = 1 cold dark matter (CDM) cosmogony is calculated. The resulting power spectra are in good agreement with each other, with more power on large scales than in the standard inflation plus CDM model. Calculation of related statistics (two-point correlation functions, mass variances, cosmic Mach number) indicates that the texture plus CDM model compares more favorably than standard CDM with observations of large-scale structure. Texture produces coherent velocity fields on large scales, as observed. Excessive small-scale velocity dispersions, and voids less empty than those observed may be remedied by including baryonic physics. The topology of the cosmic structure agrees well with observation. The non-Gaussian texture induced density fluctuations lead to earlier nonlinear object formation than in Gaussian models and may also be more compatible with recent evidence that the galaxy density field is non-Gaussian on large scales. On smaller scales the density field is strongly non-Gaussian, but this appears to be primarily due to nonlinear gravitational clustering. The velocity field on smaller scales is surprisingly Gaussian.

Gooding, Andrew K.↗

NASA NTRS1992

Large-scale structure in the Southern Sky Redshift Survey

The power spectrum from the Southern Sky Redshift Survey and the CfA samples are measured in order to explore the amplitude of fluctuation in the galaxy density. At lambda of less than or equal to 30/h Mpc the observed power spectrum is quite consistent with the standard CDM model. At larger scales the data indicate an excess of power over the standard CDM model. The observed power spectrum from these optical galaxy samples is in good agreement with that drawn from the sparsely sampled IRAS galaxies. The shape of the power spectrum is also studied by examining the relation between the genus per unit volume and the smoothing length. It is found that, over Gaussian smoothing scales from 6 to 14/h Mpc, the power spectrum has a slope of about -1. The topology of the galaxy density field is studied by measuring the shift of the genus curve from the Gaussian case. Over all smoothing scales studied, the observed genus curves are consistent with a random phase distribution of the galaxy density field, as predicted by the inflationary scenarios.

Park, Changbom↗

NASA NTRS1992

Large-scale clustering of galaxies in the CfA Redshift Survey

The power spectrum of the galaxy distribution in the Center for Astrophysics Redshift Survey (de Lapparent et al., 1986; Geller and Huchra, 1989; and Huchra et al., 1992) is measured up to wavelengths of 200/h Mpc. Results are compared with several cosmological simulations with Gaussian initial conditions. It is shown that the power spectrum of the standard CDM model is inconsistent with the observed power spectrum at the 99 percent confidence level.

Vogeley, Michael S.↗

NASA NTRS1992

The topology of large-scale structure. VI - Slices of the universe

Results of an investigation of the topology of large-scale structure in two observed slices of the universe are presented. Both slices pass through the Coma cluster and their depths are 100 and 230/h Mpc. The present topology study shows that the largest void in the CfA slice is divided into two smaller voids by a statistically significant line of galaxies. The topology of toy models like the white noise and bubble models is shown to be inconsistent with that of the observed slices. A large N-body simulation was made of the biased cloud dark matter model and the slices are simulated by matching them in selection functions and boundary conditions. The genus curves for these simulated slices are spongelike and have a small shift in the direction of a meatball topology like those of observed slices.

Park, Changbom↗

NASA NTRS1992

The topology of large-scale structure. V - Two-dimensional topology of sky maps

A 2D algorithm is applied to observed sky maps and numerical simulations. It is found that when topology is studied on smoothing scales larger than the correlation length, the topology is approximately in agreement with the random phase formula for the 2D genus-threshold density relation, G2(nu) varies as nu(e) exp-nu-squared/2. Some samples show small 'meatball shifts' similar to those seen in corresponding 3D observational samples and similar to those produced by biasing in cold dark matter simulations. The observational results are thus consistent with the standard model in which the structure in the universe today has grown from small fluctuations caused by random quantum noise in the early universe.

Gott, J. R., III↗

NASA NTRS1991

The three-point correlation function for Abell clusters - Observations and simulations

Results are reported of a 3D study tracing the three-point correlation function of Abell clusters and of a comparison of this with the biased cold dark matter (CDM) simulations of Park (1990). For the observations, the maximum likelihood fits are Z11 = 0.85 and Q111 = 0.1, in excellent agreement with the result of the 2D study of Toth et al. (1989). For Park's simulation, maximum likelihood fits of Q11 = 0.9 and Q111 = 0.0 are found, which is in excellent agreement with the observational result. It is concluded that the standard biased CDM gravitational instability model reproduces the observed form of the three-point correlation functions for Abell clusters remarkably well. The number of triples as a function of the sides of triangles for Abell clusters, and the number of triples as a function of the sides of triangles for clusters in Park's simulation are illustrated on graphs.

Gott, J. R., III↗

NASA NTRS1991

Constraints on cosmological models from the IRAS QDOT survey results

The results of the recent IRAS survey are used to explore constraints on the nature of the Galaxy density field. Realistic simulations of the survey made from N-body simulations of the n = -1 power-law power spectrum and the Omega = 1 CDM models show that the power-law model is basically consistent with all QDOT variance results, while the CDM model has a smaller variance than the observation at the 20/h Mpc Gaussian smoothing scale. It is concluded that the QDOT results are best explained if the power spectrum of the Galaxy density field has a slope of about -1 near a wavelength of about 100/h Mpc, while the CDM model has a slope of about 0 at that scale. The possibility of marginal non-Gaussian behavior at the 20/h Mpc scale reported by Saunders et al. (1990) is examined for gravitational instability models with Gaussian initial conditions. It is argued that the observed (delta exp 3) versus (delta exp 2) in redshift space is not what these models would predict.

Park, Changbom↗

NASA NTRS1991

Primordial fluctuations and non-linear structure

Several aspects of nonlinear gravitational instability are explored using two numerical experiments, each of which employs a series of 3D cosmological N-body simulations. In the first experiment, all of the initial high-frequency power is truncated above some critical wavenumber, in the second experiment, initial Fourier components are replaced with wavenumbers greater than critical by waves taken from an independent realization with the same power spectrum but with unrelated phases. These initial conditions are evolved for different values of critical wavenumbers to see how the progressive elimination or substitution of initial high-frequency components affects the final, nonlinear structure.

Little, Blane↗

NASA NTRS1991

Dynamical evolution of topology of large-scale structure

The nonlinear effects of statistical biasing and gravitational evolution on the genus are studied. The biased galaxy subset is picked for the first time by actually identifying galaxy-sized peaks above a fixed threshold in the initial conditions, and their subsequent evolution is followed. It is found that in the standard cold dark matter (CDM) model the statistical biasing in the locations of galaxies produces asymmetry in the genus curve and coupling with gravitational evolution gives rise to a shift in the genus curve to the left in moderately nonlinear regimes. Gravitational evolution alone reduces the amplitude of the genus curve due to strong phase correlations in the density field and also produces asymmetry in the curve. Results on the genus of the mass density field for both CDM and hot dark matter models are consistent with previous work by Melott, Weinberg, and Gott (1987).

Park, Changbom↗

NASA NTRS1991

The biasing scheme in N-body simulations

A popular prescription for the galaxy formation, i.e., identifying peaks in the linear density field as sites of galaxy formation, is numerically justified under the Cold Dark Matter cosmogony. In particular, the peak-background scheme, originally developed to simplify analytic calculations of peak properties in a Gaussian random density field, is proven to be an excellent prescription for assigning peak tracers in low-resolution N-body simulations through many statistical comparisons. It is found that statistical properties of peak tracers allocated by the peak-background scheme closely resemble those of true peaks when the background smoothing length is about three times the galaxy scale and the correspondence improves as they evolve gravitationally. It is also shown that these peak particles are indeed strongly associated with nonlinear objects that are presently collapsed.

Park, Changbom↗

NASA NTRS1991

Large-scale structure in a texture-seeded cold dark matter cosmogony

This paper studies the formation of large-scale structure by global texture in a flat universe dominated by cold dark matter. A code for evolution of the texture fields was combined with an N-body code for evolving the dark matter. The results indicate some promising aspects: with only one free parameter, the observed galaxy-galaxy correlation function is reproduced, clusters of galaxies are found to be significantly clustered on a scale of 20-50/h Mpc, and coherent structures of over 50/h Mpc in the galaxy distribution were found. The large-scale streaming motions observed are in good agreement with the observations: the average magnitude of the velocity field smoothed over 30/h Mpc is 430 km/sec. Global texture produces a cosmic Mach number that is compatible with observation. Also, significant evolution of clusters at low redshift was seen. Possible problems for the theory include too high velocity dispersions in clusters, and voids which are not as empty as those observed.

Park, Changbom↗

NASA NTRS1991

Simulation of deep one- and two-dimensional redshift surveys

It is shown that slice or pencil-beam redshift surveys of galaxies can be simulated in a box with nonequal sides. This method saves a lot of computer time and memory while providing essentially the same results as from whole-cube simulations. A 2457.6/h Mpc-long rod (out to a redshift z = 0.58 in two opposite directions) is simulated using the standard biased cold dark matter model as an example to mimic the recent deep pencil-beam surveys by Broadhurst et al. (1990). The structures (spikes) seen in these simulated samples occur when the narrow pencil-beam pierces walls, filaments, and clusters appearing randomly along the line-of-sight. A statistical test for goodness of fit to a periodic lattice has been applied to the observations and the simulations. It is found that the statistical significance level (P = 15.4 percent) is not strong enough to reject the null hypothesis that the observations and the simulations were drawn at random from the same set.

Park, Changbom↗

NASA NTRS1990

Weak gravitational lensing due to large-scale structure of the universe

The effect of the large-scale structure of the universe on the propagation of light rays is studied. The development of the large-scale density fluctuations in the omega = 1 universe is calculated within the cold dark matter scenario using a smooth particle approximation. The propagation of about 10 to the 6th random light rays between the redshift z = 5 and the observer was followed. It is found that the effect of shear is negligible, and the amplification of single images is dominated by the matter in the beam. The spread of amplifications is very small. Therefore, the filled-beam approximation is very good for studies of strong lensing by galaxies or clusters of galaxies. In the simulation, the column density was averaged over a comoving area of approximately (1/h Mpc)-squared. No case of a strong gravitational lensing was found, i.e., no 'over-focused' image that would suggest that a few images might be present. Therefore, the large-scale structure of the universe as it is presently known does not produce multiple images with gravitational lensing on a scale larger than clusters of galaxies.

Jaroszynski, Michal↗

NASA NTRS1990

Topology of microwave background fluctuations - Theory

Topological measures are used to characterize the microwave background temperature fluctuations produced by 'standard' scenarios (Gaussian) and by cosmic strings (non-Gaussian). Three topological quantities: total area of the excursion regions, total length, and total curvature (genus) of the isotemperature contours, are studied for simulated Gaussian microwave background anisotropy maps and then compared with those of the non-Gaussian anisotropy pattern produced by cosmic strings. In general, the temperature gradient field shows the non-Gaussian behavior of the string map more distinctively than the temperature field for all topology measures. The total contour length and the genus are found to be more sensitive to the existence of a stringy pattern than the usual temperature histogram. Situations when instrumental noise is superposed on the map, are considered to find the critical signal-to-noise ratio for which strings can be detected.

Gott, J. Richard, III↗