Engineering topics

Fry, J. N.

Publications and source records attributed to Fry, J. N..

13 records

NASA NTRS1994

Skewness in large-scale structure and non-Gaussian initial conditions

We compute the skewness of the galaxy distribution arising from the nonlinear evolution of arbitrary non-Gaussian intial conditions to second order in perturbation theory including the effects of nonlinear biasing. The result contains a term identical to that for a Gaussian initial distribution plus terms which depend on the skewness and kurtosis of the initial conditions. The results are model dependent; we present calculations for several toy models. At late times, the leading contribution from the initial skewness decays away relative to the other terms and becomes increasingly unimportant, but the contribution from initial kurtosis, previously overlooked, has the same time dependence as the Gaussian terms. Observations of a linear dependence of the normalized skewness on the rms density fluctuation therefore do not necessarily rule out initially non-Gaussian models. We also show that with non-Gaussian initial conditions the first correction to linear theory for the mean square density fluctuation is larger than for Gaussian models.

Fry, J. N.↗

NASA NTRS1994

Redshift distortions of galaxy correlation functions

To examine how peculiar velocities can affect the two-, three-, and four-point redshift correlation functions, we evaluate volume-average correlations for configurations that emphasize and minimize redshift distortions for four different volume-limited samples from each of the CfA, SSRS, and IRAS redshift catalogs. We present the results as the correlation length r(sub 0) and power index gamma of the two-point correlations, bar-xi(sub 0) = (r(sub 0)/r)(exp gamma), and as the hierarchical amplitudes of the three- and four-point functions, S(sub 3) = bar-xi(sub 3)/bar-xi(exp 2)(sub 2) and S(sub 4) = bar-xi(sub 4)/bar-xi(exp 3)(sub 2). We find a characteristic distortion for bar-xi(sub 2), the slope gamma is flatter and the correlation length is larger in redshift space than in real space; that is, redshift distortions 'move' correlations from small to large scales. At the largest scales (up to 12 Mpc), the extra power in the redshift distribution is compatible with Omega(exp 4/7)/b approximately equal to 1. We estimate Omega(exp 4/7)/b to be 0.53 +/- 0.15, 1.10 +/- 0.16, and 0.84 +/- 0.45 for the CfA, SSRS, and IRAS catalogs. Higher order correlations bar-xi(sub 3) and bar-xi(sub 4) suffer similar redshift distortions but in such a way that, within the accuracy of our ananlysis, the normalized amplitudes S(sub 3) and S(sub 4) are insensitive to this effect. The hierarchical amplitudes S(sub 3) and S(sub 4) are constant as a function of scale between 1 and 12 Mpc and have similar values in all samples and catalogs, S(sub 3) approximately equal to 2 and S(sub 4) approximately equal to 6, despite the fact that bar-xi(sub 2), bar-xi(sub 3), and bar-xi(sub 4) differ from one sample to another by large factors (up to a factor of 4 in bar-xi(sub 2), 8 for bar-xi(sub 3), and 12 for bar-xi(sub 4)). The agreement between the independent estimations of S(sub 3) and S(sub 4) is remarkable given the different criteria in the selection of galaxies and also the difference in the resulting range of densities, luminosities, and locations between samples.

Fry, J. N.↗

NASA NTRS1994

The minimal power spectrum: Higher order contributions

It has been an accepted belief for some time that gravity induces a minimal tail P(k) approximately k(exp 4) in the power spectrum as k approaches 0 for distributions with no initial power on large scales. In a recent numerical experiment with initial power confined to a restricted range in k, Shandarin and Melott (1990) found a k approaches 0 tail that at early stages of evolution behaves as k(exp 4) and grows with time as a(exp 4)(t), where a(t) is the cosmological expansion factor, and at late times depends on scale as k(exp 3) and grows with time as a(exp 2)(t). I compute analytically several contributions to the power spectrum of higher order than those included in earlier work, and I apply the results to the particular case of initial power restricted to a finite range of k. As expected, in the perturbative regime P(k) approximately a(exp 4)k(exp 4) from the first correction to linear perturbation theory is the dominant term as k approaches 0. Numerical investigations show that the higher order contributions go as k(exp 4) also. However, perturbation theory alone cannot tell whether the P approximately a(exp 2)k(exp 3) result is 'nonperturbative' or a numerical artifact.

Fry, J. N.↗

NASA NTRS1993

Biasing and hierarchical statistics in large-scale structure

In this paper we consider the consequences for galaxy formation of an arbitrary, effectively local biasing transformation of a hierarchical underlying matter distribution. We show that a general form of such a transformation preserves the hierarchical properties and the shape of the dispersion in the limit of small fluctuations, i.e., on large scales, although the values of the hierarchical amplitudes may change arbitrarily. We present expressions for the induced hierarchical amplitudes S(g,j) of the galaxy distribution in terms of the matter amplitudes S(j) and biasing parameters for j = 3-7. For higher order correlations, j greater than 2, restricting to a linear bias is not a consistent approximation even at very large scales. To draw any conclusions from the galaxy distribution about matter correlations of order j, properties of biasing must be specified completely to order j - 1.

Fry, J. N.↗

NASA NTRS1993

The three-point correlation function in an ensemble of three-dimensional simulations

We evaluate the three-point function in Fourier space for an ensemble of three-dimensional 128 exp 3 numerical simulations with initial power spectra characterized by spectral index n = +1, 0, -1, -2, -3, with no high-frequency cutoff and with cutoff k(c) = 16 or k(c) = 4. To remove dependences on scale and on time, we present results as the reduced amplitude Q in the hierarchical model as a function of the dimensionless variable kd(rms), where d(rms) is the mean square displacement of a particle from its initial position. For scale-free initial conditions, there is no evolution in Q. For initial conditions with a cutoff, Q evolves until the scale of the cutoff is in the nonlinear regime; the results afterwards are no different from those with no initial cutoff. The transition from quasi-linear to nonlinear regimes is followed. In the quasi-linear regime, our results agree well with gravitational perturbation theory predictions, including a marked dependence on the shape of the configuration. In the nonlinear regime, the value of Q for scale-invariant initial conditions is remarkably independent of evolution epoch, of scale, and of configuration shape, and depends on spectral index roughly as Q = 3/(3 + n).

Fry, J. N.↗

NASA NTRS1992

The three-point function in an ensemble of numerical simulations

The three-point function in Fourier space is evaluated for an ensemble of 2D numerical simulations with nine initial power spectra distinguished by spectral index and cutoff. To remove the main dependences on scale and time, results are presented as the reduced amplitude Q in the hierarchical model. To lowest nonvanishing order in perturbation theory, Q is a constant, independent of length scale, of time, and of initial spectrum. The results show that in the nonlinear regime of evolution, normalizing to Q does remove the main variations, but systematic dependences on spectral index and cutoff remain at late times that depend on properties of the initial spectrum. Models with initial power cut off on a scale that has been evolved far into the nonlinear regime are indistinguishable from models with no cutoff.

Fry, J. N.↗

NASA NTRS1989

Void statistics, scaling, and the origins of large-scale structure

The probability that a volume of the universe of given size and shape spaced at random will be void of galaxies is used here to study various models of the origin of cosmological structures. Numerical simulations are conducted on hot-particle and cold-particle-modulated inflationary models with and without biasing, on isothermal or initially Poisson models, and on models where structure is seeded by loops of cosmic string. For the Pisces-Perseus redshift compilation of Giovanelli and Haynes (1985), it is found that hierarchical scaling is obeyed for subsamples constructed with different limiting magnitudes and subsamples taken at random. This result confirms that the hierarchical ansatz holds valid to high order and supports the idea that structure in the observed universe evolves by a regular process from an almost Gaussian primordial state. Neutrino models without biasing show the effect of a strong feature in the initial power spectrum. Cosmic string models do not agree well with the galaxy data.

Fry, J. N.↗

NASA NTRS1988

Cosmological structure formation from soft topological defects

Some models have extremely low-mass pseudo-Goldstone bosons that can lead to vacuum phase transitions at late times, after the decoupling of the microwave background.. This can generate structure formation at redshifts z greater than or approx 10 on mass scales as large as M approx 10 to the 18th solar masses. Such low energy transitions can lead to large but phenomenologically acceptable density inhomogeneities in soft topological defects (e.g., domain walls) with minimal variations in the microwave anisotropy, as small as delta Y/T less than or approx 10 to the minus 6 power. This mechanism is independent of the existence of hot, cold, or baryonic dark matter. It is a novel alternative to both cosmic string and to inflationary quantum fluctuations as the origin of structure in the Universe.

Hill, Christopher T.↗

NASA NTRS1986

Statistics of voids in hierarchical universes

As one alternative to the N-point galaxy correlation function statistics, the distribution of holes or the probability that a volume of given size and shape be empty of galaxies can be considered. The probability of voids resulting from a variety of hierarchical patterns of clustering is considered, and these are compared with the results of numerical simulations and with observations. A scaling relation required by the hierarchical pattern of higher order correlation functions is seen to be obeyed in the simulations, and the numerical results show a clear difference between neutrino models and cold-particle models; voids are more likely in neutrino universes. Observational data do not yet distinguish but are close to being able to distinguish between models.

Fry, J. N.↗

NASA NTRS1986

On statistical searches for filaments

The presence or absence of an excess of filamentary structure in the galaxy distribution has important implications for the origin of such structure. In an attempt to answer this question, many statistics have been devised to quantify the visual impression of filaments seen in galaxy maps, but few of these are at all well understood. Two of these, a quadrupole elongation statistic and a nearest-neighbor alignment statistic, are analyzed in the common language of the irreducible N-point correlation functions of the galaxy distribution, and it is argued that there has as yet been no success in isolating filaments in particular from clustering in general.

Fry, J. N.↗

NASA NTRS1985

Statistical comparison of galaxy formation models - The bispectrum

To discriminate between galaxy-formation models that give similar two-point correlation functions, higher moments, specifically the three-point function in transform space or bispectrum, are looked to for an ensemble of numerical simulations. Different behaviors of this statistic are found that can be used to distinguish between classes of models. Up to the uncertainty in identifying the galaxy distribution with the mass distribution in the models, the results seem to prefer the isothermal or the cold-particle models. No model, however, agrees in all detail with the observational bispectrum of the Shane-Wirtanen galaxy catalog.

Fry, J. N.↗

NASA NTRS1985

Cosmological density fluctuations and large-scale structure From N-point correlation functions to the probability distribution

Knowledge of N-point correlation functions for all N allows one to invert and obtain the probability distribution of mass fluctuations in a fixed volume. The hierarchical sequence of higher order is applied to correlations with dimensionless amplitudes suggested by the BBGKY equations. The resulting distribution is significantly non-Gaussian, even for quite small mean square fluctuations. The qualitative and to some degree quantitative results are to a large degree independent of the exact sequence of amplitudes. An ensemble of such models compared with N-body simulations fails in detail to account for the low-density frequency distribution.

Fry, J. N.↗

NASA NTRS1984

Supermassive monopole stars

In this paper, the evolution of a superheavy monopole-dominated universe is reexamined; in particular, the evolution of rotation-stabilized monopole-burning 'stars', balancing effects of radiation and annihilation are examined. In contrast to earlier results, it is found that this can lead to complete burning of all poles present in such an object within finite time. If monopoles can be brought within acceptable limits by dynamical processes, an inflationary epoch of the early universe need not be associated with grand unification.

Fry, J. N.↗