Engineering topics

Hamilton, A. J. S.

Publications and source records attributed to Hamilton, A. J. S..

18 records

NASA NTRS2005

"Cosmological Parameters from Large Scale Structure"

This grant has provided primary support for graduate student Mark Neyrinck, and some support for the PI and for colleague Nick Gnedin, who helped co-supervise Neyrinck. This award had two major goals. First, to continue to develop and apply methods for measuring galaxy power spectra on large, linear scales, with a view to constraining cosmological parameters. And second, to begin try to understand galaxy clustering at smaller. nonlinear scales well enough to constrain cosmology from those scales also. Under this grant, the PI and collaborators, notably Max Tegmark. continued to improve their technology for measuring power spectra from galaxy surveys at large, linear scales. and to apply the technology to surveys as the data become available. We believe that our methods are best in the world. These measurements become the foundation from which we and other groups measure cosmological parameters.

Hamilton, A. J. S.↗

NASA NTRS2001

Precision Measurement of Large Scale Structure

The purpose of this grant was to develop and to start to apply new precision methods for measuring the power spectrum and redshift distortions from the anticipated new generation of large redshift surveys. A highlight of work completed during the award period was the application of the new methods developed by the PI to measure the real space power spectrum and redshift distortions of the IRAS PSCz survey, published in January 2000. New features of the measurement include: (1) measurement of power over an unprecedentedly broad range of scales, 4.5 decades in wavenumber, from 0.01 to 300 h/Mpc; (2) at linear scales, not one but three power spectra are measured, the galaxy-galaxy, galaxy-velocity, and velocity-velocity power spectra; (3) at linear scales each of the three power spectra is decorrelated within itself, and disentangled from the other two power spectra (the situation is analogous to disentangling scalar and tensor modes in the Cosmic Microwave Background); and (4) at nonlinear scales the measurement extracts not only the real space power spectrum, but also the full line-of-sight pairwise velocity distribution in redshift space.

Hamilton, A. J. S.↗

NASA NTRS1996

Non-Linear Cosmological Power Spectra in Real and Redshift Space

We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zero-crossing of the quadrupole, where our model breaks down.

Taylor, A. N.↗

NASA NTRS1993

Omega from the anisotropy of the redshift correlation function in the IRAS 2 Jansky survey

Peculiar velocities distort the correlation function of galaxies in redshift space. In the linear regime, the distortion has a characteristic quadrupole plus hexadecapole form, with amplitude depending on the cosmological density parameter Omega. I report here measurements of the anisotropy of the correlation function in the IRAS 2 Jy redshift survey. The inferred value of Omega is Omega = 0.5 + 0.5 or - 0.25.

Hamilton, A. J. S.↗

NASA NTRS1993

Omega from the anisotropy of the redshift correlation function

Peculiar velocities distort the correlation function of galaxies observed in redshift space. In the large scale, linear regime, the distortion takes a characteristic quadrupole plus hexadecapole form, with the amplitude of the distortion depending on the cosmological density parameter omega. Preliminary measurements are reported here of the harmonics of the correlation function in the CfA, SSRS, and IRAS 2 Jansky redshift surveys. The observed behavior of the harmonics agrees qualitatively with the predictions of linear theory on large scales in every survey. However, real anisotropy in the galaxy distribution induces large fluctuations in samples which do not yet probe a sufficiently fair volume of the Universe. In the CfA 14.5 sample in particular, the Great Wall induces a large negative quadrupole, which taken at face value implies an unrealistically large omega 20. The IRAS 2 Jy survey, which covers a substantially larger volume than the optical surveys and is less affected by fingers-of-god, yields a more reliable and believable value, omega = 0.5 sup +.5 sub -.25.

Hamilton, A. J. S.↗

NASA NTRS1993

Ways to improve your correlation functions

This paper describes a number of ways to improve on the standard method for measuring the two-point correlation function of large scale structure in the Universe. Issues addressed are: (1) the problem of the mean density, and how to solve it; (2) how to estimate the uncertainty in a measured correlation function; (3) minimum variance pair weighting; (4) unbiased estimation of the selection function when magnitudes are discrete; and (5) analytic computation of angular integrals in background pair counts.

Hamilton, A. J. S.↗

NASA NTRS1992

Measuring Omega and the real correlation function from the redshift correlation function

Peculiar velocities distort the correlation function of galaxies in redshift space. In the linear regime, the distortion has a characteristic quadrupole plus hexadecapole form. The amplitude of the distortion depends on the cosmological density parameter Omega. Practical formulas are derived here which can be applied to redshift galaxy catalogs to measure Omega in the linear regime. The formulas also yield the real underlying correlation function in the linear regime, corrected for peculiar velocities.

Hamilton, A. J. S.↗

NASA NTRS1991

HEAO 1 A-2 low-energy detector X-ray spectra of the Lupus Loop and SN 1006

The Lupus Loop and SN 1006 were observed by the A-2 low-energy detector proportional counters on the HEAO 1 satellite as part of the all-sky survey. As a result of a major advance in understanding of detector response and background accurate analysis of the data has become possible. Soft X-ray spectra for both supernova remnants were constructed from the PHA data taken during the scanning observations. Single-temperature and two-temperature Raymond-Smith models were fitted to the observed spectra. In addition, power-law and power-law plus one-temperature models were fitted to the spectrum of SN 1006. Only two-component models provide an adequate description for both Lupus Loop and SN 1006 spectra. The temperatures, column densities, and emission measures are significantly more accurate than previous results.

Leahy, D. A.↗

NASA NTRS1991

Reconstructing the primordial spectrum of fluctuations of the universe from the observed nonlinear clustering of galaxies

It was discovered that the nonlinear evolution of the two point correlation function in N-body experiments of galaxy clustering with Omega = 1 appears to be described to good approximation by a simple general formula. The underlying form of the formula is physically motivated, but its detailed representation is obtained empirically by fitting to N-body experiments. In this paper, the formula is presented along with an inverse formula which converts a final, nonlinear correlation function into the initial linear correlation function. The inverse formula is applied to observational data from the CfA, IRAs, and APM galaxy surveys, and the initial spectrum of fluctuations of the universe, if Omega = 1.

Hamilton, A. J. S.↗

NASA NTRS1988

The topology of fractal universes

It is shown how the genus per unit volume of isodensity surfaces in general nonlinear universes is related to the entire hierarchy of correlation functions. The general relation between the correlation function, the probability distribution of densities at several points, and the probability distributions of density and its derivatives at a point are given. Formulas for the area and genus per unit volume of isodensity surfaces are presented. As an application, after first reviewing the case of Gaussian fields, analytic results are reported for one particular example of a thoroughly nonlinear universe, Mandelbrot's Rayleigh-Levy random-walk fractal. While this fractal bears little resemblance to the real universe of galaxies, it possesses the singular and theoretically interesting property that in it cluster-cluster correlations are identically equal to galaxy-galaxy correlations to all orders.

Hamilton, A. J. S.↗

NASA NTRS1988

On hierarchical solutions to the BBGKY hierarchy

It is thought that the gravitational clustering of galaxies in the universe may approach a scale-invariant, hierarchical form in the small separation, large-clustering regime. Past attempts to solve the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy in this regime have assumed a certain separable hierarchical form for the higher order correlation functions of galaxies in phase space. It is shown here that such separable solutions to the BBGKY equations must satisfy the condition that the clustered component of the solution has cluster-cluster correlations equal to galaxy-galaxy correlations to all orders. The solutions also admit the presence of an arbitrary unclustered component, which plays no dyamical role in the large-clustering regime. These results are a particular property of the specific separable model assumed for the correlation functions in phase space, not an intrinsic property of spatially hierarchical solutions to the BBGKY hierarchy. The observed distribution of galaxies does not satisfy the required conditions. The disagreement between theory and observation may be traced, at least in part, to initial conditions which, if Gaussian, already have cluster correlations greater than galaxy correlations.

Hamilton, A. J. S.↗

NASA NTRS1988

Cluster-cluster correlations and constraints on the correlation hierarchy

The hypothesis that galaxies cluster around clusters at least as strongly as they cluster around galaxies imposes constraints on the hierarchy of correlation amplitudes in hierachical clustering models. The distributions which saturate these constraints are the Rayleigh-Levy random walk fractals proposed by Mandelbrot; for these fractal distributions cluster-cluster correlations are all identically equal to galaxy-galaxy correlations. If correlation amplitudes exceed the constraints, as is observed, then cluster-cluster correlations must exceed galaxy-galaxy correlations, as is observed.

Hamilton, A. J. S.↗

NASA NTRS1988

Evidence for biasing in the CfA survey

Intrinsically bright galaxies appear systematically more correlated than faint galaxies in the Center for Astrophysics redshift survey. The amplification of the two-point correlation function behaves exponentially with luminosity, being essentially flat up to the knee of the luminosity function, then increasing markedly. The amplification reaches a factor of 3.5e + or - 0.4 in the very brightest galaxies. The effect is dominated by spirals rather than ellipticals, so that the correlation function of bright spirals becomes comparable to that of normal ellipticals. Similar results are obtained whether the correlation function is measured in two or three dimensions. The effect persists to separations of a correlation length or more, and is not confined to the cores of the Virgo, Coma, and Abell 1367 clusters, suggesting that the effect is caused by biasing, that is, galaxies kindle preferentially in more clustered regions, rather than by gravitational relaxation.

Hamilton, A. J. S.↗

NASA NTRS1986

The topology of the large-scale structure of the universe

It has been suggested recently that the topology of a distribution of galaxies can be characterized by the mean Gaussian curvature per unit volume of surfaces of constant density. An expression is derived which relates the mean curvature of isodensity surfaces to the power spectrum of density fluctuations in the linear regime of Gaussian fluctuations with random phases. The result may be compared to real galaxy catalogs if the galaxy density is smoothed over scales larger than a correlation length. The implications of the result for understanding the large-scale structure of the universe are discussed.

Hamilton, A. J. S.↗

NASA NTRS1986

The X-ray spectrum of SN 1006

The supernova (SN) of A.D. 1006 represents the brightest in recorded history. The X-ray observations of its remnant appear to be full of puzzles. The present paper has the objective to reevaluate published X-ray data on SN 1006, using detailed nonequilibrium spectral computations and a self-consistent hydrodynamic SNR model. In a summary of the main conclusions, it is pointed out that an observed power-law continuum can be understood as mainly free-free emission from a reverse shock into SN ejecta with an initially uniform density profile. The spectral index is correctly predicted by such a model. Most of the continuum is produced by fully ionized gas in the dense outer layers of ejecta. The X-ray spectrum is not consistent with a solar composition or a uniform composition but is consistent with a layered composition of ejecta containing carbon on the outside, and processed heavy elements on the inside. There is no difficulty in including a large mass of iron.

Hamilton, A. J. S.↗

NASA NTRS1986

The X-ray spectrum of Tycho

Baade (1945) has identified Tycho's supernova (SN) of A.D. 1572 as Type I, taking into account an analysis of the light curve recorded by Tycho. However, in spite of the obvious interest of Tycho's spectrum, to date the spectrum remains poorly understood. The present study is concerned with a reevaluation of the X-ray spectrum of Tycho. Attention is given to detailed nonequilibrium calculations and a self-consistent hydrodynamic model for ejecta consisting of pure heavy elements moving into a uniform external medium. The model provides a satisfactory fit to the spectrum, and avoids any requirement for a large mass of material in Tycho. It is demonstrated that the observed iron line emission is compatible with the presence of perhaps 0.7 solar mass of iron, of which 0.3 solar mass is shocked.

Hamilton, A. J. S.↗

NASA NTRS1985

X-ray spectra of young Type I supernova remnants - Exploded white dwarfs?

It is argued that the X-ray spectra of young Type I supernova remnants can be understood consistently in terms of thermal emission mainly from a reverse shock into initially uniform density ejecta. The inferred mass of ejecta is then consistent with 1.4 solar mass in SN 1006, Tycho, and Kepler. A substantial mass of iron, perhaps 0.8 solar mass, may be present provided that the ejecta are chemically inhomogeneous, with iron confined to inner layers of ejecta. The marked difference between the X-ray spectra of SN 1006 and Tycho is explained by the lower interstellar density around SN 1006.

Hamilton, A. J. S.↗

NASA NTRS1982

Gravitational spin precession in binary systems

The precessional behavior of a binary system is modeled along the lines of one orbital angular and two spin angular non-dissipatively coupled momenta. It is found that the precessional behavior consists of a periodic nutation superimposed on an overall precession of the system about the axis of total angular momentum. A periodic nutation, superimposed on an overall precession of the system about the axis of total angular momentum, is found to characterize system behavior. It is also shown that the nutation associated with precession in such compact object-containing binaries as the PSR 1913+16 pulsar and the Martin and Rees (1979) model of SS 433 will generally be too small to be observable.

Hamilton, A. J. S.↗