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NASA NTRS2017

Structure in the 3D Galaxy Distribution: III. Fourier Transforming the Universe: Phase and Power Spectra

We demonstrate the effectiveness of a relatively straightforward analysis of the complex 3D Fourier transform of galaxy coordinates derived from redshift surveys. Numerical demonstrations of this approach are carried out on a volume-limited sample of the Sloan Digital Sky Survey redshift survey. The direct unbinned transform yields a complex 3D data cube quite similar to that from the Fast Fourier Transform (FFT) of finely binned galaxy positions. In both cases deconvolution of the sampling window function yields estimates of the true transform. Simple power spectrum estimates from these transforms are roughly consistent with those using more elaborate methods. The complex Fourier transform characterizes spatial distributional properties beyond the power spectrum in a manner different from (and we argue is more easily interpreted than) the conventional multi-point hierarchy. We identify some threads of modern large scale inference methodology that will presumably yield detections in new wider and deeper surveys.

Galactic clusters↗

NASA NTRS1994

Amplitude of primeval fluctuations from cosmological mass density reconstructions

We use the POTENT reconstruction of the mass density field in the nearby universe to estimate the amplitude of the density fluctuation power spectrum for various cosmological models. We find that sigma(sub 8) Omega(sub m sup 0.6) = 1.3(sub -0.3 sup +0.4), almost independently of the power spectrum. This value agrees well with the Cosmic Background Explorer (COBE) normalization for the standard cold dark matter model, while alternative models predict an excessive amplitude compared with COBE. Flat, low Omega(sub m) models and tilted models with spectral index n less than 0.8 are particularly discordant.

Seljak, Uros↗

NASA NTRS2023

The Atacama Cosmology Telescope: Map-Based Noise Simulations for DR6

The increasing statistical power of cosmic microwave background (CMB) datasets requires a commensurate effort in understanding their noise properties. The noise in maps from ground-based instruments is dominated by large-scale correlations, which poses a modeling challenge. This paper develops novel models of the complex noise covariance structure in the Atacama Cosmology Telescope Data Release 6 (ACT DR6) maps. We first enumerate the noise properties that arise from the combination of the atmosphere and the ACT scan strategy. We then prescribe a class of Gaussian, map-based noise models, including a new wavelet-based approach that uses directional wavelet kernels for modeling correlated instrumental noise. The models are empirical, whose only inputs are a small number of independent realizations of the same region of sky. We evaluate the performance of these models against the ACT DR6 data by drawing ensembles of noise realizations. Applying these simulations to the ACT DR6 power spectrum pipeline reveals a ≥ 20% excess in the covariance matrix diagonal when compared to an analytic expression that assumes noise properties are uniquely described by their power spectrum. Along with our public code, mnms, this work establishes a necessary element in the science pipelines of both ACT DR6 and future ground-based CMB experiments such as the Simons Observatory (SO).

CMBR experiments↗

NASA NTRS1994

On determining the spectrum of primordial inhomogeneity from the COBE DMR sky maps: Results of two-year data analysis

A new technique of Fourier analysis on a cut sky has been applied to the two-year Cosmic Background Explorer (COBE) Differential Microwave Radiometer (DMR) 53 and 90 GHz sky maps. The Bayesian power spectrum estimation results are consistent with the Harrison-Zel'dovich n = 1 model. The maximum likelihood estimates of the usual parameters defining the power spectrum of primordial perturbations are n = 1.22 (1.02) and Q(sub rms-PS) = 17 (20) microK including (excluding) the quadrupole. A spectral-index-independent normalization is naturally expressed for the two-year maps in terms of the multipole amplitude a(sub 9) = 8.2 (8.3) microK (to approximately 12 sigma significance). The marginal likelihood function on n obtained by intergration with respect to a(sub 9) renders n = 1.17 +/- 0.31 (0.96 +/- 0.36).

Gorski, K. M.↗

NASA NTRS1984

Analysis and Interpretation of Synthetic Time Strings of Oscillation Data

Artificial strings of solar oscillation data with gaps and noise, corresponding to the output of different spatial filter functions, were analyzed. Peaks in the power spectrum are identified for values of the degree l from 0 to 18, and rotational splitting is estimated. The filters prove effective in facilitating identification of essentially all the real peaks in the power spectrum. Estimates of peak frequencies and amplitudes and rotational splitting frequencies are in reasonably good agreement with the input values. Spurious peaks in autocorrelation spectra correspond to the frequency spacing between power peaks with the same order n, differing by one or two in the degree l.

Mihalas, B. W.↗

NASA NTRS1979

Turbulence in planetary occultations. IV - Power spectra of phase and intensity fluctuations

Power spectra of phase and intensity scintillations during occultation by turbulent planetary atmospheres are significantly affected by the inhomogeneous background upon which the turbulence is superimposed. Such coupling is particularly pronounced in the intensity, where there is also a marked difference in spectral shape between a central and grazing occultation. While the former has its structural features smoothed by coupling to the inhomogeneous background, such features are enhanced in the latter. Indeed, the latter power spectrum peaks around the characteristic frequency that is determined by the size of the free-space Fresnel zone and the ray velocity in the atmosphere; at higher frequencies strong fringes develop in the power spectrum. A confrontation between the theoretical scintillation spectra computed here and those calculated from the Mariner 5 Venus mission by Woo et al. (1974) is inconclusive, mainly because of insufficient statistical resolution. Phase and/or intensity power spectra computed from occultation data may be used to deduce characteristics of the turbulence and to distinguish turbulence from other perturbations in the refractive index. Such determinations are facilitated if observations are made at two or more frequencies (radio occultation) or in two or more colors (stellar occultation).

Haugstad, B. S.↗

NASA NTRS1986

Infrared helioseismology - Detection of the chromospheric mode

Time-series observations of an infrared solar OH absorption line profile have been obtained on two consecutive days using a laser heterodyne spectrometer to view a 2 arcsec portion of the quiet sun at disk center. A power spectrum of the line center velocity shows the well-known photospheric p-mode oscillations very prominently, but also shows a second feature near 4.3 mHz. A power spectrum of the line intensity shows only the 4.3 mHz feature, which is identified as the fundamental p-mode resonance of the solar chromosphere. The frequency of the mode is observed to be in substantial agreement with the eigenfrequency of current chromospheric models. A time series of two beam difference measurements shows that the mode is present only for horizontal wavelengths greater than 19 Mm. The period of a chromospheric p-mode resonance is directly related to the sound travel time across the chromosphere, which depends on the chromospheric temperature and geometric height. Thus, detection of this resonance will provide an important new constraint on chromospheric models.

Deming, D.↗

NASA NTRS2003

First Year Wilkinson Microwave Anisotropy Probe (WMAP)Observations: Preliminary Maps and Basic Results

We present full sky microwave maps in five frequency bands (23 to 94 GHz) from the WMAP first year sky survey. Calibration errors are less than 0.5% and the low systematic error level is well specified. The cosmic microwave background (CMB) is separated from the foregrounds using multifrequency data. The sky maps are consistent with the 7 in. full-width at half-maximum (FWHM) Cosmic Background Explorer (COBE) maps. We report more precise, but consistent, dipole and quadrupole values. The CMB anisotropy obeys Gaussian statistics with -58 less than f(sub NL) less than 134 (95% CL). The 2 less than or = l less than or = 900 anisotropy power spectrum is cosmic variance limited for l less than 354 with a signal-to-noise ratio greater than 1 per mode to l = 658. The temperature-polarization cross-power spectrum reveals both acoustic features and a large angle correlation from reionization. The optical depth of reionization is tau = 0.17 +/- 0.04, which implies a reionization epoch of t(sub r) = 180(sup +220, sub -80) Myr (95% CL) after the Big Bang at a redshift of z(sub r) = 20(sup +10, sub -9) (95% CL) for a range of ionization scenarios. This early reionization is incompatible with the presence of a significant warm dark matter density. A best-fit cosmological model to the CMB and other measures of large scale structure works remarkably well with only a few parameters. The age of the best-fit universe is t(sub 0) = 13.7 +/- 0.2 Gyr old. Decoupling was t(sub dec) = 379(sup +8, sub -7)kyr after the Big Bang at a redshift of z(sub dec) = 1089 +/- 1. The thickness of the decoupling surface was Delta(sub z(sub dec)) = 195 +/- 2. The matter density of the universe is Omega(sub m)h(sup 2) = 0.135(sup +0.008, sub -0.009) the baryon density is Omega(sub b)h(sup 2) = 0.0224 +/- 0.0009, and the total mass-energy of the universe is Omega(sub tot) = 1.02 +/- 0.02. There is progressively less fluctuation power on smaller scales, from WMAP to fine scale CMB measurements to galaxies and finally to the Ly-alpha forest. This is accounted for with a running spectral index, significant at the approx. 2(sigma) level. The spectral index of scalar fluctuations is fit as n(sub s) = 0.93 +/-0.03 at wavenumber k(sub o) = 0.05/Mpc ((sub eff) approx. = 700), with a slope of dn(sub s)/d I(sub nk) = -0.031(sup + 0.016, sub -0.018) in the best-fit model.

Bennett, C. L.↗

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.↗

NASA NTRS1992

The kinematics of buoyancy induced mixing

A model problem to study mixing driven by buoyancy flow fields due to a time dependent body force which consists of a steady and an oscillatory component is considered. Flow fields generated by a time dependent body force, which consists of a steady and an oscillatory component from vibrations or g-jitter, mix two fluids inside a cavity by stretching and folding the interface into various morphological patterns. These patterns show two basic structures depending on the dominant components of the body force. These structures are whirls and tendrils, corresponding to the dominance of either the steady or oscillatory component, respectively. A combination of these structures also occurs in the interaction region. In this region the effect of the steady component opposes the oscillatory component and the result is to smooth the interface, and prevent breakup of the interface. For the parametric range considered, two basic flow regimes occur: convective and chaotic. In the convective regime, the morphological patterns are topological. In the chaotic regime, mixing occurs by a repetitive sequence of bubble formation, necking, and breakup which spreads the concentration field throughout the cavity. The length stretch of the interface increases exponentially with time. The dynamical system characteristics show that in the convective regime, at a point in space, the flow field is oscillatory with elliptical phase space trajectories, and its power spectrum indicates that the flow field responds to the corresponding input frequency. Whereas, in the chaotic regime, the flow field is aperiodic, the phase space trajectories show irregular patterns, and the power spectrum shows a broadband distribution.

Duval, Walter M. B.↗

NASA NTRS1978

Synoptic analysis of interplanetary radio scintillation spectra observed at 34 MHz

Synoptic observations of the temporal power spectrum of interplanetary scintillations were made in the summer of 1976 on the University of Iowa's Cocoa Cross radio telescope and the University of Maryland's TPT array. Most of the observations were at large (larger than 40 deg) solar elongations. It was found that the power spectrum broadens when enhanced turbulence at the front of a high-speed solar wind stream sweeps over the earth. In the case with sufficient synoptic coverage, the broadening appeared to result from the relative closeness of the enhanced scattering region rather than from an increase in velocity. A small percentage of the spectra displayed two power law components with a plateau between them. These may result from a flattening in the spatial turbulence spectrum such as has been observed by spacecraft.

Gotwols, B. L.↗

NASA NTRS1991

Ultraviolet variability of NGC 5548 - Dynamics of the continuum production region and geometry of the broad-line region

Data from the 1989-1990 IUE monitoring of the Seyfert galaxy NGC 5548 are used here to analyze the continuum variability properties of the galaxy and to derive the structure or its emission-line region. The mean shape of the UV continuum is well fit by an accretion disk model with a given black hole mass and an additional component required to reproduce the observed soft X-ray flux. The continuum fluctuation power spectrum is very steep, with most of the variance coming from about 1 yr time scales. The entire optical/UV continuum rises and falls almost simultaneously, so that the logarithmic slope of the power spectrum is nearly the same for all bands, but the flux at higher photon frequencies varies with larger amplitude. The emission-line material around the nucleus may best be described by a highly ionized inner zone of high and nearly constant pressure that stretches about 4-14 light-days from the center and an outer, more weakly ionized zone of considerably lower ionization at least 20-30 light-days out.

Krolik, J. H.↗

NASA NTRS1996

The Nearest Neutron Stars

Extreme Ultraviolet Explorer (EUVE) satellite observations of the Pulsar PSR J0437-4715, the Seyfert Galaxy RX J0437.4-4711, and the Geminga Pulsar are reported on. The main purpose of the PSR J0437-4715 investigation was to examine its soft X-ray flux. The 20 day EUVE observation of RX J0437.4-4711 constitutes a uniformly sampled soft X-ray light curve of a highly variable Seyfert galaxy whose power spectrum can be examined on timescales from 3 hrs. to several days. A unique aspect of the EUVE observation of RX J0437.4-4711 is its long light curve which we have used to measure the power spectrum of soft X-ray variability at low frequencies. Approximately 2100 counts were detected for the Geminga pulsar in a period of 251,000 s by the EUVE Deep Survey instrument. Geminga presents an unusually difficult problem because its multicomponent X-ray spectrum and pulse profile are indicative of a complex distribution of surface emission, and possibly a contribution from nonthermal emission as well.

Halpern, Jules P.↗

NASA NTRS1987

Analytic and numerical calculations of quantum synchrotron spectra from relativistic electron distributions

Calculations are performed numerically and analytically of synchrotron spectra for thermal and power-law electron distributions using the single-particle synchrotron power spectrum derived from quantum electrodynamics. It is found that the photon energy at which quantum effects appear is proportional to temperature and independent of field strength for thermal spectra; quantum effects introduce an exponential roll-off away from the classical spectra. For power law spectra, the photon energy at which quantum effects appear is inversely proportional to the magnetic field strength; quantum effects produce a steeper power law than is found classically. The results are compared with spectra derived from the classical power spectrum with an energy cutoff ensuring conservation of energy. It is found that an energy cutoff is generally an inadequate approximation of quantum effects for low photon energies and for thermal spectra, but gives reasonable results for high-energy emission from power-law electron distributions.

Brainerd, J. J.↗

NASA NTRS2007

Quasi-Periodic Variability in NGC 5408 X-1

We report the discovery with XMM-Newton of quasiperiodic variability in the 0.2 - 10 keV X-ray flux from the ultraluminous X-ray source NGC 5408 X-1. The average power spectrum of all EPIC-pn data reveals a strong 20 mHz QPO with an average amplitude (rms) of 9%, and a coherence, Q identical with nu(sub 0)/sigma approximately equal to 6. In a 33 ksec time interval when the 20 mHz QPO is strongest we also find evidence for a 2nd QPO peak at 15 mHz, the first indication for a close pair of QPOs in a ULX source. Interestingly, the frequency ratio of this QPO pair is inconsistent with 3:2 at the 3 sigma level, but is consistent with a 4:3 ratio. A powerlaw noise component with slope near 1.5 is also present below 0.1 Hz with evidence for a break to a flatter slope at about 3 mHz. The source shows substantial broadband variability, with a total amplitude (rms) of about 30% in the 0.1 - 100 mHz frequency band, and there is strong energy dependence to the variability. The power spectrum of hard X-ray photons (greater than 2 keV) shows a "classic" flat-topped continuum breaking to a power law with index 1.5 - 2. Both the break and 20 mHz QPO are detected in the hard band, and the 20 mHz QPO is essentially at the break. The QPO is both strong and narrow in this band, having an amplitude (rms) of 15%, and Q approx. equal to 25. The energy spectrum is well fit by three components, a "cool" disk with kT = 0.15 keV, a steep power law with index 2.56, and a thermal plasma at kT = 0.87 keV. The disk, power law, and thermal plasma components contribute 35, 60, and 5% of the 0.3 - 10 keV flux, respectively. Both the timing and spectral properties of NGC 5408 X-1 are strikingly reminiscent of Galactic black hole systems at high inferred accretion rates, but with its characteristic frequencies (QPO and break frequencies) scaled down by a factor of 10 - 100. We discuss the implications of these findings in the context of models for ULXs, and their implications for the object's mass.

Strohmayer, Tod E.↗

NASA NTRS1998

The Development of a Degree 360 Expansion of the Dynamic Ocean Topography of the POCM_4B Global Circulation Model

This paper documents the development of a degree 360 expansion of the dynamic ocean topography (DOT) of the POCM_4B ocean circulation model. The principles and software used that led to the final model are described. A key principle was the development of interpolated DOT values into land areas to avoid discontinuities at or near the land/ocean interface. The power spectrum of the POCM_4B is also presented with comparisons made between orthonormal (ON) and spherical harmonic magnitudes to degree 24. A merged file of ON and SH computed degree variances is proposed for applications where the DOT power spectrum from low to high (360) degrees is needed.

Rapp, Richard H.↗

NASA NTRS1986

Observations of quasi-periodic oscillations from GX 5 - 1 and Cygnus X-2 with the Einstein (HEAO 2) Observatory

The bright galactic bulge X-ray source GX 5 - 1 was observed in April 1979 with the Monitor Proportional Counter on board the Einstein (HEAO 2) Observatory. Analysis of the high time resolution data from the Time Interval Processor confirms the recent Exosat discovery of quasi-periodic oscillations in the X-ray emission from GX 5 - 1. In addition, the summed 0.4 s power spectrum shows the low-frequency red noise component also discovered in the Exosat data. Low-frequency structure is also clearly present in data taken from the bright galaxtic X-ray source Cyg X-2 in December 1978. The expected power spectrum for quasi-periodic oscillations was calculated, including the low-frequency red noise component, using a simple shot noise model with oscillating shots.

Elsner, R. F.↗

NASA NTRS1993

Hemodynamic and autonomic nervous system responses to mixed meal ingestion in healthy young and old subjects and dysautonomic patients with postprandial hypotension

BACKGROUND. Although postprandial hypotension is a common cause of falls and syncope in elderly persons and in patients with autonomic insufficiency, the pathophysiology of this disorder remains unknown. METHODS AND RESULTS. We examined the hemodynamic, splanchnic blood pool, plasma norepinephrine (NE), and heart rate (HR) power spectra responses to a standardized 400-kcal mixed meal in 11 healthy young (age, 26 +/- 5 years) and nine healthy elderly (age, 80 +/- 5 years) subjects and 10 dysautonomic patients with symptomatic postprandial hypotension (age, 65 +/- 16 years). Cardiac and splanchnic blood pools were determined noninvasively by radionuclide scans, and forearm vascular resistance was determined using venous occlusion plethysmography. In healthy young and old subjects, splanchnic blood volume increased, but supine blood pressure remained unchanged after the meal. In both groups, HR increased and systemic vascular resistance remained stable. Forearm vascular resistance and cardiac index increased after the meal in elderly subjects, whereas these responses were highly variable and of smaller magnitude in the young. Young subjects demonstrated postprandial increases in low-frequency HR spectral power, representing cardiac sympatho-excitation, but plasma NE remained unchanged. In elderly subjects, plasma NE increased after the meal but without changes in the HR power spectrum. Patients with dysautonomia had a large postprandial decline in blood pressure associated with no change in forearm vascular resistance, a fall in systemic vascular resistance, and reduction in left ventricular end diastolic volume index. HR increased in these patients but without changes in plasma NE or the HR power spectrum. CONCLUSIONS. 1) In healthy elderly subjects, the maintenance of blood pressure homeostasis after food ingestion is associated with an increase in HR, forearm vascular resistance, cardiac index, and plasma NE. In both young and old, systemic vascular resistance is maintained. 2) Dysautonomic patients with postprandial hypotension fail to maintain systemic vascular resistance after a meal. This impairment in vascular response to meal ingestion may underlie the development of postprandial hypotension. 3) The measurement of mean HR or plasma NE does not adequately characterize autonomic cardiac control. Power spectral analysis suggests an impairment in the postprandial autonomic modulation of HR in healthy elderly and dysautonomic subjects, possibly predisposing to hypotension when vascular compensation is inadequate.

Non-NASA Center↗