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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.

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NASA NTRS1976

On signal design by the R sub 0 criterion for non-white Gaussian noise channels

The use of the R sub 0 criterion for modulation system design is investigated for channels with non-white Gaussian noise. A signal space representation of the waveform channel is developed, and the cut-off rate R sub 0 for vector channels with additive nonwhite Gaussian noise and unquantized demodulation is derived. When the signal unput to the channel is a continuous random vector, maximization of R sub 0 with constrained average signal energy leads to a water-filling interpretation of optimal energy distribution in signal space. The necessary condition for a finite signal set to maximize R sub 0 with constrained energy and an equally likely probability assignment of signal vectors is presented, and an algorithm is outlined for numerically computing the optimum signal set. A necessary condition on a constrained energy, finite signal set is found which maximizes a Taylor series approximation of R sub 0. This signal set is compared with the finite signal set which has the water-filling average energy distribution.

Bordelon, D. L.↗
NASA NTRS2000

Structural Characterization of Crystalline Ice Nanoclusters

Water ice nanoclusters are useful analogs for studying a variety of processes that occur within icy grains in the extraterrestrial environment. The surface of ice nanoclusters prepared in the laboratory is similar to the surface of interstellar ice grains. In cold molecular clouds, the silicate cores of interstellar grains are typically approx. 100 nm in diameter and have a coating of impure amorphous water ice. Depositional, thermal and radiolytic processes leave the surface and subsurface molecules in a disordered state. In this state, structural defects become mobile and reactions of trapped gases and small molecules can occur. The large surface area of nanocluster deposits relative to their bulk allows for routine observation of such surface-mediated processes. Furthermore, the disordered surface and subsurface layers in nanocluster deposits mimic the structure of amorphous ice rinds found on interstellar dust grains. Transmission Electron Microscopy (TEM has been used tn characterize the crystallinity, growth mechanism, and size distribution of nanoclusters formed from a mixture of water vapor with an inert carrier gas that has been rapidly cooled to 77K. E M imaging reveals a Gaussian size distribution around a modal diameter that increases from approx. 15 to 30 nm as the percentage of water vapor within the mixture increases from 0.5 to 2.007, respectively . TEM bright and dark field imaging also reveals the crystalline nature of the clusters. h4any of the clusters show a mosaic structure in which crystalline domains originate at the center Other images show mirror planes that are separated by approx. 10 nm. Electron diffraction patterns of these clusters show that the clusters are composed of cubic ice with only a small hexagonal component. Further, the crystalline domain size is approximately the same as the modal diameter suggesting that the clusters are single crystals.

Blake, David↗
NASA NTRS1999

UV Spectral Variability and the Lyman-Alpha Forest in the Lensed Quasar Q0957+561

Far-ultraviolet spectra of the gravitational lens components Q0957+561 A and B were obtained with the Hubble Space Telescope Faint Object Spectrograph (FOS) at five equally spaced epochs, one every two weeks. We confirm the flux variability of the quasar's Lyman-alpha and O VI lambda 1037 emission lines reported in IUE (International Ultraviolet Explorer) spectra. The fluxes in these lines vary on a time scale of weeks in the local rest frame (LRF), independently of each other and of the surrounding continuum. The individual spectra of each image were co-added to investigate the properties of the Lyman-alpha forest along the two lines of sight to the quasar. Absorption lines having equivalent width W (sub lambda) greater than or equal to 0.3 Angstroms in the LRF not previously identified as interstellar lines, metal lines, or higher order Lyman lines were taken to be LY-alpha forest lines. The existence of each line in this consistently selected set was then verified by its presence in two archival FOS spectra with approx. 1.5 times higher signal to noise than our co-added spectra. Ly-alpha forest lines with W (sub lambda) greater than or equal to 0.3 Angstroms appear at 42 distinct wavelengths in the spectra of the two images. Two absorption lines in the spectrum of image A have no counterpart at that wavelength in the spectrum of image B, and two lines in image B have no counterpart in image A. Based on the separation of the lines of sight at the redshift of the absorption lines appearing in only one spectrum, the density of the absorbing clouds in the direction of Q0957+561 must change significantly over a distance of 79 (+34, -26) h (sub 50) (sup -1) kpc in the simplified model where the absorbers are treated as spherical clouds and the characteristic dimension is the radius. (We adopt H (sub 0)= 50 h (sub 50) km s (sup -1) kpc (sup -1), q (sub 0) = 1/2, and LAMBDA = 0 throughout the paper.) The two limits define the 68% confidence interval on the characteristic dimension, equivalent to the 1 sigma confidence interval for a Gaussian distribution. The 95% confidence interval extends from (32 - 250) h (sub 50) (sup -1) kpc. We show in the Appendix that the fraction of Ly-alpha forest lines that appear in only one spectrum can be expressed as a rapidly converging power series in 1/r, where r the ratio of the radius of the cloud to the separation of the two LOS at the redshift of the cloud. This power series can be rewritten to give r in terms of the fraction of Ly-alpha forest wavelengths that appear in the spectrum of only one image. A simple linear approximation to the solution which everywhere agrees with the power series solution to better than 0.8% for r greater than or equal to 2 is derived in the Appendix.

Dolan, J. F.↗
NASA NTRS2006

An Ensemble-Based Smoother with Retrospectively Updated Weights for Highly Nonlinear Systems

Monte Carlo computational methods have been introduced into data assimilation for nonlinear systems in order to alleviate the computational burden of updating and propagating the full probability distribution. By propagating an ensemble of representative states, algorithms like the ensemble Kalman filter (EnKF) and the resampled particle filter (RPF) rely on the existing modeling infrastructure to approximate the distribution based on the evolution of this ensemble. This work presents an ensemble-based smoother that is applicable to the Monte Carlo filtering schemes like EnKF and RPF. At the minor cost of retrospectively updating a set of weights for ensemble members, this smoother has demonstrated superior capabilities in state tracking for two highly nonlinear problems: the double-well potential and trivariate Lorenz systems. The algorithm does not require retrospective adaptation of the ensemble members themselves, and it is thus suited to a streaming operational mode. The accuracy of the proposed backward-update scheme in estimating non-Gaussian distributions is evaluated by comparison to the more accurate estimates provided by a Markov chain Monte Carlo algorithm.

Monte Carlo↗
NASA NTRS1994

Velocity distributions among colliding asteroids

The probability distribution for impact velocities between two given asteroids is wide, non-Gaussian, and often contains spikes according to our new method of analysis in which each possible orbital geometry for collision is weighted according to its probability. An average value would give a good representation only if the distribution were smooth and narrow. Therefore, the complete velocity distribution we obtain for various asteroid populations differs significantly from published histograms of average velocities. For all pairs among the 682 asteroids in the main-belt with D greater than 50 km, we find that our computed velocity distribution is much wider than previously computed histograms of average velocities. In this case, the most probable impact velocity is approximately 4.4 km/sec, compared with the mean impact velocity of 5.3 km/sec. For cases of a single asteroid (e.g., Gaspra or Ida) relative to an impacting population, the distribution we find yields lower velocities than previously reported by others. The width of these velocity distributions implies that mean impact velocities must be used with caution when calculating asteroid collisional lifetimes or crater-size distributions. Since the most probable impact velocities are lower than the mean, disruption events may occur less frequently than previously estimated. However, this disruption rate may be balanced somewhat by an apparent increase in the frequency of high-velocity impacts between asteroids. These results have implications for issues such as asteroidal disruption rates, the amount/type of impact ejecta available for meteoritical delivery to the Earth, and the geology and evolution of specific asteroids like Gaspra.

Bottke, William F., Jr.↗
NASA NTRS1978

Gaussian step-pressure loading of rigid viscoplastic plates

The response of a thin, rigid viscoplastic plate subjected to a spatially axisymmetric Gaussian step pressure impulse loading was studied analytically. A Gaussian pressure distribution in excess of the collapse load was applied to the plate, held constant for a length of time, and then suddenly removed. The plate deforms with monotonically increasing deflections until the dynamic energy is completely dissipated in plastic work. The simply supported plate of uniform thickness obeys the von Mises yield criterion and a generalized constitutive equation for rigid viscoplastic materials. For the small deflection bending response of the plate, the governing system of equations is essentially nonlinear. Transverse shear stress is neglected in the yield condition and rotary inertia in the equations of dynamic equilibrium. A proportional loading technique, known to give excellent approximations of the exact solution for the uniform load case, was used to linearize the problem and to obtain the analytical solutions in the form of eigenvalue expansions. The effects of load concentration, of an order of magnitude change in the viscosity of the plate material, and of load duration were examined while holding the total impulse constant.

Hayduk, R. J.↗
NASA NTRS1993

Spectrophotometry of Wolf-Rayet stars. I - Continuum energy distributions

All available low-resolution IUE spectra are assembled for Galactic, LMC, and SMC W-R stars and are merged with ground-based optical and NIR spectra in order to collate in a systematic fashion the shapes of these energy distributions over the wavelength range 0.1-1 micron. They can be consistently fitted by a power law of the form F(lambda) is approximately equal to lambda exp -alpha over the range 1500-9000 A to derive color excesses E(B-V) and spectral indices by removing the 2175-A interstellar absorption feature. The WN star color excesses derived are found to be in good agreement with those of Schmutz and Vacca (1991) and Koesterke et al. (1991). Significant heterogeneity in spectral index values was generally seen with any given subtype, but the groups consisting of the combined set of Galactic and LMC W-R stars, the separate WN and WC sequences, and the Galactic and LMC W-R stars all showed a striking and consistent Gaussian-like frequency distribution of values.

Morris, Patrick W.↗
NASA NTRS2010

Maximum Likelihood Time-of-Arrival Estimation of Optical Pulses via Photon-Counting Photodetectors

Many optical imaging, ranging, and communications systems rely on the estimation of the arrival time of an optical pulse. Recently, such systems have been increasingly employing photon-counting photodetector technology, which changes the statistics of the observed photocurrent. This requires time-of-arrival estimators to be developed and their performances characterized. The statistics of the output of an ideal photodetector, which are well modeled as a Poisson point process, were considered. An analytical model was developed for the mean-square error of the maximum likelihood (ML) estimator, demonstrating two phenomena that cause deviations from the minimum achievable error at low signal power. An approximation was derived to the threshold at which the ML estimator essentially fails to provide better than a random guess of the pulse arrival time. Comparing the analytic model performance predictions to those obtained via simulations, it was verified that the model accurately predicts the ML performance over all regimes considered. There is little prior art that attempts to understand the fundamental limitations to time-of-arrival estimation from Poisson statistics. This work establishes both a simple mathematical description of the error behavior, and the associated physical processes that yield this behavior. Previous work on mean-square error characterization for ML estimators has predominantly focused on additive Gaussian noise. This work demonstrates that the discrete nature of the Poisson noise process leads to a distinctly different error behavior.

Erkmen, Baris I.↗
NASA NTRS1987

EDQNM closure: A homogeneous simulation to support it. A quasi-homogeneous simulation to disprove it

It is known that two-point closures are useful tools for understanding and predicting turbulence. Among the various closures, the Eddy Damped Quasi-Normal Markovian (EDQNM) approach is one of the simplest and, at the same time, most useful. Direct numerical simulations (DNS) can provide information that can be used to test the validity of two-point theories. It is the purpose of the present work to use DNS to validate, or improve upon, EDQNM. A case was selected for which EDQNM is known to give satisfactory results: homogeneous isotropic turbulence. Quantities were then evaluated which may be used to test the assumptions of two-point closure approximations: spectral Lagrangian time scales. The goal was to make a careful and refined study to validate the EDQNM theory. A reference case was built for which EDQNM is likely to give poor results. An attempt to generate a quasi-homogeneous turbulent field containing organized structures, was built by artifically injecting them in the initial conditions. The results of direct simulations using such initial conditions are expected to provide a challenge for EDQNM since this kind of field is simple enough to allow comparisons with two-point theories, but at the same time contains coherent structures which cannot be expected to be accurately accounted for by closures based on expansions about Gaussianity.

Bertoglio, J. P.↗
NASA NTRS1995

GHRS observations of cool, low-gravity star. 2: Flow and turbulent velocities in the outer atmosphere of gamma CRU CIS (M3.4 III)

The Goddard High Resoulution Spectrograph (GHRS) on the Hubble Space Telescope (HST) has been used to obtain medium (R = 20,000) and high (R = 85,000) resoultion UV spectra of chromosphere emission features for the M3.4 III star gamma Cru. Small Science Aperture (SSA) G270M and Echelle-B spectra of selected regions in the 2300-2850 A range were obtained to determine the kinematics of the chromosphere using lines of C2), Fe2, Co2, Si1/2), Ni2, Mn2, and Mg2. Profiles of C2) (UV 0.01) lines and fluorescently excited lines of low optical depth indicate average turbulent velocities (Doppler FWHM) of 30.2 +/- 1.3 and 28.8 +/- 1.3 km/s, respectively. The fluorescent emission lines (mean RV = 21.3 +/- 0.9 km/s) and the wings of the emission components of Fe2 lines (mean RV = 22.8 +/- 0.4 km/s) are approximately at rest relative to the radial velocity of the star (21 km/s), while the C2) lines show a modest inflow (mean RV = 23.1 +/- 0.9 km/s). The more opaque lines of Fe2 and Mg2 exhibit complex profiles resulting from line formation in an optically thick, extended expanding atmosphere. The emission wings of these lines are broadened by multiple scattering, and they are centered near the photospheric radial velocity. Closer to line center, these strong lines show a strong blueshifted self-absorption feature (already seen in IUE data), indicative of formation in an expanding chromosphere, and a previously unseen dip in the profiles on the red side of line center. The absorption components, when extracted using simple Gaussian fits, show strong correlations with the relative optical depths of the lines. The derived absorption flow velocities converge to the photospheric velocity as one examines spectra features formed deeper in the atmosphere. The blueward abosrption velocity increases in magnitude from about 7 to 14 km/s with increasing line optical depth - the strong absorptions directly map the acceleration of the outflowing stellar wind, while the interpretation of the weaker redshifted abosrptions is more ambiguous, indicating either an inflow of material or formation in an extended, spherically expanding outflow. The Mg2 and Fe2 profiles, taken together, imply that the wind speed decreases between the atmospheric layers where the Mg2 and Fe2 self-absorption components are formed. Interstellar absorptions are seen in the resonance lines of Mg2 (UV 1) and Fe2 (UV1) with zero-volt lower levels, at about -3 km/s, consistent with models of the interstellar medium in the direction of gamma Cru. Finally, we have detected the Mg2 'satellite lines' seen in solar spectra obtained above the limb. In gamma Cru these lines are probably fluorescently excited by H Ly beta.

Carpenter, Kenneth G.↗
NASA NTRS2019

An Evolving Broad Iron Line from the First Galactic Ultraluminous X-Ray Pulsar Swift J0243.6+6124

We present a spectral study of the ultraluminous Be/X-ray transient pulsar Swift J0243.6+6124 using Neutron Star Interior Composition Explorer (NICER) observations during the system's 2017–2018 giant outburst. The 1.2–10 keV energy spectrum of the source can be approximated with an absorbed cutoff power-law model. We detect strong, luminosity-dependent emission lines in the 6–7 keV energy range. A narrow 6.42 keV line, observed in the sub-Eddington regime, is seen to evolve into a broad Fe-line profile in the super-Eddington regime. Other features are found at 6.67 and 6.97 keV in the Fe-line complex. An asymmetric broad-line profile, peaking at 6.67 keV, is possibly due to Doppler effects and gravitational redshift. The 1.2–79 keV broadband spectrum from Nuclear Spectroscopic Telescope Array (NuSTAR) and NICER observations at the outburst peak is well described by an absorbed cutoff power law plus multiple Gaussian lines and a blackbody component. Physical reflection models are also tested to probe the broad iron-line feature. Depending on the mass accretion rate, we found emission sites that are evolving from ~5000 km to a range closer to the surface of the neutron star. Our findings are discussed in the framework of the accretion disk and its implication on the magnetic field, the presence of optically thick accretion curtain in the magnetosphere, jet emission, and the massive, ultrafast outflow expected at super-Eddington accretion rates. We do not detect any signatures of a cyclotron absorption line in the NICER or NuSTAR data.

Gaurava K. Jaisawal↗
NASA NTRS1972

Smoothing of functions of range and range rate measurements from earth orbiting satellites

It is shown that for satellites in circular Earth orbits with altitudes of 500 kilometers to 1500 kilometers, and for satellites in elliptical orbits with an approximate 4000 kilometer height of perigee, a high degree least squares polynomial (e.g., a 9th or 10th degree in some cases) is required to smooth both range and range rate data for purposes of input to orbit determination programs. In order to circumvent this problem, functions of range and range rate are smoothed with lower degree least squares polynomials (e.g., 3rd and 4th degree) and it is shown that under the above geometric constraints the standard deviation of fit can be reduced to levels commensurate with typical S-band tracking system resolution which is 1 to 2 meters in range and 0.005 meters/second in range rate for a 1 per second data rate. Also shown are the effects of Gaussian random noise, biases, and periodic noise. This analysis includes numerous examples applied to the 44 point data smoothing interval currently used in much of the operational preprocessing at the Goddard Space Flight Center.

Grenchik, T. J.↗
NASA NTRS1980

Propagation in a shearing plasma. II - Turbulence and the frequency range of pulsar microstructure

Numerical calculations are presented which explore the propagation of radio waves and pulses through a turbulent shearing plasma. A stochastic model is used to describe the turbulent velocity field, in which random fluctuations are superposed on a mean profile. Both Gaussian wave packets and shot-noise pulses polarized in the plane of shearing acquire quasi-periodic intensity modulations above the rest-frame plasma frequency. The frequency range over which these modulations appear is shown to depend on the spatial correlation length of the turbulent fluctuations and on their standard deviation from the mean velocity. The period of the modulations is variable from one realization of the random process to the next, and the average period is frequency dependent. The results of these calculations lend further support to a model for pulsar microstructure in which periodic micropulses are pure temporal modulations of the emitted radiation due to propagation effects in magnetospheric shearing regions. It is shown that turbulence on a scale of approximately 10 cm can produce these quasi-periodic modulations over a frequency range comparable to that of observed microstructure.

Harding, A. K.↗
NASA NTRS1995

Morphology, near-infrared luminosity, and mass of the Galactic bulge from COBE DIRBE observations

Near-infrared images of the Galactic bulge at 1.25, 2.2, 3.5, and 4.9 microns obtained by the Diffuse Infrared Background Experiment (DIRBE) onboard the Cosmic Background Explorer (COBE) satellite are used to characterize its morphology and to determine its infrared luminosity and mass. Earlier analysis of the DIRBE observations (Weiland et al. 1994) provided supporting evidence for the claim made by Blitz & Spergel (1991) that the bulge is bar-shaped with its near end in the first Galactic quadrant. Adopting various triaxial analytical functions to represent the volume emissivity of the source, we confirm the barlike nature of the bulge and show that triaxial Gaussian-type functions provide a better fit to the data than other classes of functions, including an axisymmetric spheroid. The introduction of a `boxy' geometry, such as the one used by Kent, Dame, & Fazio (1991) improves the fit to the data. Our results show that the bar is rotated in the plane with its near side in the first Galactic quadrant creating an angle of 20 deg +/- 10 deg between its major axis and the line of sight to the Galactic center. Typical axis ratios of the bar are (1:0.33 +/- 0.11:0.23 +/- 0.08), resembling the geometry of prolate spheroids. There is no statistically significant evidence for an out-of-plane tilt of the bar at 2.2 microns, and marginal evidence for a tilt of approximately equal 2 deg at 4.9 microns. The introduction of a roll around the intrinsic major axis of the bulge improves the `boxy' appearance of some functions. A simple integration of the observed projected intensity of the bulge gives a bulge luminosity of 1.2 x 10(exp 9), 4.1 x 10(exp 8), 2.3 x 10(exp 8), and 4.3 x 10(exp 7) solar luminosity, respectively, at 1.25, 2.2, 3.5, and 4.9 microns wavelength for a Galactocentric distance of 8.5 kpc. The 2.2 microns luminosity function of the bulge population in the direction of Baade's window yields a bolometric luminosity of L(sub bol) = 5.3 x 10(exp 9) solar luminosity. Stellar evolutionary models relate this luminosity to the number of main-sequence progenitor stars that currently populate the red giant branch. Combined with the recent determination of the main-sequence turnoff mass for the bulge by the Hubble Space Telescope (Holtzman et al. 1993) we derive a photometrically determined bulge mass of approximately equal to 1.3 x 10(exp 10) solar mass for a Salpeter initial mass function extended down to 0.1 solar mass.

Dwek, E.↗
NASA NTRS2020

Optically targeted search for gravitational waves emitted by core-collapse supernovae during the first and second observing runs of advanced LIGO and advanced Virgo

We present the results from a search for gravitational-wave transients associated with core-collapse supernovae observed within a source distance of approximately 20 Mpc during the first and second observing runs of Advanced LIGO and Advanced Virgo. No significant gravitational-wave candidate was detected. We report the detection efficiencies as a function of the distance for waveforms derived from multidimensional numerical simulations and phenomenological extreme emission models. The sources with neutrino-driven explosions are detectable at the distances approaching 5 kpc, and for magnetorotationally driven explosions the distances are up to 54 kpc. However, waveforms for extreme emission models are detectable up to 28 Mpc. For the first time, the gravitational-wave data enabled us to exclude part of the parameter spaces of two extreme emission models with confidence up to 83%, limited by coincident data coverage. Besides, using ad hoc harmonic signals windowed with Gaussian envelopes, we constrained the gravitational-wave energy emitted during core collapse at the levels of 4.27 × 10^(−4) Mꙩc^(2) and 1.28 × 10^(−1) Mꙩc^(2) for emissions at 235 and 1304 Hz, respectively. These constraints are 2 orders of magnitude more stringent than previously derived in the corresponding analysis using initial LIGO, initial Virgo, and GEO 600 data.

B. P. Abbott↗
NASA NTRS1989

Feasibility study of a single, elliptical heliocentric Earth-Mars trajectory

The initial intent of this design project was to evaluate the existence and feasibility of a single elliptical heliocentric Earth/Mars trajectory. This trajectory was constrained to encounter Mars twice in its orbit, within a time interval of 15 to 180 Earth days between encounters. The single ellipse restriction was soon found to be prohibitive for reasons shown later. Therefore, the approach taken in the design of the round-trip mission to Mars was to construct single-leg trajectories which connected two planets on two prescribed dates. Three methods of trajectory design were developed. Method 1 is an eclectic approach and employs Gaussian Orbit Determination (Method 1A) and Lambert-Euler Preliminary Orbit Determination (Method 1B) in conjunction with each other. Method 2 is an additional version of Lambert's Solution to orbit determination, and both a coplanar and a noncoplanar solution were developed within Method 2. In each of these methods, the fundamental variables are two position vectors and the time between the position vectors. In all methods, the motion was considered Keplerian motion and the reference frame origin was located at the sun. Perturbative effects were not considered in Method 1. The feasibility study of round-trip Earth/Mars trajectories maintains generality by considering only heliocentric trajectory parameters and planetary approach conditions. The coordinates and velocity components of the planets, for the standard epoch J2000, were computed from an approximate set of osculating elements by the procedure outlined in an ephemeris of coordinates.

Blake, M.↗
NASA NTRS1989

Higher order dispersion in the propagation of a gravity wave packet

To the first order of approximation, the complex amplitude of a wave packet in an anisotropic and dispersive medium is convected with the group of velocity. However, a gravity wave is a vector wave. Its wave packet must be formed by superposition of various wave numbers with corresponding frequencies, as is the case for scalar waves, and additionally by superposing many eigenmodes which also depend on the wave number. To represent the vector wave packet self-consistently, it is found that a gradient term must be included in the expansion. For a Guassian wave packet, this gradient term is shown to have important implications on the velocity vector as represented by its hodograph. Numerical results show that the hodograph is influenced by the location of the relative position of interest from the center of a Gaussian pulse. Higher order expansion shows that an initial Gaussian wave packet will retain its Gaussian shape as it propagates, but the pulse will spread in all directions with its major axis undergoing a rotation. Numerical results indicate that these higher order dispersive effects may be marginally observable in the atmosphere.

Yeh, K. C.↗
NASA NTRS1993

The Lyman alpha forest of the high-z quasar 0000-263

Medium-resolution (delta(v) = 45 km/s) optical spectra of the bright, high-redshift (z = 4.1) quasar 0000-263 taken at the ESO 3.5-m NTT telescope were analyzed to determine the distribution of column densities, velocities and line widths of the Lyman-alpha forest absorption components. The values of NH, b, and z were determined by fitting Voigt profiles to the lines, and convolving with a Gaussian instrumental response function. Over 350 components with log N(sub H) greater than 13.2 were identified. An analysis of the dependence of the number of components with z reveals that the number evolution of components obeys the power law dN/dz varies as (1+z)(sup gamma), where gamma = 0.5 +/- 0.4 for the sample of 182 lines with log N(sub H) greater than 14.0. The distribution of component strengths is found to obey f(N(sub H)) varies as N(sub h)(sup -beta), where beta = -1.55 for components with log(N(sub H)) is greater than 14.7, and beta = -0.68 for the components with log(N(sub H)) greater than 13.5. A distinct break in the f(N(sub H)) histogram is also observed, at log(N(sub H)) is approximately 14.7. The results are briefly considered in the context of theoretical models of quasar Lyman alpha clouds and their evolution.

Penprase, Bryan↗