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NASA NTRS1995

Nonlinear structure formation in flat cosmological models

This paper describes the formation of nonlinear structure in flat (zero curvature) Friedmann cosmological models. We consider models with two components: the usual nonrelativistic component that evolves under gravity and eventually forms the large-scale structure of the universe, and a uniform dark matter component that does not clump under gravity, and whose energy density varies with the scale factor a(t) like a(t)(sup -n), where n is a free parameter. Each model is characterized by two parameters: the exponent n and the present density parameter Omega(sub 0) of the nonrelativistic component. The linear perturbation equations are derived and solved for these models, for the three different cases n = 3, n is greater than 3, and n is less than 3. The case n = 3 is relevant to model with massive neutrinos. The presence of the uniform component strongly reduces the growth of the perturbation compared with the Einstein-de Sitter model. We show that the Meszaros effect (suppression of growth at high redshift) holds not only for n = 4, radiation-dominated models, but for all models with n is greater than 3. This essentially rules out any such model. For the case n is less than 3, we numerically integrate the perturbation equations from the big bang to the present, for 620 different models with various values of Omega(sub 0) and n. Using these solutions, we show that the function f(Omega(sub 0), n) = (a/delta(sub +))d(delta)(sub +)/da, which enters in the relationship between the present density contrast delta(sub 0) and peculiar velocity field u(sub 0) is essentially independent of n. We derive approximate solutions for the second-order perturbation equations. These second-order solutions are tested against the exact solutions and the Zel'dovich approximation for spherically symmetric perturbations in the marginally nonlinear regime (the absolute value of delta is less than or approximately 1). The second-order and Zel'dovich solutions have comparable accuracy, significantly higher than the accuracy of the linear solutions. We then investigate the dependence of the delta(sub 0) - u(sub 0) relationship upon the value of n in the nonlinear regime using the second-order solutions for marginally nonlinear, general perturbations, and the exact solutions for strongly nonlinear, spherically symmetric perturbations. In both cases, we find that the delta(sub 0) - u(sub 0) relationship remains independent of n. We speculate that this result extends to strongly nonlinear, general perturbations as well. This eliminates any hope to determine the presence of the uniform component or the value of n using dynamical methods. Finally, we compute the nonlinear evolution of the skewness of the distribution of values of delta, assuming Gaussian initial conditions. We find that the skewness is not only independent of n, but also of Omega(sub 0). Thus the skewness cannot be used to discriminate among various models with Gaussian initial conditions. However, it can be used for testing the Gaussianity of the initial conditions themselves. We conclude that the uniform component leaves no observable signature in the present large-scale structure of the universe. To determine its presence and nature, we must investigate the relationship between the past and present universe, using redshift-dependent tests.

Martel, Hugo↗

NASA NTRS1995

A compact solution to computational acoustics

This paper demonstrates that the linearized, dimensional Euler equations for acoustic computation can be accurately solved as a set of decoupled first-order wave equations, and that if ordered properly, this system of simple waves has unambiguous, easily implemented boundary conditions, allowing waves of same group speeds to pass through numerical boundaries or comply with wall conditions. Thus, the task of designing a complex multi-dimensional scheme with approximate far-field boundary conditions reduces to the design of higher order schemes for the one-dimensional simple wave equation. A compact finite-difference scheme and a characteristically exact but numerically n(th) order accurate boundary condition are introduced for solving the first order wave equation. Spanning a three-point two-level stencil, this low-dispersion implicit scheme has a third order spatial accuracy when used on nonuniform meshes, fourth order accurate on uniform meshes, and a temporal accuracy of second order due to the choice of trapezoidal integration for algorithmic simplicity. The robustness and accuracy of the scheme are demonstrated through a series of numerical experiments and comparisons with published results. When tested on the one-dimensional wave equation on a uniform grid, this scheme allows a Gaussian wave packet to pass through any finite domain with low numerical dispersion characteristic of a spatially fourth-order scheme and reflections at numerical boundaries maintained below truncation error. On highly stretched and irregular grids, only mild dispersions are found in the solution while solutions by other methods fail or are severely distorted. Yet, this scheme is no more sophisticated to solve or implement than the Crank-Nicolson scheme. This scheme has been tested on four categories of the ICASE/LaRC benchmark problems, which include propagation of acoustic and convective waves in Cartesian and cylindrical domains, reflection of acoustic wave at stationary/moving boundaries, and sound generation by gust-blade interaction.

Fung, K.-Y.↗

NASA NTRS1994

An extended source for CN jets in Comet P/Halley

We examined radial intensity profiles of CN jets in comparison with the diffuse, isotropic component of the CN coma of Comet P/Halley. All images were bias-subtracted, flat-fielded, and continuum-subtracted. We calculated the diffuse profiles by finding the azimuthal mean of the coma least contaminated by jets yielding profiles similar to those of vectorial and Haser models of simple photodissociation. We found the jet profiles by calculating a mean around a Gaussian-fitted center in r-theta space. There is an unmistakable difference between the profiles of the CN jets and the profiles of the diffuse CN. Spatial derivatives of these profiles, corrected for geometrical expansion, show that the diffuse component is consistent with a simple photodissociation process, but the jet component is not. The peak production of the jet profile occurs 6000 km from the nucleus at a heliocentric distance of 1.4 AU. Modeling of both components of the coma indicate results that are consistent with the diffuse CN photochemically produced, but the CN jets need an additional extended source. We found that about one-half of the CN in the coma of Comet P/Halley originated from the jets, the rest from the diffuse component. These features, along with the width of the jet being approximately constant, are consistent with a CHON grain origin for the jets.

Klavetter, James Jay↗

NASA NTRS1984

Center of mass estimation in closed vortices - A verification in principle and practice

The problem of tracking closed mesoscale vortices using center of mass estimation techniques is studied. Three estimators are evaluated using data from a warm core Gulf Stream ring. The comparisons show that a method based on the intersection of perpendicular bisectors and one using a least-squares fit of a conic section perform comparably. The perpendicular bisector algorithm is used in conjunction with a Gaussian ring model and a star-shaped survey pattern to produce an expected error curve as a function of vortex translation, survey speed and vortex size. For typical ring parameters, center estimation is usually possible to within + or - 5 km. The feasibility of using differing data sets to construct a history of ring motion based on a coordinate system moving with the ring is also investigated. In this way, the validity of using satellite-derived data and drifter trajectories to estimate the center of mass of a mesoscale feature is assessed. The results of the analysis demonstrate that the location of the deeper structure of the ring and the surface expression are sufficiently well correlated to permit dynamically relevant calculations based on surface measurements. It is shown that satellite-derived data can be used to approximate the center of mass trajectory to within the error in the individual center estimates for the period analyzed. The Lagrangian-drifter-derived centers are offset from the center of mass trajectory in a manner consistent with kinematic arguments.

Hooker, S. B.↗

NASA NTRS2010

On the Nature of the Compact Object in SS 433. Observational Evidence of X-Ray Photon Index Saturation

We present an analysis of the X-ray spectral properties observed from black hole , candidate (BHC) binary SS 433. We have analyzed Rossi X-ray Time Explorer (RXTE) data from this source, coordinated with Green Bank Interferometer/RATAN-600. We show that SS 433 undergoes a X-ray spectral transition from the low hard state (LHS) to the intermediate state (IS). We show that the X-ray broad-band energy spectra during all spectral states are well fit by a sum of so called "Bulk Motion Comptonization (BMC) component" and by two (broad and narrow) Gaussians for the continuum and line emissions respectively. In addition to these spectral model components we also find a strong feature that we identify as a" blackbody-like (BB)" component which color temperature is in the range of 4-5 keV in 24 IS spectra during the radio outburst decay in SS 433. Our observational results on the "high temperature BB" bump leads us to suggest the presence of gravitationally redshifted annihilation line emission in this source. In fact this spectral feature has been recently reproduced in Monte Carlo simulations by Laurent and Titarchuk. We have also established the photon index saturation at about 2.3 in index vs mass accretion correlation. This index-mass accretion correlation allows us to evaluate the low limit of black hole (BH) mass of compact object in SS 433, M(sub bh) approximately > 2 solar masses, using the scaling method using BHC GX 339-4 as a reference source. Our estimate of the BH mass in SS 433 is consistent with recent BH mass measurement using the radial-velocity measurements of the binary system by Hillwig & Gies who find that M(sub x)( = (4.3 +/- 0.8) solar masses. This is the smallest BH mass found up to now among all BH sources. Moreover, the index saturation effect versus mass accretion rate revealed in SS 433, like in a number of other BH candidates, is the strong observational evidence for the presence of a BH in SS 433.

Seifina, Elena↗

NASA NTRS2003

A Self-Contained Mapping Closure Approximation for Scalar Mixing

Scalar turbulence exhibits interplays of coherent structures and random fluctuations over a broad range of spatial and temporal scales. This feature necessitates a probabilistic description of the scalar dynamics, which can be achieved comprehensively by using probability density functions (PDFs). Therefore, the challenge is to obtain the scalar PDFs (Lundgren 1967; Dopazo 1979). Generally, the evolution of a scalar is governed by three dynamical processes: advection, diffusion and reaction. In a PDF approach (Pope 1985), the advection and reaction can be treated exactly but the effect of molecular diffusion has to be modeled. It has been shown (Pope 1985) that the effect of molecular diffusion can be expressed as conditional dissipation rates or conditional diffusions. The currently used models for the conditional dissipation rates and conditional diffusions (Pope 1991) have resisted deduction from the fundamental equations and are unable to yield satisfactory results for the basic test cases of decaying scalars in isotropic turbulence, although they have achieved some success in a variety of individual cases. The recently developed mapping closure approach (Pope 1991; Chen, Chen & Kraichnan 1989; Kraichnan 1990; Klimenko & Pope 2003) provides a deductive method for conditional dissipation rates and conditional di usions, and the models obtained can successfully describe the shape relaxation of the scalar PDF from an initial double delta distribution to a Gaussian one. However, the mapping closure approach is not able to provide the rate at which the scalar evolves. The evolution rate has to be modeled. Therefore, the mapping closure approach is not closed. In this letter, we will address this problem.

He, Guo-Wei↗

NASA NTRS2008

Multi-wavelength Observations and Modelling of a Solar Flare

Aims: The aim of this work is to investigate the dynamic behavior of a C-class solar flare through the evolution of temperature, emission measure, energy loss and velocity. In particular, the variation of these properties with time are studied using multi-wavelength observations in combination with a recently developed 0-D hydrodynamic model. Methods: The temperature and emission measure evolution were studied using several instruments covering a wide range of temperatures - the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI, >5 MK), GOES-12 (5- 30 MK), the Transition Region and Coronal Explorer (TRACE 171 A, 1 MK) and the Coronal Diagnostic Spectrometer (CDS, 0.03-8 MK). The temperature and emission measure were analysed through the systematic cooling of flare plasma through the response functions of these instruments. These parameters were then investigated using the Enthalpy Based Thermal Evolution of Loops model (EBTEL). The Doppler shifts at both flare footpoints were analysed using five emission lines seen by CDS. Results: The flare began with clear evidence for pre-flare heating. Upflows of approx.90 km/s and low level emission, both observed in Fe XIX before the main impulsive phase were explained by pre-flare gentle chromospheric evaporation. During the main impulsive phase, the flare plasma was heated to a temperature of >13 MK in approximately 10 minutes. Explosive chromospheric evaporation was observed, driving upflows of approx.80 km/s in Fe XIX and simultaneous downflows of approx.20 km/s in He I and O v. At the peak of the Rare, conduction modelled by EBTEL was found to be the dominant loss mechanism, working efficiently to both lower the temperatures and drive gentle chromospheric evaporation. As the temperature fell below approx.8 MK, radiation became the dominant loss mechanism. During the final stages of the decay phase, downflowing plasma was observed at the footpoints in He I, O v and Mg x at velocities of up to approx.40 km/s, suggesting loop draining occurred. Conclusions. This is the first extensive study of the evolution of flare plasma using both spectroscopic and broad-band instruments in conjunction with a comprehensive hydrodynamic model. The flare began with pre-flare heating and then evolved following the predictions of the standard flare model. Detailed analysis of the plasma heating mechanisms was carried out and the heating function most consistent with observations was found to be Gaussian in shape. The simulations suggested that both direct heating and heating by a non-thermal beam played significant roles in this event.

Raftery, Claire L.↗

NASA NTRS2007

High-Resolution N-Band Observations of the Nova RS Ophiuchi with the Keck Interferometer Nuller

We report new observations of the nova RS Ophiuchi (RS Oph) using the Keck Interferometer Nulling Instrument, approximately 3.8 days following the most recent outburst that occurred on 2006 February 12. The Keck Interferometer Nuller (KIN) operates in K-band from 8 to 12.5 pm in a nulling mode, which means that the central broad-band interference fringe is a dark fringe - with an angular width of 25 mas at mid band - rather than the bright fringe used ill a conventional optical interferometer. In this mode the stellar light itself is suppressed by the destructive fringe, effectively enhancing the contrast of the circumstellar material located near the star. By subsequently shifting the neighboring bright fringe onto the center of the source brightness distribution and integrating, a second spatial regime dominated by light from the central portion of the source is almost simultaneously sampled. The nulling technique is the sparse aperture equivalent of the conventional corongraphic technique used in filled aperture telescopes. By fitting the unique KIK inner and outer spatial regime data, we have obtained an angular size of the mid-infrared continuum of 6.2, 4.0. or 5.4 mas for a disk profile, gaussian profile (fwhm), and shell profile respectively. The data show evidence of enhanced neutral atomic hydrogen emission located in the inner spatial regime relative to the outer regime. There is also evidence of a 9.7 micron silicate feature seen outside of this region. Importantly, we see spectral lines excited by the nova flash in the outer region before the blast wave reaches these regions. These lines are from neutral, weakly excited atoms which support the following interpretation. We discuss the present results in terms of a unifying model of the system that includes an increase in density in the plane of the orbit of the two stars created by a spiral shock wave caused by the motion of the stars through the cool wind of the red giant star. These data show the power and potential of the nulling technique which has been developed for the detection of Earth-like planets around nearby stars for the Terrestrial Planet Finder Mission and Darwin missions.

Barry, R. K.↗

NASA NTRS2007

Antarctic Circumpolar Current Transport Variability during 2003-05 from GRACE

Gravity Recovery and Climate Experiment (GRACE) gravity data spanning January 2003-November 2005 are used as proxies for ocean bottom pressure (BP) averaged over 1 month, spherical Gaussian caps 500 km in radius, and along paths bracketing the Antarctic Circumpolar Current's various fronts. The GRACE BP signals are compared with those derived from the Estimating the Circulation and Climate of the Ocean (ECCO) ocean modeling-assimilation system, and to a non-Boussinesq version of the Regional Ocean Model System (ROMS). The discrepancy found between GRACE and the models is 1.7 cm H2O (1 cm H2O approx. 1 hPa), slightly lower than the 1.9 cmH2O estimated by the authors independently from propagation of GRACE errors. The northern signals are weak and uncorrelated among basins. The southern signals are strong, with a common seasonality. The seasonal cycle GRACE data observed in the Pacific and Indian Ocean sectors of the ACC are consistent, with annual and semiannual amplitudes of 3.6 and 0.6 cmH2O (1.1 and 0.6 cm H2O with ECCO), the average over the full southern path peaks (stronger ACC) in the southern winter, on days of year 197 and 97 for the annual and semiannual components, respectively; the Atlantic Ocean annual peak is 20 days earlier. An approximate conversion factor of 3.1 Sv (Sv equiv 10(exp 6)cu m/s) of barotropic transport variability per cm H2O of BP change is estimated. Wind stress data time series from the Quick Scatterometer (QuikSCAT), averaged monthly, zonally, and over the latitude band 40(deg)- 65(deg)S, are also constructed and subsampled at the same months as with the GRACE data. The annual and semiannual harmonics of the wind stress peak on days 198 and 82, respectively. A decreasing trend over the 3 yr is observed in the three data types.

Gravity Recovery and Climate Experiment (GRACE)↗

NASA NTRSDate not supplied

Estimation of Timing Performance with Pulsed Laser Links for Small Satellite PNT

Satellite constellations are growing in size and in utility for applications as diverse as providing reliable, low-latency internet service to rural areas orEarth science missions.This expansion of satellite constellations brings attention to the need for responsive and reliable satellite communication.Current research in the PrecisionSpace Systems Laboratory at the University of Florida focuses on using pulsed laser communications as the method of relaying time signals instead of the radio frequency (RF)signals.The upcoming CLICK (CubeSat Laser Infrared CrosslinK) missions (Massachusetts Institute of Technology, University of Florida, NASA Ames Research Center) will demonstrate a spacecraft-to-spacecraft laser communication link and time-transfer.For pre-flight technology assessment of missions such as CLICK, a simulation of a spacecraft constellation in Earth orbit has been created to estimate clock synchronization and precision orbit determination based on measured instrumentation performance.We have developed a novel MATLAB-based numerical simulator to model spacecraft-to-spacecraft laser time-transfer and estimate the offset between the spacecraft clocks over time.This simulation includes timing errors associated with laser pulse generation and detection, as well as non-Gaussian clock drift models.The two on-board clocks modeled are a cesium-based Chip-Scale Atomic Clock (CSAC) and a rubidium-based Miniature Atomic Clock (MAC), both produced by Microchip.An example case of two spacecraft in a circular, low-Earth orbit receiving GPS position, GPS timing, and laser pulse time-of-flight measurements is simulated.The positions and velocities of the two spacecraft at a reference epoch and the constant clock model coefficients are estimated.Polynomial models of different orders were used as clock models. The effect of clock model order on the root-mean-square (RMS) of the clock error is apparent in the case using GPS and lasing measurements, showing that the clock model improves with increasing clock model order. Results compare the estimated clock model of a mission operation that only uses GPS measurements and a mission operation that uses both GPS and laser pulse time-of-flight measurements between spacecraft referenced to their on-board CSACs or on-board MACs. Including lasing measurements reduces the RMS clock model error by approximately 80% of the RMS of the cases with only GPS measurements.This simulation tool can be used to optimize the lasing operations schedule based on mission timing performance objectives. During this presentation, I will discuss the details of the simulation and clock model estimation, as well as discuss the results.I will compare the results of incorporating lasing timing measurements to using only GPS measurements and the outcomes of using different orders of polynomials.

Timing Performance↗

NASA NTRS1995

Wavelet transform analysis of the small-scale X-ray structure of the cluster Abell 1367

We have developed a new technique based on a wavelet transform analysis to quantify the small-scale (less than a few arcminutes) X-ray structure of clusters of galaxies. We apply this technique to the ROSAT position sensitive proportional counter (PSPC) and Einstein high-resolution imager (HRI) images of the central region of the cluster Abell 1367 to detect sources embedded within the diffuse intracluster medium. In addition to detecting sources and determining their fluxes and positions, we show that the wavelet analysis allows a characterization of the sources extents. In particular, the wavelet scale at which a given source achieves a maximum signal-to-noise ratio in the wavelet images provides an estimate of the angular extent of the source. To account for the widely varying point response of the ROSAT PSPC as a function of off-axis angle requires a quantitative measurement of the source size and a comparison to a calibration derived from the analysis of a Deep Survey image. Therefore, we assume that each source could be described as an isotropic two-dimensional Gaussian and used the wavelet amplitudes, at different scales, to determine the equivalent Gaussian Full Width Half-Maximum (FWHM) (and its uncertainty) appropriate for each source. In our analysis of the ROSAT PSPC image, we detect 31 X-ray sources above the diffuse cluster emission (within a radius of 24 min), 16 of which are apparently associated with cluster galaxies and two with serendipitous, background quasars. We find that the angular extents of 11 sources exceed the nominal width of the PSPC point-spread function. Four of these extended sources were previously detected by Bechtold et al. (1983) as 1 sec scale features using the Einstein HRI. The same wavelet analysis technique was applied to the Einstein HRI image. We detect 28 sources in the HRI image, of which nine are extended. Eight of the extended sources correspond to sources previously detected by Bechtold et al. Overall, using both the PSPC and the HRI observations, we detect 16 extended features, of which nine have galaxies coincided with the X-ray-measured positions (within the positional error circles). These extended sources have luminosities lying in the range (3 - 30) x 10(exp 40) ergs/s and gas masses of approximately (1 - 30) x 10(exp 9) solar mass, if the X-rays are of thermal origin. We confirm the presence of extended features in A1367 first reported by Bechtold et al. (1983). The nature of these systems remains uncertain. The luminosities are large if the emission is attributed to single galaxies, and several of the extended features have no associated galaxy counterparts. The extended features may be associated with galaxy groups, as suggested by Canizares, Fabbiano, & Trinchieri (1987), although the number required is large.

Grebeney, S. A.↗

NASA NTRS2006

Antarctic Circumpolar Current Transport Variability during 2003-05 from GRACE

Gravity Recovery and Climate Experiment (GRACE) gravity data spanning January 2003 - November 2005 are used as proxies for ocean bottom pressure (BP) averaged over 1 month, spherical Gaussian caps 500 km in radius, and along paths bracketing the Antarctic Circumpolar Current's various fronts. The GRACE BP signals are compared with those derived from the Estimating the Circulation and Climate of the Ocean (ECCO) ocean modeling-assimilation system, and to a non-Boussinesq version of the Regional Ocean Model System (ROMS). The discrepancy found between GRACE and the models is 1.7 cm(sub H2O) (1 cm(sub H2O) similar to 1 hPa), slightly lower than the 1.9 cm(sub H2O) estimated by the authors independently from propagation of GRACE errors. The northern signals are weak and uncorrelated among basins. The southern signals are strong, with a common seasonality. The seasonal cycle GRACE data observed in the Pacific and Indian Ocean sectors of the ACC are consistent, with annual and semiannual amplitudes of 3.6 and 0.6 cm(sub H2O) (1.1 and 0.6 cm(sub H2O) with ECCO), the average over the full southern path peaks (stronger ACC) in the southern winter, on days of year 197 and 97 for the annual and semiannual components, respectively; the Atlantic Ocean annual peak is 20 days earlier. An approximate conversion factor of 3.1 Sv ( Sv equivalent to 10(exp 6) m(exp 3) s(exp -1)) of barotropic transport variability per cm(sub H2O) of BP change is estimated. Wind stress data time series from the Quick Scatterometer (QuikSCAT), averaged monthly, zonally, and over the latitude band 40 de - 65 deg S, are also constructed and subsampled at the same months as with the GRACE data. The annual and semiannual harmonics of the wind stress peak on days 198 and 82, respectively. A decreasing trend over the 3 yr is observed in the three data types.

oceanographic regions↗

NASA NTRSDate not supplied

Influence of Thermophysical Property Variability on Thermal Predictions of Ti-6Al-4V

The additive manufacturing (AM) industry has experienced rapid growth in recent decades as industrial interest in the process has grown. Because of this, there are many groups interested in simulations of the AM process. However, the influence of thermophysical property variability on the melt pool geometry during processing of various AM alloys is unclear. The goal of my work at NASA Langley Research Center (LaRC) was to characterize this influence on Ti-6Al-4V during AM processing alongside developing a tool to enable equivalent studies on other AM materials. To facilitate this process, a database tool was developed to contain and organize thermophysical data previously reported by primary sources. The specific thermophysical properties of interest for this study were density, specific heat capacity, and conductivity. Thermal diffusivity was calculated using the other three properties. This data was then fit with a Gaussian distribution and then randomly sampled from using Monte Carlo random value sampling. Using the Rosenthal equation, this sample data was used to simulate the temperature field during additive manufacturing and extract the melt pool geometry. Specifically, the melt pool’s length, width, and depth. This process was repeated an arbitrary number of times, with the default being 1000. Once this information was obtained, histograms were made showing the distributions of the sizes of the melt pool’s length, width, and depth. Representative statistical metrics of the distributions were calculated (mean, standard deviation, and coefficient of variance). This work found that at the simulated processing values, the melt pool’s width and depth had a 5.7% variation while the length had a 3.2% variation. Additionally, a tool was constructed to graph a thermal color map representation of the melt pool for specific, arbitrary values of density, specific heat, and conductivity. This tool allowed for more efficient plotting of individual queries of the thermophysical properties. The results that were observed in the research were that values reported in literature vary and this variance can have a significant impact on the simulation. Predictions of the melt pool’s dimensions show that length has a standard deviation of approximately 6 μm, width has a standard deviation of approximately 5 μm, and depth can vary by approximately 3 μm. Considering the mean sizes of length, width, and depth are 185 μm, 88 μm, and 44 μm respectively, such a deviation is significant. This shows that depth, for example, could be more than 10% larger or smaller than expected. This demonstrates that variability in the reported thermophysical properties are not negligible and should be expected to have an influence on the results of the laser powder bed fusion additive manufacturing process. When simulating this process in the future, measures should be taken to account for this discrepancy and the uncertainty involved

Justin Martin↗

NASA NTRS2012

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10-24 deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large separation travel times associated with upergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations,reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel time difference in the separation range 10-24 deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity for the average supergranule, 5.1 s, is constant over the distance range. This magnitude of signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 m/s extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 m/s at a depth of 2.3 Mm and a peak horizontal flow of 700 m/s at a depth of 1.6 Mm.

Duvall, T. L., Jr.↗

NASA NTRS2012

Subsurface Supergranular Vertical Flows as Measured Using Large Distance Separations in Time-Distance Helioseismology

As large-distance rays (say, 10 - 24deg) approach the solar surface approximately vertically, travel times measured from surface pairs for these large separations are mostly sensitive to vertical flows, at least for shallow flows within a few Mm of the solar surface. All previous analyses of supergranulation have used smaller separations and have been hampered by the difficulty of separating the horizontal and vertical flow components. We find that the large-separation travel times associated with supergranulation cannot be studied using the standard phase-speed filters of time-distance helioseismology. These filters, whose use is based upon a refractive model of the perturbations, reduce the resultant travel time signal by at least an order of magnitude at some distances. More effective filters are derived. Modeling suggests that the center-annulus travel-time difference [outward-going time minus inward-going time] in the separation range delta= 10 - 24deg is insensitive to the horizontally diverging flow from the centers of the supergranules and should lead to a constant signal from the vertical flow. Our measurement of this quantity, 5.1+/-0.1 seconds, is constant over the distance range. This magnitude of the signal cannot be caused by the level of upflow at cell centers seen at the photosphere of 10 ms(exp−1) extended in depth. It requires the vertical flow to increase with depth. A simple Gaussian model of the increase with depth implies a peak upward flow of 240 ms(exp−1) at a depth of 2.3 Mm and a peak horizontal flow of 700 ms(exp−1) at a depth of 1.6 Mm.

convection↗

NASA NTRS2000

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Fink, P. W.↗

NASA NTRS1997

Evolution of Structure in the Intergalactic Medium and the Nature of the LY-Alpha Forest

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.

Bi, Hongguang↗

NASA NTRS2005

Coronal Dynamics and Complete Flare Energy Budget for the M Dwarf AD Leo

This grant supported the observing and data analysis for FUSE Cycle 3 project C114 to observe the flare star AD Leo for 50 ksec coordinated with HST (Hubble Space Telescope) STIS ultraviolet spectroscopy and Chandra X-ray spectroscopy. Unfortunately, it was impossible to obtain the planned FUSE observations because AD Leo is a low declination target (delta approximately 20 degrees) and was rendered unobservable by restrictions in the sky coverage for FUSE observations. In April 2002 another M dwarf star, EV Lac, which is at significantly higher declination, was substituted for this project. EV Lac was observed by FUSE for a cumulative exposure of 35 ksec on 2002 July 1. The observation used the large LWRS aperture and collected data in time-tagged mode. The LWRS aperture is large enough that the target should remain within the aperture despite the normal level of pointing jitter and target drift experienced during FUSE observing. Our examination of the stellar signal showed that the target was well within the aperture throughout the observation. The data were split into night-time and day-time data so that the effects of airglow emission were recognizable. No obvious flaring, the primary science objective, was detected during the observation. The only stellar lines detected are 0 VI 1031.9, 1037.6 Angstrom, and the C III 1175 Angstrom, UV multiplet and the 977 Angstrom, resonance line. A comparison of the day-time and night-time spectra show that the 0 VI lines and the C III intersystem multiplet are unaffected by airglow features. The day-time data 977 Angstrom profile shows the presence of significant scattered solar C III photons, which should not be present in the night time spectrum. Emission fluxes for these lines were measured by direct summation of the emission lines. No continuum signal was detected in the region of these lines. The cleanest emission line profiles are for the O VI lines and we performed Gaussian fitting for these profiles. Both lines are clearly skewed with the emission peak shifted shortward of the line centroid and with emission extending further in the longward wing than for the shortward wing. A single Gaussian fits the 1032 Angstrom line profile reasonably and gives a line flux similar to that from direct integration with a line width (FWHM) of 0.16 Angstrom, (46 kilometers per second).

Brown, Alexander↗