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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Interactive Soil Dust Aerosol Model in the GISS GCM: Sensitivity of the Soil Dust Cycle to Radiative Properties of Soil Dust Aerosols - Part 1

The sensitivity of the soil dust aerosol cycle to the radiative forcing by soil dust aerosols is studied. Four experiments with the NASA/GISS atmospheric general circulation model, which includes a soil dust aerosol model, are compared, all using a prescribed climatological sea surface temperature as lower boundary condition. In one experiment, dust is included as dynamic tracer only (without interacting with radiation), whereas dust interacts with radiation in the other simulations. Although the single scattering albedo of dust particles is prescribed to be globally uniform in the experiments with radiatively active dust, a different single scattering albedo is used in those experiments to estimate whether regional variations in dust optical properties, corresponding to variations in mineralogical composition among different source regions, are important for the soil dust cycle and the climate state. On a global scale, the radiative forcing by dust generally causes a reduction in the atmospheric dust load corresponding to a decreased dust source flux. That is, there is a negative feedback in the climate system due to the radiative effect of dust. The dust source flux and its changes were analyzed in more detail for the main dust source regions. This analysis shows that the reduction varies both with the season and with the single scattering albedo of the dust particles. By examining the correlation with the surface wind, it was found that the dust emission from the Saharan/Sahelian source region and from the Arabian peninsula, along with the sensitivity of the emission to the single scattering albedo of dust particles, are related to large scale circulation patterns, in particular to the trade winds during Northern Hemisphere winter and to the Indian monsoon circulation during summer. In the other regions, such relations to the large scale circulation were not found. There, the dependence of dust deflation to radiative forcing by dust particles is probably dominated by physical processes with short time scales. The experiments show that dust radiative forcing can lead to significant changes both in the soil dust cycle and in the climate state. To estimate dust concentration and radiative forcing by dust more accurately, dust size distributions and dust single scattering albedo in the model should be a function of the source region, because dust concentration and climate response to dust radiative forcing are sensitive to dust radiative parameters.

Perlwitz, Jan↗
NASA NTRS1997

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS1997

Detection of "noisy" chaos in a time series

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
DOE OSTI2021

A Spatially Explicit Individual-Based Modeling Approach to Evaluate the Cumulative Effects of Wind Energy Development on the Greater Sage-Grouse: Sensitivity Analysis and Validation of Key Parameters

To address the need for an approach to evaluate cumulative ecological impacts of wind energy development, particularly those on critical wildlife habitats and species, the authors developed a proof-of-concept, landscape-based, spatially explicit individual-based modeling (IBM) framework for populations of the greater sage-grouse (Centrocercus urophasianus) in Albany County, Wyoming, based on published and other available information on the life history of the species. This sage-grouse IBM estimates the spatial and temporal movements of sage-grouse based on modeled effects of habitat characteristics and developments on sage-grouse condition, survivorship, and reproduction. After completing the initial version of the model, we conducted a series of sensitivity analyses of key model parameters and validation of lek occurrences and spatial distributions to better understand performance of the model relative to observed values of important life history characteristics. The parameter sensitivity analysis was conducted as a series of one-factor-at-a-time tests in which the values of selected parameters were individually varied to evaluate the corresponding effects on model output. We examined the model’s response to changes in parameter values to gain insight into the overall robustness of the model, identify key driver parameters, and initiate qualitative validation. Five functions selected for sensitivity analyses were (1) the rate of change in body condition in relationship to habitat suitability index (HSI) of occupied habitat (condition change rate), (2) the effect of competition between individuals with overlapping home ranges expressed as a percentage reduction in HSI (competition factor), (3) value of condition at which survivorship probability is equal to zero (zero survivorship condition), (4) the relationship between female body condition and clutch size, and (5) the relationship between female body condition and nest success. We varied the parameter values to be tested for the sensitivity analysis around the original value used in the model (i.e., tested values were higher and lower than the model’s original value) to examine the effect of this variation on the predicted output of the model. Model outputs evaluated in the sensitivity analysis included (1) predicted age-class distribution (as measured by the percentage of immature individuals within the population); (2) predicted sex ratio; (3) predicted age-sex class distribution (percent of population in each of six age-sex classes, i.e., male and female juveniles, yearlings, and adults); (4) lifespan; (5) population size; and (6) spatial distribution. Of the five parameters analyzed, condition change rate, survivorship, clutch size, and nest success did not substantially affect any of the evaluated model outputs. For the predicted age-class distribution, the percentage of immature individuals predicted by the model for these four parameters ranged from 61.9% to 65.0%, which was reasonable with respect to the reference values of 51.4 to 57.8% in published studies. The ratio of females to males ranged from 1.09 to 1.14, which was comparable to the reference values of 1.2 to 3.0 presented in an existing study. The predicted mean lifespan ranged from 1.62 to 1.74 years, which appears to be reasonable with respect to the reference values of 0.9 to 1.1 years for sharp-tail grouse and greater prairie chickens presented by published studies. The predicted population size ranged from 1,877 to 3,140. This prediction would be reasonable with respect to our estimate of 5,000 yearlings and adults, which was based on the USFWS estimate for the state of Wyoming scaled to the number of leks in the county. The predicted spatial distribution was not substantially affected by the parameter values examined. In our sensitivity analyses, the only tested parameter that had a noticeable effect on model output was competition factor. Over the range of values tested for this parameter, predicted population size exhibited the largest range (from 1,833 to 4,737) of all parameters tested. As the competition factor increased, the predicted population size decreased. This reflects the effect competition had on the number of individuals that could co occur in high-quality habitat patches. Despite this apparently significant effect, the range of values appears to be reasonable with respect to our estimate of 5,000 yearlings and adults, which was based on the USFWS estimate for the state of Wyoming scaled to the number of leks in the county.

17 WIND ENERGY↗
DOE OSTI2023

Model-Free Probabilistic Forecasting of Nodal Voltages in Distribution Systems

As the penetration of distributed energy resources (DERs) into distribution systems increases, so does the interest in forecasting relevant system variables to help mitigate the associated challenges. One such challenge is the more frequent occurrence of excessive voltages in distribution systems with higher shares of DERs. Accurate and reliable estimates together with forecasts of system states (i.e., nodal voltages) will therefore play a key role in improving the utilization of these variable and uncertain sources while mitigating potential operational risks. Whilst recent literature has explored machine learning (ML) methods for voltage estimation and their extrapolation for a short-time period into the future, few have taken uncertainty quantification into account, and these methods have not yet been translated into operations. This paper discusses the advantages offered by probabilistic voltage forecasts and proposes a non-parametric Bayesian method suitable for forecasting nodal voltages at short-term time horizons while accounting for uncertainties in load and distributed photovoltaic (PV) generation. We demonstrate the value of the proposed Gaussian process (GP) model for a case study using historical forecasts and observation data.

distribution system↗
DOE OSTI2022

Improved Line Outage Detection in Transmission Systems with Few PMUs

Unlike transmission systems, distribution systems historically lack enough measurements, making their real-time monitoring almost impossible. Recent deployment of diverse types of devices such as phasor measurement units (PMUs), smart meters, solar inverters and weather information sensors opens up new ways of monitoring these systems, with the assistance of customized machine learning (ML) applications. The paper describes a grid-model-informed machine learning (ML) tool which integrates heterogeneous data streams and creates synchronous measurement snapshots to be used by a hybrid robust state estimator (SE) which provides not only accurate state estimates but also real-time feedback for ML model refinement. Improved monitoring performance due to the use of developed computational framework is experimentally observed by simulated scenarios on an electric utility’s distribution system.

Distribution systems, graph learning, machine lear↗
DOE OSTI2022

Estimating the impacts of natural gas power generation growth on solar electricity development: PJM's evolving resource mix and ramping capability

Abstract Expansion of distributed solar photovoltaic (PV) and natural gas‐fired generation capacity in the United States has put a renewed spotlight on methods and tools for power system planning and grid modernization. This article investigates the impact of increasing natural gas‐fired electricity generation assets on installed distributed solar PV systems in the Pennsylvania–New Jersey–Maryland (PJM) Interconnection in the United States over the period 2008–2018. We developed an empirical dynamic panel data model using the system‐generalized method of moments (system‐GMM) estimation approach. The model accounts for the impact of past and current technical, market and policy changes over time, forecasting errors, and business cycles by controlling for PJM jurisdictions‐level effects and year fixed effects. Using an instrumental variable to control for endogeneity, we concluded that natural gas does not crowd out renewables like solar PV in the PJM capacity market; however, we also found considerable heterogeneity. Such heterogeneity was displayed in the relationship between solar PV systems and electricity prices. More interestingly, we found no evidence suggesting any relationship between distributed solar PV development and nuclear, coal, hydro, or electricity consumption. In addition, considering policy effects of state renewable portfolio standards, net energy metering, differences in the PJM market structure, and other demand and cost‐related factors proved important in assessing their impacts on solar PV generation capacity, including energy storage as a non‐wire alternative policy technique. This article is categorized under: Photovoltaics > Economics and Policy Fossil Fuels > Climate and Environment Energy Systems Economics > Economics and Policy

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

A Bayesian Approach for In-Situ Stress Prediction and Uncertainty Quantification for Subsurface Engineering

Many subsurface engineering applications require accurate knowledge of the in-situ state of stress for their safe design and operation. Existing methods to meet this need primarily include field measurements for estimating one or more of the principal stresses from a borehole, or optimization methods for constructing a 3D geomechanical model in terms of geophysical measurements. These methods, however, often contain considerable uncertainty in estimating the state of stress. Here, in this paper, we build on a Bayesian approach to quantify uncertainty in stress estimations for subsurface engineering applications. This approach can provide an estimate of the 3D distribution of stress throughout the volume of interest and provide an estimate of the uncertainty arising from the stress measurement, the rheology parameters, and a paucity of measurements. The value of this approach is demonstrated using stress measurements from the In Salah carbon storage site, which was one of the world’s first industrial carbon capture and storage projects. This demonstration shows the application of this Bayesian approach for estimating the initial state of stress for In Salah and quantifying the uncertainty in the estimated stress. Also, an assessment of a maximum injection pressure to prevent geomechanical risks from CO 2 injection pressures is provided in terms of the probability distribution of the minimum principal stress quantified by the approach. With the In Salah case study, this paper demonstrates that using the Bayesian approach can provide additional insights for site explorations and/or project operations to make informed-site decisions for subsurface engineering applications.

58 GEOSCIENCES↗
DOE OSTI2023

A Smart Silicon Carbide Power Module With Pulse Width Modulation Over Wi-Fi and Wireless Power Transfer-Enabled Gate Driver, Featuring Onboard State of Health Estimator and High-Voltage Scaling Capabilities: Preprint

A wide range of utility applications require controllable switches with features such as high-voltage (HV) blocking and high-current carrying capacity especially at high pulse width modulation (PWM) frequency. Low and medium voltage utility applications such as motor drives and flexible AC transmission systems (FACTS) as well as solid state transformers (SST) could also benefit from a low-cost HV switching module. Wide band gap (WBG) semiconductors such as SiC and GaN MOSFETs are considered to be the present and next generation device choices, although they have their own limitations. For relatively HV applications with demanding thermal management, SiC is still the only choice, and GaN dominates the low voltage regime. This manuscript proposes a new half bridge power MOSFET module that is suitable for conventional H-bridge of multilevel configurations used in HV applications. Constructed from bare SiC dies, this half bridge module takes advantage of (1) optimized MOSFET placement inside the module, (2) customized heat exchanger, manifold and cooling, (3) integrated gate driver module with PWM over wi-fi to eliminate the need for low voltage signals, (4) wireless power transfer (WPT) enabled gate driver and other ancillary circuits, (5) and the option to incorporate an onboard state of health (SOH) estimator module onboard. The entire architecture has been designed and built at National Renewable Energy Laboratory (NREL), Golden, CO.

baseplate design↗
NASA NTRS1985

An efficient algorithm for estimating noise covariances in distributed systems

An efficient computational algorithm for estimating the noise covariance matrices of large linear discrete stochatic-dynamic systems is presented. Such systems arise typically by discretizing distributed-parameter systems, and their size renders computational efficiency a major consideration. The proposed adaptive filtering algorithm is based on the ideas of Belanger, and is algebraically equivalent to his algorithm. The earlier algorithm, however, has computational complexity proportional to p to the 6th, where p is the number of observations of the system state, while the new algorithm has complexity proportional to only p-cubed. Further, the formulation of noise covariance estimation as a secondary filter, analogous to state estimation as a primary filter, suggests several generalizations of the earlier algorithm. The performance of the proposed algorithm is demonstrated for a distributed system arising in numerical weather prediction.

Dee, D. P.↗
DOE OSTI2024

Cost of Wind Energy Review: 2024 Edition [Slides]

The primary elements of this analysis include: Estimated LCOE for (1) a representative land-based wind energy project installed in a moderate wind resource in the United States, (2) a representative fixed-bottom offshore wind energy project installed in the U.S. North Atlantic, and (3) a representative floating offshore wind energy project installed off the U.S. Pacific Coast. It also updates the LCOE estimates for representative residential-, commercial-, and large-scale distributed wind projects installed in a moderate wind resource in the United States. A sensitivity analyses is included that shows the range of effects that basic LCOE variables could have on the cost of wind energy for land-based and offshore wind projects and provides updated Fiscal Year 2024 values for land-based and offshore wind energy used for Government Performance and Results Act (GPRA) reporting and illustrated progress toward established GPRA targets.

17 WIND ENERGY↗
NASA NTRS2016

Determination of Celestial Body Principal Axes via Gravity Field Estimation

The determination of physical parameters of celestial bodies provides critical navigational and scientific information. Determining the mass, rotation state, and density distribution is an important task of the navigation team on an operational mission. One representation of the internal density distribution, spherical harmonics, may be leveraged to compute the orientation of the principal axis frame of the celestial body, which in turn informs the dynamics of the body’s motion. Using data from NASA’s Dawn mission to the massive asteroids (1) Ceres and (4) Vesta, a method is proposed that refines the knowledge of the principal axis frame by utilizing estimated spherical harmonic coefficients. Applying an iterative rotation scheme to the solved-for body-fixed frame leads to convergence on a frame that is very close to the actual dynamical principal axis frame.

Takahashi, Yu↗
DOE OSTI2025

A derecho climatology (2004–2021) in the United States based on machine learning identification of bow echoes

Due to their persistent widespread severe winds, derechos pose significant threats to human safety and property, with impacts comparable to many tornadoes and hurricanes. Yet, automated detection of derechos remains challenging due to the absence of spatiotemporally continuous observations and the complex criteria employed to define the phenomenon. This study presents an objective derecho detection approach capable of automatically identifying derechos through both observations and model results. The approach is grounded in a physically based definition of derechos and integrates three algorithms: (1) the Python Flexible Object Tracker (PyFLEXTRKR) algorithm to track mesoscale convective systems (MCSs), (2) a semantic segmentation convolutional neural network to identify bow echoes, and (3) a comprehensive classification algorithm to detect derechos within MCS life cycles and distinguish derecho-producing from non-derecho-producing MCSs. Using this approach, we developed a novel high-resolution (4 km and hourly) observational dataset of derechos and accompanying derecho-producing MCSs over the United States east of the Rocky Mountains from 2004 to 2021. The dataset consists of two subsets based on different gust speed data sources and is analyzed to document the climatology of derechos in the United States. On average, 12–15 derechos are identified per year, aligning with previous estimations (∼6–21 events annually). The spatial distribution and seasonal variation patterns are consistent with prior studies, showing peak occurrences in the Great Plains and the Midwest during the warm season. Additionally, during the study period, derechos account for approximately 3.1 % of measured damaging gusts (≥25.93 m s−1) over the eastern United States. The dataset is publicly available at https://doi.org/10.5281/zenodo.14835362 (Li et al., 2025).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1987

Polarized fluorescence spectroscopy of O2(+)

Polarized fluorescence measurements involving the A 2Pi(u) - X 2Pi(g) and b 4Sigma(g)(-) - a 4Pi(u) transitions in O2(+) following narrow-band photoexcitation of O2/X 3Sigma(g)(-)/ are reported. The analysis, based on the conventional high-J limit, involves deducing the quadrupole alignment factor from which the relative strengths of degenerate photoexcitation channels responsible for the population distribution in the A 2Pi(u) and b 4Sigma(g)(-) states of O2(+) can be estimated. The measured A-channel polarization exhibits pronounced structure which correlates well with the known positions of Rydberg states, whereas the polarization signal in the b channel has broad and less prominent features. Discrepancies between theoretical and measured results can largely be accounted for by additional configuration mixing and autoionization considerations.

Keller, J. W.↗
DOE OSTI2025

National Modeling of Geothermal District Energy Systems with Ambient-Temperature Loops Using dGeo

Geothermal district energy systems (DES) with ambient-temperature loops, also known as thermal energy networks, are one option for decarbonizing space heating and cooling loads. Geothermal fifth-generation DES include an "ambient" temperature thermal loop that connects heat pumps at each building with thermal balancing sources such as geothermal borehole fields. Heating and cooling are provided via a water-source heat pump at each end-user. This project seeks to analyze the nationwide potential for ambient-temperature loop districts by creating a new module within the Distributed Geothermal Market Demand Model (dGeo). dGeo is an agent-based modeling tool for distributed geothermal resources; it can investigate potential on a nationwide or statewide scale using geospatial data for all 50 states and thermal demands for existing buildings. This process allows for high-level estimates of technical and economic potential for ambient-temperature loop districts across the United States. A lookup table was created using GHEDesigner to size borehole fields for different thermal loads and ground conditions experienced across the country. A cost and financing structure, along with incentives, were applied. Cost estimates include costs for the distribution network, borehole field installation and operation, and circulation pump operation, while savings are calculated based on energy bills for building owners (agents). This newly developed module can be used for assessing which areas of the country have the highest potential for agent benefits from ambient-temperature loop installation and assess the impact of future cost and price scenarios. Initial results for statewide analysis (for Vermont) and nationwide (for United States) are provided. Future work includes expanding the module to consider mixed residential and commercial districts as well as evaluating multiple cost scenarios.

ambient-temperature loop↗
DOE OSTI2024

NPFTURBULENCE: Best Estimate Aerosol Size Distribution by airborne measurements

The original data were collected during the field campaign of “Turbulent layers promoting New Particle Formation” experiment (NPFTURBULENCE; https://www.arm.gov/research/campaigns/aaf2024npfturbulence) over the Atmospheric Radiation Measurement (ARM) Southern Great Plains (SGP) Atmospheric Observatory (https://www.arm.gov/capabilities/observatories/sgp ) in north-central Oklahoma. The ARM Aerial Facility ArcticShark uncrewed aerial system (UAS) was based at Blackwell–Tonkawa Municipal Airport (IATA: BWL, ICAO: KBKN, FAA LID: BKN, 36.74475° N, 97.34918° W, 313.9 m MSL), for the field campaign from May 5 through May 29, 2024. The ArcticShark UAS performed 11 flights, including 10 research flights over the Central Facility of the ARM SGP to measure atmospheric state, turbulence, surface IT temperature and imagery, aerosol number concentration and size distribution. The current data set presents Best Estimate Aerosol Size Distribution: a merged aerosol size distribution composed of the data from 2 sensors: miniaturized Scanning Electrical Mobility Sizer (mSEMS) and Portable Optical Particle Spectrometer (POPS). The mSEMS data were interpolated to 1 second from “native” time resolution of about 15 second to match the other probe. The POPS data were converted from equivalent optical size into geometric size using value of aerosol refractive index of 1.477 from the HISCALE field campaign (same geographical area, altitudes, and time of year; http://www.arm.gov/campaigns/aaf2016hiscale ).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2015

Coupled Inertial Navigation and Flush Air Data Sensing Algorithm for Atmosphere Estimation

This paper describes an algorithm for atmospheric state estimation that is based on a coupling between inertial navigation and flush air data sensing pressure measurements. In this approach, the full navigation state is used in the atmospheric estimation algorithm along with the pressure measurements and a model of the surface pressure distribution to directly estimate atmospheric winds and density using a nonlinear weighted least-squares algorithm. The approach uses a high fidelity model of atmosphere stored in table-look-up form, along with simplified models of that are propagated along the trajectory within the algorithm to provide prior estimates and covariances to aid the air data state solution. Thus, the method is essentially a reduced-order Kalman filter in which the inertial states are taken from the navigation solution and atmospheric states are estimated in the filter. The algorithm is applied to data from the Mars Science Laboratory entry, descent, and landing from August 2012. Reasonable estimates of the atmosphere and winds are produced by the algorithm. The observability of winds along the trajectory are examined using an index based on the discrete-time observability Gramian and the pressure measurement sensitivity matrix. The results indicate that bank reversals are responsible for adding information content to the system. The algorithm is then applied to the design of the pressure measurement system for the Mars 2020 mission. The pressure port layout is optimized to maximize the observability of atmospheric states along the trajectory. Linear covariance analysis is performed to assess estimator performance for a given pressure measurement uncertainty. The results indicate that the new tightly-coupled estimator can produce enhanced estimates of atmospheric states when compared with existing algorithms.

Karlgaard, Christopher D.↗
NASA NTRS1994

Geometrical evidence for dark matter: X-ray constraints on the mass of the elliptical galaxy NGC 720

We describe (1) a new test for dark matter and alternate theories of gravitation based on the relative geometries of the X-ray and optical surface brightness distributions and an assumed form for the potential, of the optical light, (2) a technique to measure the shapes of the total gravitating matter and dark matter of an ellipsoidal system which is insensitive to the precise value of the temperature of the gas and to modest temperature gradients, and (3) a new method to determine the ratio of dark mass to stellar mass that is dependent on the functional forms for the visible star, gas and dark matter distributions, but independent of the distance to the galaxy or the gas temperature. We apply these techniques to X-ray data from the ROSAT Position Sensitive Proportional Counter (PSPC) of the optically flattened elliptical galaxy NGC 720; the optical isophotes have ellipticity epsilon approximately 0.40 extending out to approximately 120 sec. The X-ray isophotes are significantly elongated, epsilon = 0.20-0.30 for semimajor axis a approximately 100 sec. The major axes of the optical and X-ray isophotes are misaligned by approximately 30 deg +/- 15 deg. Spectral analysis of the X-ray data reveals no evidence of temperature gradients or anisotropies and demonstrates that a single-temperature plasma (T approximately 0.6 keV) having subsolar heavy element abundances and a two-temperature model having solar abundances describe the spectrum equally well. Considering only the relative geometries of the X-ray and optical surface brightness distributions and an assumed functional form for the potential of the optical light, we conclude that matter distributed like the optical light cannot produce the observed ellipticities of the X-ray isophotes, independent of the gas pressure, the gas temperature, and the value of the stellar mass; this comparison assumes a state of quasi-hydrostatic equilibrium so that the three-dimensional surfaces of the gas emissivity trace the three-dimensional isopotential surfaces -- we discuss the viability of this assumption for NGC 720. Milgrom's Modification of Newtonian Dynamics (MOND) cannot dispel this manifestation of dark matter. Hence, geometrical considerations require, without mention of pressure or temperature, the presence of an extended, massive dark matter halo in NGC 720. Employing essentially the technique of Buote & Canizares (1992; Buote 1992) we use the shape of the X-ray surface brightness to constrain the shape of the total gravitating matter. The total matter is modeled as either an oblate or prolate spheriod of constant shape and orientation having either a Ferrers (rho approximately r(exp -n)) or Hernquist density. Assuming the X-ray gas is in hydrostatic equilibrium, we construct a model X-ray gas distribution for various temperature profiles. We determine the ellipticity of the total gravitating matter to be epsilon approximately 0.50-0.70. Using the single-temperature model we estimate a total mass approximately (0.41-1.4) x 10(exp 12) h(sub 80) solar mass interior to the ellipsoid of semimajor axis 43.6 h(sub 80) kpc. Ferrers densities as steep as r(exp -3) do not fit the data, but the r(exp -2) and Hernquist models yield excellent fits. We estimate the mass distributions of the stars and the gas and fit the dark matter directly. For a given gas equation of state and functional forms for the visible stars, gas, and dark matter, these models yield a distance-independent and temperature-independent measurement of the ratio of dark mass to stellar mass M(sub DM)/M(sub stars). We estimate a minimum M(sub DM)/M(sub stars) greater than or equal to 4 which corresponds to a total mass slightly greater than that derived from the single-temperature models for distance D = 20h(sub 80) Mpc.

Buote, David A.↗