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DOE OSTI2022

Estimation of China Fusion Engineering Test Reactor performance and burning fraction in different pellet fueling scenarios by a multi-species radial transport model

Tritium self-sufficiency in future deuterium–tritium fusion reactors is a crucial challenge. As an engineering test reactor, the China Fusion Engineering Test Reactor requires a burning fraction of 3% for the goal to test the accessibility to the future fusion plant. To self-consistently simulate burning plasmas with profile changes in pellet injection scenarios and to estimate the corresponding burning fraction, a one-dimensional multi-species radial transport model is developed in the BOUT++ framework. Here several pellet-fueling scenarios are then tested in the model. The results show that the increased fueling depth improves the burning fraction by particle confinement improvement and fusion power increase. Nevertheless, by increasing the depth, the pellet cooling-down may significantly lower the temperature in the core region. Taking the density perturbation into consideration, the reasonable parameters of the fueling scenario in these simulations are estimated as pellet radius ${r}_{{\rm{p}}}=3\,{\rm{mm}},$ injection rate $=\,4\,\mathrm{Hz},$ and pellet injection velocity $=\,1000\mbox{-}2000\,{\rm{m}}\,{{\rm{s}}}^{-1}$ without drift or $450\,{\rm{m}}\,{{\rm{s}}}^{-1}$ with high-field-side drift.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Droplet burning of n-butyl acetate/n-heptane mixtures in the standard atmosphere: experiments and numerical modeling

Blending petroleum fuels with oxygenates is a common approach to stem the depletion of crude oil while also mitigating the impact of their combustion on the environment. It has recently been considered that n-butyl acetate (BA, C6H12O2 , boiling point of 399K) could be a viable oxygenate additive to diesel fuel. In this application it is important to determine the influence of the fractional amount of BA on burning of the mixture. This presentation considers this problem from an experimental and computational approach using n-heptane (C7H14 , boiling point of 372K) as an essentially single component surrogate for diesel fuel. The burning configuration considered was ostensibly spherical symmetry as promoted by burning droplets under conditions where forced and natural convection effects were minimized. In this configuration the droplet and flame are concentric spheres and soot aggregates are trapped in a shell structure between the droplet and flame. Measurements were made of the droplet, flame and soot shell diameters through video imaging of the burning process. The experimental results were used to validate a detailed numerical model of the spherically symmetric droplet burning process that incorporated a consistent combustion kinetic mechanism for BA/heptane mixtures, comprised of 402 species and 16,872 reactions inclusive of soot chemistry. A model for soot formation was also included in the simulation to predict formation of the soot shell. The simulations agreed well with measured droplet and flame diameters. It was found both experimentally and computationally that adding BA to heptane had a minimal effect on the mixture burning rate, while the flame was positioned closer to the droplet surface and the simulated soot volume fraction decreased. The implications of these results are discussed for using BA as a potential additive to diesel fuel.

09 BIOMASS FUELS↗

NASA NTRS2003

Modeling Candle Flame Behavior In Variable Gravity

The burning of a candle, as typical non-propagating diffusion flame, has been used by a number of researchers to study the effects of electric fields on flame, spontaneous flame oscillation and flickering phenomena, and flame extinction. In normal gravity, the heat released from combustion creates buoyant convection that draws oxygen into the flame. The strength of the buoyant flow depends on the gravitational level and it is expected that the flame shape, size and candle burning rate will vary with gravity. Experimentally, there exist studies of candle burning in enhanced gravity (i.e. higher than normal earth gravity, g(sub e)), and in microgravity in drop towers and space-based facilities. There are, however, no reported experimental data on candle burning in partial gravity (g < g(sub e)). In a previous numerical model of the candle flame, buoyant forces were neglected. The treatment of momentum equation was simplified using a potential flow approximation. Although the predicted flame characteristics agreed well with the experimental results, the model cannot be extended to cases with buoyant flows. In addition, because of the use of potential flow, no-slip boundary condition is not satisfied on the wick surface. So there is some uncertainty on the accuracy of the predicted flow field. In the present modeling effort, the full Navier-Stokes momentum equations with body force term is included. This enables us to study the effect of gravity on candle flames (with zero gravity as the limiting case). In addition, we consider radiation effects in more detail by solving the radiation transfer equation. In the previous study, flame radiation is treated as a simple loss term in the energy equation. Emphasis of the present model is on the gas-phase processes. Therefore, the detailed heat and mass transfer phenomena inside the porous wick are not treated. Instead, it is assumed that a thin layer of liquid fuel coated the entire wick surface during the burning process. This is the limiting case that the mass transfer process in the wick is much faster than the evaporation process at the wick surface.

Alsairafi, A.↗

NASA NTRS2021

Colorado Front Range Disasters: Understanding the Impact of Forest Management on the Cameron Peak and CalWood Fire

Along the Colorado Front Range, forest management has gained significant attention due to uncharacteristically large fires that burned late in 2020. The Cameron Peak Fire (largest in Colorado recorded history) and the CalWood Fire collectively burned an estimated 219,019 acres from August through December of 2020. Project partners at the Coalition for the Poudre River Watershed, Colorado State Forest Service, Ben Delatour Scout Ranch, The Nature Conservancy, Colorado Forest Restoration Institute, and Colorado State University were interested in understanding the effectiveness of previous forest treatments in reducing burn severity within the Cameron Peak Fire and the CalWood Fire. We first collated a forest treatment dataset from pre-existing datasets by reclassifying over 29,000 treatments, which occurred across the Northern Colorado Front Range between 1970-2020. Secondly, we mapped three burn severity indices using Landsat 8 OLI and Sentinel-2 MSI Earth observations and compared them to soil burn severity field data. Thirdly, a total of 35 topographic, disturbance, forest structure, and treatment predictor variables were generated across the fires. Finally, we assessed relationships between these predictor variables and burn severity using the random forest algorithm. Model results indicate that the primary drivers of burn severity were elevation and distance to treatment edge for the Cameron Peak Fire and fire area and forest canopy cover for the CalWood Fire. Further analysis of these variables paired with field data is necessary to understand the relationship between burn severity and treatments to guide future restoration efforts, improve forest resiliency, and mitigate fire risks.

Neal Swayze↗

NASA NTRS1972

Model atmospheres for cool supergiant stars.

The results of an exploratory grid of model atmospheres for cool giant stars are used to illustrate the effect of varying the chemical composition of the atmosphere. The effects of composition changes (depletion of C and O, enrichment of N, and increase in the ratio C/O), which might be expected from processing of the original material of a star through the CNO cycle of nuclear burning, are studied. The models also include the important CN opacity. They are illustrated by giving several representative T-P and T-tau diagrams, spectral energy curves, and column density tables of molecules.

Alexander, D. R.↗

DOE OSTI2020

Vertical profiles of light absorption and scattering associated with black carbon particle fractions in the springtime Arctic above 79° N

Despite the potential importance of black carbon (BC) for radiative forcing of the Arctic atmosphere, vertically resolved measurements of the particle light scattering coefficient (σ sp ) and light absorption coefficient (σ ap ) in the springtime Arctic atmosphere are infrequent, especially measurements at latitudes at or above 80° N. Here, relationships among vertically distributed aerosol optical properties (σap, σsp and single scattering albedo or SSA), particle microphysics and particle chemistry are examined for a region of the Canadian archipelago between 79.9 and 83.4° N from near the surface to 50 hPa. Airborne data collected during April 2015 are combined with ground-based observations from the observatory at Alert, Nunavut and simulations from the Goddard Earth Observing System (GEOS) model, GEOS-Chem, coupled with the TwO-Moment Aerosol Sectional (TOMAS) model (collectively GEOS-Chem–TOMAS; Kodros et al., 2018) to further our knowledge of the effects of BC on light absorption in the Arctic troposphere. The results are constrained for σsp less than 15 Mm -1 , which represent 98% of the observed σsp, because the single scattering albedo (SSA) has a tendency to be lower at lower σsp, resulting in a larger relative contribution to Arctic warming. At 18.4 m 2 g -1 , the average BC mass absorption coefficient (MAC) from the combined airborne and Alert observations is substantially higher than the two averaged modelled MAC values (13.6 and 9.1 m2 g -1 ) for two different internal mixing assumptions, the latter of which is based on previous observations. The higher observed MAC value may be explained by an underestimation of BC, the presence of small amounts of dust and/or possible differences in BC microphysics and morphologies between the observations and model. In comparing the observations and simulations, we present σap and SSA, as measured, and σ ap 2 and the corresponding SSA to encompass the lower modelled MAC that is more consistent with accepted MAC values. Median values of the measured σap, rBC and the organic component of particles all increase by a factor of 1.8±0.1, going from near-surface to 750 hPa, and values higher than the surface persist to 600 hPa. Modelled BC, organics and σap agree with the near-surface measurements but do not reproduce the higher values observed between 900 and 600 hPa. The differences between modelled and observed optical properties follow the same trend as the differences between the modelled and observed concentrations of the carbonaceous components (black and organic). Model-observation discrepancies may be mostly due to the modelled ejection of biomass burning particles only into the boundary layer at the sources. For the assumption of the observed MAC value, the SSA range between 0.88 and 0.94, which is significantly lower than other recent estimates for the Arctic, in part reflecting the constraint of σsp<15 Mm -1 . The large uncertainties in measuring optical properties and BC, and the large differences between measured and modelled values here and in the literature, argue for improved measurements of BC and light absorption by BC and more vertical profiles of aerosol chemistry, microphysics and other optical properties in the Arctic.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2015

Aspects of Cool-Flame Supported Droplet Combustion in Microgravity

Droplet combustion experiments performed on board the International Space Station have shown that normal-alkane fuels with negative temperature coefficient (NTC) chemistry can support quasi-steady, low-temperature combustion without any visible flame. Here we review the results for n-decane, n-heptane, and n-octane droplets burning in carbon dioxidehelium diluted environments at different pressures and initial droplet sizes. Experimental results for cool-flame burning rates, flame standoff ratios, and extinction diameters are compared against simplified theoretical models of the phenomenon. A simplified quasi-steady model based on the partial-burning regime of Lin predicts the burning rate, and flame standoff ratio reasonably well for all three normal alkanes. The second-stage cool-flame burning and extinction following the first-stage hot-flame combustion, however, shows a small dependence on the initial droplet size, thus deviating from the quasi-steady results. An asymptotic model that estimates the oxygen depletion by the hot flame and its influence on cool-flame burning rates is shown to correct the quasi-steady results and provide a better comparison with the measured burning-rate results.This work was supported by the NASA Space Life and Physical Sciences Research and Applications Program and the International Space Station Program.

cool flames↗

NASA NTRS2001

Combustion of Metals in Reduced-Gravity and Extraterrestrial Environments

As a result of the ongoing exploration of Mars and the several unmanned and possibly manned missions planned for the near future, increased attention has been given to the use of the natural resources of the planet for rocket propellant production and energy generation. Since the atmosphere of Mars consists of approximately 95% carbon dioxide (CO2), this gas is the resource of choice to be employed for these purposes. Since many metals burn vigorously with CO2, these may be used as an energy source or as propellants for a research vehicle on the surface of Mars. Shafirovich and Goldshleger conducted experiments with spherical particles up to 2.5 mm in diameter and found that the burning process was controlled by diffusion and that the particles exhibited pulsating combustion due to superheating of the Mg vapor trapped inside a protective oxide shell. They also proposed a reaction mechanism based on the gas-phase reaction, Mg + CO2 yields MgO + CO and the heterogeneous reaction Mg + CO yields MgO + C occurring on the sample surface. In all the above studies with large Mg particles, the burning process is invariably influenced by strong convective currents that accelerate the combustion reaction and shorten the burning times. Although these currents are nearly absent in the burning of small particles, the high emissivity of the flames, rapid reaction, and small length scales make the gathering of any useful information on burning rates and flame structure very difficult. The goal of this investigation is to provide a detailed study of flame structure by taking advantage of large, free-floating spherical metal samples and their corresponding long burning times available in a weightless environment. The use of reduced gravity is essential to eliminate the intrusive buoyant flows that plague high temperature metal reactions, to remove the destructive effect of gravity on the shape of molten metal samples, and to study the combustion behavior of metals in the presence of solid oxides undisturbed by natural convection. This work presents the most complete modeling of metal particle burning to date for Mg with CO2 and O2.

Branch, M. C.↗

NASA NTRS1993

Burning of a spherical fuel droplet in a uniform flowfield with exact property variation

An analytical/numerical model is developed for single droplet evaporation and burning in a convective flowfield. The model is based on the boundary-layer approach, and chemical reaction kinetics are represented by a one-step, finite-rate reaction mechanism, while variation of gas properties with temperature and gas composition is based on the kinetic theory of gases. Four droplet models differing in the degree of complexity concerning property variation and chemistry are compared. Comparisons are also provided with existing empirical correlations for convective droplet evaporation and burning.

Madooglu, K.↗

DOE OSTI2023

Isolating the effect of biomass burning aerosol emissions on 20th century hydroclimate in South America and Southeast Asia

Abstract Biomass burning is a significant source of aerosol emissions in some regions and has a considerable impact on regional climate. Earth system model simulations indicate that increased biomass burning aerosol emissions contributed to statistically significant decreases in tropical precipitation over the 20th century. In this study, we use the Community Earth System Model version 1 Large Ensemble (CESM1-LENS) experiment to evaluate the mechanisms by which biomass burning aerosol contributed to decreased tropical precipitation, with a focus on South America and Southeast Asia. We analyze the all-but-one forcing simulations in which biomass burning aerosol emissions are held constant while other forcings (e.g., greenhouse gas concentrations) vary throughout the 20th century. This allows us to isolate the influence of biomass burning aerosol on processes that contribute to decreasing precipitation, including cloud microphysics, the radiative effects of absorbing aerosol particles, and alterations in regional circulation. We also show that the 20th century reduction in precipitation identified in the CESM1-LENS historical and biomass burning experiments is consistent across Coupled Model Intercomparison Project Phase 5 models with interactive aerosol schemes and the CESM2 single-forcing experiment. Our results demonstrate that higher concentrations of biomass burning aerosol increases the quantity of cloud condensation nuclei and cloud droplets, limiting cloud droplet size and precipitation formation. Additionally, absorbing aerosols (e.g., black carbon) contribute to a warmer cloud layer, which promotes cloud evaporation, increases atmospheric stability, and alters regional circulation patterns. Corresponding convectively coupled circulation responses, particularly over the tropical Andes, contribute to further reducing the flow of moisture and moisture convergence over tropical land. These results elucidate the processes that affect the water cycle in regions prone to biomass burning and inform our understanding of how future changes in aerosol emissions may impact tropical precipitation over the 21st century.

Environmental Sciences & Ecology↗

NASA NTRS2017

Elastomeric Thermal Insulation Design Considerations in Long, Aluminized Solid Rocket Motors

An all-new sounding rocket was designed at NASA's Marshall Space Flight Center that featured an aft finocyl, aluminized solid propellant grain and silica-filled ethylene-propylene-diene monomer (SFEPDM) internal insulation. Upon the initial static firing of the first of this new design, the solid rocket motor (SRM) case failed thermally just upstream of the aft closure early in the burn time. Subsequent fluid modeling indicated that the high-velocity combustion-product jets emanating from the fin-slots in the propellant grain were likely inducing a strongly swirling flow, thus substantially increasing the severity of the convective environment on the exposed portion of the SFEPDM insulation in this region. The aft portion of the fin-slots in another of the motors were filled with propellant to eliminate the possibility of both direct jet impingement on the exposed SFEPDM and the appearance of strongly swirling flow in the aft region of the motor. When static-fired, this motor's case still failed in the same axial location, and, though somewhat later than for the first static firing, still in less than 1/3rd of the desired burn duration. These results indicate that the extreme material decomposition rates of the SFEPDM in this application are not due to gas-phase convection or shear but rather to interactions with burning aluminum or alumina slag. Further comparisons with between SFEPDM performance in this design and that in other hot-fire tests provide insight into the mechanisms of SFEPDM decomposition in SRM aft domes that can guide the upcoming redesign effort, as well as other future SRM designs. These data also highlight the current limitations of modeling elastomeric insulators solely with diffusion-controlled, gas-phase thermochemistry in SRM regions with significant viscous shear and/or condense-phase impingement or flow.

Martin, Heath T.↗

NASA NTRS1997

Heterogeneous Combustion of Porous Graphite Particles in Microgravity

Recent theoretical investigations on graphite particle combustion have employed several levels of heterogeneous reaction models, ranging from global to elementary models, to describe the oxidation of carbon to gaseous products. Unlike the counterpart homogeneous reaction models, these heterogeneous reaction models are not well developed because of the difficulties associated with decoupling the physical characteristics of the solid (e.g. surface area taking part in combustion) from the chemical kinetic data. This is certainly true for porous graphite particle combustion, where heterogeneous and homogeneous reactions occur within the pores and play an important role in the overall oxidation process. As a result, there are considerable uncertainties of physical phenomena predicted using different heterogeneous kinetic models available in the literature. A good example, discussed later in this paper, is the predicted critical particle size below which the mass burning rate becomes exponentially small. The main goal of this study is to understand the basic mechanism controlling such rapid changes in burning rates, by developing a model where physical contributions are decoupled from chemical rate constants in a consistent manner. Another important goal of the proposed study is to develop a truly intrinsic, detailed heterogeneous reaction model for porous graphite combustion at high-temperatures, and to derive a systematically reduced heterogeneous reaction model in terms of the elementary reaction rate constants of the detailed model. The validation of chemical kinetic models describing the heterogeneous and homogeneous combustion in and around a spherically symmetric porous graphite particle can be considerably simplified by experimental measurements obtained under microgravity conditions. A vital component of this study is to conduct such supporting experiments on particle burning rate and surface temperature using NASA microgravity facilities, in close coordination with the theoretical effort. The basic understanding obtained and models developed as part of this project will be useful for optimal design of coal combustion devices. These models can also be extended to investigate the role of heterogeneous chemistry on pollutant formation pathways in combustion devices. The theoretical approach developed here, with pore diffusion effects decoupled from the chemical effects, can also be extended to understand the heterogeneous combustion of other porous fuels, for example, combustion of magnesium in a CO2 environment for propulsion in the Martian atmosphere.

Chelliah, Harsha K.↗

NASA NTRSDate not supplied

FUTURE LEVELS OF AEROSOLS & RADIATIVE FORCING OVER THE ARCTIC

The Arctic Monitoring and Assessment Programme (AMAP) is currently assessing the impacts of Short-Lived Climate Forcers (SLCF) on Arctic climate and air quality. In support of the assessment, we used the NASA Goddard Institute of Space Sciences (GISS) Earth System Model (modelE2.1), with prescribed sea surface temperature and sea-ice fraction, to simulate SLCF concentrations globally between 1995 and 2015. Two simulations were conducted, using the One-Moment Aerosol (OMA) and the Multiconfiguration Aerosol TRacker of mIXing state (MATRIX) aerosol modules. OMA is a mass-based scheme in which aerosols are assumed to remain externally mixed and have a prescribed and constant size distribution, while MATRIX is an aerosol microphysics scheme based on the quadrature method of moments, which is able to explicitly simulate the mixing state of aerosols. Anthropogenic emissions from the ECLIPSE v6b emissions database were used, along with emissions from aircrafts and open biomass burning from the Coupled Model Intercomparison Project Phase 6 (CMIP6), while the natural emissions of sea salt, DMS, isoprene and dust are calculated interactively. The simulated monthly surface concentrations of sulfate (SO4), black carbon (BC), organic carbon (OA), and ozone (O3) are compared with observations from a set of Arctic stations, extracted from the EBAS and IMPROVE databases, as well as a few additional locations. Simulated aerosol optical depths (AOD) are also compared with Advanced Very-High Resolution Radiometer (AVHRR). The study will present the evaluation of the modelE2.1 in simulating SLCF levels over the Arctic using different aerosol schemes, along with observed and simulated trends of SLCFs over the Arctic between 1995 and 2015.

Aersosols↗

DOE OSTI2021

Improved Bounds for Burning Fence Graphs

Graph burning studies how fast a contagion, modeled as a set of fires, spreads in a graph. The burning process takes place in synchronous, discrete rounds. In each round, a fire breaks out at a vertex, and the fire spreads to all vertices that are adjacent to a burning vertex. Additionally, the burning number of a graph G is the minimum number of rounds necessary for each vertex of G to burn. We consider the burning number of the $m \times n$ Cartesian grid graphs, written $G_{m,n}$ . For $m = \omega (\sqrt{n})$ , the asymptotic value of the burning number of $G_{m,n}$ was determined, but only the growth rate of the burning number was investigated in the case $m = O(\sqrt{n})$ , which we refer to as fence graphs. We provide new explicit bounds on the burning number of fence graphs $G_{c\sqrt{n},n}$ , where $c > 0$ .

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2011

Inferring Absorbing Organic Carbon Content from AERONET Data

Black carbon, light-absorbing organic carbon (often called brown carbon) and mineral dust are the major light-absorbing aerosols. Currently the sources and formation of brown carbon aerosol in particular are not well understood. In this study we estimated globally the amount of light absorbing organic carbon and black carbon from AERONET measurements. We find that the columnar absorbing organic carbon (brown carbon) levels in biomass burning regions of South-America and Africa are relatively high (about 15-20 magnesium per square meters during biomass burning season), while the concentrations are significantly lower in urban areas in US and Europe. However, we estimated significant absorbing organic carbon amounts from the data of megacities of newly industrialized countries, particularly in India and China, showing also clear seasonality with peak values up to 30-35 magnesium per square meters during the coldest season, likely caused by the coal and biofuel burning used for heating. We also compared our retrievals with the modeled organic carbon by global Oslo CTM for several sites. Model values are higher in biomass burning regions than AERONET-based retrievals, while opposite is true in urban areas in India and China.

Arola, A.↗

NASA NTRS1984

The lower main sequence and the nature of secondary stars in ultracompact binaries

The possible nature of the secondary stars in ultracompact binary stellar systems (with orbital periods of less than about 1 hr) are systematically investigated. Using a simplified stellar evolution code, which assumes isentropic stellar models, nearly 3000 separate models for hydrogen-burning main-sequence stars with masses less than 0.3 solar mass are generated. The effects of the (homogeneous) chemical composition on the properties of such stars and in, particular, on the minimum main-sequence mass are explored in detail. It is found that this minimum mass is a sensitive function of the hydrogen content and can be as small as 0.035 solar mass. The properties of fully degenerate low-mass stars, as well as low-mass stars that are not in thermal equilibrium are also studied. In particular, it is shown that the thermal time scale of such nonequilibrium stars may exceed 10 billion yr. The results also confirm the existence of a second branch of the main sequence and shed new light on the thermal instability of this branch. The available observational information on the three known ultracompact binary systems (4U 1626-67, G61-29, 4U 1916-05) is summarized, and the results of the stellar model calculations are combined with the empirical results to place constraints on the properties of the secondary stars.

Rappaport, S.↗

NASA NTRS1988

The hydrogen shell game - Pulsational instabilities in hydrogen shell-burning planetary nebula nuclei

Fully nonadiabatic g-mode pulsation calculations have been obtained for evolutionary models of planetary nebula nuclei (PNN) with active hydrogen-burning shells. Expressions have been developed for the phase delays which can develop between the temperature variations and the abundance variations of agents in the CN cycle. G-mode instabilities are noted that are driven by the epsilon mechanism at the position of the nuclear burning shells in standard PNN models. The results indicate that the central stars do not retain sufficient hydrogen to support nuclear burning following ejection of the planetary nebula.

Kawaler, Steven D.↗

DOE OSTI2022

Kepler and TESS Observations of PG 1159-035

Abstract PG 1159-035 is the prototype of the PG 1159 hot (pre-)white dwarf pulsators. This important object was observed during the Kepler satellite K2 mission for 69 days in 59 s cadence mode and by the TESS satellite for 25 days in 20 s cadence mode. We present a detailed asteroseismic analysis of those data. We identify a total of 107 frequencies representing 32 ℓ = 1 modes, 27 frequencies representing 12 ℓ = 2 modes, and eight combination frequencies. The combination frequencies and the modes with very high k values represent new detections. The multiplet structure reveals an average splitting of 4.0 ± 0.4 μ Hz for ℓ = 1 and 6.8 ± 0.2 μ Hz for ℓ = 2, indicating a rotation period of 1.4 ± 0.1 days in the region of period formation. In the Fourier transform of the light curve, we find a significant peak at 8.904 ± 0.003 μ Hz suggesting a surface rotation period of 1.299 ± 0.002 days. We also present evidence that the observed periods change on timescales shorter than those predicted by current evolutionary models. Our asteroseismic analysis finds an average period spacing for ℓ = 1 of 21.28 ± 0.02 s. The ℓ = 2 modes have a mean spacing of 12.97 ± 0.4 s. We performed a detailed asteroseismic fit by comparing the observed periods with those of evolutionary models. The best-fit model has T eff = 129, 600 ± 11 100 K, M * = 0.565 ± 0.024 M ⊙ , and log g = 7.41 − 0.54 + 0.38 , within the uncertainties of the spectroscopic determinations. We argue for future improvements in the current models, e.g., on the overshooting in the He-burning stage, as the best-fit model does not predict excitation for all of the pulsations detected in PG 1159-035.

79 ASTRONOMY AND ASTROPHYSICS↗