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Influence of isoelectronic mass modulation on phonon decay and transport in layered pnictogen-carbon systems

This study systematically investigates the structural, electronic, and thermal transport properties of layered pnictogen–carbon (Pn 2 C 2 ; Pn = P, As, Sb, Bi) monolayers, revealing a profound influence of isoelectronic mass modulation on phonon dynamics and thermal conductivity. Through first-principles calculations and lattice dynamics analysis, we demonstrate that increasing the atomic mass of pnictogens leads to elongated Pn-C bonds, weakened interatomic interactions, and enhanced phonon-phonon scattering, resulting in a dramatic reduction in lattice thermal conductivity (κ). Specifically, κ decreases exponentially from 65.6 W/m-K in P 2 C 2 to an ultralow 0.37 W/m-K in Bi 2 C 2 , driven by suppressed acoustic-optical phonon gaps Δ$^{Γ}_{A-0}$, increased anharmonicity, and reduced phonon lifetimes and group velocities. The transition from semiconducting to metallic behavior in heavier pnictogen-based systems further enhances phonon-electron scattering, contributing to thermal conductivity suppression. Structural analysis highlights the strengthening of out-of-plane C—C bonds and the contraction of C—Pn—C bond angles, which disrupt in-plane phonon transport. Further, these findings establish a design framework for engineering ultralow-κ materials through chemical substitution and structural tuning, offering significant potential for thermoelectric and thermal management applications. This work provides fundamental insights into phonon decay mechanisms and thermal transport in 2D materials, paving the way for advanced phononic and energy-efficient devices.

2D materials↗

Cross-sections for 43 Sc, 44 m Sc, and 44 g Sc from two heavy ion reactions

Two different heavy ion reactions were used to produce 43 Sc (t$_{\frac12}$ = 3.891 h), 44g Sc (t$_{\frac12}$ = 4.042 h), and 44m Sc (t$_{\frac12}$ = 58.61 h) among other stable or long-lived chemically separable products. Production cross sections for 19 F + 27 Al and the reverse kinematic reaction 35 Cl + nat B were measured using an MC-SNICS ion source and the Notre Dame FN Tandem Accelerator. 19 F beams from 35 to 60 MeV were produced with beam currents between 40–80 pnA and 35 Cl beams were produced at six entrance energies with comparable beam currents. This work reports nuclear reaction cross sections 27 Al ( 19 F, x) 43 Sc, 27 Al ( 19 F, pn) 44g Sc, and 27 Al ( 19 F, pn) 44m Sc at six energies between 35 and 60 MeV lab energy. Cross sections within the same energy range were measured for 27 Al ( 19 F, 3pn) 42 K and 27 Al ( 19 F, 3p) 43 K. Comparative measurements were performed for the same compound nucleus produced from nat B( 35 Cl, x) 43 Sc, nat B( 35 Cl, pn) 44g Sc, and nat B( 35 Cl, pn) 44m Sc. The measured thin target cross sections show an overestimation by several statistical models for the scandium radioisotopes. This is corroborated by the measured thick target production rates for both entrance channels. This may be due to angular momentum effects of a heavy ion entrance channel compared to light-ion production, but additional work is required to understand this discrepancy. Finally, these measurements demonstrate that the medically useful 43 Sc, 44g Sc, and 44m Sc radioisotopes can be free of the long-lived contaminant 46 Sc without the use of enriched targets, using heavy ion beams and robust target materials.

07 ISOTOPE AND RADIATION SOURCES↗

Base-Free Catalytic Transfer Hydrogenation of Alkyl Formates and Organic Esters at Mild Temperature

The pincer-ligated ruthenium complex ( iPr PN H P)Ru(CO)H 2 ( iPr PN H P = ( i Pr 2 PC 2 H 4 ) 2 NH) is an active catalyst for the transfer hydrogenation of alkyl formates (HCO 2 R) and organic esters (RCO 2 R′) to the corresponding alcohols under base-free reaction conditions at mild temperatures. Specifically, a range of alkyl formate esters were reduced to MeOH and the corresponding alcohols in high yields using ( iPr PN H P)Ru(CO)H 2 as the catalyst and isopropanol ( i PrOH) as the hydrogen donor at 30 °C. The first step in the process is the metal-catalyzed transesterification of the alkyl formate with i PrOH to generate isopropyl formate, which is then reduced. The use of i PrOH as the hydrogen donor is crucial. ( iPr PN H P)Ru(CO)H 2 can also catalyze the transfer hydrogenation of a broad range of organic esters, including cyclic, acyclic, heteroatom-substituted, and long-chain bio-derived esters, to the corresponding alcohols in good yields using ethanol (EtOH) as the hydrogen donor at 55 °C. Computational studies were used to elucidate the proposed pathway for alkyl formate reduction and the underlying reasons why i PrOH is the most effective hydrogen donor for alkyl formate reduction, while EtOH is optimal for organic ester reduction. Overall, this work describes a highly active catalyst for alkyl formate and organic ester transfer hydrogenation and provides mechanistic insight into the factors responsible for the strong catalytic performance. Finally, these findings will be valuable for designing catalysts for both transfer hydrogenation and related reactions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Magnetic Properties Tuning via Broad Range Site Deficiency in Square Net Material UCu x Bi 2

HfCuSi 2 -type pnictogen compounds have recently been shown to be a versatile platform for designing materials with topologically nontrivial band structures. However, these phases require strict control over the electron count to tune the Fermi level, which can only be achieved in compositions with A 2+ M 2+ Pn 2 and A 3+ M + Pn 2 (A = lanthanides, M = transition metals, Pn = pnictogens P–Bi) charge distribution. While such lanthanide compounds have been thoroughly studied as candidate magnetic topological materials, their heavy element analogs with uranium and bismuth remain largely underexplored. In this report, we present the synthesis of UCu x Bi 2 single crystals and study their magnetic properties. Detailed structural analysis revealed that flux-grown crystals always form as a site-deficient UCu x Bi 2 composition, where x varies between 0.20 and 0.64. Magnetic property measurements revealed a dependence of the magnetic coupling on the Cu site deficiency, linearly changing the Néel temperature from 51 K for UCu 0.60 Bi 2 to 118 K for UCu 0.30 Bi 2 . Moreover, higher Cu concentration promotes a metamagnetic transition in highly magnetically anisotropic UCu 0.60 Bi 2 single crystals. We show that DFT calculations can successfully model site deficiency in the UCu x Sb 2 and UCu x Bi 2 systems. This work paves the way toward using the site deficiency to tune the Fermi level in more ubiquitous A 3+ M 2+ x Pn 2 phases, which previously have not been considered topological candidate materials due to unfavorable electron count.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polymerized small molecular acceptor based all-polymer solar cells with an efficiency of 16.16% via tuning polymer blend morphology by molecular design

All-polymer solar cells (all-PSCs) based on polymerized small molecular acceptors (PSMAs) have made significant progress recently. Here, we synthesize two A-DA’D-A small molecule acceptor based PSMAs of PS-Se with benzo[c][1,2,5]thiadiazole A’-core and PN-Se with benzotriazole A’-core, for the studies of the effect of molecular structure on the photovoltaic performance of the PSMAs. The two PSMAs possess broad absorption with PN-Se showing more red-shifted absorption than PS-Se and suitable electronic energy levels for the application as polymer acceptors in the all-PSCs with PBDB-T as polymer donor. Cryogenic transmission electron microscopy visualizes the aggregation behavior of the PBDB-T donor and the PSMA in their solutions. In addition, a bicontinuous-interpenetrating network in the PBDB-T:PN-Se blend film with aggregation size of 10~20 nm is clearly observed by the photoinduced force microscopy. The desirable morphology of the PBDB-T:PN-Se active layer leads its all-PSC showing higher power conversion efficiency of 16.16%.

14 SOLAR ENERGY↗

Existence of a flat band in highly correlated metal BaCo 2 P 2

We report on the observation of a flat band situated at the Fermi level E F along with the structural, electrical transport, and magnetic properties of BaCo 2 P 2 that crystallizes in the ThCr 2 Si 2 -type body-center tetragonal structure. This compound has the largest inter-layer pnictide (Pn) distance d Pn–Pn as well as the largest c/a ratio among all the known ACo 2 Pn 2 (A = alkaline earth metal) compounds, where a and c are the tetragonal lattice parameters. Hence, the magnetic and electronic properties of this compound are expected to have a quasi-two-dimensional character. Despite the evidence of the presence of sizable magnetic interactions, magnetic susceptibility χ(T) of BaCo 2 P 2 does not show magnetic ordering down to 1.8 K. The material shows good metallic conduction with a large residual resistivity ratio ρ 300 K /ρ 1.8 K ≈ 70 and a Fermi liquid behavior at low temperature. Kadowaki–Woods ratio R KW of BaCo 2 P 2 suggests the presence of sizable electronic correlations within this system. Additionally, a large many-body enhancement of 2.3 of the experimental density of states D γ (E F ) over the band-structure D band (E F ) is inferred to arise from sizable electron-electron and/or electron-phonon interactions leading to a substantial deviation from the free-electron behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spectroscopic survey of faint planetary-nebula nuclei – II. The subdwarf O central star of Fr 2-30

Fr 2-30 = PN? G126.8−15.5 is a faint emission nebula, hosting a 14th-mag central star that we identify here for the first time. Deep Hα and [O III ] images reveal a roughly elliptical nebula with dimensions of at least 22 arcmin × 14 arcmin, fading into a surrounding network of even fainter emission. Optical spectrograms of the central star show it to have a subdwarf O spectral type, with a Gaia parallax distance of 890 pc. A model-atmosphere analysis gives parameters of T eff = 60 000 K, log g = 6.0, and a low helium content of n He /n H = 0.0017. The location of the central star in the log g–T eff plane is inconsistent with a post-asymptotic-giant-branch evolutionary status. Two alternatives are that it is a helium-burning post-extreme-horizontal-branch object, or a hydrogen-burning post-red-giant-branch star. In either case, the evolutionary ages are so long that a detectable planetary nebula (PN) should not be present. We find evidence for a variable radial velocity (RV), suggesting that the star is a close binary. However, there are no photometric variations, and the spectral-energy distribution rules out a companion earlier than M2 V. The RVs of the star and surrounding nebula are discordant, and the nebula lacks typical PN morphology. We suggest that Fr 2-30 is a ‘PN mimic’ – the result of a chance encounter between the hot sdO star and an interstellar cloud. However, we note the puzzling fact that there are several nuclei of genuine PNe that are known to be in evolutionary states similar to that of the Fr 2-30 central star.

79 ASTRONOMY AND ASTROPHYSICS↗

Solid particulate mass and number from ducted fuel injection in an optically accessible diesel engine in skip-fired operation

Ducted fuel injection (DFI) is a new combustion strategy that has been shown to significantly attenuate soot formation in diesel engines. While previous studies have used optical diagnostics and optical filter smoke number methods to show that DFI reduces in-cylinder soot formation and engine-out soot emissions, respectively, this is the first study to measure solid particle number (PN) emissions in addition to particle mass (PM). Furthermore, this study quantitatively evaluates the use of transient particle instruments for measuring particles from skip-fired operation in an optical single cylinder research engine (SCRE). Engine-out PN was measured using an engine exhaust particle sizer following a catalytic stripper, and PM was measured using a photoacoustic analyzer. The study improves on earlier preliminary emissions studies by clearly showing that DFI reduces overall PM by 76%–79% and PN for particles larger than 23 nm by 77% relative to conventional diesel combustion at a 1200-rpm, 13.3-bar gross indicated mean effective pressure operating condition. The degree of engine-out PM reduction with DFI was similar across both particulate measurement instruments used in the work. Through the use of bimodal distribution fitting, DFI was also shown to reduce the geometric mean diameter of accumulation mode particles by 26%, similar to the effects of increased injection pressure in conventional diesel combustion systems. This work clearly shows the significant solid particulate matter reductions enabled by DFI while also demonstrating that engine-out PN can be accurately measured from an optical SCRE operating in a skip-fired mode. Based on these results, it is believed that DFI has the potential to enable fuel savings when implemented in multi-cylinder engines, both by lowering the required frequency of active diesel particulate filter regeneration, and by reducing the backpressure imposed by exhaust filtration systems.

33 ADVANCED PROPULSION SYSTEMS↗

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Post-flowering Soil Waterlogging Curtails Grain Yield Formation by Restricting Assimilates Supplies to Developing Grains

Soil waterlogging is among the major factors limiting the grain yield of winter wheat crops in many parts of the world, including the middle and lower reaches of the Yangtze River China. In a field study, we investigated the relationship between leaf physiology and grain development under a varying duration of post-flowering waterlogging. A winter wheat cultivar Ningmai 13 was exposed to soil waterlogging for 0 (W0), 3 (W3), 6 (W6), and 9 d (W9) at anthesis. Increasing waterlogging duration significantly reduced flag leaf SPAD (soil plant analysis development) values and net photosynthetic rate (Pn). There was a linear reduction in flag leaf Pn and SPAD as plant growth progressed under all treatments; however, the speed of damage was greater in the waterlogged leaves. For example, compared with their respective control (W0), flag leaves of W9 treatment have experienced 46% more reduction in Pn at 21 d after anthesis (DAA) than at 7 DAA. Increasing waterlogging duration also induced oxidative damage in flag leaves, measured as malondialdehyde (MDA) contents. The capacity to overcome this oxidative damage was limited by the poor performance of antioxidant enzymes in wheat leaves. Inhibited leaf Pn and capacity to sustain assimilate synthesis under waterlogged environments reduced grain development. Compared with W0, W6 and W9 plants experienced a 20 and 22% reduction in thousand grain weight (TGW) in response to W6 and W9, respectively at 7 DAA and 11 and 19%, respectively at 28 DAA. Sustained waterlogging also significantly reduced grain number per spike and final grain yield. Averaged across two years of study, W9 plants produced 28% lesser final grain yield than W0 plants. Our study suggested that wheat crops are highly sensitive to soil waterlogging during reproductive and grain filling phases due to their poor capacity to recover from oxidative injury to photosynthesis. Management strategies such as planting time, fertilization and genotype selection should be considered for the areas experiencing frequent waterlogging problems.

Ma, Shangyu↗

Spread spectrum techniques for the Space Shuttle

The Space Shuttle will employ spread spectrum techniques for both communication and navigation. During on-orbit phases of flight, two-way S-band and Ku-band communication links between the Shuttle and the ground will be available via the tracking and data relay satellite system (TDRSS). A pseudonoise (PN) code will spread the forward-link data spectrum from 32 kbps to 216 kbps to reduce the signal spectral density impinging on the earth's surface, with the S-band code search and acquisition being performed at C/NO-values of around 5 dB-Hz, and with a code length of 2047 chips at a rate of 11.232 Mchips/sec. C/NO-values in the region of 60 dB-Hz to 63 dB-Hz will characterize PN code acquisition in the Ku-band, whose forward-link PN clock is 3.03 Mchips/sec on a 1023-chip length sequence. Primary operational navigation will be provided by the Global Positioning System (GPS), which, after measuring transit time of the PN spread spectrum signal between a number of GPS satellites and itself, scales it by the velocity of light. GPS will enable position estimation accuracy to 30 feet and velocity estimation accuracy to 0.02 ft/sec.

Batson, B. H.↗

Novel improved PMR polyimides

A series of N-phenylnadimide (PN) modified PMR polyimide composites reinforced with graphite fibers was investigated. The improved flow matrix resins consist of N-phenylnadimide (PN), monomenthyl ester of 5-norbornene-2, 3-dicarboxylic acid (NE), dimethyl ester of 3,3, 4,4-benzophenonetetracarboxylic acide (BTDE), and 4,4 methylenedianiline (MDA). Five modified PMR resin systems were formulated by the addition of 4 to 20 mole percent N-phenylnadimide to the standard PMR-15 composition. These formulations and the control PMR resin were evaluated for rheological characteristics. The initial thermal and mechanical properties of the PN modified PMR and the control PMR/Celion 6000 composites were determined. The results show that the addition of N-phenylnadimide to PMR-15 significantly improved the resin flow characteristics without sacrificing the composites properties. Concentrations of 4 and 9 mole percent PN appear to improve the thermoxidative stability of PMR composites.

Pater, R. H.↗

Luminosities and masses for three central stars of planetary nebulae in the Magellanic Clouds from ultraviolet spectroscopy with the IUE

Physical parameters of the central stars of the planetary nebulae (PN) P40, N2, and N5 are determined from UV observations by the IUE spacecraft and emission line-data. The observations took place on May 23 and 26, 1981. Derived properties, such as the H-beta, color excess, nebular hydrogen emission, helium emission, and stellar continuum emission, the stellar radius, surface gravity, Zanstra temperature, luminosity, absolute bolometric magnitude, apparent visual magnitude, mass, and Zanstra parameter for the three PN central stars are presented. All the masses were over one solar mass, suggesting a specific PN nuclei mass. The finding was corroborated by all luminosities exceeding the Eddington luminosity for a 0.6 solar mass star, which has previously been calculated for the white dwarf core of a PN.

Stecher, T. P.↗

Planetary nebulae as standard candles. IV - A test in the Leo I group

In this paper, PN are used to determine accurate distances to three galaxies in the Leo I group - The E0 giant elliptical NGC 3379, its optical companion, the SB0 spiral NGC 3384, and the smaller E6 elliptical NGC 3377. In all three galaxies, the luminosity-specific PN number densities are roughly the same, and the derived stellar death rates are in remarkable agreement with the predictions of stellar evolution theory. It is shown that the shape of the forbidden O III 5007 A PN luminosity function is the same in each galaxy and indistinguishable from that observed in M31 and M81. It is concluded that the PN luminosity function is an excellent standard candle for early-type galaxies.

Ciardullo, Robin↗

Dynamic mechanical properties of N-phenylnadimide modified PMR polyimide composites

Temperature-frequency dependence of alpha, beta, and gamma transitions was determined using a Rheometrics dynamic spectrometer on a series of unidirectional Celion 6000/N-phenylnadimide (PN) modified PMR polyimide composites. The objective was to see if any correlations exist between crosslinked network structure and dynamic mechanical properties. Variation in crosslinked network structures was achieved by altering the polyimide formulation through addition of various quantities of PN into the standard PMR-15 composition. As a control, PMR-15 composite system exhibited well-defined alpha, beta, and gamma transitions in the regions of 360, 100, and -120 C, respectively. Their activation energies were estimated to be 232, 60, and 14 kcal/mole, respectively. Increasing the amount of PN concentration caused lowering of the activation energies of the three relaxations, a decrease of the glass transition temperature, and increasing intensities of the three damping peaks, compared to the control PMR-15 counterpart. These dynamic mechanical responses were in agreement with formation of a more flexible copolymer from PN and PMR-15 prepolymer.

Pater, Ruth H.↗

Gross-fragmentation of meteoroids and bulk density of Geminids from photographic fireball records

The explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid moving in any actual atmosphere was published several years ago. The solution yields the theoretical relation of l, the distance flown by the meteoroid in its trajectory, as a function of time, t, assuming that the height, h, is a known function of l. The photographic records of meteors and fireballs are coded by time marks, using a rotating shutter or a similar device to break the moving image. Time is, thus, the independent variable and for each time mark on a meteoroid trajector, the observed distance along the trajectory, l sub obs, as well as the double- or multiple- station photographs of the same meteoroid. Applying this solution to all available Prairie Network (PN) fireball-records, we recognized that the majority of them gave good solutions with standard deviations somewhat bigger than the intrinsic geometrical precision of the data. We also noticed that, on an average, previous methods of evaluation of the meteoroid velocities (interpolation polynomials, numerical differenciation of the observed l sub obs) used up to only several tens of percent of the intrinsic precision of the PN observational data. When residuals of these solutions, i.e. l sub obs - l sub com, were represented as a function of time for about 75 percent of solutions. The remaining 25 percent of residuals showed systematic changes with time exceeding one standard deviation. We tried to explain these systematic time course of residuals by using different meteoroids first computed theoretically and then analyzed by the same model as the natural PN fireballs were. The conclusion of these model computations is that systematic time changes of residuals in the nonfragmenting model exceeding one standard of deviation are caused by sudden gross fragmentation at one or more trajectory points. Thus, we generalized the explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid by allowing for one or more points, where sudden gross fragmentation can occur. Using this generalized solution, the distances along the meteoroid trajectory can be computed for any choice of input parameters and compared with the observed distances flown by the meteoroid. For the most precise and long fireball trajectories, the least-squares solution can, thus, yield the initial velocities, the ablation coefficients, the dynamical masses, the positions of gross-fragmentation points, and the terminal mass. At a gross-fragmentation point, the ratio of the main mass to all the remaining fragments can be compared with the dynamic mass determined from our gross-fragmentation model and, thus, the meteoroid bulk density can be evaluated. We applied the gross-fragmentation model to sever PN fireballs showing time changes of residuals, and we recognized that, in all these cases, the new computed bulk densities of meteoroids resulted higher in comparison with the meteoroid densities determined with the non-gross-fragmentation model. Other aspects of the study are discussed.

Ceplecha, Zdenek↗

A volume-limited survey of High Galactic latitude planetary nebulae with the Extrme Ultraviolet Explorer

We present the results of a complete survey, at extreme-ultraviolet (EUV) wavelengths (58-234 A), of the high Galactic latitude (absolute value of b greater than or = to 20 deg) planetary nebulae (PNs) with at least one determination of the distance within 1 kpc of the Sun. The sample comprises 27 objects observed during the Extreme Ultraviolet Explorer (EUVE) all-sky survey and represents the majority of PN likely to be accessible at EUV wavelengths. Six PNs (NGC 246, NGC 1360, K1-16, LoTr 5, NGC 4361, and NGC 3587) were detected in the shortest EUV band (58-174 A). A seventh PN (NGC 6853), not included in the sample, was also detected during the survey. The emission is consistent in all cases with that of a point source and therefore most probably originates from the PN central star. Accurate EUV count rates or upper limits in the two shorter EUVE bands (centered at approximately 100 and 200 A) are given for all the sources in the sample. NGC 4361 and NGC 3587 are reported here for the first time as sources of EUV radiation. As might be expected, attenuation by the interstellar medium dominates the PN distribution in the EUV sky.

Fruscione, Antonella↗

Hierarchies of Models: Toward Understanding Planetary Nebulae

Stars like our sun (initial masses between 0.8 to 8 solar masses) end their lives as swollen red giants surrounded by cool extended atmospheres. The nuclear reactions in their cores create carbon, nitrogen and oxygen, which are transported by convection to the outer envelope of the stellar atmosphere. As the star finally collapses to become a white dwarf, this envelope is expelled from the star to form a planetary nebula (PN) rich in organic molecules. The physics, dynamics, and chemistry of these nebulae are poorly understood and have implications not only for our understanding of the stellar life cycle but also for organic astrochemistry and the creation of prebiotic molecules in interstellar space. We are working toward generating three-dimensional models of planetary nebulae (PNe), which include the size, orientation, shape, expansion rate and mass distribution of the nebula. Such a reconstruction of a PN is a challenging problem for several reasons. First, the data consist of images obtained over time from the Hubble Space Telescope (HST) and spectra obtained from Kitt Peak National Observatory (KPNO) and Cerro Tololo Inter-American Observatory (CTIO). These images are of course taken from a single viewpoint in space, which amounts to a very challenging tomographic reconstruction. Second, the fact that we have two disparate and orthogonal data types requires that we utilize a method that allows these data to be used together to obtain a solution. To address these first two challenges we employ Bayesian model estimation using a parameterized physical model that incorporates much prior information about the known physics of the PN. In our previous works we have found that the forward problem of the comprehensive model is extremely time consuming. To address this challenge, we explore the use of a set of hierarchical models, which allow us to estimate increasingly more detailed sets of model parameters. These hierarchical models of increasing complexity are akin to scientific theories of increasing sophistication, with each new model/theory being a refinement of a previous one by either incorporating additional prior information or by introducing a new set of parameters to model an entirely new phenomenon. We apply these models to both a simulated and a real ellipsoidal PN to initially estimate the position, angular size, and orientation of the nebula as a two-dimensional object and use these estimates to later examine its three-dimensional properties. The efficiency/accuracy tradeoffs of the techniques are studied to determine the advantages and disadvantages of employing a set of hierarchical models over a single comprehensive model.

Knuth, Kevin H.↗