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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

MULTIFRACTAL AND MONOFRACTAL SCALING IN A LABORATORY MAGNETOHYDRODYNAMIC TURBULENCE EXPERIMENT

Both multifractal and monofractal scaling of structure function exponents are observed in the turbulent magnetic fluctuations of the Swarthmore Spheromak Experiment plasma. Structure function and probability distribution function (PDF) analysis exhibits multifractal scaling exponents in low frequency, inertial range fluctuations of the turbulence but monofractal scaling in higher frequency, dissipation range fluctuations. The transition from multifractal to monofractal scaling occurs rapidly suggesting a dissipation mechanism that is insensitive to turbulent structure scale size. Structure functions and PDFs are presented for both temporal and spatial measurements. Variations in the magnetic helicity in the plasma are also shown to modify multifractal scaling characteristics of the inertial range, but do not affect the monofractal scaling of the dissipation range.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

THE HANLE EFFECT OF Ly{alpha} IN A MAGNETOHYDRODYNAMIC MODEL OF THE SOLAR TRANSITION REGION

In order to understand the heating of the solar corona it is crucial to obtain empirical information on the magnetic field in its lower boundary (the transition region). To this end, we need to measure and model the linear polarization produced by scattering processes in strong UV lines, such as the hydrogen Ly{alpha} line. The interpretation of the observed Stokes profiles will require taking into account that the outer solar atmosphere is highly structured and dynamic, and that the height of the transition region may well vary from one place in the atmosphere to another. Here, we report on the Ly{alpha} scattering polarization signals we have calculated in a realistic model of an enhanced network region, resulting from a state-of-the-art radiation magnetohydrodynamic simulation. This model is characterized by spatially complex variations of the physical quantities at transition region heights. The results of our investigation lead us to emphasize that scattering processes in the upper solar chromosphere should indeed produce measurable linear polarization in Ly{alpha}. More importantly, we show that via the Hanle effect the model's magnetic field produces significant changes in the emergent Q/I and U/I profiles. Therefore, we argue that by measuring the polarization signals produced by scattering processes and the Hanle effect in Ly{alpha} and contrasting them with those computed in increasingly realistic atmospheric models, we should be able to decipher the magnetic, thermal, and dynamic structure of the upper chromosphere and transition region of the Sun.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2013

CHARACTERIZING THE DUST COMA OF COMET C/2012 S1 (ISON) AT 4.15 AU FROM THE SUN

We report results from broadband visible images of comet C/2012 S1 (ISON) obtained with the Hubble Space Telescope Wide Field Camera 3 on 2013 April 10. C/ISON's coma brightness follows a 1/ρ (where ρ is the projected distance from the nucleus) profile out to 5000 km, consistent with a constant speed dust outflow model. The turnaround distance in the sunward direction suggests that the dust coma is composed of sub-micron-sized particles emitted at speeds of tens of m s{sup –1}. A(θ)fρ, which is commonly used to characterize the dust production rate, was 1340 and 1240 cm in the F606W and F438W filters, respectively, in apertures <1.''6 in radius. The dust colors are slightly redder than solar, with a slope of 5.0% ± 0.2% per 100 nm, increasing to >10% per 100 nm 10,000 km down the tail. The colors are similar to those of comet C/1995 O1 (Hale-Bopp) and other long-period comets, but somewhat bluer than typical values for short-period comets. The spatial color variations are also reminiscent of C/Hale-Bopp. A sunward jet is visible in enhanced images, curving to the north and then tailward in the outer coma. The 1.''6 long jet is centered at a position angle of 291°, with an opening angle of ∼45°. The jet morphology remains unchanged over 19 hr of our observations, suggesting that it is near the rotational pole of the nucleus, and implying that the pole points to within 30° of (R.A., decl.) = (330°, 0°). This pole orientation indicates a high obliquity of 50°-80°.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Analytical Models of Frequency and Voltage in Large-Scale All-Inverter Power Systems

Low-order frequency response models for power systems have a decades-long history in optimization and control problems such as unit commitment, economic dispatch, and wide-area control. With a few exceptions, these models are built upon the Newtonian mechanics of synchronous generators, assuming that the frequency dynamics across a system are approximately homogeneous, and assume the dynamics of nodal voltages for most operating conditions are negligible, and thus are not directly computed at all buses. As a result, the use of system frequency models results in the systematic underestimation of frequency minimum nadir and maximum RoCoF, and provides no insight into the reactive power-voltage dynamics. This paper proposes a low-order model of both frequency and voltage response in grid-forming inverter-dominated power systems. The proposed model accounts for spatial-temporal variations in frequency and voltage behavior across a system and as a result, demonstrates the heterogeneity of frequency response in future renewable power systems. Electromagnetic transient (EMT) simulations are used to validate the utility, accuracy, and computational efficiency of these models, setting the basis for them to serve as fast, scalable alternatives to EMT simulation, especially when dealing with very large-scale systems, for both planning and operational studies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2018

Tundra Trait Team: A database of plant traits spanning the tundra biome

Motivation: The Tundra Trait Team (TTT) database includes field-based measurements of key traits related to plant form and function at multiple sites across the tundra biome. This dataset can be used to address theoretical questions about plant strategy and trade-offs, trait-environment relationships and environmental filtering, and trait variation across spatial scales, to validate satellite data, and to inform earth system model parameters. Main types of variable contained: The database contains 81,537 measurements of 18 plant traits. The most frequently measured traits (>1,000 observations each) include plant height, leaf area, specific leaf area, leaf fresh and dry mass, leaf dry matter content, leaf nitrogen content, leaf carbon content, leaf phosphorus content, seed mass, and stem specific density. Spatial location and grain: Measurements were collected in tundra habitats in both the northern and southern hemispheres, including Arctic sites in Alaska, Canada, Greenland, Fennoscandia, and Siberia and alpine sites in the European Alps, Colorado Rockies, Caucasus, Ural Mountains, Pyrenees, Australian Alps, and Central Otago Mountains (New Zealand). More than 99% of observations are georeferenced. Time period and grain: All data were collected between 1964 and 2016. A small number of sites have repeated trait measurements at two or more time periods. Major taxa and level of measurement: Trait measurements were made on 858 terrestrial vascular plant species growing in tundra habitats. Most observations are on individuals (87%), while a small number represent plot or site means or maximums per species. Software format: csv file and GitHub repository with data cleaning scripts in R; contribution to TRY plant trait database (www.try-db.org) to be included in the next version release.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Atomic-Level, Energy-Conversion Heat Transfer

Abstract Heat is stored in quanta of kinetic and potential energies in matter. The temperature represents the equilibrium and excited occupation (boson) of these energy conditions. Temporal and spatial temperature variations and heat transfer are associated with the kinetics of these equilibrium excitations. During energy-conversion (between electron and phonon systems), the occupancies deviate from equilibria, while holding atomic-scale, inelastic spectral energy transfer kinetics. Heat transfer physics reaches nonequilibrium energy excitations and kinetics among the principal carriers, phonon, electron (and holes and ions), fluid particle, and photon. This allows atomic-level tailoring of energetic materials and energy-conversion processes and their efficiencies. For example, modern thermal-electric harvesters have transformed broad-spectrum, high-entropy heat into a narrow spectrum of low-entropy emissions to efficiently generate thermal electricity. Phonoelectricity, in contrast, intervenes before a low-entropy population of nonequilibrium optical phonons becomes a high-entropy heat. In particular, the suggested phonovoltaic cell generates phonoelectricity by employing the nonequilibrium, low-entropy, and elevated temperature optical-phonon produced population—for example, by relaxing electrons, excited by an electric field. A phonovoltaic material has an ultranarrow electronic bandgap, such that the hot optical-phonon population can relax by producing electron-hole pairs (and power) instead of multiple acoustic phonons (and entropy). Examples of these quanta and spectral heat transfer are reviewed, contemplating a prospect for education and research in this field.

Engineering↗
DOE OSTI2014

Low-complexity atlas-based prostate segmentation by combining global, regional, and local metrics

Purpose: To improve the efficiency of atlas-based segmentation without compromising accuracy, and to demonstrate the validity of the proposed method on MRI-based prostate segmentation application. Methods: Accurate and efficient automatic structure segmentation is an important task in medical image processing. Atlas-based methods, as the state-of-the-art, provide good segmentation at the cost of a large number of computationally intensive nonrigid registrations, for anatomical sites/structures that are subject to deformation. In this study, the authors propose to utilize a combination of global, regional, and local metrics to improve the accuracy yet significantly reduce the number of required nonrigid registrations. The authors first perform an affine registration to minimize the global mean squared error (gMSE) to coarsely align each atlas image to the target. Subsequently, atarget-specific regional MSE (rMSE), demonstrated to be a good surrogate for dice similarity coefficient (DSC), is used to select a relevant subset from the training atlas. Only within this subset are nonrigid registrations performed between the training images and the target image, to minimize a weighted combination of gMSE and rMSE. Finally, structure labels are propagated from the selected training samples to the target via the estimated deformation fields, and label fusion is performed based on a weighted combination of rMSE and local MSE (lMSE) discrepancy, with proper total-variation-based spatial regularization. Results: The proposed method was applied to a public database of 30 prostate MR images with expert-segmented structures. The authors’ method, utilizing only eight nonrigid registrations, achieved a performance with a median/mean DSC of over 0.87/0.86, outperforming the state-of-the-art full-fledged atlas-based segmentation approach of which the median/mean DSC was 0.84/0.82 when applying to their data set. Conclusions: The proposed method requires a fixed number of nonrigid registrations, independent of atlas size, providing desirable scalability especially important for a large or growing atlas. When applied to prostate segmentation, the method achieved better performance to the state-of-the-art atlas-based approaches, with significant improvement in computation efficiency. The proposed rationale of utilizing jointly global, regional, and local metrics, based on the information characteristic and surrogate behavior for registration and fusion subtasks, can be extended naturally to similarity metrics beyond MSE, such as correlation or mutual information types.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2015

SU-E-T-600: Patient Specific IMRT Verification Using a Phosphor-Screen Based Geometric QA System: A Preliminary Study

Purpose: Raven QA (JPLC, MD) is a unified and comprehensive quality assurance system for QA of TG-142, which use a phosphor screen, a mirror system and a camera. It is to test if this device can be used for IMRT QA dosimetry. Methods: A lung IMRT case is used deliver dose to Raven QA. Accuracy of dose distribution of 5cm slab phantom using Eclipse planning system (Varian) has been confirmed both from a Monte Carlo Simulation and from a MapCheck (SunNuclear) measurement. Geometric distortion and variation of spatial dose response are corrected after background subtraction. A pin-hole grid plate is designed and used to determine the light scatter in the Raven QA box and the spatial dose response. Optic scatter model was not applied in this preliminary study. Dose is normalized to the response of the 10×10 field and the TMR of 5cm depth was considered. Results: Time to setup the device for IMRT QA takes less than 5 minutes as other commercially available devices. It shows excellent dose linearity and dose rate independent, less than 1 %. Background signal, however, changes for different field sizes. It is believed to be due to inaccurate correction of optic scatter. Absolute gamma (5%, 5mm) passing rate was higher than 95%. Conclusion: This study proves that the Raven QA can be used for a patient specific IMRT verification. Part of this study is supported by the Maryland Industrial Partnership Grant.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Conditioned Simulation of Ground-Motion Time Series at Uninstrumented Sites Using Gaussian Process Regression

Ground-motion time series are essential input data in seismic analysis and performance assessment of the built environment. Because instruments to record free-field ground motions are generally sparse, methods are needed to estimate motions at locations with no available ground-motion recording instrumentation. In this study, given a set of observed motions, ground-motion time series at target sites are constructed using a Gaussian process regression (GPR) approach, which treats the real and imaginary parts of the Fourier spectrum as random Gaussian variables. Model training, verification, and applicability studies are carried out using the physics-based simulated ground motions of the 1906 Mw 7.9 San Francisco earthquake and Mw 7.0 Hayward fault scenario earthquake in northern California. Additionally, the method’s performance is further evaluated using the 2019 Mw 7.1 Ridgecrest earthquake ground motions recorded by the Community Seismic Network stations located in southern California. These evaluations indicate that the trained GPR model is able to adequately estimate the ground-motion time series for frequency ranges that are pertinent for most earthquake engineering applications. The trained GPR model exhibits proper performance in predicting the long-period content of the ground motions as well as directivity pulses.

58 GEOSCIENCES↗
DOE OSTI2018

Urban Dispersion Virtual Workshop: Designing the Next Generation Urban Dispersion Field Programs

The overarching objective of this workshop is to start the process of planning and implementing the “Next Generation of Urban Dispersion Studies”. We have organized this program to bring people interested in this complex problem together. We have representation from different disciplines, different agencies, and different academic institutions. The workshop is organized around several questions: • What are the needs of the emergency response community and how do we design models and experiments to address them? • What model improvements do the user communities need? • How do we design tracer release and sampling to address questions temporal (e.g., diurnal and seasonal variation) and spatial (e.g., land/urban/water gradients) for the broadest applicability? • What are the next-generation measurements needed to improve the data sets? • How do we implement the next generation urban dispersion experiments? The Virtual workshop format is exciting. We view this as an experiment which, if successful, will bring a large group of people together from the community to design the next generation urban experiments. We have many agencies participating: DOE-BER, DHS, FEMA, NNSA, NARAC, DTRA, NYPD, and NIST. The registration list includes over 40 people including participants from well beyond the US including Spain and Canada.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Testing Dynamic Earthquake Rupture Models Generated With Stochastic Stress Drop

In this study we investigate the performance of rupture dynamics modeling using heterogenous stress for a M6.5 crustal earthquake on a strike slip vertical fault. In our simulations we used heterogenous stress drop models with correlated stochastic perturbations following the work of Pitarka et al. (2009). The stress model with multiscale variability is designed to accommodate high-stress drop asperity areas and small-scale spatial stress variations. The stress drop and size of asperities are estimated following the IM2011 (Irikura and Miyake, 2011) recipe. In our spontaneous rupture modeling we use a linear slip weakening friction law, with depth depend strength excess, dynamic stress drop and slip weakening distance Dc. Our strategy in preparing the model parameters with vertical and lateral variability is in agreement with observations of earthquake rupture that have confirmed the existence of a shallow weak rupture zone consisting of ductile crustal material, located in the upper 4 km of the crust, and brittle seismogenic zone, underlying the weak zone. The primary objective of our study is to develop a procedure for preparing dynamic rupture models with multiscale variability, and validate spontaneous rupture modeling of strike-slip faults by comparing the resulting rupture kinematics and near-fault ground motion with empirical models for this type of rupture.

58 GEOSCIENCES↗
DOE OSTI2022

Validation of Thermohydraulic Simulations using RELAP for Critical Dual Purpose Canisters

Simulations using the RELAP5-3D systems analysis code and STAR-CCM+, a high-fidelity CFD code, were performed on a model of a real-scale MPC-32 dual purpose canister undergoing a criticality event. These simulations were performed to provide code-to-code verification of the natural convection capabilities in RELAP5. The STAR-CCM+ simulations revealed various natural convection flow patterns that aided in the cooling of fission heat produced in the fuel rods in the canister. Negligible spatial temperature variations were observed across the canister in the STAR-CCM+ results, supporting the use of RELAP5 in predicting the sub-cooled regime. The surface-averaged rod temperature predicted by RELAP5 compared well with STAR-CCM+, verifying the predictive capability of RELAP5 for sub-cooled conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Tree rings reveal the transient risk of extinction hidden inside climate envelope forecasts

Given the importance of climate in shaping species’ geographic distributions, climate change poses an existential threat to biodiversity. Climate envelope modeling, the predominant approach used to quantify this threat, presumes that individuals in populations respond to climate variability and change according to species-level responses inferred from spatial occurrence data—such that individuals at the cool edge of a species’ distribution should benefit from warming (the “leading edge”), whereas individuals at the warm edge should suffer (the “trailing edge”). Using 1,558 tree-ring time series of an aridland pine (Pinus edulis) collected at 977 locations across the species’ distribution, we found that trees everywhere grow less in warmer-than-average and drier-than-average years. Ubiquitous negative temperature sensitivity indicates that individuals across the entire distribution should suffer with warming—the entire distribution is a trailing edge. Species-level responses to spatial climate variation are opposite in sign to individual-scale responses to time-varying climate for approximately half the species’ distribution with respect to temperature and the majority of the species’ distribution with respect to precipitation. These findings, added to evidence from the literature for scale-dependent climate responses in hundreds of species, suggest that correlative, equilibrium-based range forecasts may fail to accurately represent how individuals in populations will be impacted by changing climate. A scale-dependent view of the impact of climate change on biodiversity highlights the transient risk of extinction hidden inside climate envelope forecasts and the importance of evolution in rescuing species from extinction whenever local climate variability and change exceeds individual-scale climate tolerances.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

The atmospheric circulation of a nine-hot-Jupiter sample: Probing circulation and chemistry over a wide phase space

We present results from an atmospheric circulation study of nine hot Jupiters that compose a large transmission spectral survey using the Hubble and Spitzer Space Telescopes. These observations exhibit a range of spectral behavior over optical and infrared wavelengths, suggesting diverse cloud and haze properties in their atmospheres. By utilizing the specific system parameters for each planet, we naturally probe a wide phase space in planet radius, gravity, orbital period, and equilibrium temperature. First, we show that our model “grid” recovers trends shown in traditional parametric studies of hot Jupiters, particularly equatorial superrotation and increased day–night temperature contrast with increasing equilibrium temperature. We show how spatial temperature variations, particularly between the dayside and nightside and west and east terminators, can vary by hundreds of kelvin, which could imply large variations in Na, K, CO and CH{sub 4} abundances in those regions. These chemical variations can be large enough to be observed in transmission with high-resolution spectrographs, such as ESPRESSO on VLT, METIS on the E-ELT, or MIRI and NIRSpec aboard JWST. We also compare theoretical emission spectra generated from our models to available Spitzer eclipse depths for each planet and find that the outputs from our solar-metallicity, cloud-free models generally provide a good match to many of the data sets, even without additional model tuning. Although these models are cloud-free, we can use their results to understand the chemistry and dynamics that drive cloud formation in their atmospheres.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

DIRECT DETECTION OF LYMAN CONTINUUM ESCAPE FROM LOCAL STARBURST GALAXIES WITH THE COSMIC ORIGINS SPECTROGRAPH

We report on the detection of Lyman continuum radiation in two nearby starburst galaxies. Tol 0440-381, Tol 1247-232, and Mrk 54 were observed with the Cosmic Origins Spectrograph on board the Hubble Space Telescope . The three galaxies have radial velocities of ∼13,000 km s{sup −1}, permitting a ∼35 Å window on the restframe Lyman continuum shortward of the Milky Way Lyman edge at 912 Å. The chosen instrument configuration using the G140L grating covers the spectral range from 912 to 2000 Å. We developed a dedicated background subtraction method to account for the temporal and spatial background variations of the detector, which is crucial at the low flux levels around 912 Å. This modified pipeline allowed us to significantly improve the statistical and systematic detector noise and will be made available to the community. We detect Lyman continuum in all three galaxies. However, we conservatively interpret the emission in Tol 0440-381 as an upper limit due to possible contamination by geocoronal Lyman series lines. We determined the current star formation properties from the far-ultraviolet continuum and spectral lines and used synthesis models to predict the Lyman continuum radiation emitted by the current population of hot stars. We discuss various model uncertainties such as, among others, atmospheres and evolution models. Lyman continuum escape fractions were derived from a comparison between the observed and predicted Lyman continuum fluxes. Tol 1247-232, Mrk 54, and Tol 0440-381 have absolute escape fractions of (4.5 ± 1.2)%, (2.5 ± 0.72)%, and <(7.1 ± 1.1)%, respectively.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Estimating Jupiter’s Gravity Field Using Juno Measurements, Trajectory Estimation Analysis, and a Flow Model Optimization

The upcoming Juno spacecraft measurements have the potential of improving our knowledge of Jupiter’s gravity field. The analysis of the Juno Doppler data will provide a very accurate reconstruction of spatial gravity variations, but these measurements will be very accurate only over a limited latitudinal range. In order to deduce the full gravity field of Jupiter, additional information needs to be incorporated into the analysis, especially regarding the Jovian flow structure and its depth, which can influence the measured gravity field. In this study we propose a new iterative method for the estimation of the Jupiter gravity field, using a simulated Juno trajectory, a trajectory estimation model, and an adjoint-based inverse model for the flow dynamics. We test this method both for zonal harmonics only and with a full gravity field including tesseral harmonics. The results show that this method can fit some of the gravitational harmonics better to the “measured” harmonics, mainly because of the added information from the dynamical model, which includes the flow structure. Thus, it is suggested that the method presented here has the potential of improving the accuracy of the expected gravity harmonics estimated from the Juno and Cassini radio science experiments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Revisiting the Supernova Engines in the 3C 397 and W49B Supernova Remnants

The nature of the supernova remnants (SNRs) 3C 397 and W49B has long been a subject of debate, with prior studies offering conflicting interpretations between thermonuclear and core-collapse scenarios. To help settle this debate, we present a systematic, spatially resolved, spectroscopic analysis of both remnants using XMM-Newton. By applying multicomponent thermal models, we derive key physical properties including elemental abundances, ejecta temperatures, ambient densities, and explosion energetics. We compare the inferred metal abundance ratios to a wide range of core-collapse and thermonuclear nucleosynthesis models, including new models whose explosion energies differ from the canonical value of 10 51 erg. We find that the observed Fe/Si and Ca/Si ratios in both SNRs are best matched by certain thermonuclear models. However, no model fully reproduces the complete set of observed abundance patterns. In 3C 397, high Fe enrichment and spatial abundance variations suggest interaction with a dense progenitor environment, and W49B’s composition is overall consistent with a thermonuclear origin; however, both require a low-energy (∼10 50 erg) supernova explosion. We additionally map the Fe Kα line centroid energies and find a spread, with W49B falling within the core-collapse region—highlighting both environmental complexity and the limitations of this diagnostic for supernova classification. Our results highlight the need for caution in relying on any single diagnostic or nucleosynthesis model for supernova typing, underscore the need for improved nucleosynthesis models, and motivate future high-resolution, high-throughput observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Long-term Optical Polarization Variability and Multiwavelength Analysis of Blazar Mrk 421

The results of 8 yr R-band photopolarimetric data of blazar Mrk 421 collected from 2008 February to 2016 May are presented, along with extensive multiwavelength observations covering radio to TeV γ-rays around the flares observed in 2008 May, 2010 March, and 2013 April. The most important results are found in 2013, when the source displayed in the R band a very high brightness state of 11.29 ± 0.03 mag (93.60 ± 1.53 mJy) on April 10 and a polarization degree of 11.00% ± 0.44% on May 13. The analysis of the optical data shows that the polarization variability is due to the superposition of two polarized components that might be produced in two distinct emitting regions. An intranight photopolarimetric variability study carried out over seven nights after the 2013 April maximum found flux and polarization variations on the nights of April 14, 15, 16, and 19. In addition, the flux shows a minimum variability timescale of Δt = 2.34 ± 0.12 hr, and the polarization degree presents variations of ∼1%–2% on a timescale of Δ t ∼ minutes. Also, a detailed analysis of the intranight data shows a coherence length of the large-scale magnetic field of l{sub B}≃0.3 pc, which is the same order of magnitude as the distance traveled by the relativistic shocks. This result suggests that there is a connection between the intranight polarimetric variations and spatial changes of the magnetic field. Analysis of the complete R-band data along with the historical optical light curve found for this object shows that Mrk 421 varies with a period of 16.26 ± 1.78 yr.

79 ASTRONOMY AND ASTROPHYSICS↗