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Frequency and Time Domain Nuclear-Electronic Orbital Equation-of-Motion Coupled Cluster Methods: Combination Bands and Electronic-Protonic Double Excitations

The accurate description of excited vibronic states is important for modeling a wide range of photoinduced processes. The nuclear-electronic orbital (NEO) approach, which treats specified protons on the same level as the electrons, can describe excited electronic-protonic states. Herein the multicomponent equation-of-motion coupled cluster with singles and doubles (NEO-EOM-CCSD) method and its time-domain counterpart, TD-NEO-EOM-CCSD, are developed and implemented. The application of these methods to the HCN molecule highlights their capabilities. These methods predict qualitatively reasonable energies and intensities for a combination band corresponding to simultaneous excitation of two vibrational modes, as well as an overtone. These methods also describe states with double excitation character, such as excited electronic-protonic states corresponding to the simultaneous excitation of an electron and a proton. The ability of the NEO-EOM-CCSD method and its time-dependent counterpart to describe combination bands, overtones, and double excitations will enable a wide range of photochemical applications.

Pavosevic, Fabijan↗

Bounded motion design in the Earth zonal problem using differential algebra based normal form methods

Establishing long-term relative bounded motion between orbits in perturbed dynamics is a key challenge in astrodynamics to enable cluster flight with minimum propellant expenditure. Herein, we present an approach that allows for the design of long-term relative bounded motion considering a zonal gravitational model. Entire sets of orbits are obtained via high-order Taylor expansions of Poincarè return maps about reference fixed points. The high-order normal form algorithm is used to determine a change in expansion variables of the map into normal form space, in which the phase space behavior is circular and can be easily parameterized by action–angle coordinates. The action–angle representation of the normal form coordinates is then used to parameterize the original Poincarè return map and average it over a full phase space revolution by a path integral along the angle parameterization. As a result, the averaged nodal period and drift in the ascending node are obtained, for which the bounded motion conditions are straightforwardly imposed. Sets of highly accurate bounded orbits are obtained, extending over several thousand kilometers, and valid for decades.

79 ASTRONOMY AND ASTROPHYSICS↗

Mechanisms of energetic-particle transport in magnetically confined plasmas

Super-thermal ions and electrons occur in both space and fusion plasmas. Because these energetic particles (EP) have large velocities, EP orbits necessarily deviate substantially from magnetic surfaces. Orbits are described by conserved constants of motion that define topological boundaries for different orbit types. Electric and magnetic field perturbations produced by instabilities can disrupt particle orbits, causing the constants of motion to change. The statistics of the “kicks” associated with these perturbations determines the resulting cross field transport. A unifying theme of this tutorial is the importance of the perturbation’s phase at the particle’s position Θ = k • r – ωt, where k and ω are the wavevector and frequency of the perturbation, r is the EP position, and t is the time. A distinction is made between field perturbations that resonate with an aspect of the orbital motion and those that do not. Resonance occurs when the wave phase returns to its initial value in an integer multiple of an orbital period. Convective transport occurs when resonant particles experience an unvarying wave phase. Alternatively, multiple wave-particle resonances usually decorrelate the phase, resulting in diffusive transport. Large orbits increase the number of important resonances and can cause chaotic orbits even for relatively small amplitude waves. In contrast, in the case of non-resonant perturbations, orbital phase averaging reduces transport. Here, large field perturbations introduce additional effects, including nonlinear resonances at fractional values of the orbital motion. In summary, large orbits are a blessing and a curse: For non-resonant modes, orbit-averaging reduces transport but, for resonant transport, large orbits facilitate jumps across topological boundaries and enhance the number of important resonances.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The kinematics, metallicities, and orbits of six recently discovered Galactic star clusters with Magellan/M2FS spectroscopy

ABSTRACT We present Magellan/M2FS spectroscopy of four recently discovered Milky Way star clusters (Gran 3/Patchick 125, Gran 4, Garro 01, and LP 866) and two newly discovered open clusters (Gaia 9 and Gaia 10) at low Galactic latitudes. We measure line-of-sight velocities and stellar parameters ([Fe/H], log g, Teff, and [Mg/Fe]) from high-resolution spectroscopy centred on the Mg triplet and identify 20–80 members per star cluster. We determine the kinematics and chemical properties of each cluster and measure the systemic proper motion and orbital properties by utilizing Gaia astrometry. We find Gran 3 to be an old, metal-poor (mean metallicity of [Fe/H] = −1.83) globular cluster located in the Galactic bulge on a retrograde orbit. Gran 4 is an old, metal-poor ([Fe/H] = −1.84) globular cluster with a halo-like orbit that happens to be passing through the Galactic plane. The orbital properties of Gran 4 are consistent with the proposed LMS-1/Wukong and/or Helmi streams merger events. Garro 01 is metal-rich ([Fe/H] = −0.30) and on a near-circular orbit in the outer disc but its classification as an open cluster or globular cluster is ambiguous. Gaia 9 and Gaia 10 are among the most distant known open clusters at $R_{\mathrm{GC}}\sim 18,~21.2~\mathrm{\, kpc}$ and most metal-poor with [Fe/H] ∼−0.50, −0.34 for Gaia 9 and Gaia 10, respectively. LP 866 is a nearby, metal-rich open cluster ([Fe/H] = +0.10). The discovery and confirmation of multiple star clusters in the Galactic plane shows the power of Gaia astrometry and the star cluster census remains incomplete.

Pace, Andrew B. (ORCID:0000000260218760)↗

New model for the ion collection by cylindrical probes over a wide range of collisionality

Langmuir probes remain one of the most important diagnostic tools for plasma processing applications. Modern probe analysis usually relies on the electron current part of the Langmuir probe characteristic using the Druyvesteyn method. However, for electronegative plasmas or for discharges containing dust the analysis of the ion current attracted by the probe can be desirable to determine the ion density. But, even at low pressures of a few Pa, the ion current is affected by collisions due to the large cross section for charge exchange. Available theories for collisional or collision-enhanced ion currents onto probes are complex and not well validated. Thus, in this contribution, we compare available collisional probe theories for the ion current to results of particle-in-cell (PIC) simulations. To this end, the probe surrounded by a semi-infinite plasma is simulated using a modified version of the open-source code EDIPIC. A dataset of currents for different neutral gas pressures is obtained and compared to the different theories from the literature. Based on these results, we propose a simpler and more intuitive model for the ion current collected by the probe, based on the model of Gatti and Kortshagen (Phys. Rev. E 78, 046402, 2008), developed for the charging of dust particles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Subhalos in Galaxy Clusters: Coherent Accretion and Internal Orbits

Subhalo dynamics in galaxy cluster host halos govern the observed distribution and properties of cluster member galaxies. We use the IllustrisTNG simulation to investigate the accretion and orbits of subhalos found in cluster-size halos. We find that the median change in the major axis direction of cluster-size host halos is approximately 80° between a ∼ 0.1 and the present day. We identify coherent regions in the angular distribution of subhalo accretion, and ∼68% of accreted subhalos enter their host halo through ∼38% of the surface area at the virial radius. The majority of galaxy clusters in the sample have ∼2 such coherent regions. We further measure angular orbits of subhalos with respect to the host major axis and use a clustering algorithm to identify distinct orbit modes with varying oscillation timescales. The orbit modes correlate with subhalo accretion conditions. Subhalos in orbit modes with shorter oscillations tend to have lower peak masses and accretion directions somewhat more aligned with the major axis. One orbit mode, exhibiting the least oscillatory behavior, largely consists of subhalos that accrete near the plane perpendicular to the host halo major axis. Our findings are consistent with expectations from inflow from major filament structures and internal dynamical friction: most subhalos accrete through coherent regions, and more massive subhalos experience fewer orbits after accretion. Our work offers a unique quantification of subhalo dynamics that can be connected to how the intracluster medium strips and quenches cluster galaxies.

galaxy clusters↗

Two-epoch Orbit Estimation for Wide Binaries Resolved in Hipparcos and Gaia

The Hipparcos catalog and its Double and Multiple System Annex (DMSA) lists 4099 components with individual proper motions and coordinates on the epoch 1991.25. Many of these long-period binary stars are also present in Gaia Data Release 2 (DR2). Using the available relative positions and proper motions separated by 24.25 yr, the equations of relative orbital motion can be solved for the two epoch eccentric anomalies, orbital period, and eccentricity. This method employs elimination of the linear Thiele–Innes unknowns and nonlinear optimization of the remaining condition equations. The quality of these solutions is compromised by the insufficient condition and modest precision of the Hipparcos astrometric data, as revealed by Monte Carlo simulations with artificially perturbed data points. The presence of multiple systems and optical pairs can also perturb the results. Limited experiments with artificial data indicate that useful estimates can be obtained with a 25 yr epoch difference for wide binaries with orbital periods up to ~500 yr. The prospects of this method dramatically improve with the proposed next-generation space astrometry missions such as Gaia-NIR and Theia, especially when additional conditions are included from astrometric or spectroscopic measurements. An ancillary catalog of cross-identification and astrometric information for 1295 double-star pairs cross-matched in Gaia DR2 and Hipparcos is also published.

79 ASTRONOMY AND ASTROPHYSICS↗

Substructure in the stellar halo near the Sun: I. Data-driven clustering in integrals-of-motion space

Context. Merger debris is expected to populate the stellar haloes of galaxies. In the case of the Milky Way, this debris should be apparent as clumps in a space defined by the orbital integrals of motion of the stars. Aims. Our aim is to develop a data-driven and statistics-based method for finding these clumps in integrals-of-motion space for nearby halo stars and to evaluate their significance robustly. Methods. We used data from Gaia EDR3, extended with radial velocities from ground-based spectroscopic surveys, to construct a sample of halo stars within 2.5 kpc from the Sun. We applied a hierarchical clustering method that makes exhaustive use of the single linkage algorithm in three-dimensional space defined by the commonly used integrals of motion energy E, together with two components of the angular momentum, L z and L ⊥ . To evaluate the statistical significance of the clusters, we compared the density within an ellipsoidal region centred on the cluster to that of random sets with similar global dynamical properties. By selecting the signal at the location of their maximum statistical significance in the hierarchical tree, we extracted a set of significant unique clusters. By describing these clusters with ellipsoids, we estimated the proximity of a star to the cluster centre using the Mahalanobis distance. Additionally, we applied the HDBSCAN clustering algorithm in velocity space to each cluster to extract subgroups representing debris with different orbital phases. Results. Our procedure identifies 67 highly significant clusters (> 3σ), containing 12% of the sources in our halo set, and 232 subgroups or individual streams in velocity space. In total, 13.8% of the stars in our data set can be confidently associated with a significant cluster based on their Mahalanobis distance. Inspection of the hierarchical tree describing our data set reveals a complex web of relations between the significant clusters, suggesting that they can be tentatively grouped into at least six main large structures, many of which can be associated with previously identified halo substructures, and a number of independent substructures. This preliminary conclusion is further explored in a companion paper, in which we also characterise the substructures in terms of their stellar populations. Conclusions. Our method allows us to systematically detect kinematic substructures in the Galactic stellar halo with a data-driven and interpretable algorithm. The list of the clusters and the associated star catalogue are provided in two tables available at the CDS.

79 ASTRONOMY AND ASTROPHYSICS↗

X-ray induced electron and ion fragmentation dynamics in IBr

Characterization of the inner-shell decay processes in molecules containing heavy elements is key to understanding x-ray damage of molecules and materials and for medical applications with Auger-electron-emitting radionuclides. The 1s hole states of heavy atoms can be produced by absorption of tunable x rays and the resulting vacancy decays characterized by recording emitted photons, electrons, and ions. The 1s hole states in heavy elements have large x-ray fluorescence yields that transfer the hole to intermediate electron shells that then decay by sequential Auger-electron transitions that increase the ion’s charge state until the final state is reached. In molecules, the charge is spread across the atomic sites, resulting in dissociation to energetic atomic ions. We have used x-ray/ion coincidence spectroscopy to measure charge states and energies of Iq+ and Brq′+ atomic ions following 1s ionization at the I and Br K-edges of IBr. We present the charge states and kinetic energies of the two correlated fragment ions associated with core-excited states produced during the various steps of the cascades. Here, to understand the dynamics leading to the ion data, we develop a computational model that combines Monte-Carlo/Molecular-Dynamics (MC/MD) simulations with a classical over-the-barrier model to track inner-shell cascades and redistribution of electrons in valence orbitals and nuclear motion of fragments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Astrometric gravitational-wave detection via stellar interferometry

Here, we evaluate the potential for gravitational-wave (GW) detection in the frequency band from 10 nHz to 1 μ Hz using extremely high-precision astrometry of a small number of stars. In particular, we argue that nonmagnetic, photometrically stable, hot white dwarfs (WD) located at ~kpc distances may be optimal targets for this approach. Previous studies of astrometric GW detection have focused on the potential for less precise surveys of large numbers of stars; our work provides an alternative optimization approach to this problem. Interesting GW sources in this band are expected at characteristic strains around h c ~10 -17 × (μHz/ $f$ GW ). The astrometric angular precision required to see these sources is Δθ~h c after integrating for a time T~1/$f$GW. We show that jitter in the photometric center of WD of this type due to starspots is bounded to be small enough to permit this high-precision, small-N approach. We discuss possible noise arising from stellar reflex motion induced by orbiting objects and show how it can be mitigated. The only plausible technology able to achieve the requisite astrometric precision is a space-based stellar interferometer. Such a future mission with few-meter-scale collecting dishes and baselines of $\mathscr{O}$(100 km ) is sufficient to achieve the target precision. This collector size is broadly in line with the collectors proposed for some formation-flown, space-based astrometer or optical synthetic-aperture imaging-array concepts proposed for other science reasons. The proposed baseline is however somewhat larger than the km-scale baselines discussed for those concepts, but we see no fundamental technical obstacle to utilizing such baselines. A mission of this type thus also holds the promise of being one of the few ways to access interesting GW sources in this band.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Skyrmion dynamics and transverse mobility: skyrmion Hall angle reversal on 2D periodic substrates with dc and biharmonic ac drives

Here we numerically examine the dynamics of a skyrmion interacting with a two-dimensional periodic substrate under dc and biharmonic ac drives. We show that the Magnus force of the skyrmion produces circular orbits that can resonate with the ac drive and the periodicity of the substrate to create quantized motion both parallel and perpendicular to the dc drive. The skyrmion Hall angle exhibits a series of increasing and/or decreasing steps along with strongly fluctuating regimes. In the phase locked regimes, the skyrmion Hall angle is constant and the skyrmion motion consists of periodic orbits encircling an integer number of obstacles per every or every other ac drive cycle. We also observe phases in which the skyrmion moves at 90° with respect to the driving direction even in the presence of damping, a phenomenon called absolute transverse mobility that can exhibit reentrance as a function of dc drive. When the biharmonic ac drives have different amplitudes in the two directions, we find regimes in which the skyrmion Hall angle shows a sign reversal from positive to negative, as well as a reentrant pinning effect in which the skyrmion is mobile at low drives but becomes pinned at higher drives. These behaviors arise due to the combination of the Magnus force with the periodic motion of the skyrmions, which produce Shapiro steps, directional locking, and ratchet effects.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spectroscopic Observations of Obscured Populations in the Inner Galaxy: 2MASS-GC02, Terzan 4, and the 200 km s{sup −1} stellar peak

The interpretation of potentially new and already known stellar structures located at low latitudes is hindered by the presence of dense gas and dust, as observations toward these sight lines are limited. We have identified Apache Point Observatory Galaxy Evolution Experiment (APOGEE) stars belonging to the low-latitude globular clusters 2MASS-GC02 and Terzan 4, presenting the first chemical element abundances of stars residing in these poorly studied clusters. As expected, the signature of multiple populations coexisting in these metal-rich clusters is evident. We redetermine the radial velocity of 2MASS-GC02 to be −87 ± 7 km s{sup −1}, finding that this cluster’s heliocentric radial velocity is offset by more than 150 km s{sup −1} from the literature value. We investigate a potentially new low-latitude stellar structure and a kiloparsec-scale nuclear disk (or ring) that has been put forward to explain a high-velocity (V {sub GSR} ∼ 200 km s{sup −1}) peak reported in several Galactic bulge fields based on the APOGEE commissioning observations. New radial velocities of field stars at (l, b) = (−6°,0 °) are presented and combined with the APOGEE observations at negative longitudes to carry out this search. Unfortunately no prominent −200 km s{sup −1} peak at negative longitudes along the plane of the Milky Way are apparent, as predicted for the signature of a nuclear feature. The distances and Gaia EDR3 proper motions of the high-V {sub GSR} stars do not support the current models of stars on bar-supporting orbits as an explanation of the +200 km s{sup −1} peak.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Updated Visual Orbit of the Directly Imaged Exoplanet 51 Eridani b and Prospects for a Dynamical Mass Measurement with Gaia

We present a revision to the visual orbit of the young, directly imaged exoplanet 51 Eridani b using four years of observations with the Gemini Planet Imager. The relative astrometry is consistent with an eccentric (e=0.53{sub -0.13}{sup +0.09}) orbit at an intermediate inclination (i=136{sub -11}{sup +10} °), although circular orbits cannot be excluded due to the complex shape of the multidimensional posterior distribution. We find a semimajor axis of 11.1{sub -1.3}{sup +4.2} au and a period of 28.1{sub -4.9}{sup +17.2} yr, assuming a mass of 1.75 M{sub ⊙} for the host star. We find consistent values with a recent analysis of VLT/SPHERE data covering a similar baseline. We investigate the potential of using the absolute astrometry of the host star to obtain a dynamical mass constraint for the planet. The astrometric acceleration of 51 Eri derived from a comparison of the Hipparcos and Gaia catalogs was found to be inconsistent at the 2σ–3σ level with the predicted reflex motion induced by the orbiting planet. Potential sources of this inconsistency include a combination of random and systematic errors between the two astrometric catalogs and the signature of an additional companion within the system interior to current detection limits. We also explored the potential of using Gaia astrometry alone for a dynamical mass measurement of the planet by simulating Gaia measurements of the motion of the photocenter of the system over the course of the extended 8 yr mission. We find that such a measurement is only possible (>98% probability) given the most optimistic predictions for the Gaia scan astrometric uncertainties for bright stars and a high mass for the planet (≳3.6 M {sub Jup}).

79 ASTRONOMY AND ASTROPHYSICS↗

Modification of the Loss Cone for Energetic Particles in the Earth's Inner Magnetosphere

The behavior of energetic particles in the Earth's dipole and stretched magnetic-field models is explored with a focus on the shift of the atmospheric loss cone away from the magnetic-field direction and on non-adiabatic behavior occurring when the particle gyroradius becomes comparable with the gradient scale length of the local magnetic field. It is shown that the equatorial loss cone is aberrated away from the magnetic-field direction (pitch angle of 0°) by the perpendicular drift of a charged particle (which is referred to as the “Mozer transform” described in Mozer (1966, https://doi.org/10.1029/JZ071i011p02701). It is found that the Mozer coordinate transformation in pitch-angle/gyrophase-angle space better organizes the behavior of bounce times, mirror altitudes, drift speeds, and first adiabatic invariant. It also describes the loss-cone shift accurately for a certain range of values of the adiabaticity parameter ϵ, defined by the ratio of the particle gyroradius to the local radius of curvature of the magnetic field. For particles with larger ϵ, the Mozer transform (evaluated with the standard gradient-curvature drift) breaks down and the “central trajectory” theory can be used to calculate the angular shift of the loss cone, which now includes an Earthward shift. When ϵ becomes relatively large, stochastic field line curvature (FLC) scattering occurs: we show the intimate connection between the strength of FLC scattering and the loss-cone shift. Finally, by comparing ion orbits in the dipole and Tsyganenko (Ts89 and Ts04) magnetic fields, we conclude that the loss cone of ring-current ions is significantly modified during geomagnetically active times.

79 ASTRONOMY AND ASTROPHYSICS↗

An Investigation of Poorly Studied Open Cluster NGC 4337 Using Multicolor Photometric and Gaia DR2 Astrometric Data

We present a comprehensive analysis (photometric and kinematical) of the poorly studied open cluster NGC 4337 using 2MASS, WISE, APASS, and Gaia DR2 databases. By determining the membership probabilities of stars, we identified the 624 most probable members with membership probability higher than 50% by using proper motion and parallax data taken from Gaia DR2. The mean proper motion of the cluster is obtained as μ{sub x}=−8.83±0.01 and μ {sub y} = 1.49 ± 0.006 mas yr{sup −1}. We find the normal interstellar extinction toward the cluster region. The radial distribution of members provides a cluster radius of 7.′75 (5.63 pc). The estimated age of 1600 ± 180 Myr indicates that NGC 4337 is an old open cluster with a bunch of red giant stars. The overall mass function slope for main-sequence stars is found as 1.46±0.18 within the mass range 0.75−2.0 M{sub ⊙}, which is in fair agreement with Salpeter’s value (x = 1.35) within uncertainty. The present study demonstrates that NGC 4337 is a dynamically relaxed open cluster. Using the Galactic potential model, Galactic orbits are obtained for NGC 4337. We found that this object follows a circular path around the Galactic center. Under the kinematical analysis, we compute the apex coordinates (A, D) by using two methods: (i) the classical convergent point method and (ii) the AD-diagram method. The obtained coordinates are (A {sub conv}, D {sub conv}) = (96.°27 ± 0.°10, 13.°14 ± 0.°27) and (A {sub ◦}, D {sub ◦}) = (100.°282 ± 0.°10, 9.°577 ± 0.°323) respectively. We also computed the Velocity Ellipsoid Parameters, matrix elements (μ {sub ij}), direction cosines (l {sub j}, m {sub j}, n {sub j}), and the Galactic longitude of the vertex (l {sub 2}).

79 ASTRONOMY AND ASTROPHYSICS↗

Size quantization of an exciton: A toy model of the “dead layer”

In this paper, size-quantization levels of an exciton in large nanocrystals is studied theoretically. For the nanocrystal size, L , much bigger than the Bohr radius, a B , the level positions do not depend on a B . The correction to the levels in a small parameter a B / L depends on the reflection phase of the exciton from the boundary. Calculation of this phase constitutes a three-body problem: electron, hole, and the boundary. This calculation can be performed analytically in the limit when the hole is much heavier than the electron. Physically, a slow motion of the hole towards the boundary takes place in the effective potential created by the fast motion of the electron orbiting the hole and touching the boundary. As a result, the hole is reflected before reaching the boundary. The distance of the closest approach of the hole to the boundary (the dead layer) exceeds a B parametrically .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spectroscopic Orbits of Subsystems in Multiple Stars. VII

Spectroscopic orbits of main-sequence stars HIP 3150A, 6873B, 11537A, 22531A, 22534B, 31089B, 49336A, 104833C, and 107731A belonging to eight multiple systems are determined from high-resolution spectra taken with CHIRON. Two of those are twins with mass ratios above 0.95. HIP 11537 is a young three-tier quadruple system with inner periods of 22.3 and 1146 days and the outer period of 3 kyr. HIP 22531 (ι Pic) is the brightest star in a hierarchical system with six components. It is a spectroscopic binary with periods of 1.56 days and 2.75 yr, as well as a γ Dor variable with a period of 0.67 day, possibly in a 7:3 resonance with the inner orbit. HIP 22534, also member of this system, is a double-lined binary with a period of 208 days. For HIP 31089, both the spectro-interferometric 32 yr outer orbit and the 213 day orbit of the subsystem are determined. HIP 107731 is a triple system with an inner period of 470 days and a fast spatial motion, likely metal-poor. New orbits contribute to the statistics of hierarchical multiplicity in the solar neighborhood.

79 ASTRONOMY AND ASTROPHYSICS↗