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An Open Benchmark of One Million High-Fidelity Cislunar Trajectories

Cislunar space spans from geosynchronous altitudes to beyond the Moon and will underpin future exploration, science, and security operations. We describe and release an open dataset of one million numerically propagated cislunar trajectories generated with the open-source Space Situational Awareness Python package (SSAPy). The model includes high-degree Earth/Moon gravity, solar gravity, and Earth/Sun radiation pressure; other planetary gravities are omitted by design for computational efficiency. Initial conditions uniformly sample commonly used osculating-element ranges, and each trajectory is propagated for up to six years under a single, fixed start epoch. The dataset is intended as a reusable benchmark for method development (e.g., space domain awareness, navigation, and machine-learning pipelines), a reference library for statistical studies of orbit families, and a starting point for community-driven extensions (e.g., alternative epochs). We report empirically observed stability trends (e.g., a band near ~5 GEO and persistence of some co-orbital classes including L4/L5 librators) as dataset descriptors rather than new dynamical results. The chief contribution is the scale, fidelity, organization (CSV/HDF5 with full state time series and metadata), and open availability, which together lower the barrier to comparative and data-driven studies in the cislunar regime.

79 ASTRONOMY AND ASTROPHYSICS↗

Collapse and relaxation of rotating stellar systems

The evolution of initially spherical, uniform-density, and uniform-velocity-dispersion stellar systems is investigated by means of a three-dimensional N-body computer model. Some 100,000 simulation stars are used to follow the collapse and relaxation of the system for various amounts of angular momentum in solid-body rotation. For initially low values of the angular momentum satisfying the Ostriker-Pebbles stability criterion the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. The maximum flattening for these systems is equivalent only to an E2 system. For larger values of the initial angular momentum bars develop, and the systems undergo a much more drastic evolution. The apparent rotational and random velocities of the barred systems are very sensitive to the viewing direction. An additional complication is the frequent misalignment of the apparent major axis with the direction that reflects the maximum rotation.

Hohl, F.↗

Numerical simulations of the decay of satellite galaxy orbits

A multiple three-body technique is used to study the orbital evolution of satellite galaxies which is similar to the N-body method but neglects two-body forces between stars in the halo of the parent galaxy. It is found that, for satellites orbiting within the halo, Chandrasekhar's (1960) dynamical friction formula accurately describes the orbital decay rate, including its variation with satellite mass and size and with the number density and mass of halo stars. Significant frictional forces are present even outside the halo, and the orbital decay rate, instead of depending on the procedure used to place the satellite in its orbit, is determined only by the current orbital parameters. This semirestricted N-body method is sufficiently fast to have permitted the running of 200 simulations to date, many more than would have been possible by means of the conventional N-body technique.

Lin, D. N. C.↗

How Do Uncertainties in Galaxy Formation Physics Impact Field-level Galaxy Bias?

Our ability to extract cosmological information from galaxy surveys is limited by uncertainties in the galaxy–dark matter halo relationship for a given galaxy population, which are governed by the intricacies of galaxy formation. To quantify these uncertainties, we examine quenched and star-forming galaxies using two distinct approaches to modeling galaxy formation: U$\scriptsize{NIVERSE}$M$\scriptsize{ACHINE}$, an empirical semianalytic model, and the I$\scriptsize{llustris}$TNG hydrodynamical simulation. We apply a second-order hybrid N-body perturbative bias expansion to each galaxy sample, enabling direct comparison of modeling approaches and revealing how uncertainties in the galaxy–halo connection affect bias parameters and non-Poisson noise across number densities and redshifts. Notably, we find that quenched and star-forming galaxies occupy distinct parts of the bias parameter space, and that the scatter induced from these different galaxy formation models is small when conditioned on similar selections of galaxies. We also detect the signature of assembly bias in our samples; this leads to small but significant deviations from analytic bias predictions, while assembly bias-removed samples match these predictions well. This work indicates that galaxy samples from a spectrum of reasonable, physically motivated models for galaxy formation give a relatively small range of field-level galaxy bias parameters. We estimate a set of priors from these models that should be useful in extracting cosmological constraints from luminous red galaxy– and emission line galaxy–like samples. Looking forward, careful estimates of the range of impacts of galaxy formation, for a given sample and cosmological analysis, will be an essential ingredient for extracting the most precise cosmological information from current and future large galaxy surveys.

79 ASTRONOMY AND ASTROPHYSICS↗

A simulation survey of galaxy interactions

Many carefully selected samples of interacting galaxies have been observed extensively in attempts to clarify whether interaction produces activity in galaxies. Because the sample members represent a wide range of encounter parameters and times, one can then study whether there are correlations between observable encounter features and, for example, Seyfert activity. On the other hand, in theoretical studies, simulations typically deal with either time-consuming detailed modelling of single galaxy pairs or tracing a few model encounters over time. The authors extend the observational survey approach by combining it with a simulation survey. The authors are conducting a survey of model encounters, covering the most important encounter parameters over a wide range. Some parameters, such as companion structure and initial velocity, are demonstratably less important and can be ignored in a first pass. The parameter range must be richly enough sampled so that the authors can evaluate the uniqueness of the observable morphology and velocity structure of the resulting simulated pairs to diagnose unobservable companion orbit parameters. They are using a self-gravitating polar n-body code run on the Cray X-MP at the Alabama Supercomputer Network. For each simulation, the authors have stellar and gas distributions predicted over, typically, a billion years, along with information on gas motions within the disk and any material captured by the companion or lost to the system. Features of disturbed spiral galaxies are sensitive enough to time and encounter parameters so that a match of the simulation survey results to observations can be applied as starting points to infer unobservable orbital or system parameters in actual sample members. This should enable them to examine whether interesting observed properties (Seyfert activity, nuclear star-formation rate) are functions of unobservable dynamical properties which characterize each encounter. Any correlations (or lack of some expected ones) will provide strong clues as to how or whether these phenomena are related to interactions. Aside from its use with such observed samples, this survey should greatly speed determination of initial orbital parameters for more detailed subsequent simulations of individual systems.

Byrd, Gene G.↗

The R -process Alliance: Enrichment of r -process Elements in a Simulated Milky Way–like Galaxy

We study the formation of stars with varying amounts of heavy elements synthesized by the rapid neutron-capture process (r-process) based on our detailed cosmological zoom-in simulation of a Milky Way–like galaxy with an N-body/smoothed particle hydrodynamics code, asura. Most stars with no overabundance in r-process elements, as well as the strongly r-process-enhanced (RPE) r-II stars ([Eu/Fe] > +0.7), are formed in dwarf galaxies accreted by the Milky Way within the 6 Gyr after the Big Bang. In contrast, over half of the moderately enhanced r-I stars (+0.3 < [Eu/Fe] ≤ +0.7) are formed in the main in situ disk after 6 Gyr. Our results suggest that the fraction of r-I and r-II stars formed in disrupted dwarf galaxies is larger the higher their [Eu/Fe] is. Accordingly, the most strongly enhanced r-III stars ([Eu/Fe] > +2.0) are formed in accreted components. These results suggest that non-r-process-enhanced stars and r-II stars are mainly formed in low-mass dwarf galaxies that hosted either none or a single neutron star merger, while the r-I stars tend to form in the well-mixed in situ disk. We compare our findings with high-resolution spectroscopic observations of RPE metal-poor stars in the halo and dwarf galaxies, including those collected by the R-Process Alliance. We conclude that observed [Eu/Fe] and [Eu/Mg] ratios can be employed in chemical tagging of the Milky Way’s accretion history.

Chemical enrichment↗

Computer experiments on the effect of retrograde stars in disk galaxies

Using large-scale N-body calculations for flat disk galaxies, we examine the effect of reversing the angular momentum for various fractions of the stars upon the global bar-forming mode. The initial conditions for these simulations are based on stationary states of two classes of models: the isochrones studied recently by Kalnajs by means of linear theory, and a model resembling the Schmidt model of our own Galaxy. In both cases, as the fraction of retrograde stars is increased, the growth of the bar-forming mode is inhibited (although not eliminated). These N-body results for the isochrones agree with the predictions of linear theory, quantitatively as well as qualitatively.

Zang, T. A.↗

Navigation systems

The elements of the measurement and communications network comprising the global deep space navigation system (DSN) for NASA missions are described. Among the measurement systems discussed are: VLBI, two-way Doppler and range measurements, and optical measurements carried out on board the spacecraft. Processing of navigation measurement is carried out using two modules: an N-body numerical integration of the trajectory (and state transition partial derivatives) based on pre-guessed initial conditions; and partial derivatives of simulated observables corresponding to each actual observation. Calculations of velocity correction parameters is performed by precise modelling of all physical phenomena influencing the observational measurements, including: planetary motions; tracking station locations, gravity field structure, and transmission media effects. Some of the contributions to earth-relative orbit estimate errors for the Doppler/range system on board Voyager are discussed in detail. A line drawing of the DSN navigation system is provided.

Jordan, J. F.↗

The spiral-compact galaxy pair AM 2208-251: Computer simulations versus observations

The system AM2208-251 is a roughly edge-on spiral extending east-west with a smaller round compact E system about 60 arcsec east of the spiral nucleus along the major axis of the spiral. Bertola, Huchtmeier, and Zeilinger (1990) have presented optical spectroscopic as well as single dish 21 cm observations of this system. Their spectroscopic data show, via emission lines lambda lambda 3727-29A, a rising rotation curve near the nucleus. These spectroscopic observations may indicate a tidal interaction in the system. In order to learn more about such pairs, the authors simulated the interaction using the computer model developed by Miller (1976 a,b, 1978) and modified by the authors (Byrd 1986, 1987, 1988). To do the simulation they need an idea of the mutual orbits of the two galaxies. Their computer model is a two-dimensional polar N-body program. It consists of a self-gravitating disk of particles, within an inert axially symmetric stabilizing halo potential. The particles are distributed in a 24(radial) by 36(azimuthal) polar grid. Self consistent calculations can be done only within the grid area. The disk is modeled with a finite Mestel disk, where all the particles initially move in circular orbits with constant tangential velocities (Mestel 1963), resulting in a flat rotation curve. The gas particles in the spiral's disk, which make up 30 percent of its mass, collide in the following manner. The number of particles in each bin of the polar grid is counted every time step. If it is greater than a given critical density, all the particles in the bin collide, obtaining in the result the same velocities, equal to the average for the bin. This process produces clumps of gas particles-the star formation sites. The authors suppress the collision in the inner part of the disk (within the circle r = 6) to represent the hole seen in the gas in the nuclear bulge of spirals. They thus avoid spurious effects due to collisions in that region. They also varied the size of the collisional bins, which did not affect their conclusions.

Klaric, Mario↗

Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update

Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.

Source record↗

Spiral structure produced by tidal interaction of galaxies

Simulation of a close passage of two galaxies where the self-gravity of the disk stars is taken into account was performed with the aid of a large-scale N-body model (Hohl and Hockney, 1969; Hohl, 1972). The calculation was performed by perturbing an initially stable axisymmetric disk consisting of 100,000 stars by the passage of a companion galaxy having one-fourth the mass of the primary galaxy. Parameters appropriate for M 51 and its companion NGC 5195 were used. The results show the evolution of a weak two arm spiral. The effect of large random velocities on the formation of spiral structure was studied by plotting the spatial distribution of stars for various velocity intervals. The spiral structure is quite pronounced for stars with the lower velocity dispersion, but it can hardly be detected for stars with higher velocities. The tidal interaction causes only slight changes in the azimuthally averaged density distribution.

Hohl, F.↗

Simulated trajectories error analysis program, version 2. Volume 2: Programmer's manual

A series of three computer programs for the mathematical analysis of navigation and guidance of lunar and interplanetary trajectories was developed. All three programs require the integration of n-body trajectories for both interplanetary and lunar missions. The virutal mass technique is used in all three programs. The user's manual contains the information necessary to operate the programs. The input and output quantities of the programs are described. Sample cases are given and discussed.

Vogt, E. D.↗

Impact of Cosmic Filaments on Galaxy Morphological Evolution and Predictions of Early Cosmic Web Structure for Roman

We leverage the IllustrisTNG cosmological simulations to test how the large-scale cosmic web shapes galaxy morphology and to forecast the early cosmic web structure that the Nancy Grace Roman Space Telescope will reveal. In the hydrodynamic TNG50 and N-body TNG50-Dark runs, we reconstruct the cosmic web at redshifts z = 0, 0.5, 1, 2, 3, and 4 with the Monte Carlo Physarum Machine density estimator and the DisPerSE structure identification framework. We confirm that dark matter halos start out predominantly prolate (elongated), and their shapes are aligned with their nearest filaments; prolate galaxies retain strong shape alignment with their outer halos to later times. At z ≥ 1, the fraction of prolate (spheroidal) halos increases (decreases) toward lower stellar mass, higher redshift, and lower filament density. At z < 1, more spheroidal (oblate) stellar structures preferentially reside in higher-density (lower-density) filaments. We also find that higher-density filaments favor extended rotationally supported disks, whereas lower-density filaments more often host smaller dispersion-supported systems. Then, generating mock galaxy samples from TNG100 and TNG50, we predict the early cosmic web accessible to Roman. We find that the spectroscopic emission-line depth planned for the High-Latitude Wide-Area Survey (HLWAS) yields a highly incomplete galaxy sample that does not accurately trace the z = 1 cosmic web. A survey ≥2.5× deeper over a few square degrees would enable a proper reconstruction and reveal qualitatively correct filament–galaxy morphology relationships. Nevertheless, the planned HLWAS Deep field should still identify most galaxy overdensities; targeted deeper spectroscopy of these regions would efficiently and adequately map the early filamentary structure.

Hasan, Farhanul [Space Telescope Science Institute↗

Cloud-particle galactic gas dynamics and star formation

Galactic gas dynamics, spiral structure, and star formation are discussed in relation to N-body computational studies based on a cloud-particle model of the interstellar medium. On the small scale, the interstellar medium is seen as cloud-dominated and supernova-perturbed. It is noted that the cloud-particle model simulates cloud-cloud collisions, the formation of stellar associations, and supernova explosions as dominant local processes. On the large scale, in response to a spiral galactic gravitational field, global density waves and galactic shocks develop having large-scale characteristics similar to those found in continuum gas dynamical studies. Both the system of gas clouds and the system of young stellar associations forming from the clouds figure in the global spiral structure. However, with the attributes of neither assuming a continuum of gas (as in continuum gas dynamical studies) or requiring a prescribed equation of state (such as the isothermal condition), the cloud-particle picture retains much of the detail lost in earlier work. By detail is meant the small-scale features and structures so important in understanding the local, turbulent state of the interstellar medium as well as the degree of raggedness often seen to be superposed on the global spiral structure.

Roberts, W. W., Jr.↗

Collisional dynamics of perturbed particle disks in the solar system

Theoretical and computational studies were carried out on galactic and planetary disks. With the goal of addressing important open questions centered on galactic structure, the cloudy interstellar medium, giant molecular clouds, and star formation in galactic disks and the collisional dynamics of perturbed particulate matter in planetary disks, focus was largely on the self-gravitational effects, dissipative effects, and collisional dynamics of cloud-particle disks. N-body, 'cloud-particle' computational algorithms were developed for the purpose of isolating the role of gaseous self gravity from the roles of other dominant physical mechanisms and dynamical processes, e.g. the collisional dynamics and dissipative processes. The efforts focused largely on galactic disks show that observational constraints provide stringent tests of the numerical simulation techniques developed. Self gravitational effects of the galactic interstellar medium's gas clouds are included by means of Fourier Transform technique.

Roberts, William W., Jr.↗

Relaxation time in disk galaxy simulations.

An initially stationary and stable axisymmetric disk of stars with a mass spectrum of stars is used to determine the collisional relaxation time. The relaxation time as determined from the rate of energy equipartition was found to be 560 rotation periods for stars with 10 times the mean star mass and was 1700 rotation periods for stars with 0.55 times the mean star mass. These times are in general agreement with theoretical predictions for the relaxation time of the two mass groups. The results show that the model used for the large-scale gravitational N-body calculations is indeed 'collisionless.'

Hohl, F.↗

On the generation of a bubbly universe - A quantitative assessment of the CfA slice

A first attempt is made to calculate the properties of the matter distribution in a universe filled with overlapping bubbles produced by multiple explosions. Each spherical shell follows the cosmological Sedov-Taylor solution until it encounters another shell. Thereafter, mergers are allowed to occur in pairs on the basis of N-body results. At the final epoch, the matrix of overlapping shells is populated with 'galaxies' and the properties of slices through the numerically constructed cube compare well with CfA survey results for specified initial conditions. A statistic is found which measures the distance distribution from uniformly distributed points to the nearest galaxies on the projected plane which appears to provide a good measure of the bubbly character of the galaxy distribution. In a quantitative analysis of the CfA 'slice of the universe', a very good match is found between simulation and the real data for final average bubble radii of (13.5 + or - 1.5)/h Mpc with formal filling factor 1.0-1.5 or actual filling factor of 65-80 percent.

Ostriker, J. P.↗

The DECam MAGIC Survey: Uncovering the Tidal Tails of the Crater II Dwarf Galaxy

Crater II (CraII), a large and low-density dwarf spheroidal galaxy, has unusual observed properties that are difficult to reproduce in cold dark matter simulations. Ongoing tidal disruption may help explain the discrepancies, as evidenced by the recent discovery of tidal tails. Here we present metallicity-sensitive narrowband photometry of the Ca II H and K lines from the Dark Energy Camera, covering 128 deg$^{2}$ across the center and identified tidal tails of CraII as part of the Mapping the Ancient Galaxy in CaHK survey. Our combined photometric metallicity, color–magnitude, proper motion, and parallax selections identify 162 CraII candidates. Of these, 37 candidates are located in the tidal tails, which extend at least 7° (∼95 kpc) from the center of CraII, suggesting it has lost ≳25% of its initial stellar mass. We confirm low contamination rates with dedicated control fields and highlight the extremely low surface brightness stellar features that can be uncovered with CaHK data, as faint as ∼36 mag arcsec$^{−2}$. We also make the first detection of a metallicity gradient (−0.34 ± 0.17 dex deg$^{−1}$) in the center of the galaxy and infer a stream width of w ∼ 0.°8, roughly 50% larger than the CraII half-light radius. The detection of candidates in the most distant CraII pointings from its center implies that the tidal tails extend beyond our footprint. We compare the CraII stream to N-body models with “cored” and “cuspy” dark matter halo progenitors, determining that CraII’s density profile is still ambiguous and warrants further modeling.

Atzberger, Kaia R. [Virginia U., Astron. Dept.] (O↗