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At least 145 records · Page 8

A Gigaparsec-scale Hydrodynamic Volume Reconstructed with Deep Learning

The next generation of spectroscopic surveys will map the large-scale structure of the Universe at high redshifts (2 ≤ z ≤ 5) using millions of quasar spectra, enabling major advances in constraining both the standard cosmological model and its extensions. Robust cosmological analyses of these data sets require numerical simulations that both cover gigaparsec volumes and resolve features on ∼10 kpc scales and smaller. However, running such large-volume, high-resolution hydrodynamic simulations is computationally prohibitive. We present a generative deep learning model that enhances a low-resolution, gigaparsec-scale (960 h −1 Mpc) hydrodynamic simulation using a smaller (80 h −1 Mpc) high-resolution input hydrodynamic simulation as training data. The resulting enhanced simulation reproduces the line-of-sight power spectrum to within ∼10% and the three-dimensional power spectrum at the ∼20% level at intermediate to small scales (k ≲ 2 h Mpc −1 ). Our method shows strong promise for producing realistic simulations for cosmological analyses with current surveys such as the Dark Energy Spectroscopic Instrument and upcoming next-generation experiments, but further improvements are needed to accurately recover the large-scale modes. We publicly release the enhanced hydrodynamic simulation, along with a halo catalog from a companion N-body dark matter simulation to support the calibration of data analysis pipelines for these large-scale surveys.

Convolutional neural networks↗

Redshift evolution and covariances for joint lensing and clustering studies with DESI Y1

ABSTRACT Galaxy–galaxy lensing (GGL) and clustering measurements from the Dark Energy Spectroscopic Instrument Year 1 (DESI Y1) data set promise to yield unprecedented combined-probe tests of cosmology and the galaxy–halo connection. In such analyses, it is essential to identify and characterize all relevant statistical and systematic errors. We forecast the covariances of DESI Y1 GGL + clustering measurements and the systematic bias due to redshift evolution in the lens samples. Focusing on the projected clustering and GGL correlations, we compute a Gaussian analytical covariance, using a suite of N-body and lognormal simulations to characterize the effect of the survey footprint. Using the DESI one percent survey data, we measure the evolution of galaxy bias parameters for the DESI luminous red galaxy (LRG) and bright galaxy survey (BGS) samples. We find mild evolution in the LRGs in $0.4 < z < 0.8$, subdominant to the expected statistical errors. For BGS, we find less evolution for brighter absolute magnitude cuts, at the cost of reduced sample size. We find that for a redshift bin width $\Delta z = 0.1$, evolution effects on DESI Y1 GGL is negligible across all scales, all fiducial selection cuts, all fiducial redshift bins. Galaxy clustering is more sensitive to evolution due to the bias squared scaling. Nevertheless the redshift evolution effect is insignificant for clustering above the 1-halo scale of $0.1h^{-1}$ Mpc. For studies that wish to reliably access smaller scales, additional treatment of redshift evolution is likely needed. This study serves as a reference for GGL and clustering studies using the DESI Y1 sample.

79 ASTRONOMY AND ASTROPHYSICS↗

Biasing from galaxy trough and peak profiles with the DES Y3 redMaGiC galaxies and the weak lensing mass map

We measure the correspondence between the distribution of galaxies and matter around troughs and peaks in the projected galaxy density, by comparing redMaGiC galaxies (0.15 < z < 0.65) to weak lensing mass maps from the Dark Energy Survey (DES) Y3 data release. We obtain stacked profiles, as a function of angle θ, of the galaxy density contrast δ g and the weak lensing convergence κ, in the vicinity of these identified troughs and peaks, referred to as ‘void’ and ‘cluster’ superstructures. The ratio of the profiles depend mildly on θ, indicating good consistency between the profile shapes. We model the amplitude of this ratio using a function $F(\boldsymbol{\eta }, \theta )$ that depends on cosmological parameters $\boldsymbol{\eta }$, scaled by the galaxy bias. We construct templates of $F(\boldsymbol{\eta }, \theta )$ using a suite of N-body (‘Gower Street’) simulations forward-modelled with DES Y3-like noise and systematics. We discuss and quantify the caveats of using a linear bias model to create galaxy maps from the simulation dark matter shells. We measure the galaxy bias in three lens tomographic bins (near to far): $2.32^{+0.86}_{-0.27}, 2.18^{+0.86}_{-0.23}, 1.86^{+0.82}_{-0.23}$ for voids, and $2.46^{+0.73}_{-0.27}, 3.55^{+0.96}_{-0.55}, 4.27^{+0.36}_{-1.14}$ for clusters, assuming the best-fit Planck cosmology. Similar values with ∼0.1σ shifts are obtained assuming the mean DES Y3 cosmology. The biases from troughs and peaks are broadly consistent, although a larger bias is derived for peaks, which is also larger than those measured from the DES Y3 3 × 2-point analysis. This method shows an interesting avenue for measuring field-level bias that can be applied to future lensing surveys.

cosmology: observations↗

Beyond the 3rd moment: a practical study of using lensing convergence CDFs for cosmology with DES Y3

ABSTRACT Widefield surveys probe clustered scalar fields – such as galaxy counts, lensing potential, etc. – which are sensitive to different cosmological and astrophysical processes. Constraining such processes depends on the statistics that summarize the field. We explore the cumulative distribution function (CDF) as a summary of the galaxy lensing convergence field. Using a suite of N-body light-cone simulations, we show the CDFs’ constraining power is modestly better than the second and third moments, as CDFs approximately capture information from all moments. We study the practical aspects of applying CDFs to data, using the Dark Energy Survey (DES Y3) data as an example, and compute the impact of different systematics on the CDFs. The contributions from the point spread function and reduced shear approximation are $\lesssim 1~{{\ \rm per\ cent}}$ of the total signal. Source clustering effects and baryon imprints contribute 1–10 per cent. Enforcing scale cuts to limit systematics-driven biases in parameter constraints degrade these constraints a noticeable amount, and this degradation is similar for the CDFs and the moments. We detect correlations between the observed convergence field and the shape noise field at 13σ. The non-Gaussian correlations in the noise field must be modelled accurately to use the CDFs, or other statistics sensitive to all moments, as a rigorous cosmology tool.

79 ASTRONOMY AND ASTROPHYSICS↗

Pursuing Dark Energy with Large Galaxy Redshift Surveys: Baryon Acoustic Oscillations and Beyond (Final Technical Report)

We have developed and applied methods of large-scale structure from galaxy redshift surveys to the study of dark energy. This program supported my group's development of the baryon acoustic method and our participation in the Dark Energy Spectroscopic Instrument (DESI) survey. In addition to my leadership role in the DESI collaboration, my group at Harvard focused on several topics addressing key needs of the DESI science program. 1) We continued our design, validation, and documentation of DESI target selection of the luminous red galaxy and emission-line galaxy samples. 2) We applied simulations from our novel and extremely fast N-body code to make DESI catalogs. With these, we will search for possible systematic shifts in the acoustic scale due to clustering bias with an unprecedented volume of simulations. 3) We extended our method for the fast construction of covariance matrices for correlation functions. 4) We developed new large-scale structure methods, including density-field reconstruction and three-point function analysis.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

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↗

Phase-space Properties and Chemistry of the Sagittarius Stellar Stream Down to the Extremely Metal-poor ([Fe/H] ≲ -3) Regime

In this work, we study the phase-space and chemical properties of the Sagittarius (Sgr) stream, the tidal tails produced by the ongoing destruction of the Sgr dwarf spheroidal (dSph) galaxy, focusing on its very metal-poor (VMP; [Fe/H] < -2) content. We combine spectroscopic and astrometric information from SEGUE and Gaia EDR3, respectively, with data products from a new large-scale run of the StarHorse spectrophotometric code. Our selection criteria yield ~1600 stream members, including >200 VMP stars. We find the leading arm (b > 0°) of the Sgr stream to be more metal-poor, by ~0.2 dex, than the trailing one (b < 0°). With a subsample of turnoff and subgiant stars, we estimate this substructure's stellar population to be ~1 Gyr older than the thick disk's. With the aid of an N-body model of the Sgr system, we verify that simulated particles stripped earlier (>2 Gyr ago) have present-day phase-space properties similar to lower metallicity stream stars. Conversely, those stripped more recently (<2 Gyr) are preferentially akin to metal-rich ([Fe/H] > -1) members of the stream. Such correlation between kinematics and chemistry can be explained by the existence of a dynamically hotter, less centrally concentrated, and more metal-poor population in Sgr dSph prior to its disruption, implying that this galaxy was able to develop a metallicity gradient before its accretion. Finally, we identified several carbon-enhanced metal-poor ([C/Fe] > +0.7 and [Fe/H] ≤ -1.5) stars in the Sgr stream, which might be in tension with current observations of its remaining core where such objects are not found.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

Endothermic self-interacting dark matter in Milky Way-like dark matter haloes

ABSTRACT Self-interacting dark matter (SIDM) offers the potential to mitigate some of the discrepancies between simulated cold dark matter (CDM) and observed galactic properties. We introduce a physically motivated SIDM model to understand the effects of self interactions on the properties of Milky Way and dwarf galaxy sized haloes. This model consists of dark matter with a nearly degenerate excited state, which allows for both elastic and inelastic scattering. In particular, the model includes a significant probability for particles to up-scatter from the ground state to the excited state. We simulate a suite of zoom-in Milky Way-sized N-body haloes with six models with different scattering cross sections to study the effects of up-scattering in SIDM models. We find that the up-scattering reaction greatly increases the central densities of the main halo through the loss of kinetic energy. However, the physical model still results in significant coring due to the presence of elastic scattering and down-scattering. These effects are not as apparent in the subhalo population compared to the main halo, but the number of subhaloes is reduced compared to CDM.

Astronomy & Astrophysics↗

Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements

The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye–Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Impact of bar resonances in the velocity–space distribution of the solar neighbourhood stars in a self-consistent N -body Galactic disc simulation

ABSTRACT The velocity–space distribution of the solar neighbourhood stars shows complex substructures. Most of the previous studies use static potentials to investigate their origins. Instead we use a self-consistent N-body model of the Milky Way, whose potential is asymmetric and evolves with time. In this paper, we quantitatively evaluate the similarities of the velocity–space distributions in the N-body model and that of the solar neighbourhood, using Kullback–Leibler divergence (KLD). The KLD analysis shows the time evolution and spatial variation of the velocity–space distribution. The KLD fluctuates with time, which indicates the velocity–space distribution at a fixed position is not always similar to that of the solar neighbourhood. Some positions show velocity–space distributions with small KLDs (high similarities) more frequently than others. One of them locates at $(R,\phi)=(8.2\,\,\rm{\mathrm{kpc}}, 30^\circ)$, where R and ϕ are the distance from the galactic centre and the angle with respect to the bar’s major axis, respectively. The detection frequency is higher in the inter-arm regions than in the arm regions. In the velocity maps with small KLDs, we identify the velocity–space substructures, which consist of particles trapped in bar resonances. The bar resonances have significant impact on the stellar velocity–space distribution even though the galactic potential is not static.

79 ASTRONOMY AND ASTROPHYSICS↗

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↗

Numerical challenges in modeling gravothermal collapse in Self-Interacting Dark Matter halos

When dark matter has a large cross section for self scattering, halos can undergo a process known as gravothermal core collapse, where the inner core rapidly increases in density and temperature. To date, several methods have been used to implement Self-Interacting Dark Matter (SIDM) in N-body codes, but there has been no systematic study of these different methods or their accuracy in the core-collapse phase. In this paper, we compare three different numerical implementations of SIDM, including the standard methods from the GIZMO and Arepo codes, by simulating idealized dwarf halos undergoing significant dark matter self interactions (σ/m = 50 cm 2 /g). When simulating these halos, we also vary the mass resolution, time-stepping criteria, and gravitational force-softening scheme. The various SIDM methods lead to distinct differences in a halo's evolution during the core-collapse phase, as each results in spurious scattering rate differences and energy gains/losses. The use of adaptive force softening for gravity can lead to numerical heating that artificially accelerates core collapse, while an insufficiently small simulation time step can cause core evolution to stall or completely reverse. Additionally, particle numbers must be large enough to ensure that the simulated halos are not sensitive to noise in the initial conditions. Even for the highest-resolution simulations tested in this study (10 6 particles per halo), we find that variations of order 10% in collapse time are still present. Here, the results of this work underscore the sensitivity of SIDM modeling on the choice of numerical implementation and motivate a careful study of how these results generalize to halos in a cosmological context.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Piecewise interaction picture density matrix quantum Monte Carlo

The density matrix quantum Monte Carlo (DMQMC) set of methods stochastically samples the exact N-body density matrix for interacting electrons at finite temperature. We introduce a simple modification to the interaction picture DMQMC (IP-DMQMC) method that overcomes the limitation of only sampling one inverse temperature point at a time, instead allowing for the sampling of a temperature range within a single calculation, thereby reducing the computational cost. At the target inverse temperature, instead of ending the simulation, we incorporate a change of picture away from the interaction picture. The resulting equations of motion have piecewise functions and use the interaction picture in the first phase of a simulation, followed by the application of the Bloch equation once the target inverse temperature is reached. We find that the performance of this method is similar to or better than the DMQMC and IP-DMQMC algorithms in a variety of molecular test systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Allosterically coupled conformational dynamics in solution prepare the sterol transfer protein StarD4 to release its cargo upon interaction with target membranes

Complex mechanisms regulate the cellular distribution of cholesterol, a critical component of eukaryote membranes involved in regulation of membrane protein functions directly and through the physiochemical properties of membranes. StarD4, a member of the steroidogenic acute regulator-related lipid-transfer (StART) domain (StARD)-containing protein family, is a highly efficient sterol-specific transfer protein involved in cholesterol homeostasis. Its mechanism of cargo loading and release remains unknown despite recent insights into the key role of phosphatidylinositol phosphates in modulating its interactions with target membranes. We have used large-scale atomistic Molecular dynamics (MD) simulations to study how the dynamics of cholesterol bound to the StarD4 protein can affect interaction with target membranes, and cargo delivery. We identify the two major cholesterol (CHL) binding modes in the hydrophobic pocket of StarD4, one near S136&S147 (the Ser-mode), and another closer to the putative release gate located near W171, R92&Y117 (the Trp-mode). We show that conformational changes of StarD4 associated directly with the transition between these binding modes facilitate the opening of the gate. To understand the dynamics of this connection we apply a machine-learning algorithm for the detection of rare events in MD trajectories (RED), which reveals the structural motifs involved in the opening of a front gate and a back corridor in the StarD4 structure occurring together with the spontaneous transition of CHL from the Ser-mode of binding to the Trp-mode. Further analysis of MD trajectory data with the information-theory based NbIT method reveals the allosteric network connecting the CHL binding site to the functionally important structural components of the gate and corridor. Mutations of residues in the allosteric network are shown to affect the performance of the allosteric connection. These findings outline an allosteric mechanism which prepares the CHL-bound StarD4 to release and deliver the cargo when it is bound to the target membrane.

59 BASIC BIOLOGICAL SCIENCES↗

The phase space distance between collider events

How can one fully harness the power of physics encoded in relativistic N-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a Riemannian metric. This natural structure that scaffolds the space on which all collider physics events live opens up new directions for machine learning applications and implementation. Here we present a detailed construction of the phase space manifold and its differential line element, identifying particle ordering prescriptions that ensure that the metric satisfies necessary properties. We apply the phase space metric to several binary classification tasks, including discrimination of high-multiplicity resonance decays or boosted hadronic decays of electroweak bosons from QCD processes, and demonstrate powerful performance on simulated data. Our work demonstrates the many benefits of promoting phase space from merely a background on which calculations take place to being geometrically entwined with a theory’s dynamics.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗