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DEPRECATED AI-Batt-OS (Autonomous Identification of Battery Life Models - Open Source) [SWR 21-17]

DEPRECATED. This repository was archived by the owner on Jun 30, 2026. It is now read-only. Open source implementation of some of the methods utilized by AI-Batt, a battery lifetime modeling and analysis toolkit provided by the National Laboratory of the Rockies (NLR). This software demonstrates the use of bi-level optimization and symbolic regression techniques to semi-autonomously identify algebraic models predicting the capacity fade of lithium-ion batteries during calendar aging. Modeling the degradation of batteries is a complex task, due to the difficulty in separating the time-dependent and time-independent factors impacting cell level degradation, across multiple data series with different numbers of measurements and/or data quality. Bi-level optimization enables model parameters to be optimized to either the entire data set or to individual data series, allowing statistical disambiguation of global behaviors (data series independent) and local behaviors (data series dependent). Symbolic regression is used to automatically search for optimal low-dimesional models predicting the variation of locally optimized parameters versus time-independent experimental variables from millions of possible models, resulting in a more accurate and repeatable model identification process than is possible by a manual search. The provided tools also implement cross-validation and bootstrap resampling schemes, empowering statistical model comparison/selection and quantification of model uncertainties. An example script replicates the results from the manuscript "Challenging Practices of Algebraic Battery Life Models through Statistical Validation and Model Identification via Machine-Learning", submitted to ECS. All code is written in MATLAB. Requires the Statistics and Machine Learning Toolbox. Contact Dr. Paul Gasper at Paul.Gasper@nlr.gov for any questions.

Gasper, Paul [National Renewable Energy Lab. (NREL

Decorated Honeycomb Lattice and Successive Magnetic Transitions of the Delafossite Derivative K 4 Ni 5 Te 3 O 16

Here, we report the synthesis and characterization of the delafossite derivative K 4 Ni 5 Te 3 O 16 , which hosts a decorated honeycomb Ni 2+ lattice. Single-crystal X-ray diffraction, electron microscopy, and neutron diffraction establish a noncentrosymmetric Pmm2 crystal structure that combines regular honeycomb units with elongated motifs formed by Ni 2+ trimers along extended edges. Magnetic susceptibility reveals strong antiferromagnetic interactions, while heat capacity measurements identify two successive magnetic transitions at 30 and 12 K. Neutron diffraction shows that these transitions correspond to a progression from partial to full long-range magnetic order on distinct Ni sites, reflecting competition among the various exchange interactions. The resulting magnetic point group, mm2.1′, inherits the lattice polarity and permits high-order magnetoelectric coupling. Consistent with this symmetry, a quadratic magnetic-field-induced polarization is experimentally observed below the magnetic ordering temperature, likely arising from exchange-driven magnetostriction coupled to the polar lattice. These results establish K 4 Ni 5 Te 3 O 16 as an interesting platform for engineering B-site ordering in delafossite derivatives to realize complex quantum magnetism and functional responses.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Dense nuclear matter equation of state from heavy-ion collisions

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. Furthermore, this white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Proteome-wide analysis of protein stability in Escherichia coli under acid stress

Knowledge of protein acid sensitivity remains sparse and is largely derived from low-throughput, enzyme-specific assays. We used a scalable framework to map acid stability across the Escherichia coli proteome to assess the acid stability of 1,675 unique proteins, estimating pH 50 values for over 90% of them. The parameter pH50 was defined as the pH value at which only 50% of the initial protein remains in solution following acid treatment. Proteome-wide pH 50 values ranged from 2.28 to 6.33 (median 5.11). Approximately 9% of detected proteins remained stable across all tested pH conditions. Our results align with published data and the assay of citrate synthase (GltA) performed here. Protein acid stability differed significantly by subcellular localization: periplasmic proteins were relatively more abundant in the acid-stable group, cytoplasmic proteins were abundant at pH 50 values 4.5–5.5, and inner membrane proteins at higher pH 50 between 5.5 and 6.0. Outer membrane proteins were too few to draw strong conclusions regarding enrichment within specific pH 50 groups. Notably, the periplasmic binding protein of the molybdate ABC transporter (ModA), was enriched after incubation at low pH. Estimated pH 50 values showed no correlation with protein isoelectric point and molecular weight. Together, this work provides the first proteome-wide map of protein acid stability and establishes a general framework for studying different chemical stressors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Cosmological probes of Dark Radiation from Neutrino Mixing

Abstract Models of stepped dark radiation have recently been found to have an important impact on the anisotropies of the cosmic microwave background, aiding in easing the Hubble tension. In this work, we study models with a sector of dark radiation with a step in its abundance, which thermalizes after big bang nucleosynthesis by mixing with the standard model neutrinos. For this, we extend an earlier work which has focused on the background evolution only until the dark sector thermalizes by deriving the full background and perturbation equations of the model and implementing them in an Einstein-Boltzmann solving code. We expound on the behavior of this model, discussing the wide range of parameters that result in interesting and viable cosmologies that dynamically generate dark radiation during a range of epochs. We find that for the strongly self-coupled regime, there is no large cosmological impact for a tight prior on the mass, whereas larger mass ranges allow a smooth interpolation between a behavior close to the ΛCDM cosmological standard model and close to an additional component of strongly self-interacting dark radiation. In the weakly self-coupled regime we find that we can accommodate a parameter space relevant for the neutrino anomalies as well as one relevant to easing the Hubble tension.

Astronomy & Astrophysics

Impact of Advances in Anion Exchange Membranes and Ionomers on Alkaline Fuel Cells

Abstract The operation of low‐temperature electrochemical energy conversion systems (fuel cells, electrolyzers) at high pH values is of perennial interest due to the possibility of moving away from expensive platinum group metal catalysts and reducing cost. Historically, the anion exchange membranes (AEMs) and ionomers have been hampered by performance (ionic conductivity, mechanical strength) and chemical stability issues. In this context, select developments over the past decade in alternate AEM chemistries, water management methods, and production of membrane electrode assemblies (MEAs) that have enabled a significant leap in performance of alkaline fuel cells are examined. These developments are linked to performance improvements in alkaline H 2 /O 2 fuel cells and also consider developments in alkaline fuel cells using nitrogen‐containing fuels (ammonia, hydrazine), carbon‐containing fuels (alcohols, glycols), and boron‐containing fuels (sodium borohydride, ammonia borane). Finally, current challenges and bottlenecks are identified, and potential solutions are proposed.

Chemistry

Hamiltonian switching control of noisy bipartite qubit systems

Abstract We develop a Hamiltonian switching ansatz for bipartite control that is inspired by the quantum approximate optimization algorithm, to mitigate environmental noise on qubits. We demonstrate the control for a central spin coupled to bath spins via isotropic Heisenberg interactions, and then make physical applications to the protection of quantum gates performed on superconducting transmon qubits coupling to environmental two-level-systems (TLSs) through dipole-dipole interactions, as well as on such qubits coupled to both TLSs and a Lindblad bath. The control field is classical and acts only on the system qubits. We use reinforcement learning with policy gradient to optimize the Hamiltonian switching control protocols, using a fidelity objective for specific target quantum gates. We use this approach to demonstrate effective suppression of both coherent and dissipative noise, with numerical studies achieving target gate implementations with fidelities over 0.9999 (four nines) in the majority of our test cases and showing improvement beyond this to values of 0.999 999 999 (nine nines) upon a subsequent optimization by GRadient Ascent Pulse Engineering (GRAPE). We analyze how the control depth, total evolution time, number of environmental TLS, and choice of optimization method affect the fidelity achieved by the optimal protocols and reveal some critical behaviors of bipartite control of quantum gates.

Physics

Commercial and Industrial Energy Procurement in Nigeria: A Consumer's Guidebook

Across Africa, countries have incorporated a variety of new energy sources into their energy mix to account for increasing demand. In Nigeria, electricity consumption per capita has grown nearly 50% in the past 20 years. To address rising demand for energy in Nigeria, the country has passed several recent policies and regulations aimed at increasing energy generation across the country, improving the country's transmission infrastructure, and ensuring that electricity reliably reaches end users, including commercial and industrial (C&I) customers. This guidebook is designed for C&I customers in Nigeria to use in the consideration of procuring such onsite, captive energy systems to supplement their energy needs. Each section of this guidebook touches on a step of the procurement process and details the relevant stakeholders, processes, and data needed to make decisions during that step.

14 SOLAR ENERGY

A Sensitivity-driven Wide Area Protection (SWAP) Coordination Tool for High Penetration of Inverter-based Resources (IBR)

Traditionally, power system generation sources have been composed of synchronous generators, of which the fault current behavior is understood with minimal differences between generation size and types due to the physics of their construction. Present protection schemes and modeling methods are based upon these understood characteristics. Most renewable generation is composed of inverter-based resources (IBR), in which fault current is determined by switching control software and hardware limitations, each of which can vary between manufacturers and even between models of the same manufacturer. The resulting fault current is low in magnitude, low in negative-sequence current, unpredictable phase angles, and is a challenge to model. These characteristics also result in a challenge to traditional protection schemes and fault simulation software. To address several of these concerns, the project has the following goals: 1. Improve IBR models: Improve IBR models used in short circuit (SC) programs to accurately capture the response of IBRs at the bulk power system (BPS) level for fault and protection studies. 2. Develop automation tool: Develop an automation tool that allows engineers to identify protection coordination and sensitivity issues by performing SC and protection coordination studies in a high IBR-penetrated grid by applying variations to the IBR models, faults, contingencies, etc. 3. Develop schemes: Develop new protection mitigation solution schemes that complement the existing protection systems to ensure safe operation of the BPS with higher IBR penetration levels. The project team did not achieve this final goal, as the Department of Energy (DOE) stopped the project early due to changes in DOE funding priorities. The termination notice came at the beginning of the final project phase, while the team was identifying and beginning to investigate protection issues. It should be noted that the team discussed a 100% penetration scenario. However, this scenario would require the use of grid-forming IBR models that are not presently available. Since developing these models requires additional effort, the 100% penetration scenario was not pursued during this project. In the future, developing the methodology and models for the 100% scenario could benefit the industry.

14 SOLAR ENERGY

Resolving root causes of experiment discrepancies guided by machine learning

Abstract Scientists rely on accurate experimental data to explain nature and then harness this knowledge for applications addressing human needs. However, discrepancies between experiments of the same observable can impede scientific progress if one does not understand the underlying causes. Here, we developed a process that unravels data discrepancies by first using Bayesian machine learning to relate discrepancies to few of many, potentially biasing metadata features that encode experiment procedures. This machine learning output guides human experts to study discrepancy causes by simulating suspicious aspects of historical experiments or designing modern ones to address open questions. The study findings then lead to rejecting or correcting historical data on firm scientific bases. This process is demonstrated for the energy spectrum of neutrons emitted promptly (<1 ns) after fission of 252 Cf, a trusted nuclear physics Standard. It reduces the spread in experimental 252 Cf spectra by up to a factor of 6.

Neudecker, D. (ORCID:0000000339200627)

EXERGETIC: De-Risking Next-Generation Resilient Geothermal Hybrids via At-Scale Evaluation Using Virtual Emulation Digital Twin Environment for Efficient Operation

The DOE-GTO-funded project, award number 5.1.2.12, entitled "EXERGETIC - De-risking Next Generation Resilient Geothermal Hybrids via at-Scale Evaluation Using a Virtual Emulation Digital Twin Environment for Efficient Operation," advances the solution to these challenges by developing and validating a geothermal co-emulation environment implemented at the National Laboratory of the Rockies (NLR)'s Advanced Research on Integrated Energy Systems (ARIES) platform. This framework enables the de-risking of next-generation geothermal and geothermal hybrid systems through high-fidelity modeling, real-time digital emulation, advanced control strategies, and techno-economic assessment. The project focused on geothermal hybrid configurations that integrate geothermal power plants with concentrated solar power and underground thermal energy storage, enabling enhanced efficiency, flexibility, and grid support capabilities. The main goal of this project was the development of a geothermal digital co-emulation environment to demonstrate the technical and economic value of geothermal hybrid systems and their contribution to grid stability and flexibility. The EXERGETIC framework combined physics-based models, controls, and real assets at ARIES, including digital real-time simulators (DRTS), a 20-MW-scale controllable grid interface (CGI), and a 2-MW conventional generator. Detailed transient models were developed for the key subsystems of a hybrid geothermal plant, including parabolic trough solar collectors, reservoir thermal energy storage (RTES), and a binary Organic Rankine Cycle (ORC) power plant. The ORC model explicitly captured thermal inertia and off-design operation and integrated control strategies to dynamically respond to electric load profiles. The models were validated against published experimental and numerical studies, demonstrating strong agreement and confirming the accuracy and robustness of the modeling approach. The resulting digital twin represents geothermal-solar-storage systems at multiple scales (1 MW to 100 MW) and enables realistic emulation of grid-connected operation. The control architecture allows the geothermal resource to provide stable baseload generation, while solar and stored thermal energy supply flexible, dispatchable support during periods of high demand or variable grid conditions. A key contribution of the EXERGETIC project is the demonstration that geothermal hybrid systems can be designed to be active grid assets rather than passive baseload generators. Using the ARIES platform, the digital twin was evaluated under multiple grid scenarios, including load following, voltage support at the distribution level, and frequency response at the transmission level. Results show that hybrid geothermal systems can respond effectively to dynamic grid conditions, providing inertia-like behavior, primary frequency support, and voltage regulation through coordinated control. In addition to the performance and grid services capability analysis of geothermal and hybrid geothermal systems, the EXERGETIC project also focused on scalability and techno-economic analysis of geothermal hybrid plants. In particular, for the scalability analysis, machine-learning (ML)-based surrogate models were trained using data generated from the geothermal digital twin under different grid-connected scenarios and plant capacities. These ML models demonstrated strong interpolation and extrapolation capabilities across plant sizes, accurately reproducing both steady-state and transient responses with very low errors. Regarding the techno-economic analysis, plant performance results were integrated with cost models for hybrid geothermal systems, and the levelized cost of electricity (LCOE) was used as the main economic metric to evaluate system performance across a range of system capacities, solar shares, solar multiples, and storage durations. Results indicate that economies of scale significantly reduce geothermal LCOE as plant capacity increases, with large-scale systems (25-100 MW) achieving substantially lower costs than small plants. Hybridization with solar thermal energy and storage further improves economic performance by increasing capacity utilization and enabling flexible dispatch. In addition, thermal storage plays a critical role in reducing LCOE by maximizing geothermal, solar, and stored energy resources. In summary, the results from this project demonstrate that geothermal hybrid systems represent a promising alternative for increasing the energy conversion efficiency of geothermal technologies, contributing to the preservation of geothermal resources, and supporting the transition of geothermal plants from traditional baseload resources into flexible, resilient, and cost-competitive energy conversion technologies.

15 GEOTHERMAL ENERGY

A molecular conveyor belt-associated protein controls the rotational direction of the bacterial type 9 secretion system

ABSTRACT Many bacteria utilize the type 9 secretion system (T9SS) for gliding motility, surface colonization, and pathogenesis. This dual-function motor supports both gliding motility and protein secretion, where rotation of the T9SS plays a central role. Fueled by the energy of the stored proton motive force and transmitted through the torque of membrane-anchored stator units, the rotary T9SS propels an adhesin-coated conveyor belt along the bacterial outer membrane like a molecular snowmobile, thereby enabling gliding motion. However, the mechanisms controlling the rotational direction and gliding motility of T9SS remain elusive. Shedding light on this mechanism, we find that in the gliding bacteriumFlavobacterium johnsoniae, deletion of the C-terminus of the conveyor belt-associated protein GldJ controls and, in fact, reverses the rotational direction of T9SS from counterclockwise (CCW) to clockwise (CW). This suggests that the interface between the conveyor belt-associated protein GldJ and the T9SS ring protein GldK plays an important role in controlling the directionality of T9SS, potentially by modulating its interaction with the stator complex GldLM, which drives motor rotation. Combined with MD simulation of the T9SS stator units GldLM, we suggest a “tri-component gearset” model where GldJ controls the rotational direction of its driver, the T9SS, thus providing adaptive sensory feedback to influence the motility of the gliding bacterium. IMPORTANCE The type 9 secretion system (T9SS) is fundamental to bacterial gliding motility, pathogenesis, and surface colonization. Our findings reveal that the C-terminal region of the conveyor belt-associated protein GldJ functions as a molecular switch which is capable of reversing the rotational direction of T9SS. Through the coordinated actions of the T9SS stator units (akin to a driving motor), the GldK ring (the gear that converts rotational energy into linear movement), and GldJ, this machinery forms a smart conveyor belt system reminiscent of flexible or cognitive mechanical conveyors. Such advanced conveyors can alter their direction to adapt to shifting demands. Here, we show that the bacterial T9SS similarly adjusts its rotational bias based on feedback from the conveyor belt-associated protein GldJ. This dual-role feedback mechanism underscores an evolved, controllable biological snowmobile, offering new avenues for studying how bacteria fine-tune motility in dynamic environments.

Microbiology

O Corona, where art thou? eROSITA’s view of UV-optical-IR variability-selected massive black holes in low-mass galaxies

Finding massive black holes (MBHs,M BH ≈ 10 4 –10 7 M ⊙ ) in the nuclei of low-mass galaxies $\left( {{M_*}\mathop {\mathop < \limits_ }\limits_ {{10}^{10}}{M_ \odot }} \right)$ is crucial to constrain seeding and growth of black holes over cosmic time, but it is particularly challenging due to their low accretion luminosities. Variability selection via long-term photometric ultraviolet, optical, or infrared (UVOIR) light curves has proved effective and identifies lower-Eddington ratios compared to broad and narrow optical spectral lines searches. In the inefficient accretion regime, X-ray and radio searches are effective, but they have been limited to small samples. Therefore, differences between selection techniques have remained uncertain. Here, we present the first large systematic investigation of the X-ray properties of a sample of known MBH candidates in dwarf galaxies. We extracted X-ray photometry and spectra of a sample of ~200 UVOIR variability-selected MBHs and significantly detected 17 of them in the deepest available SRG/eROSITA image, of which four are newly discovered X-ray sources and two are new secure MBHs. This implies that tens to hundreds of LSST MBHs will have SRG/eROSITA counterparts, depending on the seeding model adopted. Surprisingly, the stacked X-ray images of the many non-detected MBHs are incompatible with standard disk-corona relations, typical of active galactic nuclei, inferred from both the optical and radio fluxes. They are instead compatible with the X-ray emission predicted for normal galaxies. After careful consideration of potential biases, we identified that this X-ray weakness needs a physical origin. A possibility is that a canonical X-ray corona might be lacking in the majority of this population of UVOIR-variability selected low-mass galaxies or that unusual accretion modes and spectral energy distributions are in place for MBHs in dwarf galaxies. This result reveals the potential for severe biases in occupation fractions derived from data from only one waveband combined with SEDs and scaling relations of more massive black holes and galaxies.

Astronomy & Astrophysics

Surface science insight note: Optimizing XPS instrument performance for quantification of spectra

X-ray photoelectron spectroscopy (XPS) provides quantitative information from photoemission peaks and shapes observed within the background due to the inelastic scattering of photoelectrons. To quantify the signal, both photoemission peaks and background in spectra must be adjusted for instrumental transmission variations that are a consequence of changes in efficiency when recording electrons with different kinetic energy. While it is generally assumed that correcting spectroscopic data for transmission is a necessary part of quantification by XPS, there are consequences for the quantification of spectra measured using an instrument for which transmission has significant curvature. In this Insight, the implications of curvature in transmission characteristics are discussed and a method based on XPS microscopy is proposed that ensures the transmission response of an instrument is free from significant curvature. An example of an instrument for which a flat transmission response is presented is achieved through collecting spectra using lens modes designed to measure stigmatic images.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH

Kondo effect in ferromagnetic quantum critical CeRh 6 ⁢Ge 4

The mechanism of a pressure-induced quantum critical point in the heavy fermion ferromagnet CeRh 6 ⁢Ge 4 has attracted interest, as ferromagnetic quantum criticality in a clean itinerant Ce compound is typically avoided. The localized versus itinerant character of the 4⁢𝑓 electrons is a key aspect for understanding this behavior. We investigated the electronic structure of the 4⁢𝑓 shell in CeRh 6 ⁢Ge 4 using core-level photoelectron and x-ray absorption spectroscopy, demonstrating the hybridization of Ce 4⁢𝑓 with the conduction electrons. Linearly polarized x-ray absorption reveals a temperature-dependent linear dichroism consistent with the crystal-electric-field sequence as inferred from the static susceptibility. This dichroism cannot be described by an ionic full-multiplet model alone, but is reproduced by including the Kondo effect within a single-impurity Anderson model in the noncrossing approximation. The Kondo effect mixes higher-lying crystal-field states into a resulting multiorbital ground state with 4⁢𝑓 occupancy, 𝑛 𝑓 ∼ 0.9. Deviations at low temperatures between the measured linear dichroism and calculated dichroism suggest an orbital-dependent Kondo effect. A scenario in which there is a multiorbital ground state and orbital-dependent Kondo hybridization should be a starting point for a model of pressure-induced criticality in CeRh 6 ⁢Ge 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND

Grain boundary segregation and chemical ordering in CoCrFeMnNi multi-principal element alloy

Owing to their far-from-dilute compositions, multi-principal element alloys (MPEAs) can exhibit unique combinations of engineering properties. As nearly all MPEAs are polycrystalline aggregates, it is necessary to understand the interactions of various elemental species with grain boundaries (GBs). This is of particular importance in extreme environments, such as radiation and elevated temperatures, where such interactions have implications on the properties of MPEAs. Herein, we employ atomistic simulations to generate a series of [001] asymmetric tilt GBs in a model CoCrFeMnNi MPEA and quantify solute interactions and segregation to these boundaries. We employ the Warren-Cowley order parameters to investigate the interplay between GB segregation and chemical short-range order (SRO). At temperatures above 800 K, simulation results reveal the segregation of Cr and Mn to CoCrFeMnNi GBs and show weak dependence of boundary solute excess on GB geometry, at least for the boundaries explored in this work. At temperatures in the range of 673–800 K, formation of domains rich in Cr is observed at GBs in agreement with experimental observations. Quantitative analysis shows that solute excess of various alloying elements decreases rapidly with the increase in temperature in the range of 1000–1200 K. Furthermore, we show that GB regions exhibit SRO characteristics that are distinct from the bulk crystals, leading to spatial variations in SRO. In broad terms, our study highlights the need to account for GB interactions with alloying elements when designing advanced MPEAs with novel chemistries.

Wang, Yitao [Lehigh University, Bethlehem, PA (Uni

The occurrence rate of galaxies with polar structures may be significantly underestimated

Polar-ring galaxies are photometrically and kinematically decoupled systems that are highly inclined to the major axis of the host. These galaxies have been explored since the 1970s, but the rarity of these systems has made such systematic studies difficult. However, over 250 good candidates have been identified. In this work, we examine a sample of over 18 000 galaxies from the Sloan Digital Sky Survey (SDSS) Stripe 82 for the presence of galaxies with polar structures. Using deep SDSS Stripe 82, DESI Legacy Imaging Surveys, and Hyper Suprime-Cam Subaru Strategic Program, we selected 53 good candidate galaxies with photometrically decoupled polar rings, 9 galaxies with polar halos, 6 galaxies with polar bulges, and 34 possibly forming polar-ring galaxies, versus 13 polar-ring candidates previously selected in Stripe 82. Our results suggest that the occurrence rate of galaxies with polar structures may be significantly underestimated, as revealed by the deep observations, and may amount to 1–3% of non-dwarf galaxies.

Astronomy & Astrophysics