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At least 1,027 records · Page 57

Power and particle exhaust in the ST-E1 fusion power plant

Power exhaust challenges and potential solutions for a 5 m major radius, low-aspect ratio burning tokamak have been explored. 1D edge plasma models have been used to screen for access to detachment using short and long outer divertor legs in double and single null configurations, using Ar as the primary impurity and assuming tungsten plasma-facing components (PFCs). These show that detachment access can be accessed for all but the most conservative assumptions on scrape-off layer (SOL) width and power, but that trade-offs will be required between magnet engineering and the size of the acceptable window of as-yet uncertain plasma parameters. SOLPS-ITER was used to further model selected plasma scenarios, confirming that Ar seeding can be used to achieve dissipative divertor scenarios with peak deposited heat fluxes below 15 MWm -2 . Initial scoping of first wall loads and positioning of limiters has been carried out, showing the feasibility of protecting the breeding blanket wall during steady state without impeding tritium breeding. Initial PFC technology selection is also presented, identifying this as a critical area where further work is needed to find an attractive solution for helium-cooled PFCs that can handle high heat fluxes without excessive power requirements. Key questions and trade-offs for concept development have been identified, including: how to achieve high radiation for reduction of SOL power without core performance degradation; whether power exhaust can be well-controlled in a double null plasma; mechanical design and materials challenges of high-heat flux PFCs; and control of material erosion, redeposition and tritium retention.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A discontinuous Galerkin method for general relativistic hydrodynamics in thornado

Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while still resolving strong shocks. These and other properties make DG methods attractive for solving problems involving hydrodynamics; e.g., the core-collapse supernova problem. With that in mind we are developing a DG solver for the general relativistic, ideal hydrodynamics equations under a 3+1 decomposition of spacetime, assuming a conformally-flat approximation to general relativity. With the aid of limiters we verify the accuracy and robustness of our code with several difficult test-problems: a special relativistic Kelvin-Helmholtz instability problem, a two-dimensional special relativistic Riemann problem, and a one- and two-dimensional general relativistic standing accretion shock (SAS) problem. We find good agreement with published results, where available. We also establish sufficient resolution for the 1D SAS problem and find encouraging results regarding the standing accretion shock instability (SASI) in 2D.

Dunham, Samuel↗

Experimental error mitigation using linear rescaling for variational quantum eigensolving with up to 20 qubits

Quantum computers have the potential to help solve a range of physics and chemistry problems, but noise in quantum hardware currently limits our ability to obtain accurate results from the execution of quantum-simulation algorithms. Various methods have been proposed to mitigate the impact of noise on variational algorithms, including several that model the noise as damping expectation values of observables. In this work, we benchmark various methods, including a new method proposed here. Here, we compare their performance in estimating the ground-state energies of several instances of the 1D mixed-field Ising model using the variational-quantum-eigensolver algorithm with up to 20 qubits on two of IBM's quantum computers. We find that several error-mitigation techniques allow us to recover energies to within 10% of the true values for circuits containing up to about 25 ansatz layers, where each layer consists of CNOT gates between all neighboring qubits and Y-rotations on all qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A random-sampling method as an efficient alternative to variational Monte Carlo for solving Gutzwiller wavefunctions

Abstract We present a random-sampling (RS) method for evaluating expectation values of physical quantities using the variational approach. We demonstrate that the RS method is computationally more efficient than the variational Monte Carlo method using the Gutzwiller wavefunctions applied on single-band Hubbard models as an example. Non-local constraints can also been easily implemented in the current scheme that capture the essential physics in the limit of strong on-site repulsion. In addition, we extend the RS method to study the antiferromagnetic states with multiple variational parameters for 1D and 2D Hubbard models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Dispersive interactions between standard and Dirac materials and the role of dimensionality

The van der Waals (vdW) interaction plays a prominent role between neutral objects at separations where short ranged chemical forces are negligible. This type of dispersive coupling is determined by the interplay between geometry and response properties of the materials making up the objects. Here, we investigate the vdW interaction between 1D, 2D, and 3D standard and Dirac materials within the Random Phase Approximation, which takes into account collective excitations originating from the electronic Coulomb potential. A comprehensive understanding of characteristic functionalities and scaling laws are obtained for systems with parabolic energy dispersion (standard materials) and crossing linear bands (Dirac materials). By comparing the quantum mechanical and thermal limits the onset of thermal fluctuations in the vdW interaction is discussed showing that thermal effects are significantly pronounced at smaller scales in reduced dimensions.

36 MATERIALS SCIENCE↗

2024 roadmap on 2D topological insulators

Abstract 2D topological insulators promise novel approaches towards electronic, spintronic, and quantum device applications. This is owing to unique features of their electronic band structure, in which bulk-boundary correspondences enforces the existence of 1D spin–momentum locked metallic edge states—both helical and chiral—surrounding an electrically insulating bulk. Forty years since the first discoveries of topological phases in condensed matter, the abstract concept of band topology has sprung into realization with several materials now available in which sizable bulk energy gaps—up to a few hundred meV—promise to enable topology for applications even at room-temperature. Further, the possibility of combining 2D TIs in heterostructures with functional materials such as multiferroics, ferromagnets, and superconductors, vastly extends the range of applicability beyond their intrinsic properties. While 2D TIs remain a unique testbed for questions of fundamental condensed matter physics, proposals seek to control the topologically protected bulk or boundary states electrically, or even induce topological phase transitions to engender switching functionality. Induction of superconducting pairing in 2D TIs strives to realize non-Abelian quasiparticles, promising avenues towards fault-tolerant topological quantum computing. This roadmap aims to present a status update of the field, reviewing recent advances and remaining challenges in theoretical understanding, materials synthesis, physical characterization and, ultimately, device perspectives.

Weber, Bent (ORCID:000000018586127X)↗

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Ensemble density functional theory (EDFT) is a generalization of ground-state DFT, which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional 'particle in a box' systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and local spin density approximation exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Overcoming the challenges of accessing topological hallmarks in Sb(112)

Sb is topologically non-trivial and semi-metallic, but differs from many topological semi-metals because of its continuous band gap. By measuring its (112) surface using angle- and spin-resolved photoemission spectroscopy, Sb(112) was shown to have 1D spin-polarised surface states resembling those on vicinal Bi surfaces and many topological insulators and topological semi-metals. The shape and spin-polarisation of the measured features and the calculated bands agreed. However, the measured features had a slightly steeper energy dispersion and different Fermi-momenta than the calculated bands. Both theoretical and experimental methods were necessary when determining the topology of Sb(112). The presence of projected bulk states near the Fermi-level and varying surface localisation of the electronic states meant it was challenging to deduce the topology of Sb(112) from the number of bands crossing the Fermi-level or a continuous contour in the bulk band gap. Ultimately, the calculations and measurements suggest that there are topological surface states on the Sb(112) surface.

36 MATERIALS SCIENCE↗

Finding simplicity: unsupervised discovery of features, patterns, and order parameters via shift-invariant variational autoencoders *

Abstract Recent advances in scanning tunneling and transmission electron microscopies (STM and STEM) have allowed routine generation of large volumes of imaging data containing information on the structure and functionality of materials. The experimental data sets contain signatures of long-range phenomena such as physical order parameter fields, polarization, and strain gradients in STEM, or standing electronic waves and carrier-mediated exchange interactions in STM, all superimposed onto scanning system distortions and gradual changes of contrast due to drift and/or mis-tilt effects. Correspondingly, while the human eye can readily identify certain patterns in the images such as lattice periodicities, repeating structural elements, or microstructures, their automatic extraction and classification are highly non-trivial and universal pathways to accomplish such analyses are absent. We pose that the most distinctive elements of the patterns observed in STM and (S)TEM images are similarity and (almost-) periodicity, behaviors stemming directly from the parsimony of elementary atomic structures, superimposed on the gradual changes reflective of order parameter distributions. However, the discovery of these elements via global Fourier methods is non-trivial due to variability and lack of ideal discrete translation symmetry. To address this problem, we explore the shift-invariant variational autoencoders (shift-VAEs) that allow disentangling characteristic repeating features in the images, their variations, and shifts that inevitably occur when randomly sampling the image space. Shift-VAEs balance the uncertainty in the position of the object of interest with the uncertainty in shape reconstruction. This approach is illustrated for model 1D data, and further extended to synthetic and experimental STM and STEM 2D data. We further introduce an approach for training shift-VAEs that allows finding the latent variables that comport to known physical behavior. In this specific case, the condition is that the latent variable maps should be smooth on the length scale of the atomic lattice (as expected for physical order parameters), but other conditions can be imposed. The opportunities and limitations of the shift VAE analysis for pattern discovery are elucidated.

97 MATHEMATICS AND COMPUTING↗

Enhancing dimensionality prediction in hybrid metal halides via feature engineering and class-imbalance mitigation

We present a machine learning (ML) framework for predicting the structural dimensionality of hybrid metal halides (HMHs), including organic-inorganic perovskites, using a combination of chemically-informed feature engineering and advanced class-imbalance handling techniques. This study is motivated by the small and highly imbalanced nature of experimentally available HMH datasets, which limits the applicability and reliability of conventional ML approaches. The dataset, consisting of 494 HMH structures, is highly imbalanced across dimensionality classes (0D, 1D, 2D, 3D), posing significant challenges to predictive modeling. To mitigate this limitation, the dataset was augmented to 1336 samples using the synthetic minority oversampling technique, enabling improved learning of underrepresented dimensionality classes while preserving chemically meaningful feature relationships. We developed interaction-based descriptors designed to capture coupled steric and polarity effects relevant to dimensionality prediction, which are not readily captured by standard single-parameter or composition-only descriptors. These descriptors are integrated into a multi-stage workflow combining feature selection, ensemble stacking, and performance optimization. Our approach significantly improves F1-scores for underrepresented classes, achieving robust cross-validation performance across all dimensionalities. This work demonstrates a generalizable strategy for extracting reliable and interpretable structure–dimensionality relationships from limited experimental data, enabling pre-synthesis screening of organic cations and providing a practical blueprint for small-data ML in hybrid materials systems.

36 MATERIALS SCIENCE↗

RCSB Protein Data Bank: improved annotation, search and visualization of membrane protein structures archived in the PDB

Abstract Motivation Membrane proteins are encoded by approximately one fifth of human genes but account for more than half of all US FDA approved drug targets. Thanks to new technological advances, the number of membrane proteins archived in the PDB is growing rapidly. However, automatic identification of membrane proteins or inference of membrane location is not a trivial task. Results We present recent improvements to the RCSB Protein Data Bank web portal (RCSB PDB, rcsb.org) that provide a wealth of new membrane protein annotations integrated from four external resources: OPM, PDBTM, MemProtMD and mpstruc. We have substantially enhanced the presentation of data on membrane proteins. The number of membrane proteins with annotations available on rcsb.org was increased by ∼80%. Users can search for these annotations, explore corresponding tree hierarchies, display membrane segments at the 1D amino acid sequence level, and visualize the predicted location of the membrane layer in 3D. Availability and implementation Annotations, search, tree data and visualization are available at our rcsb.org web portal. Membrane visualization is supported by the open-source Mol* viewer (molstar.org and github.com/molstar/molstar). Supplementary information Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗

Molecular-Resolution Electron Imaging of Defects and Dynamics at the Ice-Water Interface

Water crystallization into hexagonal ice (type I h ) is one of the most critical processes relevant to the Earth’s environment and human activities. However, despite recent breakthroughs in imaging non-equilibrium condensed ice structures, the ice-water interface has never been imaged at a molecular resolution. This is primarily due to the low stability of the hydrogen bonds in ice under high-resolution microscopy conditions and a lack of methods to prepare compatible samples. Here, this presentation describes the first molecular-resolution imaging of ice crystallized from liquid water and the ice-water interface using high-resolution transmission electron microscopy (HRTEM). By encapsulating deionized (DI) water between two amorphous carbon (a-C) TEM grids and subsequently freezing it with liquid N 2 on a cryo sample stage, we generated two types of ice: non-equilibrium, condensed ice from the atmosphere and encapsulated ice from the DI water (Fig. 1A). Condensed ice usually shows irregular, spherulitic shapes (Fig. 1B). Selected area electron diffraction (SAED) shows that they are a mixture of cubic and hexagonal crystals (Fig. 1C). On the contrary, encapsulated ice forms thin films that contain large-area single-crystalline regions of hexagonal ice oriented along the [0001] zone axis (Fig. 1D). Differential electron energy-loss spectroscopy (EELS) confirmed the high purity of the encapsulated ice free from organic contaminations that are common in other encapsulation methods for HRTEM such as graphene liquid cells. These single-crystalline areas are robust under the electron beam up to ~100 e/Å 2 s. Aberration-corrected HRTEM imaging in these areas achieved a line resolution of ~1.3 Å (Fig. 1E and F). This platform allows us to study near-equilibrium ice structures and dynamics at an unprecedented spatial resolution (Fig. 2). For example, we discovered subdomain-rich regions near the defective crystal edges despite the structure appearing single-crystalline according to diffraction criteria. These subdomains connect via low-angle grain boundaries with flat energy landscapes as a function of tilt angles (according to simulations), showing the high tolerance of ice to defect structures. When we tuned the sample temperature and electron flux rate, we observed radiolysis-controlled bubble generation and dissolution in ice single crystals near a steady state of bubble dynamics. Furthermore, rich beam-induced melting and recrystallization dynamics were observed at the ice-water interface with lattice resolution. These data represent the first observation of the ice-water phase transformation at the sub-nanometer level. In summary, the methods developed in this work enabled molecular-resolution observations of ice and the ice-water interface and shed light on the microstructures and phase transformation pathways. Finer control on the temperature, electron irradiation profile, and imaging detector could eventually lead to real-time observation of ice nucleation in water and address long-standing questions in the nucleation pathways.

74 ATOMIC AND MOLECULAR PHYSICS↗

A large, deep 3 deg2 survey of H α, [O iii ], and [O ii ] emitters from LAGER: constraining luminosity functions

ABSTRACT We present our measurements of the H α, [O iii], and [O ii] luminosity functions as part of the Lyman Alpha Galaxies at Epoch of Reionization (LAGER) survey using our samples of 1577 z = 0.47 H α-, 3933 z = 0.93 [O iii]-, and 5367 z = 1.59 [O ii]-selected emission line galaxies in a 3 deg2 single, CTIO/Blanco DECam pointing of the COSMOS field. Our observations reach 5σ depths of 8.2 × 10−18 erg s−1 cm−2 and comoving volumes of (1−7) × 105 Mpc3 making our survey one of the deepest narrow-band surveys. We select our emission line galaxies via spectroscopic confirmation, photometric redshifts, and colour–colour selections. We measure the observed luminosity functions for each sample and find best fits of $\phi ^\star = 10^{-3.16^{+0.09}_{-0.09}}$ Mpc−3 and $L^\star = 10^{41.72^{+0.09}_{-0.09}}$ erg s−1 for H α, $\phi ^\star = 10^{-2.16^{+0.10}_{-0.12}}$ Mpc−3 and $L^\star = 10^{41.38^{+0.07}_{-0.06}}$ erg s−1 for [O iii], and $\phi ^\star = 10^{-1.97^{+0.07}_{-0.07}}$ Mpc−3 and $L^\star = 10^{41.66^{+0.03}_{-0.03}}$ erg s−1 for [O ii], with α fixed to −1.75, −1.6, and −1.3, respectively. An excess of bright >1042 erg s−1 [O iii] emitters is observed and may be due to active galactic nucleus (AGN) contamination. Corrections for dust attenuation are applied assuming AHα = 1 mag. We also design our own empirical rest-frame g − r calibration using SDSS DR12 data, test it against our z = 0.47 H α emitters with zCOSMOS 1D spectra, and calibrate it for (g − r) between −0.8 and 1.3 mag. Dust and AGN-corrected star formation rate densities (SFRDs) are measured as log10ρSFR/(M⊙ yr−1 Mpc−3) = −1.63 ± 0.04, −1.07 ± 0.06, and −0.90 ± 0.10 for H α, [O iii], and [O ii], respectively. We find our [O iii] and [O ii] samples fully trace cosmic star formation activity at their respective redshifts in comparison to multiwavelength SFRDs, while the H α sample traces ∼70 per cent of the total z = 0.47 SFRD.

Khostovan, A. A.↗

Using quasar X-ray and UV flux measurements to constrain cosmological model parameters

ABSTRACT Risaliti and Lusso have compiled X-ray and UV flux measurements of 1598 quasars (QSOs) in the redshift range 0.036 ≤ z ≤ 5.1003, part of which, z ∼ 2.4 − 5.1, is largely cosmologically unprobed. In this paper we use these QSO measurements, alone and in conjunction with baryon acoustic oscillation (BAO) and Hubble parameter [H(z)] measurements, to constrain cosmological parameters in six different cosmological models, each with two different Hubble constant priors. In most of these models, given the larger uncertainties, the QSO cosmological parameter constraints are mostly consistent with those from the BAO + H(z) data. A somewhat significant exception is the non-relativistic matter density parameter Ωm0 where QSO data favour Ωm0 ∼ 0.5 − 0.6 in most models. As a result, in joint analyses of QSO data with H(z) + BAO data the 1D Ωm0 distributions shift slightly towards larger values. A joint analysis of the QSO + BAO + H(z) data is consistent with the current standard model, spatially-flat ΛCDM, but mildly favours closed spatial hypersurfaces and dynamical dark energy. Since the higher Ωm0 values favoured by QSO data appear to be associated with the z ∼ 2 − 5 part of these data, and conflict somewhat with strong indications for Ωm0 ∼ 0.3 from most z < 2.5 data as well as from the cosmic microwave background anisotropy data at z ∼ 1100, in most models, the larger QSO data Ωm0 is possibly more indicative of an issue with the z ∼ 2 − 5 QSO data than of an inadequacy of the standard flat ΛCDM model.

79 ASTRONOMY AND ASTROPHYSICS↗

Two-dimensional simulations of internal gravity waves in the radiation zones of intermediate-mass stars

Intermediate-mass main-sequence stars have large radiative envelopes overlying convective cores. This configuration allows internal gravity waves (IGWs) generated at the convective–radiative interface to propagate towards the stellar surface. The signatures of these waves can be observed in the photometric and spectroscopic data from stars. Here, we have studied the propagation of these IGWs using two-dimensional (2D) fully non-linear hydrodynamical simulations with realistic stellar reference states from the 1D stellar evolution code, Modules for Stellar Astrophysics (MESA). When a single wave is forced, we observe wave self-interaction. When two waves are forced, we observe non-linear interaction (i.e. triadic interaction) between these waves forming waves at different wavelengths and frequencies. When a spectrum of waves similar to that found in numerical simulations is forced, we find that the surface IGW frequency slope is consistent with recent observations. This power law is similar to that predicted by linear theory for the wave propagation, with small deviations that can be an effect of non-linearities. When the same generation spectrum is applied to 3 M ⊙ models at different stellar rotation and ages, the surface IGW spectrum slope is very similar to the generation spectrum slope.

79 ASTRONOMY AND ASTROPHYSICS↗

Core-collapse supernova neutrino emission and detection informed by state-of-the-art three-dimensional numerical models

ABSTRACT Based on our recent three-dimensional core-collapse supernova (CCSN) simulations including both exploding and non-exploding models, we study the detailed neutrino signals in representative terrestrial neutrino observatories, namely Super-Kamiokande (Hyper-Kamiokande), DUNE, JUNO, and IceCube. We find that the physical origin of difference in the neutrino signals between 1D and 3D is mainly proto-neutron-star convection. We study the temporal and angular variations of the neutrino signals and discuss the detectability of the time variations driven by the spiral standing accretion shock instability (spiral SASI) when it emerges for non-exploding models. In addition, we determine that there can be a large angular asymmetry in the event rate (${\gtrsim} 50 {{\ \rm per\ cent}}$), but the time-integrated signal has a relatively modest asymmetry (${\lesssim} 20 {{\ \rm per\ cent}}$). Both features are associated with the lepton-number emission self-sustained asymmetry and the spiral SASI. Moreover, our analysis suggests that there is an interesting correlation between the total neutrino energy (TONE) and the cumulative number of neutrino events in each detector, a correlation that can facilitate data analyses of real observations. We demonstrate the retrieval of neutrino energy spectra for all flavours of neutrino by applying a novel spectrum reconstruction technique to the data from multiple detectors. We find that this new method is capable of estimating the TONE within the error of ∼20 per cent if the distance to the CCSN is ≲6 kpc.

79 ASTRONOMY AND ASTROPHYSICS↗

Evidence for sub-Chandrasekhar Type Ia supernovae from the last major merger

ABSTRACT We investigate the contribution of sub-Chandrasekhar mass Type Ia supernovae to the chemical enrichment of the Gaia Sausage galaxy, the progenitor of a significant merger event in the early life of the Milky Way. Using a combination of data from Nissen & Schuster, the GALactic Archaeology with HERMES (GALAH) Data Release 3 [with 1D non-local thermal equilibrium (NLTE) abundance corrections], and the Apache Point Observatory Galactic Evolution Experiment (APOGEE) Data Release 16, we fit analytic chemical evolution models to a nine-dimensional chemical abundance space (Fe, Mg, Si, Ca, Cr, Mn, Ni, Cu, and Zn) in particular focusing on the iron-peak elements, Mn and Ni. We find that low [Mn/Fe] $\sim -0.15\, \mathrm{dex}$ and low [Ni/Fe] $\sim -0.3\, \mathrm{dex}$ Type Ia yields are required to explain the observed trends beyond the [α/Fe] knee of the Gaia Sausage (approximately at [Fe/H] $=-1.4\, \mathrm{dex}$). Comparison to theoretical yield calculations indicates a significant contribution from sub-Chandrasekhar mass Type Ia supernovae in this system (from ${\sim} 60\, \mathrm{per\, cent}$ to $100\, \mathrm{per\, cent}$ depending on the theoretical model with an additional ${\pm} 10\, \mathrm{per\, cent}$ systematic from NLTE corrections). We compare to results from other Local Group environments including dwarf spheroidal galaxies, the Magellanic Clouds, and the Milky Way’s bulge, finding the Type Ia [Mn/Fe] yield must be metallicity dependent. Our results suggest that sub-Chandrasekhar mass channels are a significant, perhaps even dominant, contribution to Type Ia supernovae in metal-poor systems, whilst more metal-rich systems could be explained by metallicity-dependent sub-Chandrasekhar mass yields, possibly with additional progenitor mass variation related to star formation history, or an increased contribution from Chandrasekhar mass channels at higher metallicity.

Sanders, Jason L.↗

Rotation curves and scaling relations of extremely massive spiral galaxies

We study the kinematics and scaling relations of a sample of 43 giant spiral galaxies that have stellar masses exceeding $10^{11} \, {\rm M}_\odot$ and optical discs up to 80 kpc in radius. We use a hybrid 3D–1D approach to fit 3D kinematic models to long-slit observations of the H α-$\rm{[N\, \small {II}]}$ emission lines and we obtain robust rotation curves of these massive systems. We find that all galaxies in our sample seem to reach a flat part of the rotation curve within the outermost optical radius. We use the derived kinematics to study the high-mass end of the two most important scaling relations for spiral galaxies: the stellar/baryonic mass Tully–Fisher relation and the Fall (mass-angular momentum) relation. All galaxies in our sample, with the possible exception of the two fastest rotators, lie comfortably on both these scaling relations determined at lower masses, without any evident break or bend at the high-mass regime. When we combine our high-mass sample with low-mass data from the Spitzer Photometry & Accurate Rotation Curves catalogue, we find a slope of α = 4.25 ± 0.19 for the stellar Tully–Fisher relation and a slope of γ = 0.64 ± 0.11 for the Fall relation. Our results indicate that most, if not all, of these rare, giant spiral galaxies are scaled up versions of less massive discs and that spiral galaxies are a self-similar population of objects up to the very high-mass end.

79 ASTRONOMY AND ASTROPHYSICS↗