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At least 19 records

Thermodynamic Modeling of Aqueous LiCl, LiBr, LiI, and LiNO 3 Solutions

Thermodynamic models are essential to facilitate the advancement of process design, optimization, and operation of electrolyte systems. In this work, a comprehensive thermodynamic framework based on the Electrolyte Nonrandom Two-Liquid model is developed to calculate phase equilibria behavior and salt solubility of aqueous LiCl, LiBr, LiI, and LiNO 3 solutions. The model describes the non-ideality of the electrolyte solutions by using two binary interaction parameters for each electrolyte-molecule pair in the system. Each binary interaction parameter is further expressed with up to three temperature coefficients which are regressed from experimental data. To take into account the hydration of lithium ion, two separate chemistries for the dissociation of lithium salts are investigated. In the first case, the lithium ion is considered as a bare ion, Li + , while in the second case hydration of the lithium ion from Li + to Li(H 2 O) + is considered. Here, the calculated thermodynamic properties compare adequately with the experimental data for both sets of chemistries for concentrations up to saturation and temperatures from 273.15 K up to 623.15 K. Moderate to significant improvements are observed with the incorporation of the hydration chemistry for aqueous LiCl, LiBr, and LiI solutions when compared to the non-hydrated lithium ion model results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamic modeling of calcium carbonate scale precipitation: aqueous Na + -Ca 2+ -Cl – -HCO 3 – -CO 3 2– -CO 2 system

To allow for accurate calculations of calcium carbonate scaling in highly saline produced waters, we present a comprehensive thermodynamic model based on the electrolyte nonrandom two-liquid (eNRTL) activity coefficient equation for the aqueous Na ⁺ -Ca ²⁺ -Cl – -HCO 3 – -CO 3 ²– -CO 2 system. The eNRTL binary interaction parameters for the H 2 O:(Na ⁺ -CO 3 2– ) pair, the H 2 O:(Na ⁺ -HCO 3 – ) pair, the (Na⁺-Cl–):(Na ⁺ -CO 3 2– ) pair, and the (Na ⁺ -Cl – ):(Na ⁺ -HCO 3 – ) pair are identified in this work via the regression of thermodynamic, calorimetric, and phase equilibria experimental data. The binary interaction parameters associated with the H 2 O:(Na ⁺ -Cl – ) pair, the CO 2 :(Na ⁺ -Cl – ) pair, the H 2 O:(Ca ²⁺ -Cl – ) pair, and the (Na ⁺ -Cl – ):(Ca ²⁺ -Cl – ) pair are retrieved from the literature. The remaining binary interaction parameters are retrieved from Aspen Plus or set to zero. In addition, the solubility product constants are identified for Na 2 CO 3 ·10H 2 O (s) , Na 2 CO 3 · 7H 2 O (s) , Na 2 CO 3 ·H 2 O (s) , Na 2 CO 3 ·NaHCO 3 2H 2 O (s) , Na 2 CO 3 ·3NaHCO 3 (s) , and CaCO 3(s) via regression of solubility data. Here, the model is capable of accurately calculating all phase equilibria and calorimetric properties at temperatures up to 473.15 K and salt concentrations up to saturation.

42 ENGINEERING↗

Extended thermodynamic model for high salinity produced waters

To support the development of desalination processes for high salinity produced waters, we developed a comprehensive thermodynamic model that reliably predicts the thermodynamic properties and phase behavior of produced water. Here this study extends a previously developed thermodynamic model for the aqueous hexary oceanic salt system by incorporating the Sr 2+ and Ba 2+ ions. Based on the electrolyte nonrandom two-liquid theory, the model requires two adjustable binary interaction parameters for each water-electrolyte and electrolyte-electrolyte pair that has a common ion. The binary interaction parameters for the electrolyte-electrolyte pairs involving Sr 2+ and Ba 2+ ions were identified using thermodynamic and salt solubility data. The model was validated for temperatures from 273.15 K to 473.15 K and electrolyte concentrations from infinite dilution to salt saturation. Extension of the model to include HCO 3 − , CO 3 2− , and CO 2 is currently in progress.

42 ENGINEERING↗

Empirical estimation of densities in NaCl-KCl-UCl 3 and NaCl-KCl-YCl 3 molten salts using Redlich-Kister expansion

Densities of molten KCl-NaCl-UCl 3 and KCl-NaCl-YCl 3 ternary systems have been estimated using a multidimensional Redlich-Kister model. Temperature and composition dependent Redlich-Kister functions have been used to generate binary interaction parameters in the outlined ternary salt systems. These binary interactions have been used in the extrapolation to ternary system densities. The results of the density extrapolations by Muggianu interpolation scheme provide agreement within 2–3% for the NaCl-KCl-YCl 3 liquids and 11% in NaCl-KCl-UCl 3 liquids compared to the available experimental data. Modeling NaCl-KCl-UCl 3 molten phase density with a ternary interaction parameter improved the agreement within 4%. Thermophysical modeling used in this study has shown promising results for use in other material properties, such as viscosity, thermal conductivity, and heat capacity of the molten salts. Lastly, the outlined modeling method applied in these specific molten salt ternaries can be used for quaternary or higher multicomponent molten salt systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Nonrandom two‐liquid activity coefficient model with association theory

Abstract Considered one of the most versatile and widely used classical thermodynamic models to correlate phase equilibria behavior of nonideal systems, the nonrandom two‐liquid (NRTL) theory does not explicitly account for specific chemical associations such as hydrogen bonding. This deficiency has been recognized as the cause for unsatisfactory representation of association systems like methanol–alkanes binaries. This work presents a practical approach to integrate Wertheim's perturbation theory for association contribution with the classical NRTL model. Specifically, the association contribution is calculated from pre‐determined molecule‐specific association strengths while the physical interaction contribution is captured with NRTL binary interaction parameters. The resulting association NRTL model correlates fluid phase equilibria of association systems with few adjustable parameters and offers improved predictive capability for higher order systems.

Hao, Yifan↗

Speed of Sound Measurements of Binary Mixtures of Hydrofluorocarbons [Pentafluoroethane (R-125), 1,1-Difluoroethane (R-152a), or 1,1,1,2,3,3,3-Heptafluoropropane (R-227ea)] with Hydrofluoroolefins [2,3,3,3-Tetrafluoropropene (R-1234yf) or trans-1,3,3,3-Tetrafluoropropene (R-1234ze(E))]

In this article, speed of sound data measured using a dual-path pulse-echo instrument are reported for three binary refrigerant mixtures, R-125/1234yf, R-1234yf/152a, and R-1234ze(E)/227ea, at compositions of (0.33/0.67) and (0.67/0.33) mole fraction. The speed of sound was studied at temperatures ranging from 230 K to 345 K from pressures slightly above the bubble point curve up to 20 MPa for the mixtures containing R-1234yf and 49 MPa for the R-1234ze(E)/227ea mixtures. The relative combined expanded speed of sound uncertainty ranged from 0.039 % to 0.317 % with a mean uncertainty over all state points of less than 0.10 %. The reported data are compared to the most recent mixture models in REFPROP for each blend studied. Comparisons of available mixture models for the R-125/1234yf and R-1234yf/152a blends exhibit average absolute deviation values ranging from 0.10 % to 0.27 %, and the average absolute deviations for R-1234ze(E)/227ea blends range from 0.62 % to 0.94 %. The comparisons show that only minor adjustments are required to the R-125/1234yf and R-1234yf/152a mixture models to represent the speed of sound data within its uncertainty. However, significant adjustments are needed to improve the current mixture models for the R-1234ze(E)/227ea blend. Deficiencies with the R-1234ze(E)/227ea mixture model are not unexpected since it (1) utilizes a pure-fluid EOS R-1234ze(E) that has been shown to inaccurately represent R-1234ze(E) speed of sound values and (2) uses binary interaction parameters for the chemically similar mixture of R-1234yf/227ea.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Speed of Sound Measurements of R-1130(E) and an Azeotropic Blend of R-1336mzz(Z)/1130(E)

Sound speed data measured using a dual-path pulse-echo instrument are reported for pure trans-1,2-dichloroethene (R-1130(E)) and an azeotropic blend of cis-1,1,1,4,4,4-hexafluorobutene (R-1336mzz(Z)) and R-1130(E) with a composition of 74.8 mass % R-1336mzz(Z) with the balance being R-1130(E). The azeotropic blend of R-1336mzz(Z)/1130(E) is classified as R-514A in ANSI/ASHRAE standard 34. Liquid phase speed of sound data are reported from just above the saturation pressure of pure R-1130(E) or the bubble point pressure of R-514A to a maximum pressure of 26.7 MPa. The relative combined expanded uncertainty in the speed of sound varies from 0.032 % to 0.148 % with the greatest deviations occurring at the lowest sound speeds. At present, no reference Helmholtz-energy-explicit equation of state (EOS) is available for R-1130(E). Therefore, the reported data for pure R-1130(E) are compared to an extended corresponding states (ECS) model. Deviations between the pure R-1130(E) sound speed data and the ECS model were found to be consistently negative ranging between − 4.1 % and − 3.5 %. The R-514A data are compared to a multifluid model inclusive of the established reference Helmholtz-energy-explicit EOS for R-1336mzz(Z) and ECS model for R-1130(E) with estimated binary interaction parameters. Deviations between the experimental speed of sound data and the multifluid model were also found to be consistently negative. However, deviations from the multifluid model were found to be as great as − 17.1 %. The large deviations from the ECS model and multifluid model underscore the need for a robust Helmholtz-energy-explicit EOS for R-1130(E).

42 ENGINEERING↗

Influence of Equation-of-States on Supercritical CO2 Combustion Mixtures

Abstract Fossil fuel based direct-fired supercritical CO2 (sCO2) cycles are gaining the attention of industry, academia, and government due to their remarkable efficiency and carbon capture at high-source temperatures. Modeling plays an important role in the development of sCO2 combustors because experiments are very expensive at the designed operating conditions of these direct-fired cycles. Inaccurate density estimates are detrimental to the simulation output. Hence, this work focuses on comprehensive evaluation of the influence and applicability of various equation-of-states (EOS) which are being used in the supercritical combustion modeling literature. A state-of-the-art supercritical combustion modeling methodology is used to simulate counter-flow supercritical CO2 flames by using various equation-of-states. The results show that using the corresponding state principle to evaluate compressibility factor is not accurate. Also, van der Waal type EOSs predictions can be as accurate as complex Benedict–Webb–Rubin EOSs; hence van der Waal EOSs are more suitable to simulate sCO2 combustor simulations. Non-ideal effects are significant under the operating conditions considered in this work. The choice of EOS significantly influences the flame structure and heat release rate. Also, assuming the binary interaction parameter as zero is reasonable in sCO2 combustion simulations.

Energy & Fuels↗

Application of the Redlich-Kister expansion for estimating the density of molten fluoride psuedo-ternary salt systems of nuclear industry interest

The development of next-generation molten salt reactors relies on accurate knowledge of the thermophysical properties of the candidate coolant and fueled molten salts. These thermophysical properties include density, viscosity, thermal conductivity, and heat capacity. Because of difficulties in measuring thermophysical properties of molten salts, there are many gaps in the current state of thermophysical property knowledge of these salts, particularly those that contain actinides or beryllium. Therefore, leveraging modeling techniques to estimate unknown molten salt thermophysical properties and guide future experimental measurements has high value for the nuclear industry. Here, the densities of molten fluoride pseudo-ternary salt systems, which are of interest to the nuclear industry, were estimated using Redlich-Kister expansion and Muggianu interpolation techniques. The pseudo-ternary systems considered for estimation in this study were NaF-LiF-ZrF 4 , LiF-BeF 2 -ZrF 4 , LiF-BeF 2 -ThF 4 , NaF-LiF-BeF 2 , NaF-KF-BeF 2 , NaF-ZrF 4 -UF 4 , and NaF-BeF 2 -UF 4 . This Redlich-Kister estimation approach accounts for nonideal mixing behavior based on pseudo-binary subsystem interaction parameters determined from experimentally measured pseudo-binary system density data sets. The Redlich-Kister estimation was compared with the method of additive molar volumes, which assumes ideal mixing. Additionally, the Redlich-Kister approach was used to determine previously unknown binary and ternary interaction parameters based on experimentally measured density data sets for select pseudo-ternary salt systems. The results of this study show improvement in density estimation using the Redlich-Kister approach for all systems considered compared with estimation by additive molar volumes. Furthermore, this analysis allowed for the estimation of nonideal density behavior in experimentally unstudied ZrF 4 -UF 4 and BeF 2 -UF 4 , as well as the quantification of ternary interaction in NaF-LiF-ZrF 4 , NaF-BeF 2 -UF 4 , and NaF-ZrF 4 -UF 4 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamic analysis of hydrogel swelling in aqueous sodium chloride solutions

Here, a comprehensive thermodynamic model is presented for swelling and salt partitioning of poly (n-isopropyl acrylamide) hydrogels in aqueous sodium chloride (NaCl) solutions at 298 K. Together with a Helmholtz energy expression for network elastic energy, a modified electrolyte Nonradom Two-Liquid activity coefficient model is used to represent both the long-range electrostatic interactions and the short-range van der Waals interactions present in the gel phase. The model parameters include one network parameter per hydrogel system plus two binary parameters per interaction pair in the polymer–solvent-salt systems. With semiquantitave agreement with experimental data for both hydrogel swelling and salt partitioning up to salt saturation, the analysis suggests the ion hydration between NaCl and water is the root cause for hydrogel deswelling in aqueous NaCl solution at high NaCl concentrations, i.e., NaCl weight fraction >0.03. On the other hand, the strong repulsive interaction between NaCl and hydrogel polymer is the dominant factor for salt partitioning.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A modified electrolyte non-random two-liquid model with analytical expression for excess enthalpy: Application to the MEA-H 2 O-CO 2 system

We report accurate thermodynamic properties of electrolyte systems are critical for the design and operation of many chemical processes. A comprehensive description of the thermodynamic framework for multi-electrolyte mixed solvent systems is presented, where the parameter structure of the symmetric electrolyte-Non-Random Two Liquid (e-NRTL) model is reformulated and a thermodynamically consistent and analytically derived formulation for the excess enthalpy is developed from the e-NRTL model. The refined parameter structure of the e-NRTL model avoids numerical singularities of the analytical formulation for the excess enthalpy in the absence of ionic species and extends the derived excess enthalpy formulation to non-electrolyte systems. The thermodynamic framework is demonstrated for the MEA-H 2 O-CO 2 case study using experimental data on thermodynamic quantities for the binary MEA-H 2 O system and the ternary MEA-H 2 O-CO 2 system. The model is implemented in Pyomo and will be available for release in the Institute for the Design of Advanced Energy Systems (IDAES) computational platform.

Monoethanolamine↗

Igniting Weak Interactions in Neutron Star Postmerger Accretion Disks

The merger of two neutron stars or a neutron star and a black hole typically results in the formation of a postmerger accretion disk. Outflows from disks may dominate the overall ejecta from mergers and be a major source of r-process nuclei in our universe. We explore the parameter space of such disks and their outflows and r-process yields by performing 3D general-relativistic magnetohydrodynamic simulations with weak interactions and approximate neutrino transport. We discuss the mapping between the initial binary parameters and the parameter space of the resulting disks, chiefly characterized by their initial accretion rate. We demonstrate the existence of an ignition threshold for weak interactions at around ~10 -3 M⊙ s -1 for typical parameters by means of analytic calculations and numerical simulations. We find a degenerate, self-regulated, neutrino-cooled regime above the threshold and an advection-dominated regime below the threshold. Excess heating in the absence of neutrino cooling below the threshold leads to ≳60% of the initial disk mass being ejected in outflows, with typical velocities of ~(0.1–0.2)c, compared to ≲40% at ~(0.1–0.15)c above the threshold. While disks below the threshold show suppressed production of light r-process elements, disks above the threshold can produce the entire range of r-process elements, in good agreement with the observed solar system abundances. Disks below the ignition threshold may produce an overabundance of actinides seen in actinide-boost stars. As gravitational-wave detectors start to sample the neutron star merger parameter space, different disk realizations may be observable via their associated kilonova emission.

79 ASTRONOMY AND ASTROPHYSICS↗

Phase coexistence implications of violating Newton’s third law

Newton’s third law, action = reaction, is a foundational statement of classical mechanics. However, in natural and living systems, this law appears to be routinely violated for constituents interacting in a nonequilibrium environment. Here, we use computer simulations to explore the macroscopic phase behavior implications of breaking microscopic interaction reciprocity for a simple model system. We consider a binary mixture of attractive particles and introduce a parameter that is a continuous measure of the degree to which interaction reciprocity is broken. In the reciprocal limit, the species are indistinguishable, and the system phase separates into domains with distinct densities and identical compositions. Furthermore, increasing nonreciprocity is found to drive the system to explore a rich assortment of phases, including phases with strong composition asymmetries and three-phase coexistence. Many of the states induced by these forces, including traveling crystals and liquids, have no equilibrium analogs. By mapping the complete phase diagram for this model system and characterizing these unique phases, our findings offer a concrete path forward toward understanding how nonreciprocity shapes the structures found in living systems and how this might be leveraged in the design of synthetic materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulations of Interacting Binary Systems—Pathways to Radio-bright Gamma-Ray Burst Progenitors

Although the association of gamma-ray bursts (GRBs) with massive stellar death is on firm footing, the nature of the progenitor system and the key ingredients required for a massive star to produce a GRB remain open questions. Here, we investigate the evolution of a 15–25M ⊙ massive star with a 10–15M ⊙ black hole (BH) using Modules for Experiments in Stellar Astrophysics. We quantify companion-influenced angular-momentum evolution over a stellar lifetime for orbital periods where tides are significant, varying stellar and BH masses, initial stellar spin, and accretion and dynamo prescriptions while tracking mass loss and angular momentum. The final spin is set by tidal torques versus stellar winds. For binaries that initially avoid Roche-lobe overflow, tides can spin up the star, but a late-stage expansion can drive tidal stripping; associated mass and angular-momentum loss can suppress spin-up. We find that massive-star BH binaries at comparable mass ratios may be potential GRB progenitors for short orbital periods (∼20–5 × 10 2 days) and long orbital periods (∼2 × 10 3 –4 × 10 3 days), where our suite of lifetime simulations reveals a favored parameter space with negligible mass loss and enough spin angular momentum to power a GRB jet. For initially nonrotating stars, this provides a lower limit on the final spin above a threshold estimate consistent with forming a postcollapse BH mass of 5–10M ⊙ with a spin parameter ≥ 0.5. For initially rapidly rotating stars, tidal interactions may sustain high spin when mass loss is negligible because the binary is not tidally synchronized.

Hernandez, Angel [Univ. of Colorado, Boulder, CO (↗

Toward Accelerated Nuclear-physics Parameter Estimation from Binary Neutron Star Mergers: Emulators for the Tolman–Oppenheimer–Volkoff Equations

Abstract Gravitational-wave observations of binary neutron-star (BNS) mergers have the potential to revolutionize our understanding of the nuclear equation of state (EOS) and the fundamental interactions that determine its properties. However, Bayesian parameter estimation frameworks do not typically sample over microscopic nuclear-physics parameters that determine the EOS. One of the major hurdles in doing so is the computational cost involved in solving the neutron-star structure equations, known as the Tolman–Oppenheimer–Volkoff (TOV) equations. In this paper, we explore approaches to emulating solutions for the TOV equations: multilayer perceptrons (MLPs), Gaussian processes, and a data-driven variant of the reduced basis method (RBM). We implement these emulators for three different parameterizations of the nuclear EOS, each with a different degree of complexity represented by the number of model parameters. We find that our MLP-based emulators are generally more accurate than the other two algorithms, whereas the RBM results in the largest speedup with respect to the full high-fidelity TOV solver. We employ these emulators for a simple parameter inference using a potentially loud BNS observation and show that the posteriors predicted by our emulators are in excellent agreement with those obtained from the full TOV solver.

79 ASTRONOMY AND ASTROPHYSICS↗

Topological approach to electron correlations at fractional quantum Hall effect

Highlights: • Braids in 2D electron systems in magnetic field acquire a cyclotron metrics. • Commensurability of 2D braids with Wigner crystal of electrons leads to FQHE. • Homotopy invariants define the hierarchy of FQHE universal in all 2D Hall systems. • Composite fermions illustrate multiloop braids in the simplest homotopy case. • Correlations in FQHE reveal long-range quantum entanglement of all electrons. The classification of homotopy invariants in interacting multi-electron 2D systems at quantizing magnetic fields is presented, explaining the topologically protected correlations occurring at integer and fractional quantum Hall effects. The long-range quantum entanglement is essential for homotopy correlated phases in contrast to the binary entanglement for conventional phases with local order parameters. The classification of homotopy long-range correlated phases induced by the Coulomb interaction of electrons has been derived in terms of homotopy invariants, which are universal and robust against local disorder and single-particle crystal field, as illustrated by experimental observations in various materials with different microscopic structure, like GaAs 2DES, graphene monolayer and bilayer and in Chern topological insulators. The homotopy phases are demonstrated to be topologically protected and immune to single-particle perturbations, temperature chaos and variation of the electron interaction strength. The nonzero repulsive interaction between electrons is shown, however, to be essential for the definition of the homotopy invariants, which disappear in gaseous systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Fate of supernova progenitors in massive binary systems

ABSTRACT How massive stars end their lives depends on the core mass, core angular momentum, and hydrogen envelopes at death. However, these key physical facets of stellar evolution can be severely affected by binary interactions. In turn, the effectiveness of binary interactions itself varies greatly depending on the initial conditions of the binaries, making the situation much more complex. We investigate systematically how binary interactions influence core–collapse progenitors and their fates. Binary evolution simulations are performed to survey the parameter space of supernova progenitors in solar metallicity binary systems and to delineate major evolutionary paths. We first study fixed binary mass ratios ($q=M_2/M_1$ = 0.5, 0.7, and 0.9) to elucidate the impacts of initial mass and initial separation on the outcomes, treating separately Type Ibc supernova, Type II supernova, accretion-induced collapse (AIC), rapidly rotating supernova (Ibc-R), black hole formation, and long gamma ray burst (long GRB). We then conduct 12 binary population synthesis model calculations, varying the initial condition distributions and binary evolution parameters, to estimate various supernova fractions. We obtain a Milky Way supernova rate $R_{\rm SN} = (1.78$–$2.47) \times 10^{-2} \, {\rm yr}^{-1}$ which is consistent with observations. We find the rates of AIC, Ibc-R, and long GRB to be $\sim 1/100$ the rate of regular supernovae. Our estimated long GRB rates are higher than the observed long GRB rate and close to the low luminosity GRB rate, although care must be taken considering our models are computed with solar metallicity. Furthering binary modelling and improving the inputs one by one will enable more detailed studies of these and other transients associated with massive stars.

Astronomy & Astrophysics↗

From Feast to Famine: A Systematic Study of Accretion onto Oblique Pulsars with 3D GRMHD Simulations

Disk-fed accretion onto neutron stars can power a wide range of astrophysical sources ranging from X-ray binaries, to accretion-powered millisecond pulsars, ultraluminous X-ray sources, and gamma-ray bursts. A crucial parameter controlling the gas–magnetosphere interaction is the strength of the stellar dipole. In addition, coherent X-ray pulsations in many neutron star systems indicate that the star's dipole moment is oblique relative to its rotation axis. Therefore, it is critical to systematically explore the 2D parameter space of the star's magnetic field strength and obliquity, which is what this work does, for the first time, in the framework of 3D general-relativistic magnetohydrodynamics. If the accretion disk carries its own vertical magnetic field, this introduces an additional factor: the relative polarity of the disk and stellar magnetic fields. We find that depending on the strength of the stellar dipole and the star–disk relative polarity, the neutron star's jet power can either increase or decrease with increasing obliquity. For weak dipole strength (equivalently, high accretion rate), the parallel polarity results in a positive correlation between jet power and obliquity, whereas the antiparallel orientation displays the opposite trend. For stronger dipoles, the relative-polarity effect disappears, and jet power always decreases with increasing obliquity. The influence of the relative polarity gradually disappears as obliquity increases. Highly oblique pulsars tend to have an increased magnetospheric radius, a lower mass accretion rate, and enter the propeller regime at lower magnetic moments than aligned stars.

79 ASTRONOMY AND ASTROPHYSICS↗