Partial Redistribution Research Articles

BSC: Belief Shift Clustering

It is still a challenging problem to characterize uncertainty and imprecision between specific (singleton) clusters with arbitrary shapes and sizes. In order to solve such a problem, we propose a belief shift clustering (BSC) method for dealing with object data. The BSC method is considered as the evidential version of mean shift or mode seeking under the theory of belief functions. First, a new notion, called belief shift, is provided to preliminarily assign each query object as the noise, precise, or imprecise one. Second, a new evidential clustering rule is designed to partial credal redistribution for each imprecise object. To avoid the “uniform effect” and useless calculations, a specific dynamic framework with simulated cluster centers is established to reassign each imprecise object to a singleton cluster or related meta-cluster. Once an object is assigned to a meta-cluster, this object may be in the overlapping or intermediate areas of different singleton clusters. Consequently, the BSC can reasonably characterize the uncertainty and imprecision between singleton clusters. The effectiveness has been verified on several artificial, natural, and image segmentation/classification datasets by comparison with other related methods.

Scalable matrix-free solver for 3D transfer of polarized radiation in stellar atmospheres

We present an efficient and massively parallel solution strategy for the transfer problem of polarized radiation, for a 3D stationary medium out of local thermodynamic equilibrium. Scattering processes are included accounting for partial frequency redistribution effects. Such a setting is one of the most challenging ones in radiative transfer modeling. The problem is formulated for a two-level atomic model, which allows linearization. The discrete ordinate method alongside an exponential integrator are used for discretization. Efficient solution is obtained with a Krylov method equipped with a tailored physics-based preconditioner. A matrix-free approach results in a lightweight implementation, suited for tackling large problems. Near-optimal strong and weak scalability are obtained with two complementary decompositions of the computational domain. The presented approach made it possible to perform simulations for the Ca i line at 4227Å with more than 109 degrees of freedom in less than half an hour on massively parallel machines, always converging in a few iterations for the proposed tests.

Interfacial electronic coupling in Mn3O4/C@FeOOH nano-octahedrals regulates intermediate adsorption for highly efficient oxygen evolution reaction

Exploiting high-efficient low-cost metal-based electrocatalysts for oxygen evolution reaction (OER) in alkaline media is still urgent and challenging. Herein, a hierarchical nanostructure of manganese oxide/carbon@iron oxyhydroxide (denoted as Mn3O4/C@FeOOH) nano-octahedrons via a three-step approach. The optimal electrocatalyst Mn3O4/C@FeOOH was achieved and delivered a low overpotential of 295 mV at 10 mA cm−2, a small Tafel slope of 47.6 mV dec−1 and a decent stability toward long-term electrolysis of 16 h with only 2.2% degradation. The excellent OER performance of the hybrid Mn3O4/C@FeOOH could be attributed to the synergistic effects of the individual counterparts, namely, the structural support of the amorphous carbon skeleton to maintain the integrity of microstructures, the enhanced conductivity imparted by the uniformly dispersed Mn3O4 and graphite nanoparticles, and the partial electron redistribution between the Mn3O4/C and FeOOH interface, optimizing the adsorption/desorption of intermediate oxygenated species. This work provides a novel strategy to prepare an efficient and stable electrocatalyst for OER in alkaline media.

The Circular Polarization of the Mn 1 Resonance Lines around 280 nm for Exploring Chromospheric Magnetism

We study the circular polarization of the Mn i resonance lines at 279.56, 279.91, and 280.19 nm (hereafter, UV multiplet) by means of radiative transfer modeling. In 2019, the CLASP2 mission obtained unprecedented spectropolarimetric data in a region of the solar ultraviolet including the Mg ii h and k resonance lines and two lines of a subordinate triplet, as well as two Mn i resonance lines. The first analysis of such data, in particular those corresponding to a plage region, allowed the inference of the longitudinal magnetic field from the photosphere to the upper chromosphere just below the transition region. This was achieved by applying the weak field approximation to the circular polarization profiles of the Mg ii and Mn i lines. While the applicability of this approximation to the Mg ii lines was already demonstrated in previous works, this is not the case for the Mn i UV multiplet. These lines are observed as absorptions between the Mg ii h and k lines, a region whose intensity is shaped by their partial frequency redistribution effects. Moreover, the only Mn i stable isotope has nuclear spin I = 5/2 and thus hyperfine structure must be, a priori, taken into account. Here we study the generation and transfer of the intensity and circular polarization of the Mn i resonance lines accounting for these physical ingredients. We analyze their sensitivity to the magnetic field by means of their response function, and we demonstrate the applicability of the weak field approximation to determine the longitudinal component of the magnetic field.

The polarization signals of the solar K I D lines and their magnetic sensitivity

Aims. This work aims to identify the relevant physical processes in shaping the intensity and polarization patterns of the solar K I D lines through spectral syntheses, placing particular emphasis on the D2 line. Methods. The theoretical Stokes profiles were obtained by numerically solving the radiative transfer problem for polarized radiation considering one-dimensional semi-empirical models of the solar atmosphere. The calculations account for scattering polarization, partial frequency redistribution (PRD) effects, hyperfine structure (HFS), J- and F-state interference, multiple isotopes, and magnetic fields of arbitrary strength and orientation. Results. The intensity and circular polarization profiles of both D lines can be suitably modeled while neglecting both J-state interference and HFS. The magnetograph formula can be applied to both lines, without including HFS, to estimate weak longitudinal magnetic fields in the lower chromosphere. By contrast, modeling the scattering polarization signal of the D lines requires the inclusion of HFS. The amplitude of the D2 scattering polarization signal is strongly depolarized by HFS, but it remains measurable. A small yet appreciable error is incurred in the scattering polarization profile if PRD effects are not taken into account. Collisions during scattering processes have a clear depolarizing effect, although a quantitative analysis is left for a forthcoming publication. Finally, the D2 scattering polarization signal is particularly sensitive to magnetic fields with strengths around 10 G and it strongly depends on their orientation. Despite this, its center-to-limb variation relative to the amplitude at the limb is largely insensitive to the field strength and orientation. Conclusions. These findings highlight the value of the K I D2 line polarization for diagnostics of the solar magnetism, and show that the linear and circular polarization signals of this line are primarily sensitive to magnetic fields in the lower chromosphere and upper photosphere, respectively.

Effects of Spectral Resolution on Simple Magnetic Field Diagnostics of the Mg ii H and K Lines

We study the effects of finite spectral resolution on the magnetic field values retrieved through the weak-field approximation (WFA) from the cores of the Mg ii h and k lines. The retrieval of the line-of-sight component of the magnetic field, B LOS, from synthetic spectra generated in a uniformly magnetized FAL-C atmosphere is accurate when restricted to the inner lobes of Stokes V. As we degrade the spectral resolution, partial redistribution effects, which more prominently affect the outer lobes of Stokes V, are brought into the line core through spectral smearing, degrading the accuracy of the WFA and resulting in an inference bias, which is more pronounced as the resolution becomes poorer. When applied to a diverse set of spectra emerging from a sunspot simulation, we find good accuracy in the retrieved B LOS when comparing it to the model value at the height where the optical depth in the line core is unity. The accuracy is preserved up to field strengths of B ∼ 1500 G. Limited spectral resolution results in a small bias toward weaker retrieved fields. The WFA for the transverse component of the magnetic field is also evaluated. Reduced spectral resolution degrades the accuracy of the inferences, because spectral mixing results in the line effectively probing deeper layers of the atmosphere.

Radiative losses in the chromosphere during a C-class flare

Context. Solar flares release an enormous amount of energy (∼1032 erg) into the corona. A substantial fraction of this energy is transported to the lower atmosphere, which results in chromospheric heating. The mechanisms that transport energy to the lower solar atmosphere during a flare are still not fully understood. Aims. We aim to estimate the temporal evolution of the radiative losses in the chromosphere at the footpoints of a C-class flare, in order to set observational constraints on the electron beam parameters of a RADYN flare simulation. Methods. We estimated the radiative losses from hydrogen, and singly ionized Ca and Mg using semiempirical model atmospheres, which were inferred from a multiline inversion of observed Stokes profiles obtained with the CRISP and CHROMIS instruments on the Swedish 1-m Solar Telescope. The radiative losses were computed taking into account the effect of partial redistribution and non-local thermodynamic equilibrium. To estimate the integrated radiative losses in the chromosphere, the net cooling rates were integrated between the temperature minimum and the height where the temperature reaches 10 kK. We also compared our time series of radiative losses with those from the RADYN flare simulations. Results. We obtained a high spatial-resolution map of integrated radiative losses around the flare peak time. The stratification of the net cooling rate suggests that the Ca IR triplet lines are responsible for most of the radiative losses in the flaring atmosphere. During the flare peak time, the contribution from Ca II H and K and Mg II h and k lines are strong and comparable to the Ca IR triplet (∼32 kW m−2). Since our flare is a relatively weak event, the chromosphere is not heated above 11 kK, which in turn yields a subdued Lyα contribution (∼7 kW m−2) in the selected limits of the chromosphere. The temporal evolution of total integrated radiative losses exhibits sharply rising losses (0.4 kW m−2 s−1) and a relatively slow decay (0.23 kW m−2 s−1). The maximum value of total radiative losses is reached around the flare peak time, and can go up to 175 kW m−2 for a single pixel located at footpoint. After a small parameter study, we find the best model-data consistency in terms of the amplitude of radiative losses and the overall atmospheric structure with a RADYN flare simulation in the injected energy flux of 5 × 1010 erg s−1 cm−2.

Contaminant release, mixing and microbial fluctuations initiated by infiltrating water within a replica field-scale legacy radioactive waste trench

Numerous legacy near-surface radioactive waste sites dating from the mid 20th century have yet to be remediated and present a global contamination concern. Typically, there is insufficient understanding of contaminant release and redistribution, with invasive investigations often impractical due to the risk of disturbing the often significantly radiotoxic contaminants. Consequently, a replica waste trench (~5.4 m3), constructed adjacent to a legacy radioactive waste site (Little Forest Legacy Site, LFLS), was used to assist our understanding of the release and mixing processes of neodymium (Nd) — a chemical analogue for plutonium(III) and americium(III), two significant radionuclides in many contaminated environments. In order to clarify the behaviour of contaminants released from buried objects such as waste containers, a steel drum, representative of the hundreds of buried drums within the LFLS, was placed within the trench. Dissolved neodymium nitrate was introduced as a point-source contaminant to the base of the trench, outside the steel drum. Hydrologic conditions were manipulated to simulate natural rainfall intensities with dissolved lithium bromide added as a tracer. Neodymium was primarily retained both at its point of release at the bottom of the trench (>97 %) as well as at a steel container corrosion point, simulated through the emplacement of steel wool. However, over the 8-month field experiment, advective mixing initiated by surface water intrusions rapidly redistributed a small proportion of Nd to shallower waters (~1.5–1.7 %), as well as throughout the buried steel drum. Suspended particulate forms of Nd (>0.2 μm) were measured at all depths in the suboxic trench and were persistent across the entire study. Analyses of the microbial communities showed that their relative abundances and metabolic functions were strongly influenced by the prevailing geochemical conditions as a result of fluctuating water depths associated with rainfall events. The site representing steel corrosion exhibited divergent biogeochemical results with anomalous changes (sharp decrease) observed in both dissolved contaminant concentration as well as microbial diversity and functionality. This research demonstrates that experimental trenches provide a safe and unique method for simulating the behaviour of subsurface radioactive contaminants with results demonstrating the initial retention, partial shallow water redistribution, and stability of particulate form(s) of this radioactive analogue. These results have relevance for appropriate management and remediation strategies for the adjacent legacy site as well as for similar sites across the globe.

Combined Analysis of Hydrogen and Oxygen 102.6 nm Emission at Mars

AbstractWater is lost from the Mars upper atmosphere to space as hydrogen and oxygen, both of which can be observed in scattered ultraviolet sunlight at 102.6 nm. We present Emirates Mars Mission Emirates Mars Ultraviolet Spectrometer (EMM/EMUS) insertion orbit observations of this airglow, resolving the independent altitude contributions of H and O for the first time. We present the first airglow modeling of the complete H and O 102.6 nm system and the first 3D azimuthally symmetric modeling of the O emission, retrieving temperatures and densities typical of northern spring. Our model reproduces the emission well above 200 km, but does not incorporate partial frequency redistribution needed to reproduce the observed O brightness at lower altitudes and on the disk. These results support future EMM/EMUS science orbit retrievals of H loss and the use of 102.6 nm observations to constrain planetary atmospheres across the solar system.

The transfer of polarized radiation in resonance lines with partial frequency redistribution, J-state interference, and arbitrary magnetic fields

Aims. We present the theoretical framework and numerical methods we have implemented to solve the problem of the generation and transfer of polarized radiation in spectral lines without assuming local thermodynamical equilibrium, while accounting for scattering polarization, partial frequency redistribution (due to both the Doppler effect and elastic collisions), J-state interference, and hyperfine structure. The resulting radiative transfer code allows one to model the impact of magnetic fields of an arbitrary strength and orientation through the Hanle, incomplete Paschen-Back, and magneto-optical effects. We also evaluate the suitability of a series of approximations for modeling the scattering polarization in the wings of strong resonance lines at a much lower computational cost, which is particularly valuable for the numerically intensive case of three-dimensional radiative transfer. Methods. We examine the suitability of the considered approximations by using our radiative transfer code to model the Stokes profiles of the Mg II h & k lines and of the H I Lyman-α line in magnetized one-dimensional models of the solar atmosphere. Results. Neglecting Doppler redistribution in the scattering processes that are unperturbed by elastic collisions (i.e., treating them as coherent in the observer’s frame) produces a negligible error in the scattering polarization wings of the Mg II resonance lines and a minor one in the Lyman-α wings, although it is unsuitable to model the cores of these lines. For both lines, the scattering processes that are perturbed by elastic collisions only give a significant contribution to the intensity component of the emissivity. Neglecting collisional as well as Doppler redistribution (so that all scattering processes are coherent) represents a rough but suitable approximation for the wings of the Mg II resonance lines, but a very poor one for the Lyman-α wings. The magnetic sensitivity in the scattering polarization wings of the considered lines can be modeled by accounting for the magnetic field in only the ηI and ρV coefficients of the Stokes-vector transfer equation (i.e., using the zero-field expression for the emissivity).

Numerical solutions to linear transfer problems of polarized radiation

Context. The polarization signals produced by the scattering of anistropic radiation in strong resonance lines encode important information about the elusive magnetic fields in the outer layers of the solar atmosphere. An accurate modeling of these signals is a very challenging problem from the computational point of view, in particular when partial frequency redistribution (PRD) effects in scattering processes are accounted for with a general angle-dependent treatment. Aims. We aim at solving the radiative transfer problem for polarized radiation in nonlocal thermodynamic equilibrium conditions, taking angle-dependent PRD effects into account. The problem is formulated for a two-level atomic model in the presence of arbitrary magnetic and bulk velocity fields. The polarization produced by scattering processes and the Zeeman effect is considered. Methods. The proposed solution strategy is based on an algebraic formulation of the problem and relies on a convenient physical assumption, which allows its linearization. We applied a nested matrix-free GMRES iterative method. Effective preconditioning is obtained in a multifidelity framework by considering the light-weight description of scattering processes in the limit of complete frequency redistribution (CRD). Results. Numerical experiments for a one-dimensional (1D) atmospheric model show near optimal strong and weak scaling of the proposed CRD-preconditioned GMRES method, which converges in few iterations, independently of the discretization parameters. A suitable parallelization strategy and high-performance computing tools lead to competitive run times, providing accurate solutions in a few minutes. Conclusions. The proposed solution strategy allows the fast systematic modeling of the scattering polarization signals of strong resonance lines, taking angle-dependent PRD effects into account together with the impact of arbitrary magnetic and bulk velocity fields. Almost optimal strong and weak scaling results suggest that this strategy is applicable to realistic 3D models. Moreover, the proposed strategy is general, and applications to more complex atomic models are possible.

TIC: A Stokes Inversion Code for Scattering Polarization with Partial Frequency Redistribution and Arbitrary Magnetic Fields

We present the Tenerife Inversion Code (TIC), which has been developed to infer the magnetic and plasma properties of the solar chromosphere and transition region via full Stokes inversion of polarized spectral lines. The code is based on the HanleRT forward engine, which takes into account many of the physical mechanisms that are critical for a proper modeling of the Stokes profiles of spectral lines originating in the tenuous and highly dynamic plasmas of the chromosphere and transition region: the scattering polarization produced by quantum level imbalance and interference (atomic polarization), the effects of frequency coherence in polarized resonance scattering (partial redistribution), and the impact of arbitrary magnetic fields on the atomic polarization and the radiation field. We present first results of atmospheric and magnetic inversions, and discuss future developments for the project.

Steady State Photoisomerization Quantum Yield of Model Rhodopsin: Insights from Wavepacket Dynamics?

We simulate the nonequilibrium steady state cis-trans photoisomerization of retinal chromophore in rhodopsin on the basis of a two-state, two-mode model coupled to a thermal environment. By analyzing the systematic trends within an inhomogeneously broadened ensemble of systems, we find that the steady state reaction quantum yield (QY) correlates strongly with the excess energy above the crossing point of the system, in agreement with the prediction of the short-time dynamical wavepacket picture. However, the nontrivial dependence of the QY on the system-environment interaction indicates that a pure dynamical picture is insufficient and that environment-induced partial internal energy redistribution takes place before the reaction concludes. These results imply that a proper treatment of the photoisomerization reaction, particularly its high QY, must account for the redistribution and dissipation of energy beyond the dynamical wavepacket motion that is typically employed in the literature and that is appropriate only in the transient regime.

Interfacial defective Ti3+ on Ti/TiO2 as visible-light responsive sites with promoted charge transfer and photocatalytic performance

Defect sites on oxide semiconductors play a crucial role in promoting photocatalytiperformance and modulating the bandgap structure of photocatalysts. However, the role of interfacial coordinatively unsaturated defect sites between metal and oxide in photocatalysis is still under debate. So, we designed an experiment to probe the role of interfacial coordinatively unsaturated defect sites. In this work, a series of Ti/TiO2 photocatalysts with varying concentrations of interfacial Ti3+ sites were prepared through an epitaxial growth method under hydrothermal conditions. Through experimental and computational investigations, the roles of interfacial defect sites were discussed in detail. On the one hand, the interfacial coordinatively unsaturated Ti3+ sites could act as visible-light-responsive sites in photocatalytic reactions due to the overlap and hybridization of multiple electronic orbitals. On the other hand, the Ti/TiO2 interface exhibited a certain degree of metallic character near the Fermi level because of the partial delocalization and redistribution of electrons, facilitating the charge migration and separation across the metal-oxide interface. Consequently, the obtained Ti/TiO2 catalysts showed notably enhanced charge transfer efficiency and visible light photocatalytic activity compared to their pristine counterparts. This work may provide a new perspective to interfacial defect engineering in classic metal/oxide heterojunction photocatalysts and figure a more precise direction to synthesize higher effective photocatalysts for environmental governance.

Формирование китайского направления политики ЕС: роль стран Центральной и Восточной Европы

The Chinese direction of the EU policy-making process is often explained by the return of great power competition and the balance of power strategy in the contemporary word politics. The EU is thus considered as a quasi-state actor with geopolitical aspirations either to balance Chinese growth in cooperation with the US or to strive for an independent role in a polycentric structure. The presented research aims to assess domestic driving forces influencing the EU common position vis-a-vis China through the prism of accommodating national interests of the CEE member-states. The authors hypothesize that cooperation between the CEE countries and China is not a reason for hardening the position of the EU, but a mobilization pretext contributing to the organizational resource of Brussels against the backdrop of global changes. The study provides the analysis of interests behind the policy of CEE countries towards China, and the degree of its possible influence on the Chinese direction of the EU policy making. The research aimes to fill the gap in academic literature in understanding mechanisms of dependency of the EU policy on economic interests of its member states as well as on political aspirations to leverage the EU institutions. The authors explain the main reasons for special relations of the CEE countries with China, and then analyze the ratio of national and pan-European policy tracks towards Beijing in order to illustrate their mutual influence. The EU and its member-states are prone to economic cooperation with China seen as a critical resource for their development. At the same time Brussels is concerned about the destabilizing potential of such a cooperation for the EU normative consensus which exacerbates the problem of intraunion consolidation. This paradox contributes to the exaggeration of restrictive conditions for further EU–China cooperation and to the partial redistribution of resources within the European Union.

Modeling the scattering polarization of the solar Ca I 4227 Å line with angle-dependent partial frequency redistribution

Context. The correct modeling of the scattering polarization signals observed in several strong resonance lines requires taking partial frequency redistribution (PRD) phenomena into account. Modeling scattering polarization with PRD effects is very computationally demanding and the simplifying angle-averaged (AA) approximation is therefore commonly applied. Aims. This work aims to assess the impact and the range of validity of the AA approximation with respect to the general angle-dependent (AD) treatment of PRD effects in the modeling of scattering polarization in strong resonance lines, with a focus on the solar Ca I 4227 Å line. Methods. Spectral line polarization was modeled by solving the radiative transfer problem for polarized radiation, under nonlocal thermodynamic equilibrium conditions, taking PRD effects into account in static one-dimensional semi-empirical atmospheric models presenting arbitrary magnetic fields. The problem was solved through a two-step approach. In step 1, the problem was solved for the intensity only, considering a multilevel atom. In step 2, the problem was solved including polarization, considering a two-level atom with an unpolarized and infinitely sharp lower level, and fixing the lower level population calculated at step 1. Results. The results for the Ca I 4227 Å line show a good agreement between the AA and AD calculations for the Q/I and U/I wings’ signals. However, AA calculations reveal an artificial trough in the line-core peak of the linear polarization profiles, whereas AD calculations show a sharper peak in agreement with the observations. Conclusions. An AD treatment of PRD effects is essential to correctly model the line-core peak of the scattering polarization signal of the Ca I 4227 Å line. By contrast, in the considered static case, the AA approximation seems to be suitable to model the wing scattering polarization lobes and their magnetic sensitivity through magneto-optical effects.

Cardiac Sarcoidosis Mimicking Anterior Myocardial Infarction.

A 58-year-old asymptomatic man with electrocardiogram (ECG) abnormality was referred to our institution for cardiac exams. His ECG showed a bifascicular block, and the echocardiography demonstrated a wall motion abnormality in apex. Stress-rest myocardial perfusion imaging (MPI) showed a significant defect in anterior wall with partial redistribution at rest. He was suspected of having an anterior myocardial infarction (MI) and underwent cardiac catheterization. However, coronary angiography (CAG) revealed no significant coronary atherosclerosis. Cardiovascular magnetic resonance imaging (CMR) was performed to evaluate the extent of myocardial infarction. Late gadolinium enhancement (LGE) demonstrated a significant epicardial and midmyocardial LGE in the multiple site including anterior, anteroseptal, lateral, inferior wall, and basal right ventricle junction, which strongly indicated that the fibrosis was due to cardiac sarcoidosis (CS).A myocardial perfusion defect in anterior wall shown in the MPI revealed the fibrosis as an atypical finding mimicking anterior MI.

Evidence for differentiation of the most primitive small bodies

Context. Dynamical models of Solar System evolution have suggested that the so-called P- and D-type volatile-rich asteroids formed in the outer Solar System beyond Neptune’s orbit and may be genetically related to the Jupiter Trojans, comets, and small Kuiper belt objects (KBOs). Indeed, the spectral properties of P- and D-type asteroids resemble that of anhydrous cometary dust. Aims. We aim to gain insights into the above classes of bodies by characterizing the internal structure of a large P- and D-type asteroid. Methods. We report high-angular-resolution imaging observations of the P-type asteroid (87) Sylvia with the Very Large Telescope Spectro-Polarimetric High-contrast Exoplanet REsearch (SPHERE) instrument. These images were used to reconstruct the 3D shape of Sylvia. Our images together with those obtained in the past with large ground-based telescopes were used to study the dynamics of its two satellites. We also modeled Sylvia’s thermal evolution. Results. The shape of Sylvia appears flattened and elongated (a/b ~1.45; a/c ~1.84). We derive a volume-equivalent diameter of 271 ± 5 km and a low density of 1378 ± 45 kg m−3. The two satellites orbit Sylvia on circular, equatorial orbits. The oblateness of Sylvia should imply a detectable nodal precession which contrasts with the fully-Keplerian dynamics of its two satellites. This reveals an inhomogeneous internal structure, suggesting that Sylvia is differentiated. Conclusions. Sylvia’s low density and differentiated interior can be explained by partial melting and mass redistribution through water percolation. The outer shell should be composed of material similar to interplanetary dust particles (IDPs) and the core should be similar to aqueously altered IDPs or carbonaceous chondrite meteorites such as the Tagish Lake meteorite. Numerical simulations of the thermal evolution of Sylvia show that for a body of such a size, partial melting was unavoidable due to the decay of long-lived radionuclides. In addition, we show that bodies as small as 130–150 km in diameter should have followed a similar thermal evolution, while smaller objects, such as comets and the KBO Arrokoth, must have remained pristine, which is in agreement with in situ observations of these bodies. NASA Lucy mission target (617) Patroclus (diameter ≈140 km) may, however, be differentiated.

Chromospheric activity in 55 Cancri: II. Theoretical wave studies versus observations

ABSTRACT In this study, we consider chromospheric heating models for 55 Cancri in conjunction with observations. The theoretical models, previously discussed in Paper I, are self-consistent, non-linear, and time-dependent ab-initio computations encompassing the generation, propagation, and dissipation of waves. Our focus is the consideration of both acoustic waves and longitudinal flux tube waves amounting to two-component chromosphere models. 55 Cancri, a K-type orange dwarf, is a star of low activity, as expected by its age, which also implies a relatively small magnetic filling factor. The Ca ii K fluxes are computed (multi-ray treatment) assuming partial redistribution and time-dependent ionization. The theoretical Ca ii H+K fluxes are subsequently compared with observations. It is found that for stages of lowest chromospheric activity the observed Ca ii fluxes are akin, though not identical, to those obtained by acoustic heating, but agreement can be obtained if low levels of magnetic heating – consistent with the expected photospheric magnetic filling factor – are considered as an additional component; this idea is in alignment with previous proposals conveyed in the literature.

Chromospheric activity in 55 Cancri – I. Results from theoretical wave studies

ABSTRACT We present theoretical models of chromospheric heating for 55 Cancri, an orange dwarf of relatively low activity. Self-consistent, non-linear, and time-dependent ab initio numerical computations are pursued encompassing the generation, propagation, and dissipation of waves. We consider longitudinal waves operating among arrays of flux tubes as well as acoustic waves pertaining to non-magnetic stellar regions. Additionally, flux enhancements for the longitudinal waves are also taken into account as supplied by transverse tube waves. The Ca ii K fluxes are computed (multi-ray treatment) assuming partial redistribution as well as time-dependent ionization (TDI). The self-consistent treatment of TDI (especially for hydrogen) greatly impacts the atmospheric temperatures and electron densities (especially behind the shocks); it also affects the emergent Ca ii fluxes. Particularly, we focus on the influence of magnetic heating on the stellar atmospheric structure and the emergent Ca ii emission, as well as the impact of non-linearities. Our study shows that a higher photospheric magnetic filling factor entails a larger Ca ii emission; however, an increased initial wave energy flux (e.g. associated with mode coupling) is of little difference. Comparisons of our theoretical results with observations will be conveyed in forthcoming Paper II.