Search

In this paper we study the structure of Gabriel quivers of tame symmetric algebras of period four. More precisely, we focus on algebras having Gabriel quiver {\it biregular}, i.e. the numbers of arrows starting and ending at any vertex are equal, and do not exceed $2$. We describe the local structure of biregular Gabriel quivers of tame symmetric algebras of period four, including certain idempotent algebras. The main result of this paper shows that, in fact, these Gabriel quivers have local structure exactly as Gabriel quivers of so called {\it weighted surface algebras}, which partially extends known characterization of algebras of generalized quaternion type.

We show that finite element discretizations of incompressible flow problems can be designed to ensure preservation/dissipation of kinetic energy not only globally but also locally. In the context of equal-order (piecewise-linear) interpolations, we prove the validity of a semi-discrete energy inequality for a quadrature-based approximation to the nonlinear convective term, which we combine with the Becker--Hansbo pressure stabilization. An analogy with entropy-stable algebraic flux correction schemes for the compressible Euler equations and the shallow water equations yields a weak `bounded variation' estimate from which we deduce the semi-discrete Lax--Wendroff consistency and convergence towards dissipative weak solutions. The results of our numerical experiments for standard test problems confirm that the method under investigation is non-oscillatory and exhibits optimal convergence behavior.

Optical spectra of the Very Late Thermal Pulse (VLTP) object V4334 Sgr have shown a rapidly changing spectrum resulting from shocks in the outflow, which created a new bipolar nebula inside the old nebula. We see C II and C III emission lines emerging typical of a [WC 11-10]-type star. The strong increase of [O III] and [S III] emission lines indicate the possible onset of photoionisation in the new ejecta., Comment: 2 pages, 3 figures, accepted for publication in the proceedings of IAU Symposium 384: Planetary Nebulae: a Universal Toolbox in the Era of Precision Astrophysics

The very late thermal pulse (VLTP) affects the evolution of $\sim$20\% of 1--8\,$\mathrm M_\odot$ stars, repeating the last phases of the red giant within a few years and leading to the formation of a new, but hydrogen-poor nebula within the old planetary nebula (PN). The strong dust formation in the latter obscures the optical and near-infrared radiation of the star. We aimed to determine the reheating timescale of the central star in Sakurai's object, which is an important constraint for the poorly understood VLTP evolution. We observed the radio continuum emission of Sakurai's object for almost 20 years from 2004 to 2023. Continuous, multi-frequency observations proved to be essential to distinguish between phases dominated by photoionization and shock ionization. The flux density fluctuates by more than a factor 40 within months to years. The spectral index remained negative between 2006 and 2017 and is close to zero since 2019. The emission region is barely resolved since 2021. Non-thermal radio emission observed from 2004 to 2017 traces shocks induced by wind interactions due to discrete mass-loss events. Thermal emission dominates during the period 2019--2023 and may indicate photoionization of the nebula by the central star., Comment: 6 pages, 3 figures, 2 tables, Astronomy & Astrophysics, accepted after minor revision

Aims. Numerous planetary nebulae show complicated inner structures not obviously explained. For one such object we undertake a detailed 3D photoionization and kinematical model analysis for a better understanding of the underlying shaping processes. Methods. We obtained 2D ARGUS/IFU spectroscopy covering the whole nebula in selected, representative emission lines. A 3D photoionization modelling was used to compute images and line profiles. Comparison of the observations with the models was used to fine-tune the model details. This predicts the approximate nebular 3D structure and kinematics. Results. We found that within a cylindrical outer nebula there is a hidden, very dense, bar-like or cylindrical inner structure. Both features are co-axial and are inclined to the sky by 40 deg. A wide asymmetric one-sided plume attached to one end of the bar is proposed to be a flat structure. All nebular components share the same kinematics, with an isotropic velocity field which monotonically increases with distance from the star before reaching a plateau. The relatively low velocities indicate that the observed shapes do not require particularly energetic processes and there is no indication for the current presence of a jet. The 3D model reproduces the observed line ratios and the detailed structure of the object significantly better than previous models., Comment: accepted for publication in A&A, 8 pages, 8 figures

Close binary central stars of planetary nebulae (PNe) must have formed through a common envelope evolution during the giant phase experienced by one of the stars. Transfer of the angular momentum from the binary system to the envelope leads to the shortening of the binary separations from the radius of red giant to the radius of the order of few tenths of AU. Thus, close binary central stars of planetary nebulae are laboratories to study the common envelope phase of evolution. The close binary fraction in the Galaxy has been measured in various sky surveys, but the close binary fraction is not yet well constrained for the Magellanic Clouds, and our results may help the study of common envelope evolution in low-metallicity environments. This paper presents a continuation of our study of variability in the Magellanic Cloud planetary nebulae on the basis of data from the OGLE survey. Previously, we had analysed the OGLE data in the Small Magellanic Cloud. Here, the study is extended to the Large Magellanic Cloud (LMC). In this paper we search for close binary central stars with the aim to constrain the binary fraction and period distribution in the LMC. We identified 290 counterparts of PNe in the LMC in the I-band images from the OGLE-III and OGLE-IV surveys. However, the light curves of ten objects were not accessible in the OGLE database, and thus we analysed the time series photometry of 280 PNe. In total, 32 variables were found, but 5 of them turned out to be foreground objects. Another 18 objects show irregular or regular variability that is not attributable to the binarity of their central stars. Their status and the nature of their variability will be verified in the follow-up paper. Nine binary central stars of PNe with periods between 0.24 and 23.6 days were discovered. The obtained fraction for the LMC PNe is 3.3^(+2.6)_(-1.6)% without correcting for incompleteness., Comment: 10 pages, 4 figures

The second data release of the LOFAR Two-Metre Sky Survey (LoTSS) covers 27% of the northern sky, with a total area of $\sim 5,700$ deg$^2$. The high angular resolution of LOFAR with Dutch baselines (6 arcsec) allows us to carry out optical identifications of a large fraction of the detected radio sources without further radio followup; however, the process is made more challenging by the many extended radio sources found in LOFAR images as a result of its excellent sensitivity to extended structure. In this paper we present source associations and identifications for sources in the second data release based on optical and near-infrared data, using a combination of a likelihood-ratio cross-match method developed for our first data release, our citizen science project Radio Galaxy Zoo: LOFAR, and new approaches to algorithmic optical identification, together with extensive visual inspection by astronomers. We also present spectroscopic or photometric redshifts for a large fraction of the optical identifications. In total 4,116,934 radio sources lie in the area with good optical data, of which 85% have an optical or infrared identification and 58% have a good redshift estimate. We demonstrate the quality of the dataset by comparing it with earlier optically identified radio surveys. This is by far the largest ever optically identified radio catalogue, and will permit robust statistical studies of star-forming and radio-loud active galaxies., Comment: 29 pages. Accepted by A&A; data products available at https://lofar-surveys.org/dr2_release.html

We present high angular-resolution observations of Sakurai's object using the Atacama Large Millimeter Array, shedding new light on its morpho-kinematical structure. The millimetre continuum emission, observed at an angular resolution of 20 milliarcsec (corresponding to 70 AU), reveals a bright compact central component whose spectral index indicates that it composed of amorphous carbon dust. Based on these findings, we conclude that this emission traces the previously suggested dust disc observed in mid-infrared observations. Therefore, our observations provide the first direct imaging of such a disc. The H$^{12}$CN($J$=4$\rightarrow$3) line emission, observed at an angular resolution of 300 milliarcsec (corresponding to 1000 AU), displays bipolar structure with a north-south velocity gradient. From the position-velocity diagram of this emission we identify the presence of an expanding disc and a bipolar molecular outflow. The inclination of the disc is determined to be $i$=72$^\circ$. The derived values for the de-projected expansion velocity and the radius of the disc are $v_{\rm exp}$=53 km s$^{-1}$ and $R$=277 AU, respectively. On the other hand, the de-projected expansion velocity of the bipolar outflow detected in the H$^{12}$CN($J$=4$\rightarrow$3) emission of approximately 1000 km s$^{-1}$. We propose that the molecular outflow has an hourglass morphology with an opening angle of around 60$^{\circ}$. Our observations unambiguously show that an equatorial disc and bipolar outflows formed in Sakurai's object in less than 30 years after the born-again event occurred, providing important constraints for future modelling efforts of this phenomenon., Comment: 9 pages, 5 figures. Accepted for publication as a Letter in Astronomy and Astrophysics

In this paper we are concerned with the structure of tame symmetric algebras of period four (TSP4 algebras, for short). We will mostly focus on the case when the Gabriel quiver of $A$ is biserial, i.e. there are at most two arrows ending and at most two arrows starting at each vertex, but some of the results can be easily extended to the general case. This serves as a basis for upcoming series of articles devoted to solve the problem of classification of all TSP4 algebras with biserial Gabriel quiver. We present a range of properties (with relatively short proofs) which must hold for the Gabriel quiver of a tame symmetric algebra of period four. Amongst others we show that triangles (and squares) appear naturally in the Gabriel quivers of such algebras, such as for weighted surface algebras [6, 8, 9]., Comment: 15 pages

In this paper, we give sufficient conditions for global-in-time existence of classical solutions for the fully parabolic chemorepulsion system posed on a convex, bounded three-dimensional domain. Our main result establishes global-in-time existence of regular nonnegative solutions provided that $\nabla\sqrt{u} \in L^4(0, T; L^2(\Omega))$. Our method is related to the Bakry--\'Emery calculation and appears to be new in this context., Comment: 14 pages; incorporated referee comments and added alternative proof

We present the detection of 68 sources from the most sensitive radio survey in circular polarisation conducted to date. We use the second data release of the 144 MHz LOFAR Two-metre Sky Survey to produce circularly-polarised maps with median 140 $\mu$Jy beam$^{-1}$ noise and resolution of 20$''$ for $\approx$27% of the northern sky (5634 deg$^{2}$). The leakage of total intensity into circular polarisation is measured to be $\approx$0.06%, and our survey is complete at flux densities $\geq1$ mJy. A detection is considered reliable when the circularly-polarised fraction exceeds 1%. We find the population of circularly-polarised sources is composed of four distinct classes: stellar systems, pulsars, active galactic nuclei, and sources unidentified in the literature. The stellar systems can be further separated into chromospherically-active stars, M dwarfs, and brown dwarfs. Based on the circularly-polarised fraction and lack of an optical counterpart, we show it is possible to infer whether the unidentified sources are likely unknown pulsars or brown dwarfs. By the completion of this survey of the northern sky, we expect to detect 300$\pm$100 circularly-polarised sources., Comment: Accepted for publication in A&A, 15 pages, 8 figures, 1 table. The catalogue will be publicly available at http://lofar-surveys.org/ and via Vizier shortly

The Sun is the source of different types of radio bursts that are associated with solar flares, for example. Among the most frequently observed phenomena are type III solar bursts. Their radio images at low frequencies (below 100 MHz) are relatively poorly studied due to the limitations of legacy radio telescopes. We study the general characteristics of types IIIb and U with stria structure solar radio bursts in the frequency range of 20 - 80 MHz, in particular the source size and evolution in different altitudes, as well as the velocity and energy of electron beams responsible for their generation. In this work types IIIb and U with stria structure radio bursts are analyzed using data from the LOFAR telescope including dynamic spectra and imaging observations, as well as data taken in the X-ray range (GOES and RHESSI satellites) and in the extreme ultraviolet (SDO satellite). In this study we determined the source size limited by the actual shape of the contour at particular frequencies of type IIIb and U solar bursts in a relatively wide frequency band from 20 to 80 MHz. Two of the bursts seem to appear at roughly the same place in the studied active region and their source sizes are similar. It is different in the case of another burst, which seems to be related to another part of the magnetic field structure in this active region. The velocities of the electron beams responsible for the generation of the three bursts studied here were also found to be different., Comment: Astronomy & Astrophysics, in press; 9 pages, 6 figures

After becoming ionized, low-density astrophysical plasmas will begin a process of slow recombination. Models for this still have significant uncertainties. The recombination cannot normally be observed in isolation, because the ionization follows the evolutionary time scale of the ionizing source. Laboratory experiments are unable to reach the appropriate conditions because of the required very long time scales. The extended nebula around the very late helium flash (VLTP) star V4334 Sgr provides a unique laboratory for this kind of study. The sudden loss of the ionizing UV radiation after the VLTP event has allowed the nebula to recombine free from other influences. More than 290 long slit spectra taken with FORS1/2 at the ESO VLT between 2007 and 2022 are used to follow the time evolution of lines of H, He, N, S, O, Ar. Hydrogen and helium lines, representing most of the ionized mass, do not show significant changes. A small increase is seen in [N II] (+2.8 %/yr; significance 2.7 sigma), while we see a decrease in [O III] (-1.96 %/yr; 2.0 sigma). The [S II] lines show a change of +3.0 %/yr; 1.6 sigma). The lines of [S III] and of Ar III] show no significant change. For [S III], the measurement differs from the predicted decrease by 4.5 sigma. A possible explanation is that the fraction of [S IV] and higher is larger than expected. Such an effect could provide a potential solution for the sulfur anomaly in planetary nebulae., Comment: 13 pages, 8 figures, 3 tables; Accepted for Publication in ApJ

A well-designed numerical method for the shallow water equations (SWE) should ensure well-balancedness, nonnegativity of water heights, and entropy stability. For a continuous finite element discretization of a nonlinear hyperbolic system without source terms, positivity preservation and entropy stability can be enforced using the framework of algebraic flux correction (AFC). In this work, we develop a well-balanced AFC scheme for the SWE system including a topography source term. Our method preserves the lake at rest equilibrium up to machine precision. The low-order version represents a generalization of existing finite volume approaches to the finite element setting. The high-order extension is equipped with a property-preserving flux limiter. Nonnegativity of water heights is guaranteed under a standard CFL condition. Moreover, the flux-corrected space discretization satisfies a semi-discrete entropy inequality. New algorithms are proposed for realistic simulation of wetting and drying processes. Numerical examples for well-known benchmarks are presented to evaluate the performance of the scheme.

Context. Galactic red novae are thought to be produced in stellar mergers between non-compact stars, such as main-sequence stars and cool giants. They are hoped to help in explaining physical processes involved in common envelope evolution and stellar binary collisions. Aims. We investigate the presence of lithium in three best-observed Galactic red nova remnants. Explaining the origin of lithium may point to mixing mechanism present before, during, or after the merger. Methods. The lithium line at 6707.81 A was compared to a feature of [Ca I at 6572.78 A to derive relative abundances in circumstellar gas. Absolute abundances were next calculated assuming the Solar calcium to lithium abundance ratio. Results. Lithium abundances were measured in the merger remnants of V838 Mon with A(Li)=2.3, CK Vul with A(Li)=2.5, and V1309 Sco with A(Li)=1.8. Conclusions. Lithium is overabundant in red novae, suggesting that at least some merger products activate the Cameron-Fowler mechanism whereby convective mixing can reach the deep stellar interior. Whether deep convection and associated diffusion alone or some other processes (e.g. spin down) can be responsible for driving the Cameron-Fowler mechanism in the remnants requires further studies. Early observations of lithium in V838 Mon hint that these mechanisms can activate early, perhaps already in the common envelope phase. These observations should be taken into account in modelling these complex systems., Comment: submitted to A&A; comments welcome

Scale-up of flow-electrode capacitive deionization is hindered due to the reliance on thick brittle graphite current collectors. Inspired by developments of electrochemical technologies we present the use of flexible membrane electrode assemblies (MEA) to solve these limitations. We tested different carbon-fiber fabrics as current collectors and laminated them successfully with ion-exchange membranes. The use of thinner ion-exchange membranes is now possible due to the reinforcement with the carbon fiber fabric. Desalination experiments reveal that a MEA setup can achieve salt transfer rates equal to standard setups. Hence, we deduce that charge percolation also acts outside the electric field. In a single point of contact, ionic and electric charges are exchanged at the carbon surface of the MEA. The use of thinner membranes leads to a reduced potential drop. Together with a more homogeneous electric field across the feed water section, this can compensate for the reduction of contact surface between flow electrode and current collector.

In this data release from the LOFAR Two-metre Sky Survey (LoTSS) we present 120-168MHz images covering 27% of the northern sky. Our coverage is split into two regions centred at approximately 12h45m +44$^\circ$30' and 1h00m +28$^\circ$00' and spanning 4178 and 1457 square degrees respectively. The images were derived from 3,451hrs (7.6PB) of LOFAR High Band Antenna data which were corrected for the direction-independent instrumental properties as well as direction-dependent ionospheric distortions during extensive, but fully automated, data processing. A catalogue of 4,396,228 radio sources is derived from our total intensity (Stokes I) maps, where the majority of these have never been detected at radio wavelengths before. At 6" resolution, our full bandwidth Stokes I continuum maps with a central frequency of 144MHz have: a median rms sensitivity of 83$\mu$Jy/beam; a flux density scale accuracy of approximately 10%; an astrometric accuracy of 0.2"; and we estimate the point-source completeness to be 90% at a peak brightness of 0.8mJy/beam. By creating three 16MHz bandwidth images across the band we are able to measure the in-band spectral index of many sources, albeit with an error on the derived spectral index of +/-0.2 which is a consequence of our flux-density scale accuracy and small fractional bandwidth. Our circular polarisation (Stokes V) 20" resolution 120-168MHz continuum images have a median rms sensitivity of 95$\mu$Jy/beam, and we estimate a Stokes I to Stokes V leakage of 0.056%. Our linear polarisation (Stokes Q and Stokes U) image cubes consist of 480 x 97.6 kHz wide planes and have a median rms sensitivity per plane of 10.8mJy/beam at 4' and 2.2mJy/beam at 20"; we estimate the Stokes I to Stokes Q/U leakage to be approximately 0.2%. Here we characterise and publicly release our Stokes I, Q, U and V images in addition to the calibrated uv-data., Comment: 23 figures, 1 table and 29 pages. The catalogues, images and uv-data associated with this data release are publicly available via https://lofar-surveys.org/

The empirical relationship between the non-thermal 5GHz radio luminosity and the soft X-ray luminosity of active stellar coronae, canonically called the G\"udel-Benz relationship (G\"udel & Benz 1993), has been a cornerstone of stellar radio astronomy as it explicitly ties the radio emission to the coronal heating mechanisms. The relationship extends from microflares on the Sun to the coronae of the most active stars suggesting that active coronae are heated by a flare-like process (Benz & G\"udel 1994). The relationship is thought to originate from a consistent partition of the available flare energy into relativistic charges, that emit in the radio-band via the incoherent gyrosynchrotron mechanism, and heating of the bulk coronal plasma, that emits in the X-ray band via the Bremsstrahlung mechanism. Consequently, coherent emission from stellar and sub-stellar objects is not expected to adhere to this empirical relationship, as is observed in ultracool dwarf stars and brown dwarfs. Here we report a population of radio-detected chromospherically active stars that surprisingly follows the G\"udel-Benz relationship despite their radio emission being classified as coherent emission by virtue of its high circularly polarised fraction and high brightness temperature. Our results prompt a re-examination of the physics behind the G\"udel-Benz relationship, its implication for the mechanism of coronal heating and particle acceleration in active stars and the phenomenological connection between solar and stellar flares., Comment: Under review, ApJL

We identify explicitly the fractional power spaces for the $L^2$ Dirichlet Laplacian and Dirichlet Stokes operators using the theory of real interpolation. The results are not new, but we hope that our arguments are relatively accessible., Comment: 10 pages. Most of this previously appeared as part of arXiv:1904.03337v1, which was subsequently split for publication

The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. The desired properties are enforced by applying a limiter to antidiffusive fluxes that represent the difference between the high-order baseline scheme and a property-preserving approximation of Lax--Friedrichs type. In the first step of the limiting procedure, the given target fluxes are adjusted in a way that guarantees preservation of local and/or global bounds. In the second step, additional limiting is performed, if necessary,to ensure the validity of fully discrete and/or semi-discrete entropy inequalities. The limiter-based entropy fixes considered in this work are applicable to finite element discretizations of scalar hyperbolic equations and systems alike. The underlying inequality constraints are formulated using Tadmor's entropy stability theory. The proposed limiters impose entropy-conservative or entropy-dissipative bounds on the rate of entropy production by antidiffusive fluxes and Runge--Kutta (RK) time discretizations. Two versions of the fully discrete entropy fix are developed for this purpose. To motivate the use of limiter-based entropy fixes, we prove a finite element version of the Lax--Wendroff theorem and perform numerical studies for standard test problems. In our numerical experiments, entropy-dissipative schemes converge to correct weak solutions of scalar conservation laws, of the Euler equations, and of the shallow water equations.

We present observations of planetary nebulae with the LOw Frequency ARray (LOFAR) between 120 and 168 MHz. The images show thermal free-free emission from the nebular shells. We have determined the electron temperatures for spatially resolved, optically thick nebulae. These temperatures are 20 to 60% lower than those estimated from collisionally excited optical emission lines. This strongly supports the existence of a cold plasma component, which co-exists with hot plasma in planetary nebulae. This cold plasma does not contribute to the collisionally excited lines, but does contribute to recombination lines and radio flux. Neither of the plasma components are spatially resolved in our images, although we infer that the cold plasma extends to the outer radii of planetary nebulae. However, more cold plasma appears to exist at smaller radii. The presence of cold plasma should be taken into account in modeling of radio emission of planetary nebulae. Modelling of radio emission usually uses electron temperatures calculated from collisionally excited optical and/or infrared lines. This may lead to an underestimate of the ionized mass and an overestimate of the extinction correction from planetary nebulae when derived from the radio flux alone. The correction improves the consistency of extinction derived from the radio fluxes when compared to estimates from the Balmer decrement flux ratios., Comment: 20 pages, 10 figures, ApJ, accepted

We present stability and error analysis for algebraic flux correction schemes based on monolithic convex limiting. For a continuous finite element discretization of the time-dependent advection equation, we prove global-in-time existence and the worst-case convergence rate of 1/2 w.r.t. the L2 error of the spatial semi-discretization. Moreover, we address the important issue of stabilization for raw antidiffusive fluxes. Our a priori error analysis reveals that their limited counterparts should satisfy a generalized coercivity condition. We introduce a limiter for enforcing this condition in the process of flux correction. To verify the results of our theoretical studies, we perform numerical experiments for simple one-dimensional test problems. The methods under investigation exhibit the expected behavior in all numerical examples. In particular, the use of stabilized fluxes improves the accuracy of numerical solutions and coercivity enforcement often becomes redundant.

CK Vul is the remnant of an energetic eruption known as Nova 1670 that is thought to be caused by a stellar merger. The remnant is composed of (1) a large hourglass nebula of recombining gas (of 71\arcsec size), very similar to some classical planetary and pre-planetary nebulae (PPNe), and (2) of a much smaller and cooler inner remnant prominent in millimeter-wave emission from molecules. We investigate the three-dimensional spatio-kinematic structure of both components. The analysis of the hourglass structure yields a revised distance to the object of >2.6 kpc, at least 3.7 times greater than so far assumed. At this distance, the stellar remnant has a bolometric luminosity >12 L$_{\odot}$ and is surrounded by molecular material of total mass >0.8 M$_{\odot}$ (the latter value has a large systematic uncertainty). We also analyzed the architecture of the inner molecular nebula using ALMA observations of rotational emission lines obtained at subarcsecond resolution. We find that the distribution of neutral and ionized gas in the lobes can be reproduced by several nested and incomplete shells or jets with different velocity fields and varying orientations. The analysis indicates that the molecular remnant was created in several ejection episodes, possibly involving an interacting binary system. We calculated the linear momentum ($\approx$10$^{40}$ g cm s$^{-1}$) and kinetic energy ($\approx$10$^{47}$ erg) of the CK Vul outflows and find them within the limits typical for classical PPNe. Given the similarities of the CK Vul outflows to PPNe, we suggest there may CK Vul analogs among wrongly classified PPNe with low intrinsic luminosities, especially among PPNe with post-red-giant-branch central stars., Comment: 12 pages, animations at: https://bit.ly/3hR6jSF and https://shorturl.at/gwzOT . Comments welcomed

We obtained new spectra of fourteen Magellanic Cloud planetary nebulae with the South African Large Telescope to determine heating rates of their central stars and to verify evolutionary models of post-asymptotic giant branch stars. We compared new spectra with observations made in previous years. Five planetary nebulae showed an increase in excitation over time. Four of their central stars exhibit [WC] features in their spectra, including three new detections. This raises the total number of [WC] central stars of PNe in the Magellanic Clouds to ten. We compared determined heating rates of the four [WC] central stars with the He-burning post-asymptotic giant branch evolutionary tracks and the remaining star with the H-burning tracks. Determined heating rates are consistent with the evolutionary models for both H and He-burning post-asymptotic giant branch stars. The central stars of the PNe that show the fastest increase of excitation are also the most luminous in the sample. This indicates that [WC] central stars in the Magellanic Clouds evolve faster than H-burning central stars, and they originate from more massive progenitors., Comment: 11 pages, 2 figures

SwSt 1 (PN G001.5-06.7) is a bright and compact planetary nebula containing a late [WC]-type central star. Previous studies suggested that the nebular and stellar lines are slowly changing with time. We studied new and archival optical and ultraviolet spectra of the object. The [OIII] 4959 and 5007 A to $\mathrm{H}\beta$ line flux ratios decreased between about 1976 and 1997/2015. The stellar spectrum also shows changes between these epochs. We modeled the stellar and nebular spectra observed at different epochs. The analyses indicate a drop of the stellar temperature from about 42 kK to 40.5 kK between 1976 and 1993. We do not detect significant changes between 1993 and 2015. The observations show that the star performed a loop in the H-R diagram. This is possible when a shell source is activated during its post-AGB evolution. We infer that a late thermal pulse (LTP) experienced by a massive post-AGB star can explain the evolution of the central star. Such a star does not expand significantly as the result of the LTP and does not became a born-again red giant. However, the released energy can remove the tiny H envelope of the star., Comment: 18 pages, 15 figures, published in MNRAS

We selected a sample of post-AGB candidates in the Magellanic Clouds on the basis of their near- and mid-infrared colour characteristics. Fifteen of the most optically bright post-AGB candidates were observed with the South African Large Telescope in order to determine their stellar parameters and thus to validate or discriminate their nature as post-AGB objects in the Magellanic Clouds. The spectral types of absorption-line objects were estimated according to the MK classification, and effective temperatures were obtained by means of stellar atmosphere modelling. Emission-line objects were classified on the basis of the fluxes of the emission lines and the presence of the continuum. Out of 15 observed objects, only 4 appear to be genuine post-AGB stars (27\%). In the SMC, 1 out of 4 is post-AGB, and in the LMC, 3 out 11 are post-AGB objects. Thus, we can conclude that the selected region in the colour-colour diagram, while selecting the genuine post-AGB objects, overlaps severely with other types of objects, in particular young stellar objects and planetary nebulae. Additional classification criteria are required to distinguish between post-AGB stars and other types of objects. In particular, photometry at far-IR wavelengths would greatly assist in distinguishing young stellar objects from evolved ones. On the other hand, we showed that the low-resolution optical spectra appear to be sufficient to determine whether the candidates are post-AGB objects., Comment: 19 pages, 19 figures, A&A in press

In this work we present a framework for enforcing discrete maximum principles in discontinuous Galerkin (DG) discretizations. The developed schemes are applicable to scalar conservation laws as well as hyperbolic systems. Our methodology for limiting volume terms is similar to recently proposed methods for continuous Galerkin approximations, while DG flux terms require novel stabilization techniques. Piecewise Bernstein polynomials are employed as shape functions for the DG spaces, thus facilitating the use of very high order spatial approximations. We discuss the design of a new, provably invariant domain preserving DG scheme that is then extended by state-of-the-art subcell flux limiters to obtain a high-order bound preserving approximation. The limiting procedures can be formulated in the semi-discrete setting. Thus convergence to steady state solutions is not inhibited by the algorithm. We present numerical results for a variety of benchmark problems. Conservation laws considered in this study are linear and nonlinear scalar problems, as well as the Euler equations of gas dynamics and the shallow water system.

We describe the structure and properties of the finite-dimensional symmetric algebras over an algebraically closed field $K$ which are socle equivalent to the general weighted surface algebras of triangulated surfaces, investigated in Erdmann and Skowro\'nski (J. Algebra 544:170-227, 2020). In particular, we prove that all these algebras are tame periodic algebras of period 4. The main results of this paper form an essential step towards a classification of all symmetric tame periodic algebras of period 4., Comment: 26 pages

We approximate functions defined on smooth bounded domains by elements of the eigenspaces of the Laplacian or the Stokes operator in such a way that the approximations are bounded and converge in both Sobolev and Lebesgue spaces. We prove an abstract result referred to fractional power spaces of positive, self-adjoint, compact-inverse operators on Hilbert spaces, and then obtain our main result by using the explicit form of these fractional power spaces for the Dirichlet Laplacian and Stokes operators. As a simple application, we prove that all weak solutions of the incompressible convective Brinkman--Forchheimer equations posed on a bounded domain in ${\mathbb R}^3$ satisfy the energy equality., Comment: 17 pages

We prove a robustness of regularity result for the $3$D convective Brinkman-Forchheimer equations $$ \partial_tu -\mu\Delta u + (u \cdot \nabla)u + \nabla p + \alpha u + \beta\abs{u}^{r - 1}u = f, $$ for the range of the absorption exponent $r \in [1, 3]$ (for $r > 3$ there exist global-in-time regular solutions), i.e. we show that strong solutions of these equations remain strong under small enough changes of the initial condition and forcing function. We provide a smallness condition which is similar to the robustness conditions given for the $3$D incompressible Navier-Stokes equations by Chernyshenko et al. (2007) and Dashti & Robinson (2008)., Comment: 22 pages

We present Atacama Large Millimeter-Submillimeter Array (ALMA) observations of CK Vulpeculae which is identified with "Nova Vulpeculae 1670". They trace obscuring dust in the inner regions of the associated nebulosity. The dust forms two cocoons, each extending ~5 arcsec north and south of the presumed location of the central star. Brighter emission is in a more compact east-west structure (2 arcsec by 1 arcsec) where the cocoons intersect. We detect line emission in NH$_2$CHO, CN, four organic molecules and C$^{17}$O. CN lines trace bubbles within the dusty cocoons; CH$_3$OH a north-south S-shaped jet; and other molecules a central cloud with a structure aligned with the innermost dust structure. The major axis of the overall dust and gas bubble structure has a projected inclination of ~24 degrees with respect to a 71 arcsec extended "hourglass" nebulosity, previously seen in H alpha. Three cocoon limbs align with dark lanes in the inner regions of the same H alpha images. The central 2 arcsec by 1 arcsec dust is resolved into a structure consistent with a warped dusty disc. The velocity structure of the jets indicates an origin at the centre of this disc and precession with an unknown period. Deceleration regions at both the northern and southern tips of the jets are roughly coincident with additional diffuse dust emission over regions approximately 2 arcsec across. These structures are consistent with a bipolar outflow expanding into surrounding high density material. We suggest that a white dwarf and brown dwarf merged between 1670 and 1672, with the observed structures and extraordinary isotopic abundances generated as a result., Comment: 10 pages, 4 figures, accepted for publication in MNRAS 14th September 2018

Radio continuum observations trace thermal emission of ionized plasma in planetary nebulae and bring useful information on nebular geometries. A model of homogeneous sphere or shell cannot fit the nebular spectra and brightness temperatures. Two alternative models have been proposed in the literature: the first one consists of two homogeneous components, while the other one is a model of a shell with a significant radial density gradient. On the other side, prolate ellipsoidal shell model can successfully fit the surface brightness distribution of selected objects. We verify the existing models using data collected in radio surveys covering wide range of frequencies. In about 50% cases, density gradient can be excluded, and none of the remaining objects could be confirmed. None of the observed planetary nebulae show the spectral index of 0.6 in the optically thick part of the spectrum, which is a value predicted for a shell containing strong radial density gradient. Radio spectra can be fitted with a model of prolate ellipsoidal shell, but also by a shell containing temperature variations in planetary nebulae. At least eight planetary nebulae show two component spectra, with one compact component showing much higher optical thickness than the other one. Unexpectedly, a group of planetary nebulae with lowest surface brightness show non-negligible optical thickness. Their emission comes from compact and dense structures, comprising only small part of total nebular mass., Comment: 22 pages, 20 figures

V4334 Sgr (a.k.a. Sakurai's object) is the central star of an old planetary nebula that underwent a very late thermal pulse a few years before its discovery in 1996. We have been monitoring the evolution of the optical emission line spectrum since 2001. The goal is to improve the evolutionary models by constraining them with the temporal evolution of the central star temperature. In addition the high resolution spectral observations obtained by X-shooter and ALMA show the temporal evolution of the different morphological components., Comment: 2 pages, 2 figures to appear in the Proceedings of the IAU Symp. 323: "Planetary nebulae: Multi-wavelength probes of stellar and galactic evolution". Eds. X.-W. Liu, L. Stanghellini and A. Karakas

In this paper we give a simple proof of the existence of global-in-time smooth solutions for the convective Brinkman-Forchheimer equations (also called in the literature the tamed Navier-Stokes equations) $$ \partial_tu -\mu\Delta u + (u \cdot \nabla)u + \nabla p + \alpha u + \beta|u|^{r - 1}u = 0 $$ on a $3$D periodic domain, for values of the absorption exponent $r$ larger than $3$. Furthermore, we prove that global, regular solutions exist also for the critical value of exponent $r = 3$, provided that the coefficients satisfy the relation $4\mu\beta \geq 1$. Additionally, we show that in the critical case every weak solution verifies the energy equality and hence is continuous into the phase space $L^2$. As an application of this result we prove the existence of a strong global attractor, using the theory of evolutionary systems developed by Cheskidov., Comment: 17 pages

We aimed to verify the nature and derive the basic parameters of the symbiotic star candidate [JD2002] 11. For this purpose, we obtained and analysed an X-Shooter spectrum of [JD2002] 11. We also used optical and infrared photometry available for the object. Emission-line diagnostic ratios are characteristic of a dusty type symbiotic star and reveal a two-component nebula (low- and high-density). The spectral energy distribution is well fitted with a two-component blackbody spectrum with the respective temperatures of 1150 K and 600 K. The total luminosity of $\rm 3000\,L_{\odot}$ is consistent with the expected luminosity of a typical Mira star, embedded in an optically thick dust shell. We conclude that [JD2002] 11 is the ninth symbiotic star in total and only the second dusty type symbiotic star discovered in the Small Magellanic Cloud., Comment: 10 pages, 4 figures, published in Acta Astronomica