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The evolution of massive stars is heavily influenced by their binarity, and the massive eccentric binary system MACHO 80.7443.1718 (ExtEV) serves as a prime example. This study explores whether the light variability of ExtEV, observed near the periastron during its 32.8-day orbit, can be explained by a wind-wind collision (WWC) model and reviews other potential explanations. Using broadband photometry, TESS data, ground-based $UBV$ time-series photometry, and high-resolution spectroscopy, we analysed the system's parameters. We ruled out the presence of a Keplerian disk and periodic Roche-lobe overflow. Our analysis suggests the primary component has a radius of about $30\,{\rm R}_\odot$, luminosity of $\sim6.6\times10^5\,{\rm L}_\odot$, and mass between $25$ and $45\,{\rm M}_\odot$, with a high wind mass-loss rate of $4.5\times10^{-5}\,{\rm M}_\odot\,{\rm yr}^{-1}$, likely enhanced by tidal interactions, rotation, and tidally excited oscillations. We successfully modelled ExtEV's light curve, identifying atmospheric eclipse and light scattering in the WWC cone as key contributors. The system's mass-loss rate exceeds theoretical predictions, indicating that ExtEV is in a rare evolutionary phase, offering insights into enhanced mass loss in massive binary systems., Comment: Accepted for publication in the Bulletin de la Soci\'et\'e Royale des Sciences de Li\`ege, Proceedings of the 41st Li\`ege Astrophysical Colloquium, held in Li\`ege 15-19 July 2024, edited by Y. Naz\'e, & E. Bozzo

Blue large-amplitude pulsators (BLAPs) are a newly discovered group of compact pulsating stars whose origin needs to be explained. Of the existing evolutionary scenarios that could lead to the formation of BLAPs, there are two in which BLAPs are the products of the merger of two stars, either a main sequence star and a helium white dwarf or two low-mass helium white dwarfs. Among over a hundred known BLAPs, three equidistant in frequency modes had been found in one, OGLE-BLAP-001. We show that similar three equidistant in frequency modes exist in yet another BLAP, ZGP-BLAP-08. This perfect separation in frequency is a strong argument to explain the modes in terms of an oblique pulsator model. This model is supported by the character of the changes of the pulsation amplitude and phase with the rotational phase. Consequently, we hypothesize that these two BLAPs are magnetic, as equidistant in frequency pulsation modes should be observed in the presence of a magnetic field whose axis of symmetry does not coincide with the rotation axis. A logical consequence of this hypothesis is to postulate that these two BLAPs could have originated in a merger scenario, just how the origin of magnetic white dwarfs is explained. We also find that period changes in both stars cannot be interpreted by a constant rate of period change and discuss the possible origin of these changes., Comment: 13 pages, 11 figures, 2 tables, accepted for publication in A&A

Blue large-amplitude pulsators (BLAPs) are a recently discovered group of hot stars pulsating in radial modes. Their origin needs to be explained, and several scenarios for their formation have already been proposed. We investigate whether BLAPs can originate as the product of a merger of two low-mass white dwarfs (WDs) and estimate how many BLAPs can be formed in this evolutionary channel. We used the MESA code to model the merger of three different double extremely low-mass (DELM) WDs and the subsequent evolution of the merger product. We also performed a population synthesis of Galactic DELM WDs using the COSMIC code. We find that BLAPs can be formed from DELM WDs provided that the total mass of the system ranges between 0.32 and 0.7 M$_\odot$. BLAPs born in this scenario either do not have any thermonuclear fusion at all or show off-centre He burning. The final product evolves to hot subdwarfs and eventually finishes its evolution either as a cooling He WD or a hybrid He/CO WD. The merger products become BLAPs only a few thousand years after coalescence, and it takes them 20 to 70 thousand years to pass the BLAP region. We found the instability of the fundamental radial mode to be in fair agreement with observations, but we also observed instability of the radial first overtone. From the population synthesis, we found that up to a few hundred BLAPs born in this scenario can exist at present in the Galaxy. Given the estimated number of BLAPs formed in the studied DELM WD merger scenario, there is a good chance to observe BLAPs that originated through this scenario. Since strong magnetic fields can be generated during mergers, this scenario could lead to the formation of magnetic BLAPs. This fits well with the discovery of two likely magnetic BLAPs whose pulsations can be explained in terms of the oblique rotator model., Comment: 14 pages, 9 figures, 2 tables, accepted for publication in A&A

Understanding the mechanisms behind opinion formation is crucial for gaining insight into the processes that shape political beliefs, cultural attitudes, consumer choices, and social movements. This work aims to explore a nuanced model that captures the intricacies of real-world opinion dynamics by synthesizing principles from cognitive science and employing social network analysis. The proposed model is a hybrid continuous-discrete extension of the well-known Naming Game opinion model. The added latent continuous layer of opinion strength follows cognitive processes in the human brain, akin to memory imprints. The discrete layer allows for the conversion of intrinsic continuous opinion into discrete form, which often occurs when we publicly verbalize our opinions. We evaluated our model using real data as ground truth and demonstrated that the proposed mechanism outperforms the classic Naming Game model in many cases, reflecting that our model is closer to the real process of opinion formation.

Evolution of massive stars is dominated by interactions within binary systems. Therefore, it is necessary to investigate all forms of interaction in binary systems that may affect the evolution of the components. One of such laboratories is the massive eccentric binary system MACHO$\,$80.7443.1718 (ExtEV). We examine whether the light variability of the ExtEV can be explained by a wind-wind collision (WWC) binary system model. We conducted an analysis of broadband multi-color photometry of ExtEV, time-series space photometry from TESS, ground-based Johnson $UBV$ photometry, and time-series spectroscopy. We fitted an analytical model of light variations to the TESS light curve of ExtEV. We rule out the possibility of the presence of a disk around the primary component. We also argue that the non-linear wave-breaking scenario may not be consistent with the observations of ExtEV. We refine the orbital parameters of ExtEV and find evidence for the presence of a tertiary component. Using evolutionary models we demonstrate that the primary component's mass is between 25 and 45$\,$M$_\odot$. We successfully reproduce light curve of ExtEV with our model, showing that the dominant processes shaping its light curve are atmospheric eclipse and light scattered in the WWC cone. We also estimate the primary's mass-loss rate due to stellar wind for $4.5\cdot 10^{-5}\,$M$_\odot\,{\rm yr}^{-1}$. We conclude that ExtEV is not an extreme eccentric ellipsoidal variable, but an exceptional WWC binary system. The mass loss rate we derived exceeds theoretical predictions by up to two orders of magnitude. This implies that the wind is likely enhanced by tidal interactions, rotation, and possibly also tidally excited oscillations. ExtEV represents a rare evolutionary phase of a binary system that may help to understand the role of a companion-driven enhanced mass loss in the evolution of massive binary systems., Comment: Accepted for publication in Astronomy&Astrophysics, 23 pages, 15 figures, 10 tables

$\delta$ Orionis is the closest massive multiple stellar system and one of the brightest members of the Orion OB association. The primary (Aa1) is a unique evolved O star. In this work, we applied a two-step disentangling method to a series of spectra in the blue region (430 to 450 nm), and we detected spectral lines of the secondary (Aa2). For the first time, we were able to constrain the orbit of the tertiary (Ab) - to 55 450 d or 152 yr - using variable $\gamma$ velocities and new speckle interferometric measurements, which have been published in the Washington Double Star Catalogue. In addition, the Gaia DR3 parallax of the faint component (Ca+Cb) constrains the distance of the system to (381 $\pm$ 8) pc, which is just in the centre of the Orion OB1b association, at (382 $\pm$ 1) pc. Consequently, we found that the component masses according to the three-body model are 17.8, 8.5, and 8.7 M$_{\odot}$, for Aa1, Aa2, and Ab, respectively, with the uncertainties of the order of $1$ M$_{\odot}$. We used new photometry from the BRITE satellites together with astrometry, radial velocities, eclipse timings, eclipse duration, spectral line profiles, and spectral energy distribution to refine radiative properties. The components, classified as O9.5 II + B2 V + B0 IV, have radii of 13.1, 4.1, and 12.0 R$_{\odot}$, which means that $\delta$ Ori A is a pre-mass-transfer object. The frequency of 0.478 cycles per day, known from the Fourier analysis of the residual light curve and X-ray observations, was identified as the rotation frequency of the tertiary. $\delta$ Ori could be related to other bright stars in Orion, in particular, $\zeta$ Ori, which has a similar architecture, or $\varepsilon$ Ori, which is a single supergiant, and possibly a post-mass-transfer object., Comment: 22 pages, 22 figures

Massive and intermediate-mass stars reside in binary systems much more frequently than low-mass stars. Binaries containing massive main-sequence (MS) component(s) are often characterised by eccentric orbits, and can be observed as eccentric ellipsoidal variables (EEVs). The orbital phase-dependent tidal potential acting on the components of EEV can induce tidally excited oscillations (TEOs). We investigate how the history of resonances between the eigenmode spectra of the EEV components and the tidal forcing frequencies depends on the initial parameters of the system. We synthesised 20,000 evolutionary models of the EEVs across the MS. Later, we calculated the eigenfrequencies for each model. We focused only on the $l=2$, $m=0,+2$ modes. Knowing the temporal changes in the orbital parameters of simulated EEVs and the changes of the eigenfrequency spectra for both components, we were able to determine so-called `resonance curves', which describe the overall chance of a resonance occurring. We analysed the resonance curves by constructing basic statistics for them and analysing their morphology using machine learning methods, including the Uniform Manifold Approximation and Projection tool. The EEV resonance curves from our sample are characterised by striking diversity, including the occurrence of exceptionally long resonances or the absence of resonances for long evolutionary times. Both components may be subject to increased resonance rates as they approach the TAMS. On average, we should observe TEOs more frequently in EEVs containing massive components than intermediate-mass ones. TEOs will be particularly well-pronounced for EEVs with the component(s) close to the TAMS. Given the total number of resonances and their rates, TEOs may play an important role in the transport of angular momentum within massive and intermediate-mass stars (mainly near TAMS)., Comment: 24 pages, 15 figures, accepted for publication in A&A

We present a complex study of the eclipsing binary system, AB Cas. The analysis of the whole TESS light curve, corrected for the binary effects, reveals 112 significant frequency peaks with 17 independent signals. The dominant frequency $f_1 = $17.1564 d$^{-1}$ is a radial fundamental mode. The $O-C$ analysis of the times of light minima from over 92 years leads to a conclusion that due to the ongoing mass transfer the system exhibits a change of the orbital period at a rate of 0.03 s per year. In order to find evolutionary models describing the current stage of AB Cas, we perform binary evolution computations. Our results show the AB Cas system as a product of the rapid non-conservative mass transfer with about 5-26 % of transferred mass lost from the system. This process heavily affected the orbital characteristics of this binary and its components in the past. In fact, this system closely resembles the formation scenarios of EL CVn type binaries. For the first time, we demonstrate the effect of binary evolution on radial pulsations and determine the lines of constant frequency on the HR diagram. From the binary and seismic modelling, we obtain constraints on various parameters. In particular, we constrain the overshooting parameter, $f_{\rm ov}\in [0.010,~0.018]$, the mixing-length parameter, $\alpha_{\rm MLT}\in[1.2,~1.5]$ and the age, $t \in [2.3,~3.4]$ Gyr., Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society Main Journal

Blue large-amplitude pulsators (BLAPs) form a small group of hot objects pulsating in a fundamental radial mode with periods of the order of 30 minutes. Proposed evolutionary scenarios explain them as evolved low-mass stars: either ~0.3 M$_\odot$ shell-hydrogen-burning objects with a degenerated helium core, or more massive (0.5 - 0.8) M$_\odot$ core-helium-burning stars, or ~0.7 M$_\odot$ surviving companions of type Ia supernovae. Therefore, their origin remains to be established. Using data from Transiting Exoplanet Survey Satellite, we discovered that HD 133729 is a binary consisting of a late B-type main-sequence star and a BLAP. The BLAP pulsates with a period of 32.37 min decreasing at a rate of $(-7.11 \pm 0.33)\times 10^{-11}$. Due to light dilution by a brighter companion, the observed amplitude of pulsation is much smaller than in other BLAPs. From available photometry, we derived times of maximum light, which revealed the binary nature of the star via O-C diagram. The diagram shows variations with a period of 23.08433 d that we attribute to the light-travel-time effect in the system. The analysis of these variations allowed to derive the spectroscopic parameters of the BLAP's orbit around the center of the mass of the binary. The presence of a hot companion in the system was confirmed by the analysis of its spectral energy distribution, which was also used to place the components in the H-R diagram. The obtained position of the BLAP fully agrees with the location of the other members of the class. With the estimated V~11 mag and the Gaia distance of less than 0.5 kpc, the BLAP is the brightest and the nearest of all known BLAPs. It may become a clue object in the verification of the evolutionary scenarios for this class of variable. We argue that low-mass progenitors of the BLAP are excluded if the components are coeval and no mass transfer between the components took place., Comment: 11 pages, 7 figures, accepted for publication in A&A

We present time-series photometry of 21 nearby Type II Cepheids in the near-infrared J, H and Ks passbands. We use this photometry, together with the Third Gaia Early Data Release parallaxes, to determine for the first time period-luminosity relations (PLRs) for Type II Cepheids from field representatives of these old pulsating stars in the near-infrared regime. We found PLRs to be very narrow for BL Herculis stars, which makes them candidates for precision distance indicators. We then use archival photometry and the most accurate distance obtained from eclipsing binaries to recalibrate PLRs for Type II Cepheids in the Large Magellanic Cloud (LMC). Slopes of our PLRs in the Milky Way and in the LMC differ by slightly more than 2{\sigma} and are in a good agreement with previous studies of the LMC, Galactic Bulge and Galactic Globular Clusters Type II Cepheids samples. We use PLRs of Milky Way Type II Cepheids to measure the distance to the LMC and we obtain a distance modulus of 18.540$\pm$0.026(stat.)$\pm$0.034(syst.)mag in the WJKs Wesenheit index. We also investigate the metallicity effect within our Milky Way sample and we find rather significant value of about -0.2mag/dex in each band meaning that more metal-rich Type II Cepheids are intrinsically brighter than their more metal-poor counterparts, in agreement with the value obtained from Type II Cepheids in Galactic Globular Clusters. The main source of systematic error on our Milky Way PLRs calibration and the LMC distance is the current uncertainty of the Gaia parallax zero point., Comment: Accepted for ApJ

We present a collection of 991 heartbeat star (HBS) candidates found in the Optical Gravitational Lensing Experiment (OGLE) project data archive. We discuss the selection process of the HBS candidates and the structure of the catalog itself. It consists of 512 stars located toward the Galactic bulge (GB), 439 stars located in the Large Magellanic Cloud (LMC), and 40 in the Small Magellanic Cloud (SMC). The collection contains two large groups of HBSs with different physical properties. The main distinction between the two groups is the evolutionary status of the primary star. The first group of about 100 systems contains a hot main-sequence (MS) or a Hertzsprung-gap primary star, while the second group of about 900 systems includes a red giant (RG). For each star, we provide two-decade-long time-series photometry, in the Cousins $I$- and Johnson $V$-band filters, obtained by the OGLE project. We also present basic observational information as well as orbital parameters derived from the light curve modeling., Comment: 13 pages (17 pages in arXiv version), 11 figures, 5 tables. The full machine-readable tables are provided by the publisher. The catalog is available via OGLE website: https://astrouw.edu.pl/ogle/ogle4/OCVS/. Erratum; in the publisher version of the paper, there are wrong reference numbers to the figures from Paper II: Figures 8--9 --> Figures 9--10, Figure 10 --> Figure 11, Figure 11 --> Figure 12

We present an analysis of 991 heartbeat stars (HBSs) from the OGLE Collection of Variable Stars (OCVS). The sample consists of 512 objects located toward the Galactic bulge (GB), 439 in the Large Magellanic Cloud (LMC) and 40 in the Small Magellanic Cloud (SMC). We model the $I$-band OGLE light curves using an analytical model of flux variations, reflecting tidal deformations between stars. We present distributions of the model parameters that include the eccentricity, orbital inclination, and argument of the periastron, but also the period-amplitude diagrams. On the Hertzsprung-Russell (HR) diagram, our HBS sample forms two separate groups of different evolutionary status. The first group of about 90 systems, with short orbital periods ($P\lesssim50$~days), consists of an early-type primary star lying on (or close to) the main sequence (MS). The second group of about 900 systems, with long orbital periods ($P\gtrsim100$~days), contains a red giant (RG). The position of RG HBSs on the period-luminosity diagram strongly indicates their binary nature. They appear to be a natural extension of confirmed binary systems that include the OGLE ellipsoidal and Long Secondary Period (LSP) variables. We also present a time-series analysis leading to detection of tidally-excited oscillations (TEOs). We identify such pulsations in about 5\% of stars in the sample with a total number of 78 different modes. This first relatively large homogeneous sample of TEOs allowed us to construct a diagram revealing the correlation between the TEO's orbital harmonic number and the eccentricity of the host binary system., Comment: 22 pages (29 pages in arXiv version), 12 figures, 3 tables

Eccentric ellipsoidal variables (aka heartbeat stars) is a class of eccentric binaries in which proximity effects, tidal distortion due to time-dependent tidal potential in particular, lead to measurable photometric variability close to the periastron passage. The varying tidal potential may also give rise to tidally-excited oscillations (TEOs). TEOs may play an important role in the dynamical evolution of massive eccentric systems. Our study is aimed at the detection of TEOs and characterisation of the long-term behaviour of their amplitudes and frequencies in the extreme-amplitude heartbeat star MACHO 80.7443.1718, consisting of a blue supergiant and a late O-type massive dwarf. We use two seasons of Transiting Exoplanet Survey Satellite (TESS) observations of the target to obtain new 30-min cadence photometry by means of the difference image analysis of TESS full-frame images. In order to extend the analysis to longer time scales, we supplement the TESS data with 30-years long ground-based photometry of the target. We confirm the detection of the known $n=23$, 25, and 41 TEOs and announce the detection of two new TEOs, with $n=24$ and 230, in the photometry of MACHO 80.7443.1718. Amplitudes of all TEOs were found to vary on a time scale of years or months. For $n=25$ TEO amplitude and frequency changes are related, which may indicate that the main cause of the amplitude drop of this TEO in TESS observations is the change of its frequency and increase of detuning parameter. The light curve of the $n=230$ TEO is strongly non-sinusoidal. Its high frequency may indicate that the oscillation is a strange mode. We also find that the orbital period of the system decreases at the rate of about 11 s(yr)$^{-1}$, which can be explained by a significant mass loss or mass transfer in the system with a possible contribution from tidal dissipation., Comment: 19 pages, 17 figures, 6 tables, accepted for publication in A&A

Heartbeat stars are eccentric binaries exhibiting characteristic shape of brightness changes during periastron passage caused by tidal distortion of the components. Variable tidal potential can drive tidally excited oscillations (TEOs), which are usually gravity modes. Studies of heartbeat stars and TEOs open a new possibility to probe interiors of massive stars. There are only a few massive (masses of components $\gtrsim 2 $M$_\odot$) systems of this type known. Using TESS data from the first 16 sectors, we searched for new massive heartbeat stars and TEOs using a sample of over 300 eccentric spectroscopic binaries. We analysed TESS 2-min and 30-min cadence data. Then, we fitted Kumar's analytical model to the light curves of stars showing heartbeats and performed times-series analysis of the residuals searching for TEOs and periodic intrinsic variability. We found 20 massive heartbeat systems, of which seven show TEOs. The TEOs occur at harmonics of orbital frequencies in the range between 3 and 36, with the median value equal to 9, lower than those in known Kepler systems with TEOs. The most massive system in this sample is the quadruple star HD 5980, a member of Small Magellanic Cloud. With the total mass of $\sim$150 M$_{\odot}$ it is the most massive system showing a heartbeat. Six stars in the sample of the new heartbeat stars are eclipsing. Comparison of the parameters derived from fitting Kumar's model and from light-curve modelling shows that Kumar's model does not provide reliable parameters. Finally, intrinsic pulsations of $\beta$ Cep, SPB, $\delta$ Sct, and $\gamma$ Dor-type were found in nine heartbeat systems. This opens an interesting possibility of studies of pulsation-binarity interaction and the co-existence of forced and self-excited oscillations., Comment: 23 pages, 15 figures, 5 tables, accepted for publication in A&A

We present the discovery and asteroseismic analysis of a new g-mode hot B subdwarf (sdB) pulsator, EC 21494-7018 (TIC 278659026), monitored in TESS first sector using 120-second cadence. The light curve analysis reveals that EC 21494-7018 is a sdB pulsator counting up to 20 frequencies associated with independent g-modes. The seismic analysis singles out an optimal model solution in full agreement with independent measurements provided by spectroscopy (atmospheric parameters derived from model atmospheres) and astrometry (distance evaluated from Gaia DR2 trigonometric parallax). Several key parameters of the star are derived. Its mass (0.391 +/- 0.009 Msun) is significantly lower than the typical mass of sdB stars, and suggests that its progenitor has not undergone the He-core flash, and therefore could originate from a massive (>2 Msun) red giant, an alternative channel for the formation of hot B subdwarfs. Other derived parameters include the H-rich envelope mass (0.0037 +/- 0.0010 Msun), radius (0.1694 +/- 0.0081 Rsun), and luminosity (8.2+/-1.1 Lsun). The optimal model fit has a double-layered He+H composition profile, which we interpret as an incomplete but ongoing process of gravitational settling of helium at the bottom of a thick H-rich envelope. Moreover, the derived properties of the core indicate that EC 21494-7018 has burnt ~43% (in mass) of its central helium and possesses a relatively large mixed core (Mcore = 0.198 +/- 0.010 Msun), in line with trends already uncovered from other g-mode sdB pulsators analysed with asteroseismology. Finally, we obtain for the first time an estimate of the amount of oxygen (in mass; X(O)core = 0.16 -0.05 +0.13) produced at this stage of evolution by an helium-burning core. This result, along with the core-size estimate, is an interesting constraint that may help to narrow down the still uncertain C12(alpha,gamma)O16 nuclear reaction rate., Comment: Published in A&A

We present the first results from the Transiting Exoplanet Survey Satellite (TESS) on the rotational and pulsational variability of magnetic chemically peculiar A-type stars. We analyse TESS 2-min cadence data from sectors 1 and 2 on a sample of 83 stars. Five new rapidly oscillating Ap (roAp) stars are announced. One of these pulsates with periods around 4.7 min, making it the shortest period roAp star known to date. Four out of the five new roAp stars are multiperiodic. Three of these, and the singly-periodic one show the presence of rotational mode splitting. Individual frequencies are provided in all cases. In addition, seven previously known roAp stars are analysed. Additional modes of oscillation are found in some stars, while in others we are able to distinguish the true pulsations from possible aliases present in the ground-based data. We find that the pulsation amplitude in the TESS filter is typically a factor 6 smaller than that in the $B$ filter which is usually used for ground-based observations. For four roAp stars we set constraints on the inclination angle and magnetic obliquity, through the application of the oblique pulsator model. We also confirm the absence of roAp-type pulsations down to amplitude limits of 6 and 13 micromag, respectively, in two of the best characterised non-oscillating Ap (noAp) stars. We announce 27 new rotational variables along with their rotation periods, and provide different rotation periods for seven other stars. Finally, we discuss how these results challenge state-of-the-art pulsation models for roAp stars., Comment: 29 pages, accepted for publication in the MNRAS