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Several models have been proposed to explain missing red giants (RGs) near the Galactic centre. Recently, a scenario has been suggested that predicts, among other processes, a long-term ablation of the surface layers of RGs during their repetitive passages through the Galactic jet (Zaja\v{c}ek et al., 2020). In this study, we perform detailed three-dimensional numerical modelling of this phenomenon. We calculate the ablation rate of the surface layers of a RG orbiting the supermassive black hole (SMBH) as it passes through the nuclear jet. In particular, we model the jet-star interaction for approximately 10 passages for the closer orbital distance of $10^{-3}\,\text{pc}$ and 2 passages for $10^{-2}\,\text{pc}$. We find that the mass loss due to ablation by the jet behaves with time as $\Delta M_{\star}\propto \sqrt{t}$ and the total ablated mass during a single active galactic nucleus (AGN) phase ($10^5$ years) is $\sim 10^4\,M_{\odot}$. We arrive at similar rates of the stellar ablation for the relatively smaller jet luminosity $10^{42}\,\text{erg}\,\text{s}^{-1}$ as in the previous analytical calculations. For larger jet luminosities of $10^{44}$ and $10^{48}\,\text{erg}\,\text{s}^{-1}$, the ablation rates inferred from $\sim 10$ interactions as well as extrapolated power-law fits are significantly lower than analytical values. For the smallest orbital distance of $10^{-3}\,\text{pc}$, we also track the thermal behaviour of the stellar surface layer, whose temperature appears to grow rapidly during the first 10 passages from $\sim 3600\,{\rm K}$ (spectral type M) to $\sim 8500\,{\rm K}$ (spectral type A). RG-jet interactions can thus lead to observable changes in the nuclear late-type stellar population., Comment: 19 pages, 20 figures, 2 tables; submitted to MNRAS; comments welcome

Auroral emission lines result from the interaction between magnetic field and stellar wind, offering valuable insights into physical properties and processes occurring within magnetospheres of celestial bodies. While extensively studied in planetary and exoplanetary atmospheres, in ultra-cool dwarfs, and as radio emission from early-type stars, the presence of specific auroral emission lines in hot star spectra remains unexplored. In this study, we utilized TLUSTY code to simulate the auroral lines, while modelling the effect of the interaction between stellar wind and magnetosphere through X-ray irradiation. Utilizing high-resolution synthetic spectra generated from model atmospheres, we identified potential candidate lines indicative of auroral emission, which were absent in non-irradiated spectra. Emission lines in synthetic spectra were present primarily in the infrared domain. The most prominent line generated by irradiation was He ii 69458 A, which appeared in all our model atmospheres with effective temperatures ranging from 15 kK to 30 kK. We also calculated the minimum irradiation required to detect emission in this most prominent line. The presence of emission lines was interpreted by considering changes in the population of different excited states of given atoms. Besides the appearance of infrared emission lines, high-energy irradiation causes infrared excess. To complement our simulations, we also searched for auroral lines in Far Ultraviolet Spectroscopic Explorer (FUSE) observations, which are deposited in the Multimission Archive at Space Telescope (MAST) catalogue. The comparison of observed spectra with synthetic spectra did not identify any possible candidate emission lines in FUSE spectra., Comment: 13 pages, accepted for publication in Monthly Notices of the Royal Astronomical Society

Betelgeuse, a red supergiant star of semi-regular variability, reached a historical minimum brightness in February 2020, known as the Great Dimming. Even though the brightness has returned to the values prior to the Great Dimming now, it continues to exhibit highly unusual behavior. Our goal is to study long-term dynamics of the photosphere, including during the Great Dimming. We applied the tomographic method, which allows different layers in the stellar atmosphere to be probed in order to reconstruct depth-dependent velocity fields. The method is based on the construction of spectral masks by grouping spectral lines from specific optical depths. These masks are cross-correlated with the observed spectra to recover the velocity field inside each atmospheric layer. We obtained about 2800 spectra over the past 15 years that were observed with the STELLA robotic telescope in Tenerife. We analyzed the variability of five different layers of Betelgeuse's photosphere. We found phase shift between the layers, as well as between the variability of velocity and photometry. The time variations of the widths of the cross-correlation function reveal propagation of two shockwaves during the Great Dimming. For about two years after the dimming, the timescale of variability was different between the inner and outer photospheric layers. By 2022, all the layers were pulsating with higher frequency corresponding with the first overtone. The combination of the extensive high-resolution spectroscopic data set with the tomographic method revealed the variable velocity fields in the photosphere of Betelgeuse, for the first time in such detail. Our results demonstrate that powerful shocks are the triggering mechanism for episodic mass-loss events, which may be the missing component to explain the mass-loss process in red supergiants., Comment: 14 pages, accepted for publication in Astronomy & Astrophysics

Context: Radiative transfer modelling of expanding stellar envelopes is an important task in their analysis. To account for inhomogeneities and deviations from spherical symmetry, it is necessary to develop a 3D approach to radiative transfer modelling. Aims: We present a 3D Monte Carlo code for radiative transfer modelling, which is aimed to calculate the plasma ionisation and excitation state with the statistical equilibrium equations, moreover, to implement photon-matter coupling. As a first step, we present our Monte Carlo radiation transfer routines developed and tested from scratch. Methods: The background model atmosphere (the temperature, density, and velocity structure) can use an arbitrary grid referred to as the model grid (modGrid). The radiative transfer was solved using the Monte Carlo method in a Cartesian grid, referred to as the propagation grid (propgrid). This Cartesian grid was created based on the structure of the modgrid; correspondence between these two grids was set at the beginning of the calculations and then kept fixed. The propgrid can be either regular or adaptive; two modes of adaptive grids were tested. The accuracy and calculation speed for different propgrids was analysed. Photon interaction with matter was handled using the Lucy's macroatom approach. Test calculations using our code were compared with the results obtained by a different Monte Carlo radiative transfer code. Results: Our method and the related code for the 3D radiative transfer using the Monte Carlo and macroatom methods offer an accurate and reliable solution for the radiative transfer problem, and are especially promising for the inclusion and treatment of 3D inhomogeneities., Comment: 21 pages

Betelgeuse is a pulsating red supergiant whose brightness is semi periodically variable and in February 2020 reached a historical minimum, the Great Dimming. The aims of this study are to characterize Betelgeuse's variability based on available archival data and to study possible causes of light variability. Many spectra, from ultraviolet and optical regions, were evaluated for spectral analysis. The spectra were used primarily to determine radial velocities from different layers of atmosphere and their long{-}term evolution. Additionally, photometric data were analyzed in different filters as well, to construct light curves and to determine periods of the variability. Spectroscopic and photometric variability are compared to each other and given into a context with the Great Dimming. The two most dominant photometric periods are $ P_{1} = 2190 \pm 270 \: \rm d $ and $ P_{2} = 417 \pm 17 \: \rm d $, while the dominant optical radial velocity periods are $ P_{1, v_{\rm r}} = 2510 \pm 440 \: \rm d $ and $ P_{2, v_{\rm r}} = 415 \pm 11 \: \rm d $. In the same time, the radial velocity determined from ultraviolet spectra also shows variability and is distinctively different from the variability of photospheric velocity, undergoing longer periods of variability. We attribute these velocities to the velocities at the base of outflowing wind. We also report a maximum of stellar wind velocity during the Great Dimming, accompanied by the previously reported minimum of brightness and the maximum of photospheric radial velocity. After the Dimming, Betelgeuse mode of variability has fundamentally changed and is now instead following a shorter period of $ \sim 200 \: \rm d $., Comment: 12 pages, 4 figures, 5 tables

Line-driven wind instability is expected to cause small-scale wind inhomogeneities, X-ray emission, and wind line profile variability. The instability can already develop around the sonic point if it is initiated close to the photosphere due to stochastic turbulent motions. In such cases, it may leave its imprint on the light curve as a result of wind blanketing. We study the photometric signatures of the line-driven wind instability. We used line-driven wind instability simulations to determine the wind variability close to the star. We applied two types of boundary perturbations: a sinusoidal one that enables us to study in detail the development of the instability and a stochastic one given by a Langevin process that provides a more realistic boundary perturbation. We estimated the photometric variability from the resulting mass-flux variations. The variability was simulated assuming that the wind consists of a large number of independent conical wind sectors. We compared the simulated light curves with TESS light curves of OB stars that show stochastic variability. We find two typical signatures of line-driven wind instability in photometric data: a knee in the power spectrum of magnitude fluctuations, which appears due to engulfment of small-scale structure by larger structures, and a negative skewness of the distribution of fluctuations, which is the result of spatial dominance of rarefied regions. These features endure even when combining the light curves from independent wind sectors. The stochastic photometric variability of OB stars bears certain signatures of the line-driven wind instability. The distribution function of observed photometric data shows negative skewness and the power spectra of a fraction of light curves exhibit a knee. This can be explained as a result of the line-driven wind instability triggered by stochastic base perturbations., Comment: 9 pages, accepted for publication in Astronomy & Astrophysics

Massive stars lose a significant fraction of mass during their evolution. However, the corresponding mass-loss rates are rather uncertain. To improve this, we calculated global line-driven wind models for Galactic B supergiants. Our models predict radial wind structure directly from basic stellar parameters. The hydrodynamic structure of the flow is consistently determined from the photosphere in nearly hydrostatic equilibrium to supersonically expanding wind. The radiative force is derived from the solution of the radiative transfer equation in the comoving frame. We provide a simple formula that predicts theoretical mass-loss rates as a function of stellar luminosity and effective temperature. The mass-loss rate of B supergiants slightly decreases with temperature down to about 22.5 kK, where the region of recombination of Fe IV to Fe III starts to appear. In this region, which is about 5 kK wide, the mass-loss rate gradually increases by a factor of about 6. The increase of the mass-loss rate is associated with a gradual decrease of terminal velocities by a factor of about 2. We compared the predicted wind parameters with observations. While the observed wind terminal velocities are reasonably reproduced by the models, the situation with mass-loss rates is less clear. The mass-loss rates derived from observations that are uncorrected for clumping are by a factor of 3 to 9 higher than our predictions on cool and hot sides of the studied sample, respectively. These observations can be reconciled with theory assuming a temperature-dependent clumping factor. On the other hand, the mass-loss rate estimates that are not sensitive to clumping agree with our predictions much better. Our predictions are by a factor of about 10 lower than the values currently used in evolutionary models appealing for reconsideration of the role of winds in the stellar evolution., Comment: 13 pages, accepted for publication in Astronomy & Astrophysics, ver. 2 (inclusion of more precise values in Table 3)

The upper main sequence stars CU Virginis is the most enigmatic object among magnetic chemically peculiar (mCP) stars. It is an unusually fast rotator showing strictly periodic light variations in all regions of the electromagnetic spectrum, as well as spectroscopic and spectropolarimetric changes. At same time, it is also the first radio main-sequence pulsar. Exploiting information hidden in phase variations, we monitored the secular oscillation of the rotational period during the last 53 years. Applying own phenomenological approach, we analyzed 37\,975 individual photometric and spectroscopic measurements from 72 data sources and improved the O-C model. All the relevant observations indicate that the secular period variations can be well approximated by the fifth degree polynomial., Comment: 6 pages, 3 figures, improved version of the proceeding contribution 2019ASPC..518..125M

The inhomogeneous surface distribution of heavy elements is known to cause periodic light variability of magnetic chemically peculiar stars. It is unclear to what extent the same paradigm applies to mercury-manganese (HgMn) stars. We aim to model the photometric variability of the HgMn star {\phi}Phe using abundance maps obtained from high-resolution spectroscopy and to study how this variability evolves with time. We compute a grid of ATLAS12 model atmospheres and the corresponding SYNSPEC synthetic spectra. Interpolating within this grid and integrating the specific intensity over the visible stellar surface at different rotational phases, we obtain theoretical light curves of the star. We predict the variability of {\phi} Phe in the ultraviolet and in the visible spectral regions with amplitude of the order of millimagnitudes, mainly caused by absorption in lines of yttrium, chromium, and titanium. We also show how this variability is affected by changes of the distribution of the heavy elements over time. The main characteristics of the predicted light variability of {\phi} Phe correspond roughly to the variability of the star observed with the TESS satellite.

HD\,37776 (V901\,Ori, B2\,Vp), also known as Landstreet's Star, is possibly the most remarkable magnetic chemically peculiar (mCP) star known. Zeeman Doppler Imaging revealed this young, rapidly rotating star's surface magnetic field to be not only the strongest ($\sim 30$ kG) of the He-strong class of hot mCP stars but also by far the most topologically complex. In contrast to the overwhelming majority of mCP stars, which are well described by tilted dipoles, Landstreet's Star's non-axisymmetric surface magnetic field is entirely dominated by high-order spherical harmonics. It is one of the handful of stars for which rotational period change has been measured, and over the past two decades of monitoring, the object has demonstrated an unexpected acceleration in its rotation that so far defies explanation. Recently acquired TESS data have provided a photometric data set of unprecedented precision. These data have revealed a highly stable yet multi-featured light curve, making Landstreet's Star the prototype of hot mCP stars whose light curves are difficult to reproduce using the standard model of chemical/photometric spots modulated by solid-body rotation., Comment: 8 pages, 8 figures, JDL workshop proceedings

Massive stars are characterized by a significant loss of mass either via spherically symmetric stellar winds or pre-explosion pulses, or by aspherical forms of circumstellar matter (CSM) such as bipolar lobes or outflowing circumstellar equatorial disks. A significant fraction of most massive stars end their lives by a core collapse; supernovae (SNe) are always located inside circumstellar envelopes created by their progenitors. We study the dynamics and thermal effects of collision between expanding ejecta of SNe and CSM that may be formed during, for example, a sgB[e] star phase, a luminous blue variable phase, around PopIII stars, or by various forms of accretion. For time-dependent hydrodynamic modeling we used our own code built with a finite volumes method. The code is highly efficient for calculations of shocks and physical flows with large discontinuities. The initial geometry of the disks corresponds to a density structure of a material that orbits in Keplerian trajectories. We examine the behavior of the density, pressure, velocity of expansion, and temperature structure in the interaction zone under various geometrical configurations of dense equatorial disks. Our `low density' model shows significant asphericity in the case of the disk mass-loss rate $\dot{M}_\text{csd}=10^{-6}\,M_\odot\,\text{yr}^{-1}$. The models also show the zones of overdensity in the SN - disk contact region and indicate the development of Kelvin-Helmholtz instabilities within the zones of shear between the disk and the more freely expanding material outside the disk.

We present a comprehensive overview of the properties of a sample of 41 magnetic chemically peculiar stars that have been recently identified in the Kepler field by our team (H\"{u}mmerich et al. 2018). The stars populate the whole age range from zero-age to terminal-age main sequence in the mass interval from 1.5 to 4 Ms. Several of the studied objects exhibit a hitherto unobserved wealth of detail in their light curves indicative of persisting complex surface structures. Monoperiodic variability and light curve stability were identified as cardinal criteria for selecting mCP star candidates among early-type objects in photometric surveys. Subsequent studies will be concerned with an exhaustive follow-up analysis of the new mCP stars, which we expect to lead to new insights on the physics of the CP star phenomenon., Comment: 8 pages, 11 figures, Astronomical Society of the Pacific Conference Series, proceedings from a conference "Physics of Magnetic Stars", Special Astrophysical Observatory, Russia, 1-5 October, 2018

In wind-powered X-ray binaries, the radiatively driven stellar wind from the primary may be inhibited by the X-ray irradiation. This creates the feedback that limits the X-ray luminosity of the compact secondary. Wind inhibition might be weakened by the effect of small-scale wind inhomogeneities (clumping) possibly affecting the limiting X-ray luminosity. We study the influence of X-ray irradiation on the stellar wind for different radial distributions of clumping. We calculate hot star wind models with external irradiation and clumping using our global wind code. The models are calculated for different parameters of the binary. We determine the parameters for which the X-ray wind ionization leads to a decrease of the radiative force. This causes a decrease of the wind velocity and even of the mass-loss rate in the case of extreme X-ray irradiation. Clumping weakens the effect of X-ray irradiation because it favours recombination and leads to an increase of the wind mass-loss rate. The best match between the models and observed properties of high-mass X-ray binaries (HMXB) is derived with radially variable clumping. We describe the influence of X-ray irradiation on the terminal velocity and on the mass-loss rate in a parametric way. The X-ray luminosities predicted within the Bondi theory agree nicely with observations when accounting for X-ray irradiation. The ionizing feedback regulates the accretion onto the compact companion resulting in a relatively stable X-ray source. The wind-powered accretion model can account for large luminosities in HMXBs only when introducing the ionizing feedback. There are two possible states following from the dependence of X-ray luminosity on the wind terminal velocity and mass-loss rate. One state has low X-ray luminosity and a nearly undisturbed wind, and the second state has high X-ray luminosity and exhibits a strong influence of X-rays on the flow., Comment: 15 pages, accepted for publication in Astronomy & Astrophysics

We provide mass-loss rate predictions for O stars from Large and Small Magellanic Clouds. We calculate global (unified, hydrodynamic) model atmospheres of main sequence, giant, and supergiant stars for chemical composition corresponding to Magellanic Clouds. The models solve radiative transfer equation in comoving frame, kinetic equilibrium equations (also known as NLTE equations), and hydrodynamical equations from (quasi-)hydrostatic atmosphere to expanding stellar wind. The models allow us to predict wind density, velocity, and temperature (consequently also the terminal wind velocity and the mass-loss rate) just from basic global stellar parameters. As a result of their lower metallicity, the line radiative driving is weaker leading to lower wind mass-loss rates with respect to the Galactic stars. We provide a formula that fits the mass-loss rate predicted by our models as a function of stellar luminosity and metallicity. On average, the mass-loss rate scales with metallicity as $ \dot M\sim Z^{0.59}$. The predicted mass-loss rates are lower than mass-loss rates derived from H$\alpha$ diagnostics and can be reconciled with observational results assuming clumping factor $C_\text{c}=9$. On the other hand, the predicted mass-loss rates either agree or are slightly higher than the mass-loss rates derived from ultraviolet wind line profiles. The calculated \ion{P}{v} ionization fractions also agree with values derived from observations for LMC stars with $T_\text{eff}\leq40\,000\,$K. Taken together, our theoretical predictions provide reasonable models with consistent mass-loss rate determination, which can be used for quantitative study of stars from Magellanic Clouds., Comment: accepted for publication in A&A, 12 pages, 8 figures

Context. Evolution of massive stars is affected by a significant loss of mass either via (nearly) spherically symmetric stellar winds or by aspherical mass-loss mechanisms, namely the outflowing equatorial disks. However, the scenario that leads to the formation of a disk or rings of gas and dust around massive stars is still under debate. Aims. We study the hydrodynamic and thermal structure of optically thick, dense parts of outflowing circumstellar disks that may be formed around various types of critically rotating massive stars, for example, Be stars, B[e] supergiant (sgB[e]) stars or Pop III stars. Methods. We specify the optical depth of the disk along the line-of-sight from stellar poles. Within the optically thick dense region we calculate the vertical disk thermal structure using the diffusion approximation while for the optically thin outer layers we assume a local thermodynamic equilibrium with the impinging stellar irradiation. We use two of our own types of hydrodynamic codes: two-dimensional operator-split numerical code and unsplit code based on the Roe's method. Results. Our models show the geometric distribution and contribution of viscous heating that begins to dominate in the central part of the disk. In the models of dense viscous disks the viscosity increases the central temperature up to several tens of thousands of Kelvins. The high mass-loss rates and high viscosity lead to instabilities with significant waves or bumps in density and temperature in the very inner disk region. Conclusions. The two-dimensional radial-vertical models of dense outflowing disks including the full Navier-Stokes viscosity terms show very high temperatures that are however limited to only the central disk cores inside the optically thick area, while near the edge of the optically thick region the temperature may be low enough for the existence of neutral hydrogen., Comment: 24 pages, 21 figures

We calculate global (unified) wind models of main-sequence, giant, and supergiant O stars from our Galaxy. The models are calculated by solving hydrodynamic, kinetic equilibrium (also known as NLTE) and comoving-frame (CMF) radiative transfer equations from the (nearly) hydrostatic photosphere to the supersonic wind. For given stellar parameters, our models predict the photosphere and wind structure and in particular the wind mass-loss rates without any free parameters. Our predicted mass-loss rates are by a factor of 2--5 lower than the commonly used predictions. A possible cause of the difference is abandoning of the Sobolev approximation for the calculation of the radiative force, because our models agree with predictions of CMF NLTE radiative transfer codes. Our predicted mass-loss rates agree nicely with the mass-loss rates derived from observed near-infrared and X-ray line profiles and are slightly lower than mass-loss rates derived from combined UV and H$\alpha$ diagnostics. The empirical mass-loss rate estimates corrected for clumping may therefore be reconciled with theoretical predictions in such a way that the average ratio between individual mass-loss rate estimates is not higher than about $ 1.6 $. On the other hand, our predictions are by factor of $ 4.7 $ lower than pure H$\alpha$ mass-loss rate estimates and can be reconciled with these values only assuming a microclumping factor of at least eight., Comment: 13 pages, 5 figures, accepted for publication in Astronomy & Astrophysics

The magnetic chemically peculiar (mCP) stars of the upper main sequence exhibit periodic light, magnetic, radio, and spectroscopic variations that can be adequately explained by a model of a rigidly rotating magnetized star with persistent surface structures. The majority of mCP stars rotate at strictly constant periods. However, there are a few mCP stars whose rotation periods vary on timescales of decades while the shape of their phase curves remains unchanged. In the case of CU Vir and V901 Ori, we have detected cyclic period variations. We demonstrate that the period oscillations of CU Vir may be a consequence of the interaction of the internal magnetic field and differential rotation., Comment: 4 pages, 2 figures, ASPCS, proceedings of the conference: STARS: FROM COLLAPSE TO COLLAPSE, 3-7 October, 2016 @ Karachay-Cherkess Republic

Rayleigh scattering is a result of an interaction of photons with bound electrons. Rayleigh scattering is mostly neglected in calculations of hot star model atmospheres because most of the hydrogen atoms are ionized and the heavier elements have a lower abundance than hydrogen. In atmospheres of some chemically peculiar stars, helium overabundant regions containing singly ionized helium are present and Rayleigh scattering can be a significant opacity source. We evaluate the contribution of Rayleigh scattering by neutral hydrogen and singly ionized helium in the atmospheres of hot stars with solar composition and in the atmospheres of helium overabundant stars. We computed several series of model atmospheres using the TLUSTY code and emergent fluxes using the SYNSPEC code. These models describe atmospheres of main sequence B-type stars with different helium abundance. We used an existing grid of models for atmospheres with solar chemical composition and we calculated an additional grid for helium-rich stars with $N$(He)/$N$(H)=10. Rayleigh scattering by neutral hydrogen can be neglected in atmospheres of hot stars, while Rayleigh scattering by singly ionized helium can be a non-negligible opacity source in some hot stars, especially in helium-rich stars., Comment: Astronomy & Astrophysics, the second version, cross section (9) and (15) were corrected

Hot stars emit large amounts of X-rays, which are assumed to originate in the supersonic stellar wind. Part of the emitted X-rays is subsequently absorbed in the wind and influences its ionization state. Because hot star winds are driven radiatively, the modified ionization equilibrium affects the radiative force. We review the recent progress in modelling the influence of X-rays on the radiative equilibrium and on the radiative force. We focus particularly on single stars with X-rays produced in wind shocks and on binaries with massive components, which belong to the most luminous objects in X-rays., Comment: 9 pages, 5 figures, accepted for publication in Advances in Space Research

Context: The presence of heavier chemical elements in stellar atmospheres influences the spectral energy distribution (SED) of stars. An uneven surface distribution of these elements, together with flux redistribution and stellar rotation, are commonly believed to be the primary causes of the variability of chemically peculiar (CP) stars. Aims: We aim to model the photometric variability of the CP star PHI Dra based on the assumption of inhomogeneous surface distribution of heavier elements and compare it to the observed variability of the star. We also intend to identify the processes that contribute most significantly to its photometric variability. Methods: We use a grid of TLUSTY model atmospheres and the SYNSPEC code to model the radiative flux emerging from the individual surface elements of PHI Dra with different chemical compositions. We integrate the emerging flux over the visible surface of the star at different phases throughout the entire rotational period to synthesise theoretical light curves of the star in several spectral bands. Results: The synthetic light curves in the visible and in the near-UV regions are in very good agreement with the observed variability of the star. The lack of usable far-UV measurements of the star precludes making any conclusions about the correctness of our model in this spectral region. We also obtained 194 new BVRI observations of PHI Dra and improved its rotational period to P=1.716500(2). Conclusions: We show that the inhomogeneous distribution of elements, flux redistribution, and rotation of the star are fully capable of explaining the stellar variability in the visible and the near-UV regions. The flux redistribution is mainly caused by bound--free transitions of silicon and bound--bound transitions of iron.

Binaries with hot massive components are strong X-ray sources. Besides the intrinsic X-ray emission of individual binary members originating in their winds, X-ray emission stems from the accretion on the compact companion or from wind collision. Since hot star winds are driven by the light absorption in the lines of heavier elements, wind acceleration is sensitive to the ionization state. Therefore, the over-ionization induced by external X-ray source strongly influences the winds of individual components. We studied the effect of external X-ray irradiation on hot star winds. We used our kinetic equilibrium (NLTE) wind models to estimate the influence of external X-ray ionization for different X-ray luminosities and source distances. The models are calculated for parameters typical of O stars. The influence of X-rays is given by the X-ray luminosity, by the optical depth between a given point and the X-ray source, and by a distance to the X-ray source. Therefore, the results can be interpreted in the diagrams of X-ray luminosity vs.~the optical depth parameter. X-rays are negligible in binaries with low X-ray luminosities or at large distances from the X-ray source. The influence of X-rays is stronger for higher X-ray luminosities and in closer proximity of the X-ray source. There is a forbidden area with high X-ray luminosities and low optical depth parameters, where the X-ray ionization leads to wind inhibition. There is excellent agreement between the positions of observed stars in these diagrams and our predictions. All wind-powered high-mass X-ray binary (HMXB) primaries lie outside the forbidden area. Many of them lie close to the border of the forbidden area, indicating that their X-ray luminosities are self-regulated. We discuss the implications of our work for other binary types., Comment: 16 pages, accepted for publication in A&A

BS Cir is a representative of moderately cool magnetic chemically peculiar stars which displays very strong light variations in Stroemgren index c1 indicating large changes in the height of the Balmer jump. We present two-spot model of light variations fitting successfully all of nine light curves obtained in the spectral region 335-750 nm. We also discuss the nature of the observed variations of intensities of Fe, Cr, Ti, Si, Mg and RE spectral lines and possible mechanisms matching the observed light variations. It was confirmed that the observed period of BS Cir 2.204 d is rising with the rate of dP/dt=5.4(4)x10^-9. The found minor secular changes in the shape of light curve should be compatible with the period changes caused by precessional motion due to magnetic distortion of the star., Comment: 8 pages, 5 figures, conference proceedings ASP CS, 494 (2015)

Evolutionary models of fast-rotating stars show that the stellar rotational velocity may approach the critical speed. Critically rotating stars cannot spin up more, therefore they lose their excess angular momentum through an equatorial outflowing disk. The radial extension of such disks is unknown, partly because we lack information about the radial variations of the viscosity. We study the magnetorotational instability, which is considered to be the origin of anomalous viscosity in outflowing disks. We used analytic calculations to study the stability of outflowing disks submerged in the magnetic field. The magnetorotational instability develops close to the star if the plasma parameter is large enough. At large radii the instability disappears in the region where the disk orbital velocity is roughly equal to the sound speed. The magnetorotational instability is a plausible source of anomalous viscosity in outflowing disks. This is also true in the region where the disk radial velocity approaches the sound speed. The disk sonic radius can therefore be roughly considered as an effective outer disk radius, although disk material may escape from the star to the insterstellar medium. The radial profile of the angular momentum-loss rate already flattens there, consequently, the disk mass-loss rate can be calculated with the sonic radius as the effective disk outer radius. We discuss a possible observation determination of the outer disk radius by using Be and Be/X-ray binaries., Comment: 8 pages, accepted for publication in Astronomy & Astrophysics

During their evolution massive stars can reach the phase of critical rotation when a further increase in rotational speed is no longer possible. Direct centrifugal ejection from a critically or near-critically rotating surface forms a gaseous equatorial decretion disk. Anomalous viscosity provides the efficient mechanism for transporting the angular momentum outwards. The outer part of the disk can extend up to a very large distance from the parent star. We study the evolution of density, radial and azimuthal velocity, and angular momentum loss rate of equatorial decretion disks out to very distant regions. We investigate how the physical characteristics of the disk depend on the distribution of temperature and viscosity. We calculated stationary models using the Newton-Raphson method. For time-dependent hydrodynamic modeling we developed the numerical code based on an explicit finite difference scheme on an Eulerian grid including full Navier-Stokes shear viscosity. The sonic point distance and the maximum angular momentum loss rate strongly depend on the temperature profile and are almost independent of viscosity. The rotational velocity at large radii rapidly drops accordingly to temperature and viscosity distribution. The total amount of disk mass and the disk angular momentum increase with decreasing temperature and viscosity. The time-dependent one-dimensional models basically confirm the results obtained in the stationary models as well as the assumptions of the analytical approximations. Including full Navier-Stokes viscosity we systematically avoid the rotational velocity sign change at large radii. The unphysical drop of the rotational velocity and angular momentum loss at large radii (present in some models) can be avoided in the models with decreasing temperature and viscosity.

Hot star wind mass-loss rates depend on the abundance of individual elements. This dependence is usually accounted for assuming scaled solar chemical composition. However, this approach may not be justified in evolved rotating stars. The rotational mixing brings CNO-processed material to the stellar surface, increasing the abundance of nitrogen at the expense of carbon and oxygen, which potentially influences the mass-loss rates. We study the influence of the modified chemical composition resulting from the rotational mixing on the wind parameters, particularly the wind mass-loss rates. We use our NLTE wind code to predict the wind structure and compare the calculated wind mass-loss rate for the case of scaled solar chemical composition and the composition affected by the CNO cycle. We show that for a higher mass-fraction of heavier elements $Z/Z_\odot\gtrsim0.1$ the change of chemical composition from the scaled solar to the CNO-processed scaled solar composition does not significantly affect the wind mass-loss rates. The missing line force caused by carbon and oxygen is compensated for by nitrogen line force. However, for a very low-mass fraction of heavier elements $Z/Z_\odot\lesssim0.1$ the rotational mixing significantly affects the wind mass-loss rates. Moreover, the decrease of the mass-loss rate with metallicity is stronger at such low metallicities. We study the relevance of the wind momentum-luminosity relationship for different metallicities and show that for a metallicity $Z/Z_\odot\lesssim0.1$ the relationship displays a large scatter, which depreciates the use of this relationship at the lowest metallicities., Comment: 7 pages, 5 figures, accepted for publication in Astronomy & Astrophysics

We calculate radiatively driven wind models of main-sequence B stars and provide the wind mass-loss rates and terminal velocities. The main-sequence mass-loss rate strongly depends on the stellar effective temperature. For the hottest B stars the mass-loss rate amounts to $10^{-9}\,\text{M}_\odot\,\text{year}^{-1}$, while for the cooler ones themass-loss rate is lower by more than three orders of magnitude. Main-sequence B stars with solar abundance and effective temperatures lower than about$15\,000\,\text{K}$ (later than spectral type B5) do not have any homogeneous line-driven wind. We predict the wind mass-loss rates for the solar chemical composition and for the modified abundance of heavier elements to study the winds of chemically peculiar stars. The mass-loss rate may either increase or decrease with increasing abundance, depending on the importance of the induced emergent flux redistribution. Stars with overabundant silicon may have homogeneous winds even below the solar abundance wind limit at $15\,000\,\text{K}$. The winds of main-sequence B stars lie below the static limit, that is, a static atmosphere solution is also possible. This points to an important problem regarding the initiation of these winds. We discuss the implications of our models for rotational braking, filling the magnetosphere of Bp stars, and for chemically peculiar stars., Comment: 10 pages, 7 figures, Astronomy&Astrophysics, in press, discussion extended and languange corrections included

The majority of magnetic chemically peculiar (mCP) stars exhibit periodic light, magnetic, radio, and spectroscopic variations that can be adequately modelled as a rigidly-rotating main-sequence star with persistent surface structures. Nevertheless, there is a small sample of diverse mCP stars whose rotation periods vary on timescales of decades while the shapes of their phase curves remain unchanged. Alternating period increases and decreases have been suspected in the hot CP stars CU Vir and V901 Ori, while rotation in the moderately cool star BS Cir has been decelerating. These examples bring new insight into this theoretically unpredicted phenomenon. We discuss possible causes of such behaviour and propose that dynamic interactions between a thin, outer, magnetically-confined envelope braked by the stellar wind, and an inner faster-rotating stellar body are able to explain the observed rotational variability, Comment: 10 pages, 4 figures, contribution for the proceedings of the conference Putting A Stars into Context, June 3-7, 2013, Moscow, Russia

Massive stars may during their evolution reach the phase of critical rotation when the further increase in rotational speed is no longer possible. The ejection of matter in the equatorial region forms the gaseous outflowing disk, which allows the star to remove the excess of its angular momentum. The outer part of the disk can extend up to large distance from the parent star. We study the evolution of density, radial and azimuthal velocity and angular momentum loss rate of equatorial decretion disk up to quite distant outer regions. We calculate the evolution of density, radial and azimuthal velocity from the initial Keplerian state until the disk approaches the final stationary state., Comment: Conference proceedings article: Massive stars: from alpha to Omega, 10-14 June 2013, Rhodes, Greece

Vela X-1 is the archetype of high-mass X-ray binaries, composed of a neutron star and a massive B supergiant. The supergiant is a source of a strong radiatively-driven stellar wind. The neutron star sweeps up this wind, and creates a huge amount of X-rays as a result of energy release during the process of wind accretion. Here we provide detailed NLTE models of the Vela X-1 envelope. We study how the X-rays photoionize the wind and destroy the ions responsible for the wind acceleration. The resulting decrease of the radiative force explains the observed reduction of the wind terminal velocity in a direction to the neutron star. The X-rays create a distinct photoionized region around the neutron star filled with a stagnating flow. The existence of such photoionized bubbles is a general property of high-mass X-ray binaries. We unveiled a new principle governing these complex objects, according to which there is an upper limit to the X-ray luminosity the compact star can have without suspending the wind due to inefficient line driving, Comment: accepted for publication in ApJ, 6 pages, 4 figures

Different diagnostics of hot star wind mass-loss rates provide results that are difficult to reconcile with each other. The widely accepted presence of clumping in hot star winds implies a significant reduction of observational mass-loss rate estimates from diagnostics that depend on the square of the density. Moreover, the ultraviolet Pv resonance lines indicate a possible need for even stronger reduction of hot star mass-loss rates, provided that Pv is a dominant ionization stage of phosphorus at least in some hot stars. The latter assumption is challenged by a possible presence of the XUV radiation. Here we study the influence of the XUV radiation on the Pv ionization fraction in the hot star winds. By a detailed solution of the hydrodynamical, radiative transfer, and statistical equilibrium equations we confirm that sufficiently strong XUV radiation source may decrease the Pv ionization fraction, possibly depreciating the Pv lines as a reliable mass-loss rate indicator. On the other hand, the XUV radiation influences also the ionization fraction of heavier ions that drive the wind, leading to a decrease of the wind terminal velocity. Consequently, we conclude that the XUV radiation alone can not bring theory and observations in accord. We fit our predicted wind mass-loss rates by a suitable formula and compare the results with the observational mass-loss rate diagnostics. We show that for supergiants and giants the theoretical predictions do not contradict the mass-loss rate estimates based on X-ray line profiles or density squared diagnostics. On the other hand, for main-sequence stars the predicted mass-loss rates are still significantly higher than that inferred from Pv or X-ray lines. This indicates that the "weak wind problem" recently detected in low-luminosity main-sequence stars may occur to some extent also for the stars with higher luminosity., Comment: Accepted for publication in MNRAS. The definitive version is available at www.blackwell-synergy.com. 8 pages, 5 figures

CU Vir and V901 Ori belong among these few magnetic chemically peculiar stars whose rotation periods vary on timescales of decades. We aim to study the stability of the periods in CU Vir and V901 Ori using all accessible observational data containing phase information. We collected all available relevant archived observations supplemented with our new measurements of these stars and analysed the period variations of the stars using a novel method that allows for the combination of data of diverse sorts. We found that the shapes of their phase curves were constant, while the periods were changing. Both stars exhibit alternating intervals of rotational braking and acceleration. The rotation period of CU Vir was gradually shortening until the year 1968, when it reached its local minimum of 0.52067198 d. The period then started increasing, reaching its local maximum of 0.5207163 d in the year 2005. Since that time the rotation has begun to accelerate again. We also found much smaller period changes in CU Vir on a timescale of several years. The rotation period of V901 Ori was increasing for the past quarter-century, reaching a maximum of 1.538771 d in the year 2003, when the rotation period began to decrease. A theoretically unexpected alternating variability of rotation periods in these stars would remove the spin-down time paradox and brings a new insight into structure and evolution of magnetic upper-main-sequence stars., Comment: 5 pages, 3 figures

The velocity law of hot star winds is usually parameterized via the so-called beta velocity law. Although this parameterization stems from theoretical considerations, it is not the most accurate description of the wind velocity law that follows from hydrodynamical calculations. We show that the velocity profile of our hydrodynamical wind models is described much better by polynomial approximation. This approximation provides a better fit than the beta velocity law already for the same number of free parameters., Comment: 3 pages, 2 figures, accepted for publication in Astronomy & Astrophysics

Photometrically and spectroscopically variable chemically peculiar (CP) stars are the optimum laboratories for testing the rotational evolution of main sequence stars. A vast majority of well-studied CP stars have quite steady rotational periods (e.g. SrCrEu star CQ UMa). However, there are several CP stars that exhibit apparent period variations. The origin of the period variations is unclear in many cases. We describe the observed period variations of several individual CP stars, especially V901 Ori, sigma Ori E, HR 7355, CU Vir, SX Ari, and EE Dra. The CP stars with unsteady periods now represent a very diverse group with dissimilar O-C diagrams and time scales. We also discuss the causes of the period changes found and a possible cyclicity or chaoticity of them., Comment: 9 pages, 10 figures, Proceedings of the conference "Magnetic Stars" held in SAO RAS Nizhnij Arkhyz, Russia, Aug./Sept. 2010, Editors I.I.Romanyuk, D.0.Kudrzavtsev

We provide hot star wind models with radiative force calculated using the solution of comoving frame (CMF) radiative transfer equation. The wind models are calculated for the first stars, O stars, and the central stars of planetary nebulae. We show that without line overlaps and with solely thermal line broadening the pure Sobolev approximation provides a reliable estimate of the radiative force even close to the wind sonic point. Consequently, models with the Sobolev line force provide good approximations to solutions obtained with non-Sobolev transfer. Taking line overlaps into account, the radiative force becomes slightly lower, leading to a decrease in the wind mass-loss rate by roughly 40%. Below the sonic point, the CMF line force is significantly lower than the Sobolev one. In the case of pure thermal broadening, this does not influence the mass-loss rate, as the wind mass-loss rate is set in the supersonic part of the wind. However, when additional line broadening is present (e.g., the turbulent one) the region of low CMF line force may extend outwards to the regions where the mass-loss rate is set. This results in a decrease in the wind mass-loss rate. This effect can at least partly explain the low wind mass-loss rates derived from some observational analyses of luminous O stars., Comment: 10 pages, accepted for publication in Astronomy & Astrophysics, correction of some typos

During the evolution of rotating first stars, which initially consisted of only hydrogen and helium, CNO elements may emerge to their surface. These stars may therefore have winds that are driven only by CNO elements. We study weak wind effects (Gayley-Owocki heating and multicomponent effects) in stellar winds of first generation stars driven purely by CNO elements. We apply our NLTE multicomponent models and hydrodynamical simulations. The multicomponent effects (frictional heating and decoupling) are important particularly for low metallicity winds, but they influence mass loss rate only if they cause decoupling for velocities lower than the escape velocity. The multicomponent effects also modify the feedback from first stars. As a result of the decoupling of radiatively accelerated metals from hydrogen and helium, the first low-energy cosmic ray particles are generated. We study the interaction of these particles with the interstellar medium concluding that these particles easily penetrate the interstellar medium of a given minihalo. We discuss the charging of the first stars by means of their winds. Gayley-Owocki heating, frictional heating, and the decoupling of wind components occur in the winds of evolved low-metallicity stars and the solar metallicity main-sequence stars., Comment: 10 pages, accepted for publication in Astronomy & Astrophysics

We calculate NLTE models of stellar winds of hot compact stars (central stars of planetary nebulae and subdwarf stars). The studied range of subdwarf parameters is selected to cover a large part of these stars. The models predict the wind hydrodynamical structure and provide mass-loss rates for different abundances. Our models show that CNO elements are important drivers of subdwarf winds, especially for low-luminosity stars. We study the effect of X-rays and instabilities on these winds. Due to the line-driven wind instability, a significant part of the wind could be very hot., Comment: 7 pages, to appear in Astrophysics and Space Science. The final publication will be available at springerlink.com.

Magnetic chemically peculiar (mCP) stars of the upper part of the main sequence usually exhibit strictly periodic variations of their light, spectrum and magnetic field. These changes can be well explained using the oblique rotator model of the rigidly rotating star with persistent photometric spots, uneven horizontal abundance of chemical elements and dipole-like magnetic field. Long-term observations of mCP stars variability enable to determine their rotational periods with an extraordinary accuracy and reliability. We compare rotational periods of mCP stars with those of normal main sequence stars of the same spectral type and discuss the found discrepancies. We also discuss the cases of mCP stars V901 Ori, SX Ari, CU Vir, (and possibly also EE Dra), which have been reported to display an increase of their rotational periods., Comment: 13 pages, pictures included, conference proceedings

We study the influence of X-rays on the wind structure of selected O stars. For this purpose we use our non-local thermodynamic equilibrium (NLTE) wind code with inclusion of additional artificial source of X-rays, assumed to originate in the wind shocks. We show that the influence of shock X-ray emission on wind mass-loss rate is relatively small. Wind terminal velocity may be slightly influenced by the presence of strong X-ray sources, especially for stars cooler than Teff < 35 000 K. We discuss the origin of the Lx/L \sim 10^-7 relation. For stars with thick wind this relation can be explained assuming that the cooling time depends on wind density. Stars with optically thin winds exhibiting the "weak wind problem" display enhanced X-ray emission which may be connected with large shock cooling length. We propose that this effect can explain the "weak wind problem". Inclusion of X-rays leads to a better agreement of the model ionization structure with observations. However, we do not found any significant influence of X-rays on Pv ionization fraction implying that the presence of X-rays cannot explain the Pv problem. We study the implications of modified ionization equilibrium due to shock emission on the line transfer in the X-ray region. We conclude that the X-ray line profiles of helium-like ions may be affected by the line absorption within the cool wind., Comment: 16 pages, accepted for publication in MNRAS

During the evolution of first stars, the CNO elements may emerge on their surfaces due to the mixing processes. Consequently, these stars may have winds driven purely by CNO elements. We study the properties of such stellar winds and discuss their influence on the surrounding environment. For this purpose, we used our own NLTE models and tested which stellar parameters of the first stars at different evolutionary stages result in CNO winds. If such winds are possible, we calculate their hydrodynamic structure and predict their parameters. We show that, while the studied stars do not have any wind driven purely by hydrogen and helium, CNO driven winds exist in more luminous stars. On the other hand, for very hot stars, CNO elements are too ionized to drive a wind. In most cases the derived mass-loss rate is much less than calculated with solar mixture of elements. This is because wind mass-loss rate in present hot stars is dominated by elements heavier than CNO. We conclude that, until a sufficient amount of these elements is created, the influence of line-driven winds is relatively small on the evolution of hot stars (which are not close to the Eddington limit)., Comment: 10 pages, accepted for publication in A&A; corrected typos

Thermal wind emission in the form of free-free and free-bound emission is known to show up in the infrared and radio continuum of hot and massive stars. For OB supergiants with moderate mass loss rates and a wind velocity distribution with \beta = 0.8...1.0, no influence of the wind to the optical continuum, i.e. for \lambda < 1 micron, is expected. Investigations of stellar and wind parameters of OB supergiants over the last few years suggest, however, that for many objects \beta is much higher than 1.0, reaching values up to 3.5. We investigate the influence of the free-free and free-bound emission on the emerging radiation, especially at optical wavelengths, from OB supergiants having wind velocity distributions with \beta > 1. For the case of a spherically symmetric, isothermal wind in local thermodynamical equilibrium (LTE) we calculate the free-free and free-bound processes and the emerging wind and total continuum spectra. We localize the generation region of the optical wind continuum and especially focus on the influence of a \beta-type wind velocity distribution with \beta > 1 on the formation of the wind continuum at optical wavelengths. The optical wind continuum is found to be generated within about 2 R_* which is exactly the wind region where \beta strongly influences the density distribution. We find that for \beta > 1, the continuum of a typical OB supergiant can indeed be contaminated with thermal wind emission, even at optical wavelengths. The strong increase in the optical wind emission is dominantly produced by free-bound processes., Comment: 8 pages, 12 figures, accepted for publication in A&A

We study the influence of clumping on the predicted wind structure of O-type stars. For this purpose we artificially include clumping into our stationary wind models. When the clumps are assumed to be optically thin, the radiative line force increases compared to corresponding unclumped models, with a similar effect on either the mass-loss rate or the terminal velocity (depending on the onset of clumping). Optically thick clumps, alternatively, might be able to decrease the radiative force., Comment: 3 pages, to appear in the proceedings of workshop 'Clumping in Hot Star Winds', eds. W.-R. Hamann, A. Feldmeier, & L. Oskinova

The influence of the wind to the total continuum of OB supergiants is discussed. For wind velocity distributions with \beta > 1.0, the wind can have strong influence to the total continuum emission, even at optical wavelengths. Comparing the continuum emission of clumped and unclumped winds, especially for stars with high \beta values, delivers flux differences of up to 30% with maximum in the near-IR. Continuum observations at these wavelengths are therefore an ideal tool to discriminate between clumped and unclumped winds of OB supergiants., Comment: 3 pages, to appear in the workshop proceedings 'Clumping in Hot Star Winds', eds. W.-R. Hamann, A. Feldmeier, & L. Oskinova

We calculate the uvby light curves of the helium-strong chemically peculiar (CP) star HD 37776. Assuming that the chemical peculiarity influences the monochromatic radiative flux due to mainly the bound-free processes and using the model of the surface distribution of helium and silicon on HD 37776, as derived from spectroscopy, we calculate the emergent fluxes for a series of its rotational phases. We show that it is possible to consistently simulate light curves of a chemically peculiar star and that the basic properties of variability of helium CP stars can be understood in terms of the model of spots with a peculiar chemical composition., Comment: 5 pages, will be published in Magnetic Stars, eds. Iosif Romanyuk & Dmitry Kudryavtsev

We compare the hot star wind models calculated assuming older solar abundance determination with models calculated using the recently published values derived from 3D hydrodynamical model atmospheres. We show that the use of new abundances with lower metallicity improves the agreement between wind observation and theory in several aspects: (1) The predicted wind mass-loss rates are lower by a factor of 0.76. This leads to a better agreement with mass-loss rate determinations derived from observations with account of clumping. (2) As a result of the lowering of mass-loss rates, there is a better agreement between predicted modified wind momentum-luminosity relationship and that derived from observations with account of clumping. (3) Both the lower mass fraction of heavier elements and lower mass-loss rates lead to a decrease of the opacity in the X-ray region. This has influence on the prediction of the X-ray line profile shapes. (4) There is a better agreement between predicted PV ionization fractions and those derived from observations., Comment: 4 pages, accepted for publication in Astronomy & Astrophysics Letters

We study the influence of the frictional heating on the wind line-profiles of SMC stars. For this purpose we use our NLTE wind code to obtain consistent occupation numbers of studied levels and our radiative transfer code to solve the radiative transfer equation in moving media. We compare predicted wind line profiles calculated with and without frictional heating for a low-luminosity SMC star with a weak wind and discuss the relevance of frictional heating as a solution of a "weak-wind problem" for this star., Comment: 2 pages; to appear in the proceedings of workshop "Mass loss from stars and the evolution of stellar clusters", A. de Koter, L. Smith & R. Waters, eds

We study the influence of X-ray radiation on the wind parameters of O stars. For this purpose we use our own NLTE wind code. The X-ray emission (assumed to be generated in wind shocks) is treated as an input quantity. We study its influence on the mass-loss rate, terminal velocity and ionization state of the stellar wind of Galactic O stars., Comment: 2 pages; to appear in the proceedings of workshop "Mass loss from stars and the evolution of stellar clusters", A. de Koter, L. Smith & R. Waters, eds