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 Hα 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 massloss rate estimates is not higher than about 1.6. On the other hand, our predictions are by factor of 4.7 lower than pure Hα mass-loss rate estimates and can be reconciled with these values only assuming a microclumping factor of at least eight.

Aims. Both empirical evidence and theoretical findings indicate that the stellar winds of massive early-type stars are inhomogeneous, i.e., porous and clumpy. For relatively dense winds, empirically derived mass-loss rates might be reconciled with predictions if these empirical rates are corrected for clumping. The predictions, however, do not account for structure in the wind. To allow for a consistent comparison, we investigate and quantify the effect of clumpiness and porosity of the outflow on the predicted wind energy and the maximal effect on the mass-loss rate of O-type stars. Methods. Combining non-LTE model atmospheres and a Monte Carlo method to compute the transfer of momentum from the photons to the gas, the effect of clumping and porosity on the energy transferred from the radiation field to the wind is computed in outflows in which the clumping and porosity stratification is parameterized by heuristic prescriptions. Results. The impact of structure in the outflow on the wind energy is complex and is a function of stellar temperature, the density of gas in the clumps, and the physical scale of the clumps. If the medium is already clumped in the photosphere, the emergent radiation field will be softer, slightly increasing the wind energy of relatively cool O stars (30 000 K) but slightly decreasing it for relatively hot O stars (40 000 K). More important is that as a result of recombination of the gas in a clumped wind the line force increases. However, because of porosity the line force decreases, simply because photons may travel in-between the clumps, avoiding interactions with the gas. If the changes in the wind energy only affect the mass-loss rate and not the terminal velocity of the flow, we find that the combined effect of clumpiness and porosity is a small reduction in the mass-loss rate if the clumps are smaller than 1/100th the local density scale height H ρ . In this case, empirical mass-loss determinations based on Hα fitting and theory match for stars with dense winds (Ṁ > ∼ 10 −7 M yr −1 ) if the overdensity of gas in the clumps, relative to the case of a smooth wind, is modest. For clumps larger than 1/10th H ρ , the predicted mass-loss rates exhibit almost the same dependence on clumpiness as do empirical rates. We show that this implies that empirical and predicted mass-loss rates can no longer be matched. Very high overdensities of gas in clumps of such large size may cause the predictedṀ to decrease by a factor of from 10 to 100. This type of structure is likely not to be the cause of the "weak-wind problem" in early-type stars, unless a mechanism can be identified that causes extreme structure to develop in winds for whichṀ < ∼ 10 −7 M yr −1 (weak winds) that is not active in denser winds.

1Ú stav teoretické fyziky a astrofyziky, Masarykova univerzita, Kotlářská 2, CZ-611 37 Brno, Czech Republic and ABSTRACT 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.

Context. Recent studies of O-type stars have demonstrated that discrepant mass-loss rates are obtained when different diagnostic methods are employed. Fitting the unsaturated UV resonance lines (e.g., P v) gives drastically lower values than obtained from the Hα emission. Wind inhomogeneity (so-called "clumping") may be the main cause of this discrepancy. Aims. In a previous paper, we presented 3D Monte-Carlo calculations for the formation of scattering lines in a clumped stellar wind. In the present paper we select five O-type supergiants (from O4 to O7) and test whether the reported discrepancies can be resolved this way. Methods. In the first step, the analyses started with simulating the observed spectra with Potsdam Wolf-Rayet (PoWR) non-LTE model atmospheres. The mass-loss rates are adjusted to fit to the observed Hα emission lines best. For the unsaturated UV resonance lines (i.e., P v) we then applied our 3D Monte-Carlo code, which can account for wind clumps of any optical depths ("macroclumping"), a non-void interclump medium, and a velocity dispersion inside the clumps. The ionization stratifications and underlying photospheric spectra were adopted from the PoWR models. The properties of the wind clumps were constrained by fitting the observed resonance line profiles.Results. Our results show that with the mass-loss rates that fit Hα (and other Balmer and He ii lines), the UV resonance lines (especially the unsaturated doublet of P v) can also be reproduced with no problem when macroclumping is taken into account. There is no need to artificially reduce the mass-loss rates or to assume a subsolar phosphorus abundance or an extremely high clumping factor, unlike what was claimed by other authors. These consistent mass-loss rates are lower by a factor of 1.3 to 2.6, compared to the mass-loss rate recipe from Vink et al. Conclusions.Macroclumping resolves the previously reported discrepancy between Hα and P v mass-loss diagnostics.

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∼ 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 find any significant influence of X‐rays on P v ionization fraction implying that the presence of X‐rays cannot explain the P v 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.

Context. The true mass-loss rates from massive stars are important for many branches of astrophysics. For the correct modeling of the resonance lines, which are among the key diagnostics of stellar mass-loss, the stellar wind clumping has been found to be very important. To incorporate clumping into a radiative transfer calculation, three-dimensional (3D) models are required. Various properties of the clumps may have a strong impact on the resonance line formation and, therefore, on the determination of empirical mass-loss rates. Aims. We incorporate the 3D nature of the stellar wind clumping into radiative transfer calculations and investigate how different model parameters influence the resonance line formation. Methods. We develop a full 3D Monte Carlo radiative transfer code for inhomogeneous expanding stellar winds. The number density of clumps follows the mass conservation. For the first time, we use realistic 3D models that describe the dense as well as the tenuous wind components to model the formation of resonance lines in a clumped stellar wind. At the same time, we account for nonmonotonic velocity fields. Results. The 3D density and velocity wind inhomogeneities show that there is a very strong impact on the resonance line formation. The different parameters describing the clumping and the velocity field results in different line strengths and profiles. We present a set of representative models for various sets of model parameters and investigate how the resonance lines are affected. Our 3D models show that the line opacity is lower for a larger clump separation and shallower velocity gradients within the clumps. Conclusions. Our model demonstrates that to obtain empirically correct mass-loss rates from the UV resonance lines, the wind clumping and its 3D nature must be taken into account.

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.

Abstract. We show that the so-called Gayley-Owocki (Doppler) heating is important for the temperature structure of the wind of main sequence stars cooler than the spectral type O6. The formula for Gayley-Owocki heating is derived directly from the Boltzmann equation as a direct consequence of the dependence of the driving force on the velocity gradient. Since Gayley-Owocki heating deposits heat directly on the absorbing ions, we also investigated the possibility that individual components of the radiatively driven stellar wind have different temperatures. This effect is negligible in the wind of O stars, whereas a significant temperature difference takes place in the winds of main sequence B stars for stars cooler than B2. Typical temperature differences between absorbing ions and other flow components for such stars is of the order 10 3 K. However, in the case when the passive component falls back onto the star, the absorbing component reaches temperatures of order 10 6 K, which allows for emission of X-rays. Moreover, we compare our computed terminal velocities with the observed ones. We found quite good agreement between predicted and observed terminal velocities. The systematic difference coming from the using of the so called "cooking formula" has been removed.