Recent work on numerical modelling of radiation-driven disk winds is summarised and discussed in the context of extreme B emission line stars.

For the modelling of the radiation fields in stellar winds and the resulting forces new efficient algorithms are presented. In the first one, the radiative transfer equation for moving 3D media is solved analytically with the assumption that the source function is known, eg. from the solution of the NLTE rate equations. For a wind with inhomogeneities an a-posteriori error controlled finite element code is described that takes scattering explicitly into account. Finally, we present possibilities for the accurate inclusion of an arbitrary number of spectral lines in a deterministic and in a stochastic way.

The Sobolev approximation for supersonic flows creates an effective opacity distribution that is nonisotropic, because the line-of-sight velocity gradient is different in different directions. To better understand the importance of this phenomenon in a simplified geometry, we consider line-driven flows in the plane-parallel zero-sound-speed limit, and solve for the wind driven by radiation with an arbitrary angular distribution. One conclusion, surprising at first glance, is that the acceleration component normal to the surface is independent of both the strength and angular profile of the driving radiation field. The flow tilt and overall mass-loss rate do depend on the character of the radiation field. Also interesting is that mass loss through a surface may be generated or enhanced by irradiation that originates above the surface.

We present the effects that inhomogeneities have on radiating atmospheres. It is shown that nonuniformities in a medium induce a reduction of the effective opacity which subsequently increases the Eddington Luminosity. The most striking effect however that arises from the dependence of the opacity on the inhomogeneities, is the possibility of a phase transition, where the atmosphere energetically favors exciting horizontally propagating waves due to large fluxes.

We discuss the evidence for the existence of bi-stable stellar winds of early type stars, both theoretically and observationally. The ratio between the terminal wind velocity and the escape velocity drops steeply from about 2.6 for stars with Teff > 21 000 K to about 1.3 at Teff < 21 000 K. This is the bi-stability jump, which is due to a change in the ionization of the wind and in the wind driving lines. The mass loss rate increases across the jump by about a factor 2 to 5 from the hotter to the cooler stars. The mass flux from rapidly rotating stars can also show the bi-stability jump at some lattitude between the pole and the equator, with a slow high density wind in the equatorial region and a faster low density wind from the poles. This might explain the disks of rapidly rotating B[e] stars, formed by the Rotation Induced Bi-stability mechanism. We discuss the RIB mechanism and its properties. We also describe some future improvements of the model.

Here we explore three types of models in which the combination of magnetic fields with line driving forces leads to faster winds than line forces alone. The fields can change the flow geometry; they can couple with rotation and transmit angular momentum; and they can carry transverse Alfvén waves. All three can lead to a deposition of momentum beyond the critical point and accelerate winds. Some history of the attempts to use magnetic fields to understand hot star winds is discussed and several new models for magnetic rotator B[e] winds are presented.

The upper main sequence chemically peculiar (CP) stars display evidence of trapped circumstellar gas and nonspherical outflows. These stars are also known to possess strong magnetic fields that are often highly inclined to the rotational axis. Their phenomenology can be understood by using the oblique rotator model, which has successfully accounted for the observed behavior of the cooler CP stars. This paper reviews some features of the oblique rotator model, in which the magnetic field is assumed to provide a rigid framework for the structuring of the stellar and circumstellar gas. Corotation of circumstellar plasma is enforced out to the Alfven radius in the magnetic equatorial plane, while for the hotter stars, a radiatively driven wind emerges from the magnetic polar caps. Some observable consequences of the model are discussed, especially the Hα and ultraviolet resonance line absorption and emission periodic variability that has been observed in the He-peculiar stars and nonthermal radio emission. Magnetospheres may also be present in O stars, e.g. θ1 Ori C, and in the Herbig Ae/Be stars.

We consider the effect of large scale magnetic fields on the circumstellar environment of hot stars. In these stars, magnetic fields of order of 100 G lead to magnetically confined wind shocks (MCWS) and then to the existence of large X-ray emitting region. MCWS lead also to the presence of corotating cooling disks around hot stars.

We discuss the case of θ1 Ori C, which is perhaps the hottest analog to Bp stars and consider the effect from rotation and instabilities. We finally discuss the case of the Herbig Ae-Be HD 104237 and show that MCWS might also explain the X-ray emission from this star.

Variability is a fundamental property of O-star winds. One of the major breakthroughs in this field of research has been the recognition that wind variability is cyclical in nature. This suggests that stellar rotation is an important piece in the unsolved puzzle of the wind-variability mechanism. The current idea is that Corotating Interacting Regions (CIRs) are responsible for the observed wind variability. These conclusions are based on detailed and extensive monitoring of ultraviolet resonance lines formed throughout the stellar wind, and subordinate lines like Hα which probe the regions close to the star.

Hot stars are known to emit X-rays with LX/Lbol ~ 10−7 for O stars, falling to ~ 10−9 for B3 stars. These stars also lose mass at large rates through their high-speed winds. Over the years, several types of production mechanisms have been proposed to explain the X-ray emission from O stars, with source locations ranging from very near the stellar surface to very far from the star. A coronal X-ray source was originally proposed (Cassinelli and Olson 1979) to explain the presence of anomalously high ionization stages observed as P Cygni line profiles in the UV spectra of O stars. At the other extreme, Chlebowski (1989) suggested that the X-rays of O stars originate far from the star, and are produced by the interaction of the stellar wind with circumstellar matter. A model in which shocks forming due to instabilities in the line-driven winds of O stars was proposed by Lucy (1982), and studied in detail by Owocki et al. (1988), Cooper (1994), and Feldmeier (1996). In this case, the X-ray emission originates in a large number of shock-heated regions distributed throughout the wind. The shocked-wind model has also been shown to be consistent with the X-ray emission from early-B stars, such as τ Sco (MacFarlane and Cassinelli 1989). However, it appears difficult for shocked wind models to explain the X-ray emission from B3 and later stars because of their presumed low mass loss rates (Cohen et al.1997).

X-ray surveys carried out with the Einstein Observatory (Chlebowski et al. 1989) and ROSAT (Berghöfer et al. 1996) have shown that all O stars are soft X-ray emitters. Since O star winds are opaque at soft X-ray energies the stars or their photospheres cannot be the origin of the observed X-ray emission, thus, this emission must be produced in their stellar winds. Obviously, the X-ray emission is connected to dynamical processes present in the winds of O stars; steady-state computations for O star winds which are able to explain many of the observational features cannot predict any X-ray emission.

Lucy & White (1980) suggested the presence of hot gas in the stellar winds which is produced in shocks developing from the growth of instabilities in the winds; supersonic wind flows in O stars are known to be intrinsically unstable. Numerical simulations confirmed this scenario. However, so far these simulations are limited to one or two dimensions and are not able to explain for instance the observed X-ray luminosity of O stars.

The manifestation of instability and nonhomogeneity of the atmospheres and winds of β Ori, HD 168607, 6 Cas and other highly luminous B7–A3 stars are considered on the basis of visible and near-infrared spectra obtained with CCD–echelle spectrometers of the 1–m and 6–m telescopes SAO RAS. Changes in the profile shapes, radial velocities and differential shifts of lines create an impression that unstable disk– or ring–shaped structures may exist at the wind bases of super-giants such as β Ori. In the process of destruction they occasionally produce more or less radial flows of escaping and infalling gas. It looks that, as the luminosity increased, the geometry and kinematics of the wind simplify. The wind becomes more symmetrical, the sings of compression diappear and even in the lower layers steady (at least over an interval of several years), although unstable expansion is observable.

We discuss why B supergiant winds are particularly well suited for wind studies, and present or refer to dynamic spectra which suggest the presence of disks, bifurcated winds, shock formation, rotationally modulated winds and the spontaneous generation of wind enhancements. They underscore the strength and richness of wind variability in B supergiants and the challenges these phenomena present to theoretical studies of stellar winds.

The profiles of the Hα and uv lines and the observed variability suggest deviations from spherical symmetry for the envelope of A-type supergiants.

Early-B hypergiants belong to the most luminous stars in the Universe. They are characterized by high mass-loss rates (Ṁ ≈ 10−5Mʘyr−1) and low terminal wind velocities (v∞ʘ400 kms−1) implying very dense winds. They represent a short-lived evolutionary phase and are of particular interest for evolutionary theories of massive stars with mass loss. Due to their high luminosity they play a key role in connection with the “wind momentum - luminosity relation”. Among the main interesting characteristics of early-B hypergiants are the various kinds of photometric and spectroscopic variations. In several recent campaigns our group has performed extensive high dispersion spectroscopy of galactic early-B hypergiants with our fiber-fed echelle spectrograph FLASH/HEROS at the ESO-50 cm telescope. The main outcome was that their dense winds behave hydrodynamically differently to the less luminous supergiants of comparable spectral type. Outwardly accelerated propagating discrete absorption components of the P Cyg-type lines are the typical features rather than rotationally modulated line profile variations. These discrete absorptions could be traced in different spectral lines from photospheric velocities up to 75% of the terminal velocity. The stellar absorption lines show a pulsation-like radial velocity variability pattern lasting up to two weeks as the typical time scale. The radius variations connected with this pulsation-like motions are correlated with the emission height of the P Cyg-type profiles.

What distinguishes WR stars from most of their progenitor phases is their dense winds, that often completely hide their small hydrostatic cores. Thus, to learn about these cores, which are especially important in an evolutionary context, we are generally limited to studying the winds only. One way to do this is to examine their ubiquitous variability. Variability studies of (single) WR stars using various techniques have revealed two main classes of wind variation: (1) large-scale and periodic, probably related to rotating disturbances (e.g. NRP or magnetic structures) close to the core surface, and (2) small (multi-) scale and stochastic, probably intrinsic to the winds themselves. The former is only seen rarely in WR stars, contrary to other hot stars. The latter appears to be universal in WR and probably (though less obvious) in all hot-star winds.

Inhomogeneities are accounted for in our non-LTE stellar wind models in a first-order approximation. When applied for spectral analyses, clumpy models yield lower mass-loss rates than homogeneous models, while other parameters are not affected. For representative WR stars, we determine the density contrast from the electron-scattering line wings and obtain mass-loss rate reductions by a factor of two, typically.

The stars known as Luminous Blue Variables include two very distinctive subgroups - the S Dor-type variables which basically define what we call an LBV and the much rarer ‘giant eruption’ LBV’s which include famous stars like η Car and P Cyg. The distinctive characteristics and long term variability of these two groups is reviewed. The lesser 1890 eruption of η Car is shown to have been much more significant than previously believed and resembles the second peak seen in the historic light curve of P Cyg. Because so many, if not all, stars in certain parts of the HR diagram appear to be luminous, blue, and variable, I suggest returning to our previous designation - S Dor variables and η Car variables for these two important groups of stars.

Following the “Great Eruption” of 1843, η Carinae underwent a second major eruption around 1890. We suggest a preliminary working model developed during this meeting (in one night, hence the term “Blitz”) that attempts to explain the temporal development of the 19th century eruptions of η Car, as well as the formation of the Homunculus nebula (note that we are not offering an explanation for the cause of the Great Eruption!). The essence of the model is that after the Great Eruption ends, the star’s extended outer envelope re-adjusts itself on a thermal time scale. This re-adjustment allows envelope material to crash back onto the surface of the star, inducing the second eruption in 1890.

LBV’s are variable on many different time scales from weeks to years or even decades. The typical LBV variations on timescales of years or longer are covered in the paper by Humphreys (this volume). Here I discuss variations of LBV’s on timescales from weeks to years.

Most classes of stars are little studied on these timescales. This also holds true for LBV’s. Therefore the hot star group of the Landessternwarte Heidelberg Started a monitoring program of a few bright LBV’s (and other objects) using the 70cm-telescopes at the Landessternwarte and later the ESO 50cm-telescope at La Silla. For more details about the project see the paper by Kaufer (this volume).