The Zeeman effect in the Sobolev approximation: applications to spherical stellar winds

Modern spectropolarimeters are capable of detecting subkilogauss field strengths using the Zeeman effect in line profiles from the static photosphere, but supersonic Doppler broadening makes it more difficult to detect the Zeeman effect in the wind lines of hot stars. Nevertheless, the recent advances in observational capability motivate an assessment of the potential for detecting the magnetic fields threading such winds. We incorporate the weak-field longitudinal Zeeman effect in the Sobolev approximation to yield integral expressions for the flux of circularly polarized emission. To illustrate the results, two specific wind flows are considered: (i) spherical constant expansion with   v ( r ) = v _∞  and (ii) homologous expansion with   v ( r ) ∝ r   . Axial and split monopole magnetic fields are used to schematically illustrate the polarized profiles. For constant expansion, optically thin lines yield the well-known 'flat-topped' total intensity emission profiles and an antisymmetric circularly polarized profile. For homologous expansion, we include occultation and wind absorption to provide a more realistic observational comparison. Occultation severely reduces the circularly polarized flux in the redshifted component, and in the blueshifted component, the polarization is reduced by partially offsetting emission and absorption contributions. We find that for a surface field of approximately 100 G, the largest polarizations result for thin but strong recombination emission lines. Peak polarizations are approximately 0.05 per cent, which presents a substantial although not inconceivable sensitivity challenge for modern instrumentation.     

The continuum re-processing efficiency of Be‐star circumstellar discs

We have calculated the total flux emitted in H α , P α and Br α by the circumstellar envelope of both an early Be star, γ Cas, and a late Be star, 1 Delphini, assuming the central star is the only source of energy input into the circumstellar envelope. These estimates are based on the Be-star models of Millar & Marlborough which have self-consistent temperature distributions determined by equating the local rates of energy gain and energy loss in the envelopes. We find that an additional source of ionizing photons, as argued by Apparao, is not necessary to account for the observed emission.     

Protodiscs around hot magnetic rotator stars

We develop equations and obtain solutions for the structure and evolution of a protodisc region that is initially formed with no radial motion and super-Keplerian rotation speed when wind material from a hot rotating star is channelled towards its equatorial plane by a dipole-type magnetic field. Its temperature is around 10⁷ K because of shock heating and the inflow of wind material causes its equatorial density to increase with time. The centrifugal force and thermal pressure increase relative to the magnetic force and material escapes at its outer edge. The protodisc region of a uniformly rotating star has almost uniform rotation and will shrink radially unless some instability intervenes. In a star with angular velocity increasing along its surface towards the equator, the angular velocity of the protodisc region decreases radially outwards and magnetorotational instability (MRI) can occur within a few hours or days. Viscosity resulting from MRI will readjust the angular velocity distribution of the protodisc material and may assist in the formation of a quasi-steady disc. Thus, the centrifugal breakout found in numerical simulations for uniformly rotating stars does not imply that quasi-steady discs with slow outflow cannot form around magnetic rotator stars with solar-type differential rotation.     

Infall and Outflow Activities in the Be star FY CMa

Unusual activity of outflow mass motion connected with infail events was recorded for the B0.5 IVe star FY CMa in February 1987 from both archival IUE spectrograms of cixcumstellar Nv resonance hnes and optical spectra of Hα and He I λ5876A emission lines which showed inverse P Cygni-type profiles. We estimate the mass loss rate using ultraviolet SiIvresonance lines with expanding atmosphere modeling calculations, and describe how the radial pressure performs the dominant role in accelerating the stellar wind. We attempt to give a qualitative explanation for the activity observed for FY CMa in terms of circumstellar matter raining down to the star.     

3D eccentric discs around Be stars

One-armed oscillation modes in the circumstellar discs of Be stars may explain the cyclical variations in their emission lines. We show that a 3D effect, involving vertical motion and neglected in previous treatments, profoundly influences the dynamics. Using a secular theory of eccentric discs that reduces the problem to a second-order differential equation, we show that confined prograde modes are obtained for all reasonable disc temperatures and stellar rotation rates. We confirm these results using a numerical analysis of the full set of linearized equations for 3D isothermal discs including viscous terms that couple the horizontal motions at different altitudes. In order to make these modes grow, viscous damping must be overcome by an excitation mechanism such as viscous overstability.     

Models of forbidden line emission profiles from axisymmetric stellar winds

A number of strong infrared forbidden lines have been observed in several evolved Wolf–Rayet (WR) star winds, and these are important for deriving metal abundances and testing stellar evolution models. In addition, because these optically thin lines form at large radius in the wind, their resolved profiles carry an imprint of the asymptotic structure of the wind flow. This work presents model forbidden line profile shapes formed in axisymmetric winds. It is well known that an optically thin emission line formed in a spherical wind expanding at constant velocity yields a flat-topped emission profile shape. Simulated forbidden lines are produced for a model stellar wind with an axisymmetric density distribution that treats the latitudinal ionization self-consistently and examines the influence of the ion stage on the profile shape. The resulting line profiles are symmetric about line centre. Within a given atomic species, profile shapes can vary between centrally peaked, doubly peaked, and approximately flat-topped in appearance depending on the ion stage (relative to the dominant ion) and viewing inclination. Although application to WR star winds is emphasized, the concepts are also relevant to other classes of hot stars such as luminous blue variables and Be/B[e] stars.     

Line profile variability of OB stars: Pulsation,rotation, clumps and magnetic fields

The variability of line profiles in spectra of bright OB stars has been studied.We obtain more than 1000 high quality spectra of δ Ori A, λ Ori A, α Cam, 19 Cep, ι Her, ρ Leo and other target stars. We revealed the line profile microvariability of small amplitude (0.5–3% in the adjacent continuum units) for all observed stars. For most stars only cyclic components of the line profile variability (LPV) at the time scales from hours to days were detected. These components seem to be connected with both the non-radial pulsations (NRP) and rotation line profile modulation. In the spectra of δ Ori A and λ Ori A we found the evidences of the stochastic LPV in spectra, probably connected with the small clumps in the stellar wind. On the basis of recent observations we discuss the origin of the magnetic field of early-type stars. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Absolute magnitudes of OB and Be stars based on Hipparcos parallaxes – II

A new method of determining absolute visual magnitudes of early-type stars, based on averaging Hipparcos parallaxes ( ESA 1997 ) inside samples of the same spectrum and luminosity (Sp/L) classes, is proposed. The used sample consists of 6262 unreddened and reddened OB stars as well as 430 Be stars of luminosity classes Ia, Iab, Ib, II, III, IV and V. The colour excesses of the reddened stars have been calculated using the mean colour indices, according to the SIMBAD data base and the intrinsic ( B − V ) values calibrated for given Sp/L classes by Papaj, Wegner & Krełowski . The values of the total-to-selective extinction   R_V = A_V / E ( B − V )  for all reddened stars were calculated from the published near-infrared photometric measurements. The calculated visual magnitudes M_V of OB and Be stars are compared to those published by Wegner in Paper I, and the earlier determinations of Schmidt-Kaler. Generally, the new values of M_V agree well with those given in Paper I, except those for O stars which are systematically brighter than the earlier estimates. The mean absolute magnitudes published by Schmidt-Kaler are generally brighter (except OB stars of luminosity class V) than those determined in this paper.     

Hα long-term monitoring of the Be star β Cephei Aa

Papers published in recent years have contributed to resolve the enigma of the hypothetical Be nature of the hot pulsating star β Cephei. This star shows variable emission in the Hα line, typical for Be stars, but its projected rotational velocity is very much lower than the critical limit, contrary to what is expected for a typical Be star. The emission has been attributed to the secondary component of the β Cephei spectroscopic binary system.
In this paper, using both our and archived spectra, we attempt to recover the Hα profile of the secondary component and to analyse its behaviour with time for a long period. To accomplish this task, we first derive the atmospheric parameters of the primary,   T _eff= 24 000 ± 250 K  and  log  g = 3.91 ± 0.10  , and then we use these values to compute its synthetic Hα profile, and finally we reconstruct the secondary's profile disentangling the observed one.
The secondary's Hα profile shows the typical two-peak emission of a Be star with a strong variability. We also analysed the behaviour versus time of some linewidth parameters: equivalent width, ratio of blue to red peak intensities, full width at half-maximum, peak separation and radial velocity of the central depression.
The projected rotational velocity  ( v sin  i )  of the secondary and the dimension of the equatorial surrounding disc have also been estimated.     

On the moving subfeatures in the Be star ζ Oph

We analyse a series of line profile observations of the He  i 6678 line in ζ Oph. A period analysis on these data using the mode and moments of the line profile confirms the two previously known periods. We describe a new method of mode identification for pulsating stars in which the calculated profiles are directly fitted to observed profiles. The method yields the full set of pulsational parameters including the spherical harmonic degree, ℓ, and azimuthal number, m . Application of the method to these data confirms the mode identifications previously suggested for the two periodicities. We find that the derived pulsational parameters are physically realistic and conclude that non-radial pulsation is the most likely explanation for the travelling subfeatures. However, a unique mode identification is still not possible – several non-sectorial modes fit the data as well as the usually adopted sectorial identifications. The predicted photometric amplitudes are in good accord with upper limits derived from photometric observations. We conclude that ζ Oph is a star in the β Cep instability strip in which two modes of high degree (probably ℓ=4 and ℓ=8) are excited. We present an interpretation of these findings in which the cause of the low-order line profile and light variations in periodic Be stars is corotating photospheric clouds, while the travelling subfeatures are incidental to the Be phenomenon and are a result of non-radial pulsation.     

X-ray emission by a shocked fast wind from the central stars of planetary nebulae

We calculate the X-ray emission from the shocked fast wind blown by the central stars of planetary nebulae (PNe) and compare with observations. Using spherically symmetric self-similar solutions, we calculate the flow structure and X-ray temperature for a fast wind slamming into a previously ejected slow wind. We find that the observed X-ray emission of six PNe can be accounted for by shocked wind segments that were expelled during the early-PN phase, if the fast wind speed is moderate,   v ₂∼ 400–600 km s⁻¹  , and the mass-loss rate is a few times  10⁻⁷ M_⊙ yr⁻¹  . We find, as proposed previously, that the morphology of the X-ray emission is in the form of a narrow ring inner to the optical bright part of the nebula. The bipolar X-ray morphology of several observed PNe, which indicates an important role of jets, rather than a spherical fast wind, cannot be explained by the flow studied here.     

3D models of radiatively driven colliding winds in massive O+O star binaries – I. Hydrodynamics

The dynamics of the wind–wind collision in massive stellar binaries are investigated using 3D hydrodynamical models which incorporate gravity, the driving of the winds, the orbital motion of the stars and radiative cooling of the shocked plasma. In this first paper, we restrict our study to main-sequence O+O binaries. The nature of the wind–wind collision region is highly dependent on the degree of cooling of the shocked plasma, and the ratio of the flow time-scale of the shocked plasma to the orbital time-scale. The pre-shock wind speeds are lower in close systems as the winds collide prior to their acceleration to terminal speeds. Radiative inhibition may also reduce the pre-shock wind speeds. Together, these effects can lead to rapid cooling of the post-shock gas. Radiative inhibition is less important in wider systems, where the winds are accelerated to higher speeds before they collide, and the resulting collision region can be largely adiabatic. In systems with eccentric orbits, cold gas formed during periastron passage can persist even at apastron, before being ablated and mixed into its surroundings and/or accelerated out of the system.