Modelling forbidden line emission profiles from colliding wind binaries

This paper presents calculations for forbidden emission-line profile shapes arising from colliding wind binaries. The main application is for systems involving a Wolf–Rayet (WR) star and an OB star companion. The WR wind is assumed to dominate the forbidden line emission. The colliding wind interaction is treated as an Archimedean spiral with an inner boundary. Under the assumptions of the model, the major findings are as follows. (i) The redistribution of the WR wind as a result of the wind collision is not flux conservative but typically produces an excess of line emission; however, this excess is modest at around the 10 per cent level. (ii) Deviations from a flat-toped profile shape for a spherical wind are greatest for viewing inclinations that are more nearly face-on to the orbital plane. At intermediate viewing inclinations, profiles display only mild deviations from a flat-toped shape. (iii) The profile shape can be used to constrain the colliding wind bow shock opening angle. (iv) Structure in the line profile tends to be suppressed in binaries of shorter periods. (v) Obtaining data for multiple forbidden lines is important since different lines probe different characteristic radial scales. Our models are discussed in relation to Infrared Space Observatory data for WR 147 and γ Vel (WR 11). The lines for WR 147 are probably not accurate enough to draw firm conclusions. For γ Vel, individual line morphologies are broadly reproducible but not simultaneously so for the claimed wind and orbital parameters. Overall, the effort demonstrates how lines that are sensitive to the large-scale wind can help to deduce binary system properties and provide new tests of numerical simulations.     

Non-thermal emission in Wolf–Rayet stars: are massive companions required?

We examine the radio spectral indices of 23 Wolf–Rayet (WR) stars to identify the nature of their radio emission. We identify nine systems as non-thermal emitters. In seven of these systems the non-thermal emission dominates the radio spectrum, while in the remaining two it is of comparable strength to the thermal, stellar wind emission, giving 'composite' spectra. Among these nine systems, seven have known spectroscopic or visual binary companions. The companions are all massive O or early B-type stars, strongly supporting a connection between the appearance of non-thermal emission in WR stars and the presence of a massive companion. In three of these binaries, the origin of non-thermal emission in a wind-collision region between the stars has been well established in earlier work. The binary systems that exhibit only thermal emission are all short‐period systems where a wind-collision zone is deep within the opaque region of the stellar wind of the WR star. To detect non-thermal emission in these systems requires optically thin lines of sight to the wind-collision region.     

3-D radiative line transfer for be star envelopes

Based on numerical three-dimensional radiative line transfer calculations H emission line profiles of circumstellar Be star envelopes have been derived. The results show that the socalled winebottle-type emission line profiles can be explained by the combination of rotational broadening and non-coherent scattering in optically thick Keplerian disks. In a further calculation the stellar wind model of Be star envelopes has been re-investigated assuming an additional expansion component in the velocity field. The resulting asymmetric winebottle-type profiles and asymmetric shell-type emission lines with blue-shifted central depressions are in contradiction with the observed line shapes. It is concluded that isotropic stationary outflows are not suitable to explain observed asymmetric emission line profiles of Be stars.     

WR 146 – observing the OB-type companion

We present new radio and optical observations of the colliding-wind system WR 146 aimed at understanding the nature of the companion to the Wolf–Rayet (WR) star and the collision of their winds. The radio observations reveal emission from three components: the WR stellar wind, the non-thermal wind–wind interaction region and, for the first time, the stellar wind of the OB companion. This provides the unique possibility of determining the mass-loss rate and terminal wind velocity ratios of the two winds, independent of distance. Respectively, these ratios are 0.20±0.06 and 0.56±0.17 for the OB-companion star relative to the WR star. A new optical spectrum indicates that the system is more luminous than had been believed previously. We deduce that the 'companion' cannot be a single, low-luminosity O8 star as suggested previously, but is either a high-luminosity O8 star, or possibly an O8+WC binary system.     

Theoretical X-ray line profiles from colliding wind binaries

We present theoretical X-ray line profiles from a range of model colliding wind systems. In particular, we investigate the effects of varying the stellar mass-loss rates, the wind speeds and the viewing orientation. We find that a wide range of theoretical line profile shapes is possible, varying with orbital inclination and phase. At or near conjunction, the lines have approximately Gaussian profiles, with small widths  (HWHM ∼ 0.1 v _∞)  and definite blueshifts or redshifts (depending on whether the star with the weaker wind is in front or behind). When the system is viewed at quadrature, the lines are generally much broader  (HWHM ∼ v _∞)  , flat-topped and unshifted. Local absorption can have a major effect on the observed profiles – in systems with mass-loss rates of a few times  10⁻⁶ M_⊙ yr⁻¹  the lower energy lines  ( E  ≲ 1 keV)  are particularly affected. This generally results in blueward-skewed profiles, especially when the system is viewed through the dense wind of the primary. The orbital variation of the linewidths and shifts is reduced in a low-inclination binary. The extreme case is a binary with   i = 0°  , for which we would expect no line profile variation.     

Exospheric models for the X-ray emission from single Wolf–Rayet stars

We review existing ROSAT detections of single Galactic Wolf–Rayet (WR) stars and develop wind models to interpret the X-ray emission. The ROSAT data, consisting of bandpass detections from the ROSAT All-Sky Survey (RASS) and some pointed observations, exhibit no correlations of the WR X-ray luminosity ( L _X) with any star or wind parameters of interest (e.g. bolometric luminosity, mass-loss rate or wind kinetic energy), although the dispersion in the measurements is quite large. The lack of correlation between X-ray luminosity and wind parameters among the WR stars is unlike that of their progenitors, the O stars, which show trends with such parameters. In this paper we seek to (i) test by how much the X-ray properties of the WR stars differ from the O stars and (ii) place limits on the temperature T _X and filling factor f _X of the X-ray-emitting gas in the WR winds. Adopting empirically derived relationships for T _X and f _X from O-star winds, the predicted X-ray emission from WR stars is much smaller than observed with ROSAT . Abandoning the T _X relation from O stars, we maximize the cooling from a single-temperature hot gas to derive lower limits for the filling factors in WR winds. Although these filling factors are consistently found to be an order of magnitude greater than those for O stars, we find that the data are consistent (albeit the data are noisy) with a trend of in WR stars, as is also the case for O stars.     

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.     

Colliding stellar wind models with non-equilibrium ionization: X-rays from WR 147

The effects of non-equilibrium ionization are explicitly taken into account in a numerical model which describes colliding stellar winds (CSW) in massive binary systems. This new model is used to analyse the most recent X-ray spectra of the WR+OB binary system WR 147. The basic result is that it can adequately reproduce the observed X-ray emission (spectral shape, observed flux) but some adjustment in the stellar wind parameters is required. Namely (i) the stellar wind velocities must be higher by a factor of 1.4–1.6 and (ii) the mass loss must be reduced by a factor of ∼2. The reduction factor for the mass loss is well within the uncertainties for this parameter in massive stars, but given the fact that the orbital parameters (e.g. inclination angle and eccentricity) are not well constrained for WR 147, even smaller corrections to the mass loss might be sufficient. Only CSW models with non-equilibrium ionization and equal (or nearly equal) electron and ion post-shock temperature are successful. Therefore, the analysis of the X-ray spectra of WR 147 provides evidence that the CSW shocks in this object must be collisionless .     

WR 7a: a V Sagittae or a qWR star?

The star WR 7a, also known as SPH 2, has a spectrum that resembles that of V Sagittae stars although no O  vi emission has been reported. The Temporal Variance Spectrum – TVS – analysis of our data shows weak but strongly variable emission of O  vi lines which is below the noise level in the intensity spectrum.
Contrary to what is seen in V Sagittae stars, optical photometric monitoring shows very little, if any, flickering. We found evidence of periodic variability. The most likely photometric period is   P _phot= 0.227(±14) d  , while radial velocities suggest a period of   P _spec= 0.204(±13) d  . One-day aliases of these periods can not be ruled out. We call attention to similarities with HD 45166 and DI Cru (= WR 46), where multiple periods are present. They may be associated to the binary motion or to non-radial oscillations.
In contrast to a previous conclusion by Pereira et al., we show that WR 7a contains hydrogen. The spectrum of the primary star seems to be detectable as the N  v 4604 Å  absorption line is visible. If so, it means that the wind is optically thin in the continuum and that it is likely to be a helium main sequence star.
Given the similarity to HD 45166, we suggests that WR 7a may be a qWR – quasi Wolf–Rayet – star. Its classification is WN4h/CE in the Smith, Shara & Moffat three-dimensional classification system.     

Spectropolarimetric modelling of hot star wind structure

A short overview is given of some recent progress in the theory of spectropolarimetry as a diagnostic of axisymmetric hot star wind density and velocity structure, covering the inferences possible from broad band polarimetry, from polarimetric light curves and simultaneous absorption line data, and from spectropolarimetric line profiles. Recent work on joint spectro-, photo-, and polari-metric study of the properties of wind inhomogeneities is also summarised. One of the most important conclusions is that the blobs necessary in WR winds to produce narrow emission line features cannot also produce polarimetric light curve features unless they originate in enhanced mass loss sources at the stellar surface rather than solely in density redistribution processes, such as turbulence, in the wind itself.     

Recombination lines and free‐free continua formed in asymptotic ionized winds: Analytic solution for the radiative transfer

In dense hot star winds, the infrared and radio continua are dominated by free‐free opacity and recombination emission line spectra. In the case of a spherically symmetric outflow that is isothermal and expanding at constant radial speed, the radiative transfer for the continuum emission from a dense wind is analytic. Even the emission profile shape for a recombination line can be derived. Key to these derivations is that the opacity scales with only the square of the density. These results are well‐known. Here an extension of the derivation is developed that also allows for line blends and the inclusion of an additional power‐law dependence beyond just the density dependence. The additional power‐law is promoted as a representation of a radius dependent clumping factor. It is shown that differences in the line widths and equivalent widths of the emission lines depend on the steepness of the clumping power‐law. Assuming relative level populations in LTE in the upper levels of He II, an illustrative application of the model to Spitzer/IRS spectral data of the carbon‐rich star WR 90 is given (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Launching of conical winds and axial jets from the disc–magnetosphere boundary: axisymmetric and 3D simulations

We investigate the launching of outflows from the disc–magnetosphere boundary of slowly and rapidly rotating magnetized stars using axisymmetric and exploratory 3D magnetohydrodynamic simulations. We find long-lasting outflows in the following cases. (1) In the case of slowly rotating stars , a new type of outflow, a conical wind , is found and studied in simulations. The conical winds appear in cases where the magnetic flux of the star is bunched up by the disc into an X-type configuration. The winds have the shape of a thin conical shell with a half-opening angle  θ∼ 30°–40°  . About 10–30 per cent of the disc matter flows from the inner disc into the conical winds. The conical winds may be responsible for episodic as well as long-lasting outflows in different types of stars. There is also a low-density, higher velocity component (a jet) in the region inside the conical wind. (2) In the case of rapidly rotating stars (the 'propeller regime'), a two-component outflow is observed. One component is similar to the conical winds. A significant fraction of the disc matter may be ejected into the winds. The second component is a high-velocity, low-density magnetically dominated axial jet where matter flows along the opened polar field lines of the star. The jet has a mass flux of about 10 per cent of that of the conical wind, but its energy flux (dominantly magnetic) can be larger than the energy flux of the conical wind. The jet's angular momentum flux (also dominantly magnetic) causes the star to spin down rapidly. Propeller-driven outflows may be responsible for the jets in protostars and for their rapid spin-down. The jet is collimated by the magnetic force while the conical winds are only weakly collimated in the simulation region. Exploratory 3D simulations show that conical winds are axisymmetric about the rotational axis (of the star and the disc), even when the dipole field of the star is significantly misaligned.     

NLTE models of line-driven stellar winds – III. Influence of X-ray radiation on wind structure of O stars

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   T _eff≲ 35 000 K  .
We discuss the origin of the   L _X/ 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.     

The circumstellar environment of Wolf–Rayet stars and gamma-ray burst afterglows

We study the evolution of the circumstellar medium of massive stars. We pay particular attention to Wolf-Rayet stars that are thought to be the progenitors of some long gamma-ray bursts (GRBs). We detail the mass-loss rates we use in our stellar evolution models and how we estimate the stellar wind speeds during different phases. With these details we simulate the interactions between the wind and the interstellar medium to predict the circumstellar environment around the stars at the time of core-collapse. We then investigate how the structure of the environment might affect the GRB afterglow. We find that when the afterglow jet encounters the free-wind/stalled-wind interface, rebrightening occurs and a bump is seen in the afterglow light curve. However, our predicted positions of this interface are too distant from the site of the GRB to reach while the afterglow remains observable. The values of the final wind density,   A _*  , from our stellar models are of the same order (≲1) as some of the values inferred from observed afterglow light curves. We do not reproduce the lowest   A _*  values below 0.5 inferred from afterglow observations. For these cases, we suggest that the progenitors could have been a WO-type Wolf–Rayet (WR) star or a very low-metallicity star. Finally, we turn our attention to the matter of stellar wind material producing absorption lines in the afterglow spectra. We discuss the observational signatures of two WR stellar types, WC and WO, in the afterglow light curve and spectra. We also indicate how it may be possible to constrain the initial mass and metallicity of a GRB progenitor by using the inferred wind density and wind velocity.     

The evolved B[e] star HD 87643: observations and a radiation-driven disc wind model for B[e] stars

New high-resolution spectroscopic and medium-resolution spectropolarimetric data of the B[e] star HD 87643 are presented, complemented with optical broad- and narrow-band imaging. The spectrum of HD 87643 exhibits the hybrid characteristics well known to be representative of the group of B[e] stars; a fast wind with an expansion velocity in excess of 1000 km s⁻¹ is measured in the hydrogen and helium lines, while a slower component is traced by lower excitation lines and forbidden lines. Clues to the geometry of the rapidly expanding circumstellar shell are provided by the startling polarization changes across Hα. Comparison with published schematic calculations indicates that the polarizing material is located in a slowly rotating, expanding disc structure. A hydrodynamical model is then presented, the results of which are consistent with the original two-wind concept for B[e] stars, and which exhibits kinematic properties that may well explain the observed spectral features in HD 87643. The model calculations use as input a B star undergoing mass loss, surrounded by an optically thick disc. The resulting configuration consists of a fast polar wind from the star and a slowly expanding disc wind. The model also predicts that the stellar wind at intermediate latitudes is slower and denser than in the polar region.     

Winds and mass-loss from evolved,low-gravity cool stars

We summarize results from several programs utilizing the Goddard High Resolution Spectrograph (GHRS) on the Hubble Space Telescope (HST) to study winds and mass-loss from evolved, low-gravity cool stars. We have found that: (i) the photons for thermally and fluorescently excited UV emission lines are created below the region of wind acceleration, (ii) the self-reversals in optically thick emission lines indicate an outflowing wind with mean velocities of 9–25 km/s, (iii) the profiles of optically thin emission lines indicate a mean chromospheric macroturbulence of 24–35 km/s, anisotropically distributed along the radial-tangential directions, (iv) significant emission from hot material (≈10⁵ K) is seen in both non-coronal and hybrid stars to the right of the Linsky-Haisch dividing line, (v) the weakness of Fe II emission lines in the carbon stars, combined with the presence of the Fe I 2807 Å feature only in carbon stars, suggests that the ionization fraction of iron is significantly lower in the outer atmospheres of carbon stars than in O-rich stars, and (vi) Fe II line profile variations indicate changes in mass-loss rate and wind opacity on a timescale of several years in two typical late-type, low-gravity stars.     

HST UV measurements of wind structure and velocities in Local Group OB stars

Archival HST FOS and GHRS data sets have been used to collect ultraviolet evidence for large- and small-scale stellar wind structure in extragalactic Local Group OB stars (i.e. SMC, LMC including R136, M31, M33 and NGC 6822). By comparison with previous studies of Galactic OB stars, wind activity is principally diagnosed in individual spectrograms via the presence of 'narrow absorption components' and saturated 'black' absorption troughs in the resonance line doublets. Their characteristics broadly suggest that these stars share the same physical mechanisms for perturbing the winds as those that act in Galactic stars. Both of these spectral indicators are also used to provide reliable measures of wind terminal velocities. These velocities are directly compared with previously published Galactic values, without reliance on model profile fitting. Relative to Galactic OB stars, the most discrepant terminal velocities (and wind line profiles) result from main-sequence early O-type stars in the SMC.     

Wind signatures in the X-ray emission-line profiles of the late-O supergiant ζ Orionis

X-ray line-profile analysis has proved to be the most direct diagnostic of the kinematics and spatial distribution of the very hot plasma around O stars. The Doppler-broadened line profiles provide information about the velocity distribution of the hot plasma, while the wavelength-dependent attenuation across a line profile provides information about the absorption to the hot plasma, thus providing a strong constraint on its physical location. In this paper, we apply several analysis techniques to the emission lines in the Chandra High Energy Transmission Grating Spectrometer (HETGS) spectrum of the late-O supergiant ζ Ori (O9.7 Ib), including the fitting of a simple line-profile model. We show that there is distinct evidence for blueshifts and profile asymmetry, as well as broadening in the X-ray emission lines of ζ Ori. These are the observational hallmarks of a wind-shock X-ray source, and the results for ζ Ori are very similar to those for the earlier O star, ζ Pup, which we have previously shown to be well fit by the same wind-shock line-profile model. The more subtle effects on the line-profile morphologies in ζ Ori, as compared to ζ Pup, are consistent with the somewhat lower density wind in this later O supergiant. In both stars, the wind optical depths required to explain the mildly asymmetric X-ray line profiles imply reductions in the effective opacity of nearly an order of magnitude, which may be explained by some combination of mass-loss rate reduction and large-scale clumping, with its associated porosity-based effects on radiation transfer. In the context of the recent reanalysis of the helium-like line intensity ratios in both ζ Ori and ζ Pup, and also in light of recent work questioning the published mass-loss rates in OB stars, these new results indicate that the X-ray emission from ζ Ori can be understood within the framework of the standard wind-shock scenario for hot stars.     

A comprehensive variability study of the enigmatic WN8 stars: final results

As a conclusion of our all-sky variability survey of the 'enigmatic' variable WN8 stars, we have carried out coordinated multisite photometric and spectroscopic observations of WN8 stars in 1989 and 1994–1995. We confirm the leading role of the stellar core in restructuring the whole wind. This emerges as a statistical trend: the higher the level of the ∼continuum (i.e. ∼core) light variations, the higher the variability of the P Cygni edges of the optical emission lines. However, the form of the correlation between the light and profile variations is generally different for each individual star. The high level of activity of WN8 stars may be supported/induced by pulsational instability.     

ROSAT observations of V471 Tauri, showing that stellar activity is determined by rotation, not age

I present pointed ROSAT PSPC observations of the pre-cataclysmic binary V471 Tauri. The hard X-ray emission (>0.4 keV) is not eclipsed by the K star, demonstrating conclusively that this component cannot be emitted by the white dwarf. Instead I show that its spectrum and luminosity are consistent with coronal emission from the tidally spun-up K star. The star is more active than other K stars in the Hyades, but equally active as K stars in the Pleiades with the same rotation periods, demonstrating that rotation — and not age — is the key parameter in determining the level of stellar activity.   The soft X-ray emission (<0.4 keV) is emitted predominately by the white dwarf and is modulated on its spin period. I find that the pulse profile is stable on time-scales of hours and years, supporting the idea that it is caused by the opacity of accreted material. The profile itself shows that the magnetic field configuration of the white dwarf is dipolar and that the magnetic axis passes through the centre of the star.   There is an absorption feature in the light curve of the white dwarf, which occurs at a time when our line of sight passes within a stellar radius of the K star. The column density and duration of this feature imply a volume and mass for the absorber that are similar to those of coronal mass ejections of the Sun.   Finally I suggest that the spin–orbit beat period detected in the optical by Clemens et al. may be the result of the interaction of the K-star wind with the magnetic field of the white dwarf.