Winds from clusters with non-uniform stellar distributions

We present the analytic and numerical models of the 'cluster wind' resulting from the multiple interactions of the winds ejected by the stars of a dense cluster of massive stars. We consider the case in which the distribution of stars (i.e. the number of stars per unit volume) within the cluster is spherically symmetric, has a power-law radial dependence, and drops discontinuously to zero at the outer radius of the cluster. We carry out comparisons between an analytic model (in which the stars are considered in terms of a spatially continuous injection of mass and energy) and 3D gasdynamic simulations (in which we include 100 stars with identical winds, located in 3D space by statistically sampling the stellar distribution function). From the analytic model, we find that for stellar distributions with steep enough radial dependencies, the cluster wind flow develops a very high central density and a non-zero central velocity, and for steeper dependencies, it becomes fully supersonic throughout the volume of the cluster (these properties are partially reproduced by the 3D numerical simulations). Therefore, the wind solutions obtained for stratified clusters can differ dramatically from the case of a homogeneous stellar distribution (which produces a cluster wind with zero central velocity, and a fully subsonic flow within the cluster radius). Finally, from our numerical simulations, we compute predictions of X-ray emission maps and luminosities, which can be directly compared with observations of cluster wind flows.     

XMM–Newton X-ray observations of the Wolf–Rayet binary system WR 147

We present results of an ≈20-ks X-ray observation of the Wolf–Rayet (WR) binary system WR 147 obtained with XMM–Newton . Previous studies have shown that this system consists of a nitrogen-type WN8 star plus an OB companion whose winds are interacting to produce a colliding wind shock. X-ray spectra from the pn and MOS detectors confirm the high extinction reported from infrared studies and reveal hot plasma including the first detection of the Fe Kα line complex at 6.67 keV. Spectral fits with a constant-temperature plane-parallel shock model give a shock temperature   kT _shock= 2.7  keV (   T _shock≈ 31  MK), close to but slightly hotter than the maximum temperature predicted for a colliding wind shock. Optically thin plasma models suggest even higher temperatures, which are not yet ruled out. The X-ray spectra are harder than can be accounted for using 2D numerical colliding wind shock models based on nominal mass-loss parameters. Possible explanations include: (i) underestimates of the terminal wind speeds or wind abundances, (ii) overly simplistic colliding wind models or (iii) the presence of other X-ray emission mechanisms besides colliding wind shocks. Further improvement of the numerical models to include potentially important physics such as non-equilibrium ionization will be needed to rigorously test the colliding wind interpretation.     

A Rigid-Field Hydrodynamics approach to modelling the magnetospheres of massive stars

We introduce a new Rigid-Field Hydrodynamics approach to modelling the magnetospheres of massive stars in the limit of very strong magnetic fields. Treating the field lines as effectively rigid, we develop hydrodynamical equations describing the one-dimensional flow along each, subject to pressure, radiative, gravitational and centrifugal forces. We solve these equations numerically for a large ensemble of field lines to build up a three-dimensional time-dependent simulation of a model star with parameters similar to the archetypal Bp star σ Ori E. Since the flow along each field line can be solved independently of other field lines, the computational cost of this approach is a fraction of an equivalent magnetohydrodynamical treatment.
The simulations confirm many of the predictions of previous analytical and numerical studies. Collisions between wind streams from opposing magnetic hemispheres lead to strong shock heating. The post-shock plasma cools initially via X-ray emission, and eventually accumulates into a warped, rigidly rotating disc defined by the locus of minima of the effective (gravitational plus centrifugal) potential. However, a number of novel results also emerge. For field lines extending far from the star, the rapid area divergence enhances the radiative acceleration of the wind, resulting in high shock velocities (up to  ∼3000 km s⁻¹  ) and hard X-rays. Moreover, the release of centrifugal potential energy continues to heat the wind plasma after the shocks, up to temperatures around twice those achieved at the shocks themselves. Finally, in some circumstances the cool plasma in the accumulating disc can oscillate about its equilibrium position, possibly due to radiative cooling instabilities in the adjacent post-shock regions.     

A numerical simulation of a wind/molecular clump interaction

It has been pointed out in the past that it is impossible to accelerate molecular material to velocities ≥ 25 km s⁻¹ with gasdynamic shocks without dissociating the gas. Because of this, it has been argued that observations of molecular emission with radial velocities ∼ 20–100 km s⁻¹ imply the presence of 'C-shocks' (which have much lower post-shock temperatures, and therefore do not dissociate the gas) and the existence of strong (∼ 10–100 μG) magnetic fields.   In this paper, we discuss an alternative mechanism for accelerating molecular material to high velocities: a high-velocity, low-density wind drives a non-dissociative shock (with shock velocity v _cs ≤ 25 km s⁻¹) into a high-density, molecular clump. Once this shock wave has gone through the clump, the molecular material is moving at a velocity ∼  v _cs and has a gas pressure approximately equal to the ram pressure of the impinging wind. The compressed molecular clump can now be accelerated directly by the ram pressure of the wind (without the passage of further shocks through the molecular material), and will eventually move at the wind velocity.   This mechanism has been previously invoked to explain high-velocity molecular emission. However, numerical simulations have shown that a wind/clump interaction leads to the fragmentation of the clump before it can be accelerated to large velocities. In our numerical simulation (which includes an approximate treatment of the relevant microphysics) we find that the fragments that are produced are still largely molecular, and that they are rapidly accelerated to velocities comparable to the wind velocity. We therefore conclude that a wind/molecular clump interaction is indeed a valid mechanism for producing high-velocity molecular features.     

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.     

Dark matter distribution in the Draco dwarf from velocity moments

If the observed relativistic plasma outflows in astrophysical jets are magnetically collimated and a single-component model is adopted, consisting of a wind-type outflow from a central object, then a problem arises with the inefficiency of magnetic self-collimation to collimate a sizeable portion of the mass and magnetic fluxes in the relativistic outflow from the central object. To solve this dilemma, we have applied the mechanism of magnetic collimation to a two-component model consisting of a relativistic wind-type outflow from a central source and a non-relativistic wind from a surrounding disc. By employing a numerical code for a direct numerical solution of the steady-state problem in the zone of super-fast magnetized flow, which allows us to perform a determination of the flow with shocks, it is shown that in this two-component model it is possible to collimate into cylindrical jets all the mass and magnetic fluxes that are available from the central source. In addition, it is shown that the collimation of the plasma in this system is usually accompanied by the formation of oblique shock fronts. The non-relativistic disc-wind not only plays the role of the jet collimator, but it also induces the formation of shocks as it collides with the initially radial inner relativistic wind and also as the outflow is reflected by the system axis. Another interesting feature of this process of magnetic collimation is a sequence of damped oscillations in the width of the jet.     

Shock breakout in Type Ibc supernovae and application to GRB 060218/SN 2006aj

Recently, a soft blackbody component was observed in the early X-ray afterglow of GRB 060218, which was interpreted as shock breakout from the thick wind of the progenitor Wolf–Rayet (WR) star of the underlying Type Ic supernova 2006aj. In this paper, we present a simple model for computing the characteristic quantities (including energy, temperature and time duration) for the transient event from the shock breakout in Type Ibc supernovae produced by the core-collapse of WR stars surrounded by dense winds. In contrast to the case of a star without a strong wind, the shock breakout occurs in the wind region rather than inside the star, caused by the large optical depth in the wind. We find that, for the case of a WR star with a dense wind, the total energy of the radiation generated by the supernova shock breakout is larger than that in the case of the same star without a wind by a factor of >10. The temperature can be either hotter or colder, depending on the wind parameters. The time duration is larger caused by the increase in the effective radius of the star due to the presence of a thick wind. Then, we apply the model to GRB 060218/SN 2006aj. We show that, to explain both the temperature and the total energy of the blackbody component observed in GRB 060218 by the shock breakout, the progenitor WR star has to have an unrealistically large core radius (the radius at optical depth of 20), larger than 100 R_⊙. In spite of this disappointing result, our model is expected to have important applications to the observations on Type Ibc supernovae in which the detection of shock breakout will provide important clues to the progenitors of Type Ibc supernovae.     

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 motion of wind-driven shells

We present a method for solving problems in which a stellar wind interacts with the surrounding environment through the production of a 'double radiative shock' structure. This condition is generally met in problems involving winds ejected from young stars. We describe a method that can be applied to problems of winds with arbitrary time and angular dependence, interacting with a stationary environment with an arbitrary density distribution. We apply the method to the interaction of: a steady wind (with an instantaneous 'turning-on') with a power-law environmental density stratification, a 'wind plus jet' ejection with a toroidal environmental density stratification, and to the interaction of an isotropic wind with a clumpy environment. These three examples illustrate the wide range of possible applications of the proposed method. We also show a comparison between some of our thin-shell solutions and three-dimensional isothermal gasdynamic simulations of the flows. These comparisons are used as an evaluation of the applicability of our thin-shell solutions to the real flows.     

Modelling the spectra of colliding winds in the Wolf–Rayet WC7+O binaries WR 42 and WR 79

We have obtained complete phase coverage of the WC7+O binaries WR 42 = HD 97152 and WR 79 = HD 152270 with high signal-to-noise ratio (S/N), moderate-resolution spectra. Remarkable orbital phase-locked profile variations of the C  iii λ 5696 line are observed and interpreted as arising from colliding wind effects. Within this scenario, we have modelled the spectra using a purely geometrical model that assumes a cone-shaped wind–wind interaction region which partially wraps around the O star. Such modelling holds the exciting promise of revealing a number of interesting parameters for WR+O binaries, such as the orbital inclination, the streaming velocity of material in the interaction region and the ratio of wind momentum flux. Knowledge of these parameters in turn leads to the possibility of a better understanding of WR star masses, mass-loss rates and wind region characteristics.     

A-star envelopes: a test of local and non-local models of convection

We present results of a fully non-local, compressible model of convection for A-star envelopes. This model quite naturally reproduces a variety of results from observations and numerical simulations which local models based on a mixing length do not. Our principal results, which are for models with T _eff between 7200 and 8500 K, are the following. First, the photospheric velocities and filling factors are in qualitative agreement with those derived from observations of line profiles of A-type stars. Secondly, the He  ii and H  i convection zones are separated in terms of convective flux and thermal interaction, but joined in terms of the convective velocity field, in agreement with numerical simulations. In addition, we attempt to quantify the amount of overshooting in our models at the base of the He  ii convection zone.     

The photometric evolution of FU Orionis objects: disc instability and wind–envelope interaction

We present the results of a photometric monitoring campaign of three well-studied FU Orionis systems (FU Orionis, V1057 Cygni and V1515 Cygni) undertaken at Maidanak Observatory between 1981 and 2003. When combined with photometric data in the literature, this data base provides a valuable resource for searching for short time-scale variability – both periodic and aperiodic – as well as for studying the secular evolution of these systems. In the case of V1057 Cyg (which is the system exhibiting the largest changes in brightness since it went into outburst) we compare the photometric data with time-dependent models. We show that prior to the end of the 'plateau' stage in 1996, the evolution of V1057 Cyg in the V –( B − V ) colour–magnitude diagram is well represented by disc instability models in which the outburst is triggered by some agent – such as an orbiting planet – in the inner disc. Following the end of the plateau phase in 1996, the dimming and irregular variations are consistent with occultation of the source by a variable dust screen, which has previously been interpreted in terms of dust condensation events in the observed disc wind. Here we instead suggest that this effect results from the interaction between the wind and an infalling dusty envelope, the existence of this envelope having been previously invoked in order to explain the mid-infrared emission of FU Orionis systems. We discuss how this model may explain some of the photometric and spectroscopic characteristics of FU Orionis systems in general.     

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.     

A HED Laboratory Astrophysics Testbed Comes of Age: JET Deflection via Cross Winds

We present new data from High-Energy Density (HED) laboratory experiments designed to explore the interaction of a heavy hypersonic radiative jet with a cross wind. The jets are generated with the MAGPIE pulsed power machine where converging conical plasma flows are produced from a cylindrically symmetric array of inclined wires. Radiative hypersonic jets emerge from the convergence point. The cross wind is generated by ablation of a plastic foil via soft-X-rays from the plasma convergence region. Our experiments show that the jets are deflected by the action of the cross wind with the angle of deflection dependent on the proximity of the foil. Shocks within the jet beam are apparent in the data. Analysis of the data shows that the interaction of the jet and cross wind is collisional and therefore in the hydrodynamic regime. We consider the astrophysical relevance of these experiments applying published models of jet deflection developed for AGN and YSOs. We also present results of 3-D numerical simulations of jet deflection using a new astrophysical Adaptive Mesh Refinement code. These simulations show highly structured shocks occurring within the beam similar to what was observed in the experiments.     

X-ray emission from planetary nebulae calculated by 1D spherical numerical simulations

We calculate the X-ray emission from both constant and time-evolving shocked fast winds blown by the central stars of planetary nebulae (PNe) and compare our calculations with observations. Using spherically symmetric numerical simulations with radiative cooling, we calculate the flow structure and the X-ray temperature and luminosity of the hot bubble formed by the shocked fast wind. We find that a constant fast wind gives results that are very close to those obtained from the self-similar solution. We show that in order for a fast shocked wind to explain the observed X-ray properties of PNe, rapid evolution of the wind is essential. More specifically, the mass-loss rate of the fast wind should be high early on when the speed is  ∼300–700 km s⁻¹  , and then it needs to drop drastically by the time the PN age reaches ∼1000 yr. This implies that the central star has a very short pre-PN (post-asymptotic giant branch) phase.     

ASCA spectroscopy of the hard X-ray emission from the colliding wind interaction in γ2 Velorum

We discuss an ASCA observation of the eccentric WC8+O7.5 III binary γ ² Velorum near apastron. The X-ray spectrum is compared with two previous observations obtained when the system was near periastron. All three spectra display a hard-emission component that undergoes strong variability over the orbital cycle. The properties of the hard X-ray emission of γ ² Vel are constrained by taking into account the contribution from contaminating soft X-ray sources in the vicinity of γ ² Vel. We find that the observed variations are in qualitative agreement with the predictions of colliding wind models. We investigate for the first time the effect of uncertainties in the chemical composition of the X-ray emitting plasma on our understanding of the high-energy properties of the wind interaction region. Our results indicate that these uncertainties significantly affect the derived shock temperature and absorption column, but play a smaller role in determining the intrinsic X-ray luminosity of the colliding wind zone. We further find that the intrinsic luminosity from the hard X-ray component in γ ² Vel does not follow the 1/ D distance relation expected from simple models of adiabatic shocks.     

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.     

Magnetized relativistic jets and long-duration GRBs from magnetar spin-down during core-collapse supernovae

We use ideal axisymmetric relativistic magnetohydrodynamic simulations to calculate the spin-down of a newly formed millisecond,   B ∼ 10¹⁵ G  , magnetar and its interaction with the surrounding stellar envelope during a core-collapse supernova (SN) explosion. The mass, angular momentum and rotational energy lost by the neutron star are determined self-consistently given the thermal properties of the cooling neutron star's atmosphere and the wind's interaction with the surrounding star. The magnetar drives a relativistic magnetized wind into a cavity created by the outgoing SN shock. For high spin-down powers  (∼10⁵¹–10⁵² erg s⁻¹)  , the magnetar wind is superfast at almost all latitudes, while for lower spin-down powers  (∼10⁵⁰ erg s⁻¹)  , the wind is subfast but still super-Alfvénic. In all cases, the rates at which the neutron star loses mass, angular momentum and energy are very similar to the corresponding free wind values (≲30 per cent differences), in spite of the causal contact between the neutron star and the stellar envelope. In addition, in all cases that we consider, the magnetar drives a collimated  (∼5–10°)  relativistic jet out along the rotation axis of the star. Nearly all of the spin-down power of the neutron star escapes via this polar jet, rather than being transferred to the more spherical SN explosion. The properties of this relativistic jet and its expected late-time evolution in the magnetar model are broadly consistent with observations of long duration gamma-ray bursts (GRBs) and their associated broad-lined Type Ic SN.     

Stellar wind accretion in GX 301−2: evidence for a high-density stream

The X-ray binary system GX 301−2 consists of a neutron star in an eccentric orbit accreting from the massive early-type star Wray 977. It has previously been shown that the X-ray orbital light curve is consistent with the existence of a gas stream flowing out from Wray 977 in addition to its strong stellar wind. Here, X-ray monitoring observations by the Rossi X-ray Timing Explorer ( RXTE )/All-Sky Monitor and pointed observations by the RXTE /Proportional Counter Array over the past decade are analysed. We analyse both the flux and column density dependence on orbital phase. The wind and stream dynamics are calculated for various system inclinations, companion rotation rates and wind velocities, as well as parametrized by the stream width and density. These calculations are used as inputs to determine both the expected accretion luminosity and the column density along the line-of-sight to the neutron star. The model luminosity and column density are compared to observed flux and column density versus orbital phase, to constrain the properties of the stellar wind and the gas stream. We find that the change between bright and medium intensity levels is primarily due to decreased mass loss in the stellar wind, but the change between medium and dim intensity levels is primarily due to decreased stream density. The mass-loss rate in the stream exceeds that in the stellar wind by a factor of ∼2.5. The quality of the model fits is better for lower inclinations, favouring a higher mass for Wray 977 in its allowed range of  40–60 M_⊙  .     

Ionization structure in accretion shocks with a composite cooling function

We have investigated the ionization structure of the post-shock regions of magnetic cataclysmic variables, using an analytic density and temperature structure model in which effects caused by bremsstrahlung and cyclotron cooling are considered. We find that in the majority of the shock-heated region where H- and He-like lines of the heavy elements are emitted, the collisional-ionization and corona-condition approximations are justified. We have calculated the line emissivity and ionization profiles for iron as a function of height within the post-shock flow. For low-mass white dwarfs, line emission takes place near the shock. For high-mass white dwarfs, most of the line emission takes place in regions well below the shock and hence it is less sensitive to the shock temperature. Thus, the line ratios are useful to determine the white dwarf masses for the low-mass white dwarfs, but the method is less reliable when the white dwarfs are massive. Line spectra can, however, be used to map the hydrodynamic structure of the post-shock accretion flow.