Dissipative models of colliding stellar winds — I. Effects of thermal conduction in wide binary systems

The influence of electron thermal conduction on the 2D gas dynamics of colliding stellar winds is investigated. It is shown that, as a result of the non-linear dependence of the electron thermal flux on the temperature, the pre-heating zones (in which the hot gas in the interaction region heats the cool winds in front of the shocks) have finite sizes. The dependence of the problem of the structure of the flow in the interaction region on the dimensionless parameters is studied, and a simple expression is derived for the size of the pre-heating zones at the axis of symmetry. It is shown that small values of the thermal conductivity do not suppress the Kelvin–Helmholtz instability if the adiabatic flow is subject to it. Further studies, both numerical and analytical, in this direction will be of great interest. The influence of thermal conduction on the X-ray emission from the interaction region is also estimated.     

A 3D dynamical model of the colliding winds in binary systems

We present a three-dimensional (3D) dynamical model of the orbital-induced curvature of the wind–wind collision region in binary star systems. Momentum balance equations are used to determine the position and shape of the contact discontinuity between the stars, while further downstream the gas is assumed to behave ballistically. An Archimedean spiral structure is formed by the motion of the stars, with clear resemblance to high-resolution images of the so-called 'pinwheel nebulae'. A key advantage of this approach over grid or smoothed particle hydrodynamic models is its significantly reduced computational cost, while it also allows the study of the structure obtained in an eccentric orbit. The model is relevant to symbiotic systems and γ-ray binaries, as well as systems with O-type and Wolf–Rayet stars.
As an example application, we simulate the X-ray emission from hypothetical O+O and WR+O star binaries, and describe a method of ray tracing through the 3D spiral structure to account for absorption by the circumstellar material in the system. Such calculations may be easily adapted to study observations at wavelengths ranging from the radio to γ-ray.     

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.     

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.     

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.     

X-rays from massive OB stars: thermal emission from radiative shocks

Chandra grating spectra of a sample of 15 massive OB stars were analysed under the basic assumption that the X-ray emission is produced in an ensemble of shocks formed in the winds driven by these objects. Shocks develop either as a result of radiation-driven instabilities or due to confinement of the wind by a relatively strong magnetic field, and since they are radiative, a simple model of their X-ray emission was developed that allows a direct comparison with observations. According to our model, the shock structures (clumps, complete or fractional shells) eventually become 'cold' clouds in the X-ray sky of the star. As a result, it is expected that for large covering factors of the hot clumps, there is a high probability for X-ray absorption by the 'cold' clouds, resulting in blueshifted spectral lines. Our analysis has revealed that such a correlation indeed exists for the considered sample of OB stars. As to the temperature characteristics of the X-ray emission plasma, the studied OB stars fall in two groups: (i) one with plasma temperature limited to ∼0.1–0.4 keV and (ii) the other with X-rays produced in plasmas at considerably higher temperatures. We argue that the two groups correspond to different mechanisms for the origin of X-rays: in radiation-driven instability shocks and in magnetically confined wind shocks, respectively.     

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.     

On the X-ray emission from massive star clusters and their evolving superbubbles – II. Detailed analytics and observational effects

In this work, we present a comprehensive X-ray picture of the interaction between a super star cluster and the interstellar medium. In order to do that, we compare and combine the X-ray emission from the superwind driven by the cluster with the emission from the wind-blown bubble. Detailed analytical models for the hydrodynamics and X-ray luminosity of fast polytropic superwinds are presented. The superwind X-ray luminosity models are an extension of the results obtained in Paper I. Here, the superwind polytropic character allows us to parametrize a wide variety of effects, for instance, radiative cooling. Additionally, X-ray properties that are valid for all bubble models taking thermal evaporation into account are derived. The final X-ray picture is obtained by calculating analytically the expected surface brightness and weighted temperature of each component. All of our X-ray models have an explicit dependence on metallicity and admit general emissivities as functions of the hydrodynamical variables. We consider a realistic X-ray emissivity that separates the contributions from hydrogen and metals. The paper ends with a comparison of the models with observational data.