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Astron. Astrophys. 338, 273-291 (1998)

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1. Introduction

Massive stars have a very substantial impact on their surrounding interstellar medium, as testified by the observations of H II regions, stellar wind bubbles, and supernova remnants. Analyzing and modeling the interaction of massive stars with the ambient gas provides a wealth of information on aspects such as the physical processes at work in the interstellar gas and dust, the energetic output of massive stars in the form of ionizing radiation and stellar winds, and the large-scale dynamics of the interstellar medium.

The supersonic motion of the star with respect to the gas adds some interesting features to the interaction between the stellar wind and the surrounding medium. One of the extensively studied cases is the motion of massive stars in dense molecular clouds, aimed at explaining the small sizes and long lifetimes of ultracompact H II regions (Van Buren et al. 1990, Mac Low et al. 1991, Van Buren & Mac Low 1992). Another interesting example is provided by the evolution of wind-blown bubbles around moving massive stars, as they undergo dramatic changes in their stellar wind properties that accompany the final stages of stellar evolution (Brighenti & D'Ercole 1995a, 1995b). A natural extension is the study of the evolution of supernova remnants inside the elongated cavities generated by moving progenitors. Numerical simulations of such events have been presented by Rozyczka et al. (1993) and Brighenti & D'Ercole (1993), and have found beautiful applications to real, well studied examples such as the Kepler supernova remnant (Borkowski et al. 1992).

Runaway stars ejected from OB associations with typical velocities of several tens of kilometers per second are common among OB stars (Blaauw 1993); their frequency decreases as a function of spectral type from about 20% among the O-types to 2.5% among B0-B0.5, and still lower among B1-B5. Their lives as fast-moving main-sequence stars can last for several million years, during which they migrate well away from their birthplaces. In their journeys through the interstellar medium before exploding as supernovae, they often find themselves in undisturbed environments with conditions very different from those characteristic of star-forming regions, in which non-runaway OB stars spend most or all of their life. In recent years, many runaway stars have been observed to produce wind bow shocks ahead of them (Van Buren et al. 1995, Noriega-Crespo et al. 1997, Kaper et al. 1997), indicative of the interaction between their strong winds and the surrounding, tenuous interstellar medium flowing around them.

Numerical expressions for the shape and physical parameters of the bow shock formed by the interaction of the wind from a moving star with its surrounding medium, neglecting thermal pressure terms, have been found by Baranov et al. (1971) and Mac Low et al. (1991). A fully analytic model describing the wind bow shock characteristics has recently been presented by Wilkin (1996). Cantó et al. (1996) have expanded this model to include the more general case of two unequal colliding winds. Wilkin models the shape of the bow shock as determined by the balance between the ram pressure of the wind, the ram pressure of the ambient medium in the reference frame of the star, and the flow of momentum along the surface of the bow shock. This provides an elegant, simple, and useful description of the shape of the bow shock and the distribution of the surface density and velocity along its surface. However, some potentially relevant aspects of the physics of the problem obviously have to be left aside in order to keep its complexity at a level that can be handled by the analytical approximation. One of these is the dynamical role of the shocked stellar wind, collisionally heated up to very high temperatures. An adequate treatment of this component, as well as of other aspects related to this problem, can only be carried out by means of numerical methods, which in turn allow to assess the validity of the proposed analytical approximations. Such numerical simulations applied to runaway stars have recently been performed by Raga et al. (1997), who took into account the very long cooling time of the shocked stellar wind, although without including the effect of thermal conduction. They also considered the dynamics of the external H II region moving along with the star, and predicted line-emission and dust-continuum maps.

In this paper, we present the results of new hydrodynamical simulations of the wind bow shock produced by a massive runaway star. Given the number of parameters defining the problem, and the large variations that may be present in some of them, we will concentrate on a few representative cases selected in such a way that they illustrate the main dependences of the resulting structures on the input parameters. Here we aim at providing a framework for the interpretative analysis of observations of actual bow shocks. Emphasis will be given to the role played by the different components appearing in the bow shock structure, the conditions under which a bow shock may not form, and to the instabilities appearing in it (cf. Dgani et al. 1996a, 1996b). We will discuss how the observations of wind bow shocks can be used to constrain parameters characterizing the stellar wind, the interstellar medium, or the stellar motion.

We present a new semi-analytical approach to the problem in Sect. 2. Section 3 gives an overview of the methods used in our numerical simulations, and introduces the set of parameters included in the models. In Sect. 4 we describe the results of the numerical simulations, and compare them to the simplified analytical model introduced earlier; furthermore, we discuss the importance of the different physical ingredients comprised in the simulations. These results are summarized and discussed in Sect. 5, and our conclusions are presented in Sect. 6.

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© European Southern Observatory (ESO) 1998

Online publication: September 8, 1998