The results presented in this work show that the interaction of the stellar wind from a supersonically moving OB star with the interstellar medium can give rise to a fairly wide variety of bow shock structures. Changes in the wind parameters, the velocity of the star, or the density of the ambient medium lead to noticeable changes in observable features of the bow shock, such as its morphology or the existence of different density and temperature domains. Understanding the formation of these structures makes it possible to model the observations of wind bow shocks and to derive the physical properties of the stellar winds and the medium in which the runaway stars move.
In short, the results encountered in our numerical simulations can be divided into three broad categories:
a) Bow shocks in which a cool, dense, and stable layer forms. This occurs in our reference case (case A, Sect. 4.1) and in the simulation with a low space velocity (case D, Sect. 4.3). The reasons for stability are rather different in both cases. In case A, the dense layer is embedded in a hotter and thicker layer more resistent to the development of instabilities. The origin of this layer is thermal evaporation at the star-facing side and the shocked interstellar gas which still has not cooled down at the other side. Stability results when this embedded layer contains a significant fraction of the mass of the bow shock, which actually is a rather marginal situation. A somewhat higher space velocity will increase the curvature radius of the bow shock, which shortens the time that the shocked gas spends in front of the star before it has cooled down, and the dense layer will thus vanish. On the other hand, a somewhat lower space velocity will decrease the curvature of the bow shock and the temperature of the shocked interstellar gas, with the result that the dense layer will become more massive and therefore unstable.
In the case of a low space velocity, the stability arises from the small compression factor of the shocked interstellar medium, which tends to favour the stability of shells confined by ram pressure on one side and thermal pressure from a hot gas on the other (Ryu & Vishniac 1987). This seems to be the case in one of the best studied bow shocks ahead of a runaway high-mass X-ray binary, Vela X-1 (Kaper et al. 1997, 1998). The observed wind bow shock has a regular and symmetric shape, although a dense filament is present in one of the wings. The new Hipparcos measurements of its proper motion indicate a space velocity of about 50 km s-1. This is a factor 2 lower than the 90 km s-1 proposed by Kaper et al. (1997), who used photographic data and did not properly correct for the differential galactic rotation. However, a space velocity of 90 km s-1 would, according to our simulations, result in a very unstable bow shock given the (accurately) observed stellar wind parameters and its small measured size. Taken together, these parameters imply a rather high density of the interstellar medium in which the star moves. The apparent contradiction regarding the stability of the Vela X-1 bow shock is solved when the space velocity is 50 km s-1; a bow shock structure similar to case D would be expected. Still, a puzzling aspect of this object is the high volume density of the interstellar medium required to keep the bow shock confined to such a short distance from the star. The Hipparcos data make this density even higher than previously assumed, given the dependence of on the ambient density and the velocity of the star in Eq. (1): a decrease in by a factor 2 must be compensated by an increase in by a factor of 4 to keep constant, if we maintain the stellar wind parameters constant. The required ambient particle density, about 20 cm-3, is more typical of a molecular cloud than of the diffuse interstellar medium (at a distance of 125 pc above the galactic plane) that we have considered throughout this paper.
b) Unstable bow shocks. Our simulations suggest that this is the general situation to be encountered among runaway stars with high velocities and strong stellar winds (cases C and E). The high velocity produces a strong compression of the shocked interstellar medium, while the strong stellar wind causes a large value of . This allows the shocked gas to stay close to the apsis for a time well exceeding its cooling time. Irregularities in observed bow shocks may be a consequence of the instabilities appearing in our simulations, but also of inhomogeneities in the interstellar medium. In this respect, our results suggest that the observation of a regular bow shock is more informative and constraining the parameters of the massive star and the ambient medium than the opposite. On the other hand, we should point out an intriguing difference with the results of Raga et al. (1997) for which we cannot find an easy explanation: in all the simulations with a finite cooling time that we have presented here, the shock defining the boundary of the freely flowing stellar wind always keeps a regular, stable shape, and is only temporarily and mildly distorted when instabilities in the dense layer of the bow shock propagate well inwards towards the star. On the contrary, the freely flowing versus shocked wind interface adopts a barrel-like morphology in the simulation presented by Raga et al. It seems unlikely to us that this discrepancy is only due to a different choice of the input parameters, given the fairly large range covered by our study, or to the apparent neglection of thermal conduction in the study of Raga et al., as our results in this respect are unchanged when suppressing thermal conduction.
c) Absence of a bow shock. Our simulations have shown two situations in which a dense bow shock does not form ahead of the star: when the star has a weak wind (case B), or when it has a high space velocity (case F). In both cases, is small, and the shocked interstellar gas flows rapidly downstream. In addition, in case F the high post-shock temperature of the interstellar gas increases its cooling time. There is a third, rather trivial possibility for the absence of a bow shock: the star may be moving in hot, low-density plasma that, according to some models of the galactic interstellar medium (e.g. McKee & Ostriker 1977), may have a considerable volume filling factor in the galactic disk. In the range of densities ( cm-3) and temperatures ( K) characteristic of this phase of the interstellar medium, runaway stars would be moving subsonically or only weakly supersonically. Then, dense bow shocks would not form due to both the small compression factors and the exceedingly long cooling times. A possible way of discarding or confirming this cause for the non-detection of a bow shock may be the detection or non-detection of a diffuse H II region around the star, given that for typical parameters of runaway OB stars in the diffuse interstellar medium the Strömgren radius by far exceeds (Raga et al. 1997). On the other hand, a combination of these three factors may well explain why the detection rate of bow-shock-like structures around runaway stars is only % (Van Buren et al. 1995).
© European Southern Observatory (ESO) 1998
Online publication: September 8, 1998