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

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6. Summary and conclusions

We have presented a study on the bow shock structures appearing as a result of the interaction between the fast stellar wind of a runaway star and the surrounding, diffuse interstellar medium. A semi-analytical approximation has been presented which takes into account the very long cooling timescale of the shocked stellar wind. The bow shock is in this case supported by the pressure of the shocked stellar wind, rather than by the momentum of the wind as its mass incorporates into the bow shock. Our analysis predicts the same shape of the bow shock as in the case where the stellar wind is allowed to cool down instantaneously, but the distributions of surface density and velocity along the bow shock are found to be very different when comparing both cases.

Two-dimensional numerical simulations of the interaction have been performed with the aim of providing a more realistic description of the characteristics and structure of the bow shock, and to test the validity of the predictions of the semi-analytical approximation. The parameters of the stellar wind, the velocity of the star, and the density of the interstellar medium have been chosen such to illustrate a representative number of possible situations. A reference case has been selected for the purpose of comparison with simulations carried out with other sets of parameters, and in order to test the agreement with the proposed semi-analytical approximation. The numerical simulations indicate that the simplifying hypothesis of a negligible thickness of the layer of shocked stellar wind is not valid in general. Nevertheless, using as a reference scale the distance of the bow shock to the star, a remarkably good agreement is found with the predictions of the semi-analytical approximation, although in the simulated cases this distance cannot be related in a simple way to the parameters defining the problem.

We have explored the consequences of changing the stellar wind power, the velocity of the star, and the density of the ambient gas on the development of a bow shock structure in front of the star. In general, the different regions found as one proceeds outwards from the star in the direction of the apsis are as follows: 1) A zone where the stellar wind flows freely; 2) A broad zone of very hot, shocked stellar wind, starting approximately at the distance of the star where the wind ram pressure balances the ram pressure of the interstellar gas moving towards the star; 3) A broad region of outward decreasing temperature and increasing density, caused by the thermal conduction of energy between the bow shock and the shocked stellar wind; 4) A thin, dense layer of gas in thermal equilibrium proceeding from the shocked interstellar medium; 5) A thick layer of moderately high temperature and density formed by the shocked stellar wind which still has not had time to cool down significantly; and 6) the unperturbed ambient gas, flowing towards the star (in the stellar rest frame). We find that, within the range of parameters that may be expected for runaway OB stars moving in a diffuse interstellar medium, the two layers composing the bow shock can have very different relative surface densities, and either of them may vanish completely under some circumstances.

In general, the bow shock structure becomes unstable when the layer of cool, dense gas inside the bow shock is strongly compressed by its confining pressures and when its surface density is high compared to that of the overlying layer of cooling shocked ambient gas. Instabilities grow close to the apsis, and are carried downstream by the overall gas flow along the bow shock. Their nature is similar to that of the blast wave overstability appearing in expanding bubbles in a medium at rest, but their evolution is different due to the stationary character of the bow shock, which transforms the overstability into a true instability.

We have also investigated the importance of the finite cooling time of the shocked gas and the transport of energy between hot and cold zones by thermal conduction with respect to the evolution of the bow shock. We find that a zero cooling time would lead to the development of extremely unstable structures, which are probably hard to recognize as bow shocks. On the other hand, the suppression of thermal conduction has two important effects: a reduction of the thickness of the layer separating the freely flowing stellar wind from the bow shock, and an increase of the thickness of the cold layer inside the bow shock due to the absence of evaporation.

Finally, we have discussed the implications our results could have for the interpretation of real observations of wind bow shocks, and their possible use as diagnostics tools to derive stellar wind strengths, stellar space velocities, and interstellar gas densities. In this respect, we predict that bow shocks are unstable for a wide range of parameters, although some of the observed irregularities may also be due to inhomogeneities in the surrounding interstellar medium. From a empirical point of view, the detection of regular, stable bow shocks seems to be more interesting; such an observation could be interpreted as an indication of a relatively low space velocity of the runaway star. We also find that it is fairly likely to observe runaway stars without apparent bow shocks, which could be a consequence of them having weak winds, high spatial velocities, or a very tenuous, hot ambient medium.

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© European Southern Observatory (ESO) 1998

Online publication: September 8, 1998