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The Circumstellar Environment of WR stars & GRB afterglows
John J Eldridge , Robert Mochkovitch , Frederic Daigne , Frank Genet (1) Queen's University Belfast, (2) Institute d'Astrophysique de Paris Email: j.eldridge@qub.ac.uk
What is the GRB Afterglow? After the initial burst of Gamma-rays an afterglow is seen at optical, x-ray and radio wavelengths that lasts for a few days and slowly fades away. Emission is from the relativistic jet as it ploughs through the environment around the progenitor. By modelling the afterglow it is deduced the density structure around some GRBs is that found in the free-wind region of the stellar wind bubbles formed around massive Wolf-Rayet stars ( r-2). Furthermore for some GRBs (e.g. GRB021004) absorption lines that are blueshifted relative to host galaxy redshift are found at velocities expected for Wolf-Rayet (WR) stellar winds (e.g. 3000 and 500 km s-1). Therefore some GRBs can be linked to massive star progenitors (Chevalier et al. 2004, van Marle et al. 2005). However there are still some unresolved problems with this picture that the surrounding medium of the GRB progenitor should be that of a massive WR star. The problem we have investigated is that for most GRB afterglow models the best fit to observations is found if the relativistic jet is propagating through a constant density medium not a stellar wind bubble. How to get a constant density medium? In stellar wind bubbles there is a constant density region. It is the stalled wind further after the jump at the freewind/stalled-wind interface. (Castor et al. 1975). The distance of this point is determined by various factors including the wind velocity, mass-loss rate and the initial density of the surrounding interstellar medium (ISM). We find that if the free-wind region size is 1017 cm the relativistic jet will traverse it in less than a day (see Figure 2). Therefore the GRB afterglow a day after the prompt emission will appear to be traversing a constant-density medium. We find that for the single star free-wind regions to reach this size the initial ISM density must be unusually high, >105 cm-3. Therefore we have investigated the other factors that effect the stellar wind bubble; rotation, duplicity and stellar motion through the ISM. This investigation was performed by using output from stellar models from the Cambridge STARS code (www.ast.cam.ac.uk/~stars) in a Zeus-2D simulation of the circumstellar medium as in Eldridge et al. (2006).
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Results & Discussion Figure 3 compares a bubble models for a single star, a single star rotating at 100 km s-1 and a star in a binary with an orbital velocity of 100 km s-1. We see the free-wind region is largely unaffected as the wind velocity is much greater (vwind=2400 km s-1) than the rotation velocity. However there is a great effect on the structure of the wind material from the red supergiant phase that has been swept up by the faster WR wind material as the velocities are of similar magnitude. Figure 4 shows the deformation of the stellar bubble if the star is travelling relative to the surrounding ISM. For the free-wind region to be shrunk enough the density of the ISM must be 103 cm-3, and the stellar velocity must be 100 km s-1. Normally this would be considered unusually high. But recent results have shown that GRB progenitors may have velocities of this order (Hammer et al., 2006). The radius where the free-wind region terminates due to the bow shock can be estimated by simple momentum arguments:

Figure 1: Simple representation of the stellar wind bubble structure. The plot is on a logarithmic scale. The free-wind density is determined by the mass-loss rate and wind velocity. The size of the bubble and the position of the interfaces are also influenced by the initial ISM density. See Castor et al. (1975) for an analytic model.

Figure 2: Example of afterglow calculations for propagation through a stellar wind bubble. Rsw is the distance from the star of the stalled-wind/free-wind interface. Taken from Eldridge et al. (2006).

Figure 3, Circumstellar environment models. In each the star had an initial mass of 70Msun, an initial metallicity mass fraction of Z=0.004 and an initial ISM density of 10-3 cm-3. Left: the normal model with no rotation. The free-wind region is inner most with the stalled wind outside. The thin and dense shell in the stalled wind region is formed from the slow and dense red supergiant wind material being swept up by the faster WR wind. Middle: a single star rotation model with a rotation velocity of 100 km s-1. Right: a binary star model with an orbital velocity of 100 km s-1. In both these cases the shell of swept up red supergiant wind material is distorted the most as the velocity is of a simialr magnitude to the rotation velocity. The plots are is 5в1020 cm by 5в1020cm.

The normal A* parameter used to define the density of the free-wind region had no direct relation to the wind momentum and therefore R0. We find that high A* WR stars (WC stars) have lower wind momentums and therefore lower R0. While lower A* WR stars (WO stars) have high wind momentums and therefore greater R0. Also we note that the density structures around very low metallicity (Z<0.001) stars may be very different to those presented here. Future Work. (1)Consider very low metallicity stellar bubbles evolution. (2)Consider other arrangements that lead to deformation of the stellar wind bubbles. References Castor J. et al., 1975, ApJ, 200, 107. Chevalier R.A. et al., 2004, ApJ, 606, 369. Eldridge J. J. et al., 2006, MNRAS, 367, 186. Hammer F. et al. 2006, astro-ph/0604461. van Marle A.J. et al., 2005, A&A, 444, 837.

Figure 4, the same stellar models as in figure 3 but with the star moving through an ISM density of 103 g cm-3 at 100 km s-1. The plot is 2в1018 cm by 1в1018cm.