Shock breakout in Type Ibc supernovae and application to GRB 060218/SN 2006aj

Recently, a soft black-body component was observed in the early X-ray afterglow of GRB 060218, which was interpreted as shock breakout from the thick wind of the progenitor Wolf-Rayet (WR) star of the underlying Type Ic SN 2006aj. In this paper we present a simple model for computing the characteristic quantities (including energy, temperature, and time-duration) for the transient event from the shock breakout in Type Ibc supernovae produced by the core-collapse of WR stars surrounded by dense winds. In contrast to the case of a star without a strong wind, the shock breakout occurs in the wind region rather than inside the star, caused by the large optical depth in the wind. We find that, for the case of a WR star with a dense wind, the total energy of the radiation generated by the supernova shock breakout is larger than that in the case of the same star without a wind by a factor > 10. The temperature can be either hotter or cooler, depending on the wind parameters. The time-duration is larger caused by the increase in the effective radius of the star due to the presence of a thick wind. Then, we apply the model to GRB 060218/SN 2006aj. We show that, to explain both the temperature and the total energy of the black-body component observed in GRB 060218 by the shock breakout, the progenitor WR star has to have an unrealistically large core radius (the radius at optical depth of 20), larger than 100 Rsun. In spite of this disappointing result, our model is expected to have important applications to the observations on Type Ibc supernovae in which the detection of shock breakout will provide important clues to the progenitors of SNe Ibc.
20 pages, including 14 figures and 1 table. Accepted by MNRAS on 13 November 2006. Revised according to the referee report. Major changes include: (1) the equation for shock deceleration is changed; (2) the opacity to starlight and the opacity relevant to the X-ray flash are distinguished; (3) the relativistic beaming effect is considered in calculation of the time-duration of shock breakout. (4) Some figures are redrawn or replaced, and one new figure is added. However, main conclusions are not changed