2. A model for the inner wind
IK Tau is a variable O-rich Mira of spectral type M6. The stellar parameters considered in this study are listed in Table 1. Its distance was derived by Le Sidaner & Le Bertre (1994) to be 220 pc while its pulsation period is 470 days (Hale et al. 1997). Le Sidaner & Le Bertre assumed a stellar temperature of 2000 K for their radiative transfer model of the IR excess, in good agreement with the value used in this study. In order to derive a radius for the star we assumed a luminosity close to the canonical value for typical Miras stars given by the Period-Luminosity relation derived by Feast (1996). The derived radius satisfies the standard pulsation equation for Miras of Fox & Wood (1982)
where we assume that the star is pulsating in its fundamental mode (Q). This gives a stellar mass of 1 , typical of O-rich Miras variables. There exists observational evidence for O-rich Miras to pulsate in their first overtone (Feast 1996) and we will study the impact of this result on our stellar and chemical model in a forthcoming paper.
Table 1. IK Tau - stellar parameters: and are defined as in Cherchneff et al. (1992) and X (Y) .
We consider the inner wind as a narrow region above the photosphere which experiences the passage of strong, periodic shocks generated by stellar pulsation. The model describes both the immediate region (thermal cooling region) and the hydrodynamical cooling region of the post-shock structure as described by Fox & Wood (1985), Bertschinger & Chevalier (1985) and WC98. More details on the model for the inner winds of AGB stars are given in Cherchneff et al. (1998). In our model of IK Tau, we choose a shock speed km s-1 in agreement with shock velocities derived from the CO IR line analysis of Hinkle et al. (1997). The periodic shocks steepen at in our model and levitate the nearby gas layers to larger radii, these regions falling down to their initial position because of stellar gravity. This periodic motion generates a pattern of gas excursions as illustrated in Fig. 1. The physical parameters characterising the shocked, inner wind are listed in Table 2.
Table 2. Pre-shock, shock front and excursion ( post-shock) gas temperature and number density as a function of position in the envelope and shock strengths. M is the Mach number associated with each shock speed.
© European Southern Observatory (ESO) 1999
Online publication: December 4, 1998