## 5. Consequences for the stellar dynamoWe do not find any remarkable gradient of the rotation frequency either in the radial or in the latitudinal direction. This raises the question about the nature of the dynamo process in this type of star, which might be quite different from the solar dynamo. The latter is believed to be of -type, producing an axisymmetric oscillating dipole field with a toroidal field component much stronger than the poloidal. This mechanism of field generation does not work in stars with weakly differential or uniform rotation. On the other hand, a fossil field can survive over a time scale where is the turbulent magnetic diffusivity and the stellar radius. Even if the efficiency of turbulent diffusion is reduced by two orders of magnitude due to the global rotation, the diffusive time scale is only about 300 years and thus much too small for a large-scale field to survive. The magnetic field of the TTS (and of the main sequence star that evolves from it) must therefore be dynamo-generated. Of the variety of known dynamo mechanisms (cf. Krause & Rädler 1980), the -dynamo seems to be the most likely one in case of uniform rotation, since for large Coriolis numbers the magnetic diffusivity decreases as while the -effect has a finite limit (Rüdiger & Kitchatinov 1993) and the dynamo must therefore necessarily become supercritical for sufficiently fast rotation. This case has been considered by Moss & Brandenburg (1995), who found that the S1 mode was the first to become supercritical, at a Coriolis number of 27.9. Since in our model for the inner 75 percent of the stellar radius, we can indeed expect the action of an -dynamo. Linear dynamo theory has shown that in case of an -dynamo in a sphere with isotropic -effect the most easily excited mode is always axisymmetric (Rädler 1986) while anisotropic leads to non-axisymmetric fields unless there is strong rotational shear (Rüdiger 1980, Brandenburg et al. 1989, Rädler et al. 1990, Rüdiger & Elstner 1994). Since for Coriolis numbers as large as in case of T Tauri stars the -tensor is indeed strongly anisotropic, the finding of Moss & Brandenburg is in agreement with the results of previous work. The actual field geometry is, however, not determined by one single mode since the back reaction of the magnetic field on the turbulent electromotive force makes the dynamo equation nonlinear and therefore there will be a coupling of different modes. Moss & Brandenburg (1995) found that in this case the field geometry always resembled the S1 mode although contributions of higher modes were present and that the field in the surrounding space was mainly that of a dipole with the axis lying perpendicular to the axis of rotation. Although the spatial structure of stellar magnetic fields is generally not observable, Doppler imaging provides some hints since it tells us about the distribution of spots on the stellar surface. Unlike the sunspots, spots on T Tauri stars appear to have lifetimes of several years and cover a significant fraction of the stellar surface. Joncour et al. (1994a,b) found large spots close to the visible poles of V 410 Tauri and HDE 283572 and hence no restriction of stellar activity to low latitudes. Moreover, the distribution of spots on the surface of V 410 Tauri is strongly non-axisymmetric and covers all latitudes. This result, also found by Rice & Strassmeier (1996), indicates that the large-scale magnetic field may indeed be non-axisymmetric. We may therefore conclude that the absence of surface differential rotation and the non-axisymmetric geometry of the magnetic field support our finding that there should not be any significant differential rotation in weak line T Tauri stars. The symmetry of the magnetic field has important consequences for stellar activity. The cyclic behaviour of solar activity is quite normal for -dynamos, which produce dynamo waves that propagate along the lines of constant rotation rate (Parker 1955, Yoshimura 1975). Non-axisymmetric field modes, however, can only propagate in longitudinal direction without any cyclic variation of the total field energy (cf. Rädler 1986). We can therefore not expect activity cycles for uniformly rotating stars. This provides a strong observational test for dynamo theory. © European Southern Observatory (ESO) 1997 Online publication: March 24, 1998 |