Buried magnetic flux tubes in giant stars near the "Coronal Dividing Line"

We apply the "solar paradigm" for stellar magnetic activity to the post-mai n-sequence evolution of stars in the mass range 1 M-circle dot less than or equal to M-star less than or equal to 3 M-circle dot. The model starts fro m a strong toroidal magnetic field generated by a dynamo working in the ove rshoot layer below the convection envelope. Once a critical field strength is exceeded, an undulatory (Parker-type) instability leads to rising flux l oops. Upon emergence at the stellar surface, they form bipolar magnetic reg ions and large-scale coronal loops. By considering the stability, dynamics, and rise of magnetic flux tubes along evolutionary sequences of stellar mo dels, we find that the flux loops become trapped in the stellar interior wh en the depth of convective envelope exceeds about 80% of the stellar radius . Trapping is caused by an increase of field line curvature at the loop sum mit, so that eventually the magnetic tension force dominates over the buoya ncy force. The magnetic loops find a stable equilibrium configuration withi n the convection zone and do not emerge at the stellar surface. The transit ion from emerging to trapped flux tubes falls in the range of spectral type s G7 to K0 for luminosity class III giants, which is close to the observed "coronal dividing line" in the Hertzsprung-Russell diagram. This result is remarkably stable within large ranges of stellar parameters (mass, rotation ) and flux tube parameters (field strength, magnetic flux) and depends prac tically exclusively on the fractional radius of the stellar radiative core. We suggest that flux tube trapping is the cause for the strong decline of stellar X-ray emission across the "coronal dividing line".