Dynamo model with a small number of modes and magnetic activity of T Tauri stars

We suggest a model based on the representation of the stellar magnetic field as a superposition of a finite number of poloidal and toroidal free decay modes to describe the dynamo action in fully convective stars. For the adopted law of stellar differential rotation, we determined the dynamo number in exceeding which the generation of a cyclically varying magnetic field is possible in stars without a radiative core and derived an expression for the period of the cycle. The dynamo cycles in fully convective stars and in stars with thin convective envelopes are shown to differ qualitatively: first, the distributions of spots in latitude during the cycle are different for these two types of stars and, second, the model predicts a great weakening of the spot formation in fully convective stars at certain phases of the cycle. To compare the theory with observations, we have analyzed the historical light curve for the weak-line T Tauri star V410 Tau and found that its long-term activity is not a well-defined cycle with a definite period—its activity is more likely quasi-cyclic with a characteristic time of ～4 yr and with a chaotic component superimposed. we have also concluded that a redistribution of spots in longitude is responsible for the secular brightness variations in the star. This does not allow the results of photometric observations to be directly compared with predictions of ourmodel, in which, for simplicity, we assumed a symmetry in longitude and investigated the temporal evolution of the spot distribution in latitude. Therefore, we discuss the questions of what and how observations can be compared with predictions of the dynamo theory.