A new model of tidally disrupted star

A new semi-analytical model of a star evolving in a tidal field is proposed. The model is a generalization of so-called 'affine' stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations. The parameters and orientations of these shells are functions of time and the radial Lagrangian coordinate of the star. The evolution equation of this model are derived from the exact integral consequences of hydrodynamical equations of motion, called virial relations under certain assumptions, and the integrals of motion are identified. It is shown that the evolution equations can be deduced from a variational principle. The evolution equations are solved numerically and compared quantitatively with the results of 3D numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows a very good agreement between main ``integral'' characteristics describing the tidal interaction event in our model and in the 3D computations. Our model is effectively a one-dimensional Lagrangian model from viewpoint of numerical computations, and therefore it can be evolved numerically $10^{2}-10^{3}$ times faster than the 3D approach allows. This enables to use our model for intensive calculations covering all parameter space of the problem.