A New Model of a Tidally Disrupted Star

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Abstract
A new semianalytical model of a star evolving in a tidal field is proposed. The model is a generalization of the so-called affine stellar model. In our model the star is composed of elliptical shells with different parameters and different orientations depending on time and on the radial Lagrangian coordinate of the shell. The evolution equations of this model are derived from the 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 three-dimensional numerical computations of the tidal interaction of a star with a supermassive black hole. The comparison shows very good agreement between the main "integral" characteristics describing the tidal interaction event in our model and in the three-dimensional computations. Our model is effectively a one-dimensional Lagrangian model from the point of view of numerical computations, and therefore it can be evolved numerically 102-103 times faster than the three-dimensional approach allows. This makes our model well suited for intensive calculations covering the whole parameter space of the problem.

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