A New Model of a Tidally Disrupted Star

A new semi-analytical model of a star evolving in a tidal field is proposed.The model is a generalization of the so-called 'affine' stellar model. In ourmodel the star is composed of elliptical shells with different parameters anddifferent orientations, depending on time and on the radial Lagrangiancoordinate of the shell. The evolution equations of this model are derived fromthe virial relations under certain assumptions, and the integrals of motion areidentified. It is shown that the evolution equations can be deduced from avariational principle. The evolution equations are solved numerically andcompared quantitatively with the results of 3D numerical computations of thetidal interaction of a star with a supermassive black hole. The comparisonshows very good agreement between the main ``integral'' characteristicsdescribing the tidal interaction event in our model and in the 3D computations.Our model is effectively a one-dimensional Lagrangian model from the point ofview of numerical computations, and therefore it can be evolved numerically$10^{2}-10^{3}$ times faster than the 3D approach allows. This makes our modelwell suited for intensive calculations covering the whole parameter space ofthe problem.Comment: This version is accepted for publication in ApJ. Stylistic and grammatical changes, new Appendix adde