Shock waves in tidally compressed stars by massive black holes

Aims. We investigate the case of a main-sequence star deeply penetrating the tidal radius of a massive black hole. We focus on the compression phase leading to a so-called pancake configuration of the star at the instant of greatest compression. The aim is to study the tidal compression process paying particular attention to the development of shock waves, to deduce reliable estimates of the thermodynamical quantities involved in the pancake star, and to solve a controversy about whether thermonuclear reactions can be triggered in the core of a tidally compressed star. Methods. We set up a one-dimensional hydrodynamical model adapted to the geometry of the problem. Based on the high-resolution shock-capturing Godunov-type approach, this model allows us to study the compression phase of the star in a direction orthogonal to its orbital plane. Results. We show the existence of two regimes depending on whether shock waves develop before or after the instant of maximum core compression. In both cases we confirm that high compression and heating factors in the stellar core are able to trigger a thermonuclear explosion. Moreover, we show that the shock waves carry a brief but very high peak of temperature outwards from the centre to the surface of the star. We tentatively conclude that the phenomenon could give rise to hard electromagnetic radiation, to be compared to some GRB-type flares already observed in their host galaxies. Finally, we estimate that the rate of pancake stars should be about 10(-5) per galaxy per year. If generated in hard X- or gamma-ray bands, several events of this kind per year should be detectable within the full observable universe.