SIMBAD references

The spiral structure of M51 (NGC 5194) is studied by 3D N-body simulations utilizing {formmu1} particles, with main interest in the stellar spirals observed in near-IR within 30arcsec of the centre of M51. A multiple-encounter tidal model for the interaction with the nearby companion (NGC 5195) is studied, capable of accounting for the main spiral structure of M51, including the morphology and kinematics of the extended Hi tail. Our model of M51 consists of a self-gravitating exponential stellar disc, embedded in an analytical {formmu2} potential {formmu3} producing the observed rotation curve with the steep rise within 15-20arcsec. When evolved in isolation, this model is stable against large-scale bar instabilities, but develops recurrent inner {formmu4} spiral structures inside about 50arcsec, although these lack continuity with the weaker outer multiarm structures. The pattern speeds of the inner spirals exceed the {formmu5} maximum, thus lacking inner Lindblad resonance (ILR). For larger disc masses, the inner spirals tend to have an oval component. These inner spirals/ovals often show a temporary leading appearance, as a result of the reflection of wave packets from the centre. The azimuthal propagation of wave packets deviates from that of Lin-Shu waves, as they do not maintain constant pattern speeds, except near the centre. Also, the shape of spirals deviates from Lin-Shu waves, the radial distance between adjacent arms adjusting close to Toomre's critical wavelength.

We show that the in situ swing amplification of the tidally induced kinematic disturbances during the highly inclined passage of the companion is limited beyond about 100arcsec. This is a result of the low frequency of external forcing, placing the ILR of the outer disc disturbances to about this distance. However, these disturbances initiate higher frequency tidal waves which propagate inward with the group velocity. The azimuthal propagation speeds increase during the inward propagation, enabling the tidal waves to pass over the {formmu6} maximum, and reach within 30arcsec, after about 500Myr of initial perturbation. The interference between separate tidal waves leads to amplitude variations along spiral arms resembling the observed variations. Inside 30arcsec, the tidal wave joins in many instances rather smoothly with the pre-existing central arms, giving a continuous structure much like the observed one. Simulations with different inner slopes of the rotation curve indicate that a steep rise in the rotation curve of M51 is essential for the formation of the tightly wound inner spiral arms.