N-body model for M51 - II. Inner structure

The spiral structure of M51 (NGC 5194) is studied by 3D N-body simulations utilizing 4 x 10(6) particles, with main interest in the stellar spirals ob served in near-IR within 30 arcsec of the centre of M51. A multiple-encount er tidal model for the interaction with the nearby companion (NGC 5195) is studied, capable of accounting for the main spiral structure of M51, includ ing the morphology and kinematics of the extended H I tail. Our model of M5 1 consists of a self-gravitating exponential stellar disc, embedded in an a nalytical bulge + halo potential (M-disc/M-tot = 0.333-0.5), producing the observed rotation curve with the steep rise within 15-20 arcsec. When evolv ed in isolation, this model is stable against large-scale bar instabilities , but develops recurrent inner m=2 spiral structures inside about 50 arcsec , although these lack continuity with the weaker outer multiarm structures. The pattern speeds of the inner spirals exceed the Omega - kappa /2 maximu m, thus lacking inner Lindblad resonance (ILR). For larger disc masses, the inner spirals tend to have an oval component. These inner spirals/ovals of ten show a temporary leading appearance, as a result of the reflection of w ave packets from the centre. The azimuthal propagation of wave packets devi ates from that of Lin-Shu waves, as they do not maintain constant pattern s peeds, except near the centre. Also, the shape of spirals deviates from Lin -Shu waves, the radial distance between adjacent arms adjusting close to To omre's critical wavelength. We show that the in situ swing amplification of the tidally induced kinemat ic disturbances during the highly inclined passage of the companion is limi ted beyond about 100 arcsec. This is a result of the low frequency of exter nal forcing, placing the ILR of the outer disc disturbances to about this d istance. However, these disturbances initiate higher frequency tidal waves which propagate inward with the group velocity. The azimuthal propagation s peeds increase during the inward propagation, enabling the tidal waves to p ass over the Omega - kappa /2 maximum, and reach within 30 arcsec, after ab out 500 Myr of initial perturbation. The interference between separate tida l waves leads to amplitude variations along spiral arms resembling the obse rved variations. Inside 30 arcsec, the tidal wave joins in many instances r ather smoothly with the pre-existing central arms, giving a continuous stru cture much like the observed one. Simulations with different inner slopes o f the rotation curve indicate that a steep rise in the rotation curve of M5 1 is essential for the formation of the tightly wound inner spiral arms.