N-body model for M51 - I. Multiple encounter versus single passage?

A numerical survey of the encounter history of the interacting grand-design system M51 (NGC 5194/5195) is performed with a 3D multiple spherical polar grid code, where both components of the pair are described with self-gravi tating star + gas discs embedded in rigid analytical halo potentials. Two c lasses of models are investigated, (1) nearly parabolic single passages, an d (2) bound encounters implying several disc-plane crossings. Both types of models can approximate the general morphology of the M51 system and simult aneously fit the projected velocity difference and separation of the compon ents. In both cases the companion disc-plane crossing responsible for the m ain spiral structure occurred nearly in the south, about 400-500 Myr ago at a distance of 25-30 kpc, but in opposite directions. In the bound encounte r model there is also a more recent crossing, at a distance of 20-25 kpc ab out 50-100 Myr ago. Our models account for some important kinematical observations of the M51 s ystem not explained by the previous models. Especially, we note that the mu ltiple-encounter model with a recent passage produces significant, out-of-p lane velocities, which manifest as an S shaped structure of the major axis rotation curve, and which also explain the high peculiar velocities in the north of the companion. In this model the resulting extended tail is tilted 40 degrees -50 degrees with respect to the inner disc, leading to a veloci ty field that appears to suggest counter-rotation of the tail with respect to the inner disc. Also some morphological features, like the direction of the: tidal extensions from the companion, are better matched by a model wit h a recent encounter. Importantly, any pre-existing spiral arms are washed out by the tidally triggered spiral arms. The multiple-encounter model assumes a high inclination (i approximate to 8 5 degrees) orbit, with a low current eccentricity (epsilon approximate to 0 .2), The possible origin of this type of bound orbital configuration is stu died by simulations including the orbital decay via the Chandrasekhar formu la for dynamical friction, and also by simulations including a self-consist ently modelled live halo for the primary. The gross features of the model, including. the tilted far tail, are preserved even when allowing for the ef fects of several earlier passages. The observed well-defined far tail seems to suggest that the previous passages have been at least 30 per cent more distant than the latest two crossings, According to our limited orbital sur vey, such an orbital decay can be accounted for, provided that M51 has an e xtended dark halo containing at least a few times the mass within the visib le disc region (total M-halo/M-disc similar to 10).