M51: the Whirlpool - and Simulation

I model the grand design spiral galaxy M51 (NGC 5194) as an interacting system and use a three component self-gravitating N-body code to simulate the gravitational interaction. The problem reduces to choosing a finite set of orbits (for NGC 5195) that can model the observed features of M51. I also include a simple gas cloud collision algorithm that permits features in the gas particles to strengthen. The code is stable and well tested. I develop an analytic method to set limits to some of the orbit parameters. This method is suitable for nearly face-on grand design galaxies with companions. I find that the entire grand design structure in M51 is consistent with a tidal passage of its companion, NGC 5195, in an osculating orbit (i = 50^circ, e = 0.1, a = 16.6 kpc) roughly 70 million years ago (H = 50 (km/sec)/Mpc). The position angle of maximum tidal action is ~300^ circ. The simulation reproduces the radii and azimuths of points along the sharp dust lane spiral arms, the general shape of the disk seen in the IR, and the clumps seen in HI north of the companion. The simulation also refines the limits for the ratio of halo mass to disk mass for M51 to be between 1.0 and 3.0. The mass of NGC 5195 must be roughly 1/10 the mass of M51 to produce a good match. This indicates that the highly disturbed companion's mass/luminosity is somewhat abnormal. The orbit and decay time estimates imply that the companion is in a shrinking orbit and will eventually merge with M51. I interpret the extended HI tail as a remnant of an earlier passage of the companion. The outer arms of M51 behave like material arms inward to ~140^ {''}. The transition between the directly excited outer tidal arms and the indirectly excited inner arms explains the symmetrically placed bends in the outer arms of M51. The inner structure is consistent with resonantly excited m = 2 Lindblad dispersion orbits. I propose three regions of spiral structure in M51: (1) the extended tidal arm created by the previous passage of NGC 5195; (2) the strong tidal arms seen in the optical and created by the most recent passage 70 to 84 million years ago; and (3) the inner density wave excited by these tidal arms.