Direct, Co-planar Encounters

We construct the 42 galaxy models with NFW halos described in §2.2 and simulate direct encounters between coplanar disks on zero energy orbits using the restricted method. The pericentric separation of the galaxies for all trajectories is 4.0 disk scale lengths (16 kpc). Figure 5 presents the results from the survey grid shown at t= +30 units (+540 Myr) after pericenter and the width of each frame is 100 units (400 kpc). (Animations of the simulations are available at http://www.cita.utoronto.ca/~dubinski/tails3/.) The grid can be divided roughly into 3 regions which distinguish the behavior of the kinematic development of the tidal tails and merging times, although there is a continuous transition between the boundaries. We refer to these three regions as I, II and III and discuss their peculiar features.

  

Figure 5: A survey of direct, co-planar galaxy collisions with NFW halos having different scale radii and maximum velocities and R_p=4.0. Each frame is 100 disk scale lengths on a side ($\sim$400 kpc). Figure 1 shows the corresponding rotation curves of these galaxies. See the text for a full explanation.

The first two columns of the simulation grid define Region I. Here, galaxies develop long tidal tails (>100 kpc in length), in many ways similar to the classic examples of interacting pairs of galaxies discussed in TT, such as NGC 4038/9 (the Antennae) and NGC 4676 (the Mice). A significant amount of mass is also stripped from the galaxies with $\sim 20$% of the original disk mass being ejected into tails. These models have no trouble producing long, massive tidal tails because the halos have low mass and are compact, resulting in a shallow potential near the disk edge. The halo mass ranges from only 2 to 13 times the stellar mass and the escape velocity within the disk is only about twice the local circular velocity. The halos at the bottom of this region have a higher central density and so dynamical friction is stronger leading to shorter merging times. The galaxies in the lower left corner are already merging by t=+30. The behavior in this region is similar to the Model A and B galaxies of DMH and, in fact, to most previous models of interacting galaxies.

The upper right corner of the simulation grid defines Region II. Here, galaxies also develop long tidal tails with the added bonus of a long connecting bridge. The interacting pair Arp 295 with its two widely separated disks and bridge looks more like these models than those in Region I. As in Region I, the escape velocity is again roughly twice the value of the circular velocity despite the higher halo mass. The circular speed is dropping off more rapidly at the disk edge as well allowing the formation of long tails and bridges. However, the potential is shallower than in Region I and the central halo density is much smaller and so the stopping power of dynamical friction is limited. The two galaxies therefore fly by each other to distances greater than 50 scale lengths (200 kpc) before falling back together, allowing the development of a long connecting bridge. The behavior is similar to the Model E galaxies discussed in MDH. For r_p=4.0 scale lengths, the galaxies take several hundred time units to merge (> 5 Gyr) because of the smaller amount of dynamical friction during the first encounter, compared with merging times of <1 Gyr for galaxies in Region I.

The lower right corner of the simulation grid defines the final Region III. Here, the formation of tidal tails is strongly suppressed, becoming more so as the halo mass and extent increases towards the lower right corner. The escape velocity is larger here than in Regions I and II with values ranging from 2.5 to 3 times the circular velocity. The potential is therefore steeper and more effective at holding onto ejected material after the strong perturbation felt during the encounter. The relative speed of the two galaxies during their encounter is 1.5 to 2 times larger than in Regions I and II and so the galaxies do not slow down appreciably after their encounter even with the heightened dynamical friction due to the higher halo densities. The behavior seen here is similar to the Model C and D galaxies discussed in DMH and is primarily a result of the steep potential at the disk edge for these high mass halos.

In summary, the galaxies in Regions I and II produce galaxies with long tidal tails during their first encounters with many similarities to observed interacting pairs. The distribution of halo mass is markedly different in these regions. Models in Region I have relatively low mass, compact halos with declining rotation curves. In contrast, models in Region II have higher mass, more extended halos, but their lower halo circular velocities result in declining rotation curves due to the disk-halo transition. Despite these differences, the controlling parameter is the ratio of escape velocity to circular velocity within the disk ( $v_e/v_c \sim 2$) rather than the actual halo:disk+bulge mass ratio, as emphasized by Springel & White (1998). The appearance of the models in Region III reflects the larger amount of dark matter in the galaxies' centers and the steep slope of their halo potential. It appears that when the escape velocity is $>2.5\times$ the circular velocity (measured at 2R_d) tidal tails do not form.