Tails and bridges in the parabolic restricted three-body problem

Abstract

After a close encounter of two galaxies, bridges and tails can be seen between or around them. A bridge would be a spiral arm between a galaxy and its companion, whereas a tail would correspond to a long and curving set of debris escaping from the galaxy. The goal of this paper is to present a mechanism, applying techniques of dynamical systems theory, that explains the formation of tails and bridges between galaxies in a simple model, the so-called parabolic restricted three-body problem, i.e. we study the motion of a particle under the gravitational influence of two primaries describing parabolic orbits. The equilibrium points and the final evolutions in this problem are recalled,and we show that the invariant manifolds of the collinear equilibrium points and the ones of the collision manifold explain the formation of bridges and tails. Massive numerical simulations are carried out and their application to recover previous results are also analysed.

Strategies to engineer the capture of a member of a binary asteroid pair using the planar parabolic restricted three-body problem

“…As collisions are taken into consideration in this paper, in a majority of prograde cases the boundaries are always collision regions. In References [48,49], without considering collisions, the authors numerically demonstrated that the boundaries between different regions should be the invariant manifolds related to + , which trend to as → +∞. This point can provide further insights into the ICMs.…”

“…The third body 3 , a massless particle, moves under the gravitational field generated by the primaries and orbits in the same plane as the primaries, without perturbing them. The problem described above is the planar parabolic restricted three-body problem (PPRTBP) [46][47][48][49]52]. Considering a binary asteroid pair approaching a central body, we can approximate the dynamics of the problem through PPRTBP, denoting the central body as 1 , the main asteroid as 2 and the minor asteroid as 3 , as shown in Fig.…”

“…An escape case occurs when the binary pair is also disrupted, however 3 escapes from 1 . Similar classification is also defined in References[46][47][48][49]. In this section, we provide some examples to illustrate different classifications of motion in the PPRTBP before detailed initial condition maps are generated.…”

S0 Galaxies: Outer Gas Accretion through Tidal Interaction and Minor Merging

“…The first simulations of galaxy gravitational interaction by Toomre and Toomre [17] demonstrated a rich collection of tails and bridges formed even without gas participation in the interactions. Later, a significant amount of other simulations were made, both pure N-body ones (e.g., [18,19]) and those taking into account gas dynamical effects in gas-rich galactic disks (e.g., [20][21][22]), and outer tails and bridges were obtained in these simulations providing gas exchange between interacting galaxies. The observations of some spectacular interacting galaxy systems also demonstrated extended outer gaseous structures, connecting the interacting galaxies-sometimes those formed from cold neutral hydrogen and seen only in the 21 cm line without optical counterparts [23][24][25], and sometimes star formation was detected in these structures beyond the galactic disks, and they were excited by young stars and seen both in UV [26] and in the ionized-gas optical emission lines (e.g., [27][28][29][30]).…”