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In the late 1920s, the observational power of 100-inches (2.5 m) class telescopes allowed Hubble to determine the existence of apparently isolated nebulae outside of our Milky-Way (Hubble 1929). These so-called "island universes" became of prime importance in the discovery of the expansion of the Universe, thanks to redshift measurements. Rapidly, many more extra-galactic objects have been classified as galaxies and sorted according to their morphology, following the famous Hubble pitch fork diagram.

2.1. Discovery of peculiarities

In the preface of his Atlas of Peculiar Galaxies, Arp (1966) noted that "when looked at closely enough, every galaxy is peculiar". While most of the luminous galaxies could be classified as either elliptical, spiral or barred-spiral, it appeared that more and more peculiar morphologies would not fit into these three families. Number of photographic plates of individual systems have been published and revealed twisted shapes and/or faint extensions outside of the central regions of the galaxies (e.g. Duncan 1923, Keenan 1935, Wild 1953, Zwicky 1956). These features have been detected in many other objets gathered in atlases and catalogues (Zwicky et al. 1961, 1963, Vorontsov-Vel'Yaminov & Arkhipova 1962, 1964, Arp 1966). This contradicted the persistent idea that the intergalactic space was entirely empty (Zwicky 1963; see also the discussion in Gold 1949 and references therein).

It rapidly appeared that many of these peculiar galaxies were actually double or multiple galaxies, i.e. pairs or small groups, observed close to each other. Really interacting galaxies have been told apart from optical pairs, for which apparent closeness is due to projection effects (Holmberg 1937; see also Zwicky 1956). The major signatures of interaction were the detection of long (~ 101-2 kpc) and thin (~ 1 kpc) filaments either connecting two galaxies or pointing away from them. The former have been named bridges and the latter, tails. This clearly distinguished them from the spiral arms which are located in the more central regions of disk galaxies. However, a confusion persisted because it was noted that tails are sometimes (but not always) in the continuation of spiral arms (Pikel'Ner 1965). Although being faint and thus often difficult to observe, these filaments appear bluer than the disks themselves, suggesting that they host ongoing star formation (Ambartsumian 1961, Zwicky 1963). But the exact reasons for such morphological features remained opened to debate over the entire 1960 decade.

2.2. A controversial scenario

Zwicky (1962) proposed that collisions of galaxies would enhance the supernovae activity, by increasing the probability of chain explosions. These blasts could then sweep out or eject the galactic material away from the nuclei. With a favorable geometry, such events could even act as "launchers of galaxies", and thus account for the intergalactic filamentary structures. However, this scenario failed to explain the thinness of the filaments and the connection to other galaxies, so that it has rapidly been ruled out (Pikel'Ner 1965).

Another explanation for the formation of bridges took jets into account (Ambartsumian 1961, Arp 1967, 1968, 1972). When a massive galaxy ejects a fraction of its matter (gaseous, stellar or both) from its nucleus, a symmetrical pair of jets is formed but rapidly slowed down by the high densities encountered along its path 1. This would create an overdensity at the tip of the jets that could condense and form a small companion galaxy (Sérsic 1968). All together, the main galaxy, its companion and one of the jets would constitute the interacting pair and the bridge. The absence of galaxy at the end of the second jet (i.e. the tail) was explained by either the escape of the companion to the intergalactic medium, its rapid dissolution, or a delayed formation that has not taken place yet (Arp 1969). Illustrative examples of this scenario are NGC 3561 ("the guitar") and M 51 ("Whirlpool galaxy"), as shown in Figure 1. However, Holmberg (1969) noted that the condensation of the gravitationally bound companion galaxy would be very unlikely when the jets reach a velocity higher than the escape velocity, which seems to be true in most of the cases. Such an activity from the nuclei of massive galaxies led some authors to classify galaxies with connecting "jets" as radio-galaxies (see e.g. Ambartsumyan 1974).

Figure 1

Figure 1. NGC 3561 (left) has been seen by Arp (1972) as a spiral galaxy having ejected two luminous jets of matter. An high surface brightness object, called "Ambartsumian's knot", can be seen at the tip of the southern jet at the bottom-edge of this image. In the case of M 51 (right), the companion is situated at the tip of a spiral arm of the main galaxy. Images from the Atlas of Peculiar Galaxies by H. Arp, available in the NASA/IPAC Extragalactic Database, Level 5.

Meanwhile, tides have been considered as a possible cause for the filaments: a close passage of one galaxy next to another would lead to different gravitational forces over the spatially extended galaxies: the side of the first galaxy facing the second is more attracted than the opposite side. These differential forces would then significantly deform the shape of the galaxies and could even trigger an exchange of some of their stars (Holmberg 1941, Zwicky 1953, 1956, Lindblad 1960, Zasov 1968, Tashpulatov 1970a). The pioneer numerical works that addressed this question concluded that, under precise circumstances, tidal structures looking like bridges and tails could form during the close encounter of two galaxies (Lindblad 1961, Yabushita 1971).

However, the tidal origin of the tails has been intensively discussed. Vorontsov-Vel'Yaminov (1962) argued that the elongation of the tails (sometimes up to a few × 100 kpc, see Mirabel et al. 1991) was too large to be produced by tides. He added that close pairs of galaxies were not systematically linked to the existence of filaments, and concluded that tails and bridges shared the same origin than the more classical spiral arms. Others followed the same line of arguments and evoked magnetic (or magnetic-like, see Vorontsov-Vel'Yaminov 1965) fields to explain the narrow shape of the tails (see e.g. Burbidge et al. 1963, Zasov 1968). Tubes of magnetic lines forming at the same time as the galaxy itself would propagate a wave that would trigger the condensation of gas along them. Such an hypothesis would explain the presence of knots of high surface brightness along the tails, as already detected by e.g. Burbidge & Burbidge (1959). Furthermore, Gershberg (1965) noted that a collision between two galaxies would heat up the gas too much (~ 107 K) to form a thin structure and ruled out this scenario as a possible cause of creation of filaments. Arp (1966) summarized the debate by suggesting that forces other than pure gravitation should be at stake in the shaping of peculiar galaxies and their intergalactic structures.

2.3. Tidal origin

The major breakthrough came in the early 1970s, in the newly-born era of computers. Thanks to a series of numerical experiments, Toomre & Toomre (1972) showed that the brief but intense tidal forces arising during the encounter of two disk galaxies would be sufficient to create structures as long and thin as the tails referenced in the catalogues. They extended the works of Pfleiderer (1963) and Tashpulatov (1970a, 1970b) by considering a bound companion galaxy on an very eccentric orbit, as well as disks inclined with respect to the orbital plane. In their study, a single galaxy is represented by a point-mass surrounded by rings of test particles whose masses are zero. When two of such galaxies are set on a given orbit, the central point-mass follows Kepler's law of motion. The test particles feel the net gravitational potential and thus, their motion is affected by both point-masses. However, in this method called restricted simulation, the mass-less test particles themselves do not affect the gravitational field of the galaxy.

Toomre & Toomre (1972) noted that close passages could induce a deformation of the disk(s), possibly leading to the creation of bridges and/or tails. By varying several parameters of the problem such as the inclination of the disks or the eccentricity of the orbit, they have shown that gravitation only was enough to reproduce the structures observed in interacting systems (see Figure 2). This showed the way to many other numerical experiments (Eneev et al. 1973, Lauberts 1974, Keenan & Innanen 1975) and allowed to conclude on the tidal origin of several observed features (Danziger & Schuster 1974, Stockton 1974, Yabushita 1977).

Figure 2

Figure 2. Restricted simulation of the Mice galaxies (NGC 4676) from Toomre & Toomre (1972). The two tails that exhibit very different shapes and thickness have been successfully reproduced numerically by considering tidal interaction only. Images of the real galaxies are shown in Figure 3, second panel, and Figure 7, panel 4.

Since then, gravitational tides have been considered as the major cause of the creation of filaments in interacting galaxies. That is why such features are often refered to as tidal structures.

An examination of the peculiar galaxies with the new light shed by numerical experiments on tides revealed that most of these galaxies would fit into an evolutionary sequence (see Figure 3), called Toomre's sequence (Toomre 1977). Each step represents a dynamical stage in the evolution of interacting galaxies toward the final coalescence of the merger 2. With time going, the tidal features created by the first encounters slowly vanish into the intergalactic medium or are captured back by their galaxy. Note however that relics of the tails remain visible for several 109 yr (Springel & White 1999).

Figure 3

Figure 3. The Tommre's sequence represents the supposed evolution of interacting galaxies. It starts with the early phases, when progenitors have just begun to interact, shows intermediate stages and finishes with the coalescence phase. From left to right, top: NGC 4038/39 (the Antennae), NGC 4676 (the Mice), NGC 3509, NGC 520; bottom: NGC 2623, NGC 3256, NGC 3921, NGC 7252 (the Atoms for Peace). Images from the Atlas of Peculiar Galaxies by H. Arp, available in the NASA/IPAC Extragalactic Database, Level 5.

2.4. Forty years of numerical simulations

In order to retrieve the steps of the Toomre's sequence and to better understand the role of each parameter involved in interacting galaxies, an important amount of work has been conducted by many authors since the very first (non-numerical) computations in the early 40's. At that time, Holmberg (1941) used the light and the property of the decay of its intensity as r-2 as a proxy for gravitation. He set a pair of two "nebulae", each made of 37 light-bulbs, and computed the equivalent gravitational acceleration by measuring the intensity of the light thanks to galvanometers at several positions. This ingenious method allowed him to spot the creation of "spirals" during a close encounter. But it is in the numerical era that most of the progresses have been done.

Despite their success in reproducing observed systems, the restricted simulations of Toomre & Toomre (1972) lacked the orbital decay due to dynamical friction. The problem was solved when considering self-consistent ("live") galaxies, i.e. models where all the particles interact with each other (e.g. White 1978, Gerhard 1981). However, the cost of such computations was very high at that time. That is why tree-codes (Barnes & Hut 1986, Hernquist 1987) and multipole expansions techniques (van Albada 1982, White 1983) have been introduced to decrease the computation time, or equivalently to increase the reachable resolution.

Barnes (1988) presented the first simulation of self-consistent multi-components galaxies. He showed that the presence of a dark-matter halo increases significantly the dynamical friction, thus favoring the merger of the galaxies.

In the same time, Hernquist & Katz (1989) gathered the tree-code method and the smooth particle hydrodynamics (SPH) technique (Lucy 1977, Gingold & Monaghan 1977) to treat both the gravitation and the hydrodynamics within a particle-based code. In SPH simulations, the physical properties of the particles are smoothed over a kernel of finite size, centered on the particle itself. Thanks to this Lagrangian approach, SPH does not suffer from the limitations of grid codes (Hockney & Eastwood 1988), i.e. mainly the waste of computational power in areas of nearly vacuum, an omnipresent situation in the case of galaxy mergers. In a similar way, the so-called "sticky-particle" method considers clouds as collisionless particles. When two clouds are in a close encounter, they loose energy via dissipation, mimicking an inelastic collision (Negroponte & White 1983).

Following this idea, Noguchi & Ishibashi (1986) proposed a galaxy model made of two types of particles: gaseous clouds and stars. When such a galaxy interacts with a point-mass encounter, these authors found the cloud-cloud collisions to be more frequent, and considered this as a burst of star formation (mostly at the times of the pericenter passages of the progenitor galaxies). Mihos et al. (1991, 1992, 1993) took one step further by considering the interstellar media (ISM) of both galaxies and monitored their interaction to characterize the formation of stars. They took advantage of the dissipative nature of their models to show that the merger phase could take place up to twice faster than in gas-free simulations.

Since then, a lot of flavors of these methods has been widely applied to many topics. Some improvements also appeared, to speed up the computation and thus to allow higher resolutions (see e.g. Dehnen 2000). More and more hybrid codes take advantage of multiples methods (e.g. Semelin & Combes 2002, Berczik et al. 2003) to increase accuracy and speed-up.

Recently, the adaptive mesh refinement (AMR) technique has been used for modeling a merger of two gas-rich galaxies at high resolution (Kim et al. 2009, Teyssier et al. 2010). AMR codes combine the power of the Lagrangian approach where dense regions are highly resolved, and the continuous description of the ISM on grids (e.g. Fryxell et al. 2000, Teyssier 2002, O'Shea et al. 2004). The computational domain is meshed on a (usually catesian) grid, which is refined at the regions of interest, typically those of highest densities. Two different snapshots of a numerical model using the AMR technique are shown on Figure 4 and Figure 11 (left panel).

As seen in the literature since Toomre & Toomre (1972), simulations of interacting galaxies can follow two approaches:

The simulation of interacting galaxies is not limited to pairs. However, numerical models of observed (compact) groups of galaxies are still very rare, due to the difficulty to set a consistent scenario for an entire group. Each galaxy-galaxy interaction has to take place in a system already perturbed by the previous interactions, such that the mass and the orbit of the progenitor are to be re-evaluated constantly during the evolution of the group. (Some attempts have been made in the case of Stephan's Quintet, see Renaud et al. 2010, Hwang et al. 2011).

Figure 4

Figure 4. Numerical simulations of the Antennae galaxies (NGC 4038/39) within four decades. From top to bottom: restricted simulation of Toomre & Toomre (1972); first self-consistent simulation of the Antennae by Barnes (1988); hydrodynamic run of Mihos et al. (1993); recent models with SPH by Karl et al. (2010) and with AMR by Teyssier et al. (2010). Improvements in both the techniques and the set of parameters allowed the models to get closer and closer to the observational data (see Figure 7, panel 6).

While they face an increasing need of resolution and accuracy, these state-of-the-art numerical methods can efficiently provide a solution to the questions raised by observations at higher and higher resolution. Simulations of interacting galaxies still represent an important part of the numerical work done in astrophysics. The models of individual galaxies are regularly updated to fit the most recent theories on galaxy formation and evolution and include better descriptions of the physical processes. Nowadays, the research on interacting galaxies is mainly threefold:

1 According to Arp (1969), the same mechanism would account for the creation of spiral arms in rotating galaxies. Back.

2 Note that the position of some of the galaxies in the sequence has been recently discussed thanks to new numerical models (see e.g. Karl et al. 2010). Back.

3 Back.

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