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4.1. Tidal dwarfs

The definition of a merger process as one which decreases the number of galaxies (see Section 3) has its drawbacks. The deformation and the possible destruction of interacting disks manifests itself also in the creation of clumps of stars and molecular gas - so-called tidal dwarfs, the by-products of mergers. One can argue that tidal dwarfs are not bona fide galaxies as they are not expected to contain a significant amount of DM. We shall stay away from this dispute. There is an additional difference between these objects and `normal' galaxies - they are expected to be made of recycled material with metals and dust, and not have the primordial composition of the first galaxies or of low-metallicity dwarfs. Tidal dwarfs are usually associated with antenna-type tidal tails of their massive parent galaxies, are gas rich, have both old and young stellar populations, and contain both Hi and H2, as noted by Braine et al. (2001) in their survey. Tidal dwarfs are characterised by a much larger ( ~ 100×) of CO luminosity compared to other dwarf galaxies of comparable optical luminosity. Because of the relative proximity of these objects, they can serve as testing labs for our understanding of the galaxy formation process, albeit different from that in the early Universe.

4.2. Polar ring galaxies and ring galaxies

While the tidal dwarfs represent a transient phenomenon during galaxy mergers, polar rings are expected to describe a rather steady-state situation when the externally acquired material finds stable orbits in the plane orthogonal to the equatorial plane of the galaxy. A number of preferentially early-type disks or ellipticals show such rings lying in their polar planes, and, therefore, kinematically distinct from their parent galaxies. The rings appear younger than their host galaxies, which seem to be depleted of cold gas. Polar rings include young stellar populations, apparently formed after the capture, and are gas-rich (a few times 109 Modot) and dusty (e.g., van Driel et al. 2002).

Two main alternative explanations, based on merger kinematics, include the accretion or capture of satellites from a nearly circular orbit, or the collisional destruction and subsequent capture of a donor from a rather radial orbit. Under special conditions, the accretion of cold gas by the host galaxy can also result in the formation of polar rings. In the accretion scenario (e.g., Schweizer et al. 1983; Reshetnikov & Sotnikova 1997), about 10% of the donor disk gas is captured in a polar ring, in less than 1 Gyr. The collision scenario of galactic disks (e.g., Bekki 1998) involves orthogonally oriented disks in a head-on, low-velocity collision. Bournaud & Combes (2003) have tested both alternatives in numerical simulations and conclude that the accretion scenario is more supported by observations, although one cannot exclude either possibility. We note that numerical simulations of galaxy formation at higher z have demonstrated routinely the formation of polar-ring galaxies as a product of merging and interaction within the computational box (e.g., Romano-Díaz et al. 2009; Roskar et al. 2010).

An interesting aspect of polar rings is that they can provide information about the DM halo shapes (e.g., Sackett & Sparke 1990). This is possible because the rings are long-lived and, therefore, have sufficient time to settle on regular orbits in the polar plane of the host galaxy, which is determined by the extended DM halo. The measured flat rotation curves of the rings point to the existence of such haloes around parent galaxies. The self-gravity of the gas settling in the rings is also a stabilising factor in their dynamics, otherwise, differential precession would destroy them in a short orbital time. This conclusion is a clear outcome of orbital analysis in a triaxial potential (e.g., Sparke 1986; Arnaboldi & Sparke 1994) and numerical simulations of ring formation and evolution (e.g., Bournaud & Combes 2003). Depending on the mass and orientation of polar rings, a number of stable and unstable equilibria are possible. If the flattening of the DM halo can be constrained independently, e.g., from lensing, one can obtain bounds on the halo (or overall mass) triaxiality, merely assuming that the observed rings are stable.

The Cartwheel galaxy represents another class of rings, most probably originating from head-on collisions involving at least one gas-rich disk. Unlike polar rings, these rings are not stationary, are frequently off-centred, and represent an expanding density wave which triggers star formation (Lynds & Toomre 1976). The relative velocity of these collisions appears to be much higher than those leading to polar rings (e.g., Horellou & Combes 2001). It is characteristic of a galaxy cluster environment, as we discuss below.

4.3. 'Mergers' in clusters: galaxy harassment

In a galaxy cluster environment, high-velocity encounters between galaxies have relative velocities vgal ~ sigmaclsigmagal, where vgal ~ 103 km s-1 is the typical relative velocity of galaxies in clusters, sigmagal ~ 100-200 km s-1 the intrinsic velocity dispersion in galaxies, and sigmacl the velocity dispersion in clusters. The corollary is that high-velocity encounters dominate in clusters and are more frequent than in the field environment, and that direct collisions are rare. Hence, one should expect that galaxies are more morphologically disturbed in clusters, which makes them vulnerable to future encounters, as well as to the effects of cluster tides. The encounter dynamics can be approximated by the impulse approximation. The cumulative effect of the above processes is called galaxy harassment. One of the main questions is whether galaxies form differently in clusters or whether environmental processes, as described above, make them different.

Observationally, in the local Universe, cluster galaxies appear redder than in the field and are more spheroid-dominated. Tidal disturbances are common from close passages. Local clusters possess no spiral disks, as reflected by their morphology-density relation (e.g., Dressler 1980). In comparison, already at z ~ 0.4, clusters contain many small disturbed spirals, which are replaced by spheroidals at the faint end of the galaxy luminosity function (LF) at z = 0. They contain a substantial population of blue, star-forming and starbursting galaxies - a reflection of the Butcher-Oemler (1978) effect. Star-forming rings are much more frequent in clusters than two-armed spirals (e.g., Oemler et al. 1997). Furthermore, in hierarchical models of structure formation, the field galaxy influx into clusters peaks around z ~ 0.4 (e.g., Kauffmann 1995), and the star formation declines abruptly around z ~ 0.5, resulting in a large population of passive, post-starburst galaxies (e.g., Dressler et al. 1999; Poggianti et al. 1999). This quenching of star formation, measured, for example, by a decline in the Halpha emission, in the cluster environment is a reflection of the overall trend in galaxy evolution which ultimately leads to the formation of the so-called red sequence. In other words, the star formation and morphological evolution in clusters appear to decouple at lower redshifts (e.g., Couch et al. 2001).

One way to understand the environmental effects on galaxy evolution is to compare and contrast the evolution of disk galaxies in rich clusters with that of field galaxies. Numerical simulations have revealed the details of galaxy harassment in such over-dense fields (e.g., Moore et al. 1998), where disks are subject to interactions with brighter and more massive neighbours - a process that injects energy and makes them vulnerable to the cluster tidal field. Moreover, the gas stripping process acts efficiently in the central regions of clusters (e.g., Tonnesen et al. 2007). These processes affect disk galaxies almost exclusively - dense ellipticals are basically immune to the effects of harassment. Furthermore, the r1/4 de Vaucouleurs surface brightness profile appears robust and invariant to harassment, even when a galaxy loses ~ 40% of its mass during an interaction (e.g., Aguilar & White 1986).

Below, we discuss how mergers influence the star formation rates (SFRs). Here we emphasise the morphological evolution these disks experience, which results in loss of the gaseous component, partly ablated and partly falling to the centre, and in a dramatic conversion of disks into spheroidals. Late-type Sc-Sd disks appear to be more affected by this process. In addition, the ram pressure by the intracluster hot gas is ~ rhohot sigmacl2, while the restoring force is propto 2pi Sigmatot, where Sigmatot is the disk total surface density (gas + stars). The stripping occurs when the ram pressure exceeds the restoring force, leading to the transformation to lenticular galaxies. When the outer hot gas, which is only loosely bound to the DM halo, is stripped, this is called strangulation.

Simulations have also demonstrated an agreement with observations both in accounting for intermediate-age stellar population in these spheroidals and in their shapes - which appear prolate and flattened by velocity dispersion anisotropy.

We now turn to the issue of merger-induced star formation. There is no doubt that mergers are responsible for the largest starbursts, e.g., the ultra-luminous infrared galaxies (ULIRGS). The most intensely star-forming galaxies are in the advanced stage of merging. But is the reverse true? In other words, does the merger rate drive the SFR?

Since z ~ 1, the cosmic SFR per unit comoving volume appears to decrease by a factor of ten (e.g., Madau et al. 1998). Because over this time period most of the star formation is associated with disk galaxies, the inevitable conclusion is that the disks are shutting down their star-forming activity. While in principle a number of processes can contribute to this evolutionary trend, here we focus on the contribution from major mergers to triggering the star formation. Because the LF of galaxies at these redshifts is dominated by `normal' galaxies (Fig. 6), the effect of mergers cannot be the principal one, as noted by Bell et al. (2005). This conclusion is based on the analysis of the deep 24 µm survey made by the MIPS (Multiband Imaging Photometer for Spitzer) Team (Rieke et al. 2004), combined with the COMBO-17 redshift and SED survey (Wolf et al. 2004) and the GEMS survey (Rix et al. 2004). The covered redshift interval is 0.65-0.75 and includes about 1500 galaxies in the CDFS (Chandra Deep Field South). About 40% of galaxies with stellar masses gtapprox 2 × 1010 Modot have been found to be undergoing a period of elevated, intense star formation at z ~ 0.7, while only ltapprox ~ 1% of similarly massive galaxies exhibit such star-forming activity at z = 0. Moreover, the IR LF and the SFR densities at z ~ 0.7 are dominated by morphologically undisturbed galaxies. More than 50% of the starbursting galaxies are spirals, but ltapprox ~ 30% appear to be strongly interacting. Hence the decline in the SFR is not `driven' by the decline in the major merger rate. Rather, factors that do not strongly alter the galaxy morphology are at play here, e.g., weak interactions and gas depletion. Bell et al. (2005) argue that the selection procedure used should not introduce any special bias against obscured starburst galaxies.

Figure 6

Figure 6. Estimated 8-1000 µm LF, split by morphological type for 397 galaxies at z ~ 0.65-0.75 (see text for details). Only galaxies detected at 24 µm are shown, and no attempt to extrapolate to lower IR luminosities has been made; the sample is grossly incomplete below 6 × 1010 Lodot as denoted by the grey dotted line. In each panel, the grey solid histogram shows the total IR LF. The shaded area shows the IR LF split by galaxy type using GEMS-derived galaxy classifications, where the extent of the shaded area explicitly shows the differences in IR LF given by the three different classifiers. The black histogram shows the IR LF, averaged over the three different classifiers and corrected to reproduce the increased fraction of clearly interacting galaxies seen in GOODS-depth data (from Bell et al. 2005).

To quantify the average enhancement in the SFR of major mergers between massive gtapprox 1010 Modot galaxies, including pre- and post-mergers, Robaina et al. (2009) used COMBO-17 and 24 µm SFR from Spitzer, in tandem with the GEMS and STAGES HST surveys, for z ~ 0.4-0.8. Major interactions have been defined here as being resolved in HST imaging, having a mass ratio of ≥ 1:4 based on the luminosity ratio, and exhibiting clear signs of interaction. Major merger remnants have been identified using a highly disturbed `train wreck' morphology, double nuclei, and tidal tails of similar length, or spheroidal remnants with large-scale tidal debris. Prominent disks with signs of merging, i.e., highly asymmetric spirals or a single tidal tail, have been assumed to be minor mergers.

In addition, the enhancement in the SFR has been evaluated as a function of the projected galaxy separation. While confirming that most starbursting galaxies are in the process of merging, Robaina et al. (2009) have found that SFRs in major-merger systems are only elevated by a factor of ~ 1.8 compared to those in non-interacting ones, when averaged over all interactions and all stages of interaction (see also Li et al. 2008; Sommerville et al. 2008). The main enhancement is visible for close pairs with projected separations of ltapprox 40 kpc. Overall, about 8% ± 3% of the total star formation has been estimated to be directly triggered by major interactions. This indeed confirms the conclusion of Bell et al. (2005), mentioned above, that major mergers are not the dominant factor in building the stellar mass at z ltapprox 1, and, therefore, they are not responsible for the decline in the SFR over this time.

We now discuss the input from numerical simulations which test the above observational results on the relation between major mergers and SFRs. Di Matteo et al. (2007) have focussed on this issue by modelling galaxy collisions of all Hubble types while varying both bulge-to-disk mass ratios and fgas. Direct and retrograde orbits have been used, and star formation in interacting and merging galaxies has been compared to that in isolated galaxies. The main outcome is that the retrograde orbits seem to produce more starbursts, and the star formation efficiency is higher (in the sense of star formation per unit mass). Moreover, these starbursts are essentially nuclear starbursts, from the gas inflow triggered by the gravitational torques from asymmetries induced by the tides.

In a comprehensive study of unequal-mass mergers, Cox et al. (2008) have quantified the effect of tidal forces on the star formation. Specifically, they have focused on the effect of mass ratio, merging orbits and galaxy structure on merger-driven starbursts. These kinematical and morphological parameters are of prime importance for the main issue - the relation between mergers and SFRs. It was found that merger-induced star formation is a strong function of the merger mass ratio, which spans over a factor of ~ 23, being negligible for small mass-ratio mergers - a straightforward dependence on the tide's strength. An additional parameter that is helpful to measure the induced star formation is starburst efficiency - the fraction of gas that is converted into stars over the interaction time. The starburst efficiency was found to be insensitive to the details of the feedback parameterisation from stellar evolution - this is very helpful because the feedback physics is sufficiently uncertain. Overall, the burst efficiencies have been reduced compared to previous studies.

However, while the burst efficiency for equal-mass mergers does not depend on the merger orbital parameters, disk orientation, or the primary galaxy properties, this differs for unequal-mass mergers. Direct coplanar-orbit mergers produce the most significant bursts at close passages. The other important factor appears to be the mass distribution in the primary galaxy. For example, a massive concentrated stellar bulge stabilises the disk and suppresses the induced star formation. More gas driven above the threshold density for star formation reduces the burst efficiency, and so is a more efficient feedback.

In summary, recent studies of mergers agree that the evolution of the merger rates after z ltapprox 1 is not responsible for the overall decrease in SFR in the Universe. The obvious direction for improving the numerical simulations of merger-induced star formation requires incorporating them into the cosmological context - so far simulations deal with isolated pairs of interacting and merging galaxies. This will allow accounting for the effect of cold-gas accretion which is expected to compete with merger-induced galaxy growth, especially at higher redshifts. Lastly, increases in the number of particles, both collisional and collisionless, are important for modelling the disk response during the interaction and merging periods. Small numbers of the particles are known to destabilise the disks owing to increased noise.

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