The galaxy distribution includes a substantial number of bound systems dominated by two galaxies (hereinafter "pairs"). These simplest systems of galaxies are excellent laboratories for studying galaxy masses (since we understand two-body dynamics better than those in clusters, and since the range of separations in pairs extends much farther than individual galaxy rotation curves), and for study of the effects of perturbations on galaxies. Overall references on this topic include the proceedings of IAU Colloquium 124 and the book Double Galaxies by Karachentsev (in Russian; there is an English version hosted by NED).
Recognizing pairs: There are special difficulties in recognizing complete sets of pairs. Various criteria have been considered, relying on either projected separation or including radial-velocity information. Early works simply used a diameter vs. separation criterion. More recent ones have incorporated isolation criteria, as illustrated in this diagram following Fig. 1 of Karachentsev's book. In this instance, the ratio of distance to the nearest galaxy (with angular diameter greater than some fraction like 1/2 of the smaller pair member) must satisfy X1i/X12 > 5 ai/a1.
The particular cutoff ratios among the relevant distances are fixed either to give some "reasonable" number of pairs, or by rough physical arguments from the ratios of expected tidal influences if mass follows light. At most, such a criterion is statistically applicable. Van Albada, for example (see the dissertation from Groningen by Soares 1990) has used the local surface density of comparably bright galaxies to assess the probability that a candidate companion is physical, while Karachentsev has included radial-velocity information; more recent redshift surveys have allowed pairs in (position, velocity) space to be identified at separations close to 1 Mpc (Charlton and Salpeter 1991 ApJ 375, 517). However, a basic problem is that the velocity dispersions of groups are comparable to the relative velocities in pairs; that is, we have no way to distinguish true two-galaxy systems from sets of group members which we happen to view as close together. Dynamical distortions provide evidence of pairing, but the converse is not true - pairs will not necessarily produce distortions at a particular time, depending on mass ratio and orbital parameters.
Some frequently used catalogs of galaxy pairs include:
Note that what you consider an appropriate, complete, or representative catalog depends on what you hope to do with it. A catalog pure enough for mass determinations will be dreadfully incomplete for interaction studies or population statistics. These catalogs are all more or less biased toward equal-luminosity pairs. Finding faint companions suffers from strong background confusion and incompleteness. These catalogs indicate that about 10% of luminous galaxies are in two-body systems, with numbers ranging from about 11% for ellipticals to 6% for later-type spirals and irregulars. The I0 or Irr II galaxies are found almost exclusively in pairs, leading to the notion that they are transient phases seen following a tidal disturbance. Compared to overall numbers, it appears that early-type (E,S0) galaxies are overrepresented in pairs (see Sulentic's 1990 review for the Sant' Agata meeting). This extension of the morphology-density relation is interesting for theories of how pairs originated.
Pairs are often used to estimate galaxy masses; if we can assume that the pair orbits in some catalog are seen at random orientations, and we understand any related selection effects, we can determine the mean M/L ratio of galaxies out to the radius of a typical companion orbit. If the pair orbit is inclined at an angle q to our line of sight, and the companion motion makes an instantaneous angle f to the line of sight, the system mass within the component separation R is given in terms of observables as follows:
where vr is the radial-velocity difference observed and R ^ is the projected separation. The analogous equation in binary-star astronomy is used to determine the mass function m sin3 q, a bit better since one can follow through cycles in f. The major problem for binaries is that we must integrate over pairs at different q, f, and catalogs will undersample some ranges of these as well as R. Trivially, a catalog will be more reliable against background contamination for smaller R ^ and hence smaller R, while for noncircular orbits a bias in q, f will also be present - so you already have to know the answer to derive it!
This means that, unfortunately, the resulting masses depend critically on how the sample is selected and on how one excludes non-bound members (for example, either by using a cutoff in measured M/L or using only those pairs in very low-density regions). Karachentsev makes a strong case for halo masses not much larger than required by the rotation curves of pair members, while L. Schweizer (1987 ApJSuppl. 64,411; 64, 417; 64, 427) argues for global M/L ratios a few times larger; she finds that the dynamical properties of pairs show correlations suggesting that the mass is concentrated well inside typical orbital radii.
The pair population is of interest for theories of galaxy formation - they are an especially clean test of where galaxy angular momentum arises (for example by tidal torquing), while their survival is related to such items as the merger rate in the past, growth of galaxies by cannibalism, and the present number of dwarf binaries. There is some evidence that we can see the effects of orbital modification by dynamical drag effects, for example in preferentially depopulating direct orbits (Keel 1991 ApJLett 375, L5; Zaritsky et al. 1993 ApJ 405, 464).
Interactions: It has been clear since at least the analog work by Holmberg (1943 ApJ) that close encounters may transfer energy between orbital and internal motions, altering both the galaxies' internal dynamics and orbits. Detailed modelling of this process started with the Toomres' (1972 ApJ 178, 623) paper using point masses and test particles, which could already reproduce structures in M51 and the Mice very well. Lots of analytic detail is given in chapter 7 of Galactic Dynamics. Tidal distortions can be traced using the stars or gas; H I maps have proven strikingly effective in showing old and extensive tidal damage.
Catalogs of galaxies showing obvious interactions have been compiled from Sky Survey material by several workers. The statistics of galaxy pairs already show that interactions occur between members of bound systems, not as chance encounters of non-related galaxies; there are simply too many observed pairs to have been formed by capture (Chatterjee 1987 Astrophys. Space Sci. 137, 267). Some important catalogs of interacting pairs are:
Models show that the responses of galaxies to tidal perturbations depend on the galaxy type (spiral vs. elliptical, for example) and direction of companion orbit. Thus, one can often diagnose a system's history from its appearance and kinematics. The basic categories for most pairs fall into a few kinds, as noted by Karachentsev in his catalog. These include common envelopes, shells, bridges, and tails, which may consist of distorted spiral arms or separate features. These tell us about the victim galaxy's dynamics and the geometry of the tidal disturbance.
For spirals, the dynamically cold disk can form long bridges and tails, depending on relative velocity, direction, and our viewing angle. This can produce things like M51, the Mice, Antennae, and even the 300-kpc tails of the Superantennae (Melnick and Mirabel 1990 A&A 231, L19). By contrast, ellipticals can form only broad fanlike distortions, but these in concert with kinematic disturbances are frequently enough for an orbital reconstruction (see, for example, Borne 1988 ApJ 330, 28).
Star formation: The following is based on the review by Keel 1990 (IAU Symp. 146, Dynamics of Galaxies and their Molecular Cloud Distributions, p. 243).
It is by now part of the lore of galaxy research that galaxy interactions can, among other interesting effects, trigger bursts of star formation. This makes such systems useful laboratories for examining star formation in unusual environments, probing the behavior of a disturbed interstellar medium, and perhaps seeing processes that were important during galaxy formation. This paper reviews the evidence for the presence and scope of enhanced star formation during interactions, and presents several mechanisms that have been proposed to account for this excess.
Since we do not have "before and after" views of interacting galaxies, we are driven to perform statistical comparisons of large samples of interacting and non-interacting (sometimes called for brevity "isolated") galaxies. This offers the hope that we might measure shifts in the (already broad) distributions of properties tracing the SFR. Selection of both interacting and comparison samples can involve some subtlety, since the SFR we wish to measure is itself a function of galaxy type and luminosity. Furthermore, selecting program galaxies for obvious morphological signs of interaction biases the sample in favor of certain kinds of interactions seen at certain stages. Conclusions from such samples may not be generalizable to the whole population of encounters. Ideally, then, we should obtain comparable observations of samples of galaxies with the same distribution of Hubble type, luminosity (as measured before any alteration by the interactions), and environment (except, of course, for the presence of companions). Since interactions induce star formation and can therefore change the luminosity of a galaxy, and tidal disturbances can change the morphology, this sort of comparison cannot be attained in practice. However, the more closely matched the properties of interacting and control samples are, the greater the confidence one may have that any differences between the two are in fact associated with the interactions. Exactly how they are associated depends to some extent on the population of systems now seen undergoing interactions: galaxies that are only now undergoing their first mutual close approach should be more like isolated systems than those that have been in fairly close, slowly decaying circular orbits for most of the Hubble time (as discussed by Karachentsev 1988 , Dvoinye Galaktiki). Thus, dynamical understanding of the entire population of binary galaxies will be important in unravelling just how interactions influence galaxy evolution.
Only for extreme "starburst" systems (loosely defined herein as those in which the SFR exceeds 4-5 times its preburst level) can we be sure that most of the star formation that we observe has been triggered by a companion, simply because only a tiny fraction of "isolated" galaxies show such a high SFR. Some of the highest values are found for apparently merging systems; more detailed interpretation of their role awaits identification of a statistically representative sample of merger candidates without recourse to quantities strongly affected by star formation (such as far-infrared luminosity). Observations of these systems can sidestep the statistical approach, since the star formation in these cases must be due predominantly to the interaction. In some cases, the SFR in these systems is so high that a global wind can be set up, thus sweeping the galaxy nearly free of gas and leaving a system that may eventually resemble an elliptical (Graham et al. 1984, Nature 310, 213).
There are several star-formation tracers for which sufficient survey material is available for statistical comparison. Further indicators (for example, in the X-ray band) should become available in the future. Note also that the discussion here is confined to luminous, gas-rich systems, which is to say spiral galaxies.
Optical colors. These reflect primarily stellar populations of age ~109 years or less, as well as being sensitive to the strength of such populations relative to any underlying older (bulge) population. Galaxies in pairs display a correlation of color indices (the Holmberg effect) tighter than that expected from the known correlation of morphological type (Holmberg 1958 Medd. Lunds Astron. Obs. Ser. 2, No. 136, Demin et al. 1984 Astron. Zh. 61, 625, Madore 1986 in Spectral Evolution of Galaxies, 97). This provides evidence of similarly recent episodes of star formation. The distributions of color indices themselves were examined by Larson and Tinsley (1978 ApJ 219, 46) for systems in the Arp and Hubble atlases, showing that the strongly interacting systems in the Arp atlas show a large dispersion in colors that could be accounted for by bursts of star formation superimposed on a normal (older) component. Finally, samples, such as the Markarian galaxies, selected for their strong near-ultraviolet continua (that is, blue color), are rich in paired and interacting galaxies (Heidmann and Kalloghlian 1974 Astrof, 9. 71; Casini and Heidmann 1975 A&A 39, 127; Kazarian and Kazarian 1988 Astrof, 28, 487; Keel and van Soest 1992 A&A Suppl 94, 553). These extreme systems probe the tail of the SFR distribution in much the same way as far-infrared flux-limited samples.
Direct counts of stars and clusters. Statistics of supernovae show excesses of type II outbursts (and hence of young, massive progenitors) in interacting galaxies (Smirnov and Tsvetkov 1981 PAZh 7, 154; Kochhar 1990 in IAU Coll. 124). Some interacting systems have extraordinarily luminous individual H II complexes (Petrosian, Saakian, and Khachikian 1985 Astrof. 21, 57), while others have a normal H II region luminosity function even if the number of H II regions is unusually high (Keel, Frattare, and Laurikainen someday). There are indications that the spatial distribution of H II regions is more centrally concentrated in interacting systems than in normal spirals (Bushouse 1987 ApJ 320, 49, Kennicutt et al. 1987 AJ 93, 1011). Recently it has become clear (as outlined in the earlier section on starbursts) that many interacting and merging systems make stars in very luminous, perhaps massive clusters which can long outlast OB stars; probing their ages is a growth industry. This is a particular area where one is tempted to compare dynamic star-forming environments today with events on the early Universe.
Nuclear and integrated emission-line properties. Recombination lines trace the number of stars producing significant ionizing radiation (OB stars), with some sensitivity to reddening, obscuration, and mass function. For both nuclei and disks, several spectroscopic and imaging surveys have shown clear (statistical) excesses of emission in interacting systems (Keel et al. 1985 AJ 90, 90, 708; Bushouse 1987; Kennicutt et al. 1987), with some tendency for the excess to be stronger for more disturbed systems. This is found in Ha luminosity, in equivalent width (normalized to optical luminosity), and in Ha surface brightness (normalized to disk area). Further, the Ha equivalent width can be combined with continuum color indices to form a 2-color diagram with a very long effective wavelength baseline, and this may be interpreted much as done by Larson and Tinsley (Kennicutt et al. 1987).
Detailed comparison of multiwavelength images shows that, for galactic nuclei, the role of obscuration is strong and complex; ionizing clusters can contribute to Ha emission while remaining completely unseen in the optical continuum. Thus, differential comparisons are likely to be more reliable than absolute measures. In particular, model comparisons yielding burst ages or IMF slopes must be regarded as highly suspect. Also, there are systems in which emission lines may be influenced by such processes as shock heating (Keel 1990 AJ 100, 356) or weak nuclear activity (Kennicutt, Keel, and Blaha 1989 AJ 97, 1022), so spectroscopic diagnostics are needed to be sure the luminosities we measure really reflect the SFR. For very dusty systems, it may not be clear how much the optical spectrum reflects the dominant energetics of the galaxy (compare the conclusions of Sanders et al. 1988 ApJ 325, 74 and Leech et al. 1989 MNRAS 240, 349 as regards the role of star formation in the most luminous IRAS galaxies).
Thermal infrared. Two ranges have been studied - the 10m window (offering excellent spatial resolution and modest sensitivity, probing high dust temperatures) and the far-infrared bands pioneered with IRAS (excellent sensitivity but poor resolution, over a much wider temperature range). Both are sensitive to a wider range of stellar masses than are H recombination lines. At 10m, Cutri and McAlary (1985 ApJ 296, 90) found that galaxies from the Karachentsev (1972, 1988) catalog of paired galaxies have systematically higher luminosities (and detection probabilities) than isolated systems, which they interpreted as reflecting dust heated by increased numbers of young stars. Similarly, Lonsdale, Persson, and Matthews (1984 ApJ 287, 1009) found enhanced 10-20m emission in galaxies selected for tidal distortions from the Arp Atlas.
There has been an enormous amount of work on the connection between IRAS emission and interactions (Soifer et al. 1984 ApJL 278, L71, Lonsdale, Persson, and Matthews 1984; Telesco, Wolstencroft, and Done 1988 ApJ 329, 174; Lawrence et al. 1989 MNRAS 240, 329), but the results for an infrared-selected sample can be somewhat misleading if taken out of context. The far-IR properties of optically-selected samples (Bushouse 1987, Kennicutt et al. 1987, Haynes and Herter 1988 AJ 96, 504; Sulentic 1989 AJ 98, 2066) show distributions much like those seen in Ha, with most systems modestly enhanced and a small percentage dramatically affected. It is this small tail of the SFR distribution that is strongly represented in FIR flux-limited samples, even though only a tiny fraction of all interacting systems are seen during such extreme bursts. These systems include many of the famous "superluminous" IRAS galaxies (Sanders et al. 1988). Above about 1011 solar luminosities in the far-IR, the source population is dominated by mergers and multi-way interactions (as seen in this WFPC2 montage of powerful IRAS galaxies). Statistical treatment of the IRAS data is limited by the poor resolution (generally requiring that pair members be treated together). In some very distorted galaxies, interpretation of the far-IR emission can be complicated by the possibility of more effective conversion of visible-wavelength radiation from an old stellar population into thermal infrared emission, when the dust is no longer confined to a single plane (e.g. Thronson et al. 1990 ApJ 375, 456).
Radio continuum emission. Spirals with high-surface-brightness radio disks are actively star-forming, and a large fraction are in interacting systems (Condon et al. 1982 ApJ 252, 102). The spectral index and surface brightness of the emission indicate a nonthermal origin, perhaps in supernova-accelerated particles radiating in fields along spiral arms. In some cases, the radio structure shows direct links to star-forming regions, and in some nearby objects, individual sources identified as supernova remnants can be found (Kronberg, Biermann and Schwab 1985 ApJ 291, 693; Noreau and Kronberg 1987 AJ 93, 1045). At least at the highest values, the surface brightness at centimeter wavelengths appears to reflect the supernova rate, and thus SFR in the relevant mass range. Over the 6-20 cm range, both disks (Hummel 1981 A&A 96, 111) and nuclei (Hummel et al. 1987 A&A Suppl 70, 517) show statistical enhancements in interacting systems.
All of these SFR indicators tell similar stories: the majority of interacting spirals have increases in SFR of order 30%, detectable only statistically, while a few experience increases of an order of magnitude. Such a wide range of responses may indicate sensitivity to internal dynamics, or to details of spin and orbit directions for particular encounters. There has been no shortage of proposed mechanisms to produce these effects, largely discussed in the starburst section.
Active Galactic Nuclei: Interactions have frequently been implicated as somehow triggering the occurrence of various kinds of nuclear activity, but just how and how often remains surprisingly unclear - see the review by Heckman (1990, IAU Coll. 124, p. 359). Confirming such a process would be quite important; not only would we learn more about how to feed the monster, but we would know that most galaxies alreday have an undernourished one. I will cite only some of the major results here.
Seyfert nuclei: Seyfert galaxies seem to have more companions than non-Seyferts of the same kind and luminosity (Dahari 1984 AJ 89, 966, MacKenty 1989 ApJ 343, 125), but the strength of this result depends critically on just how the control sample is selected (Fuentes-Williams and Stocke 1988 AJ 96, 1235). Samples of interacting galaxies are rich in Seyferts (Keel et al. 1985 AJ 90, 2208) but this survey plus those of Dahari 1985 (ApJ Suppl 57, 143) and Bushouse (1986 AJ 91, 255) also shows that very distorted galaxies almost never have Seyfert nuclei. The upshot is that perturbations make it easier to have Seyfert activity, but do not appear utterly essential (to first order, a bar acts like a small companion). When a Seyfert nucleus is present, it is usually in the brighter pair member, and preferentially in host galaxies with the most concentrated bulge masses as judged from rotation curves (Keel 1996 AJ AJ 111, 696). This panel shows the kinds of environments found for Seyferts, including luminous companions and tidal tails.
Radio galaxies: Radio galaxies are more likely to have close companions than optically similar radio-quiet galaxies (Heckman et al. 1985 ApJ 288, 122); note that here too the details of sample selection are rather important in one's result (Dressel 1981 ApJ 245, 25; Stocke 1978 AJ 83, 348; Adams et al. 1980 AJ 85, 1010). The highest-luminosity nearby radio galaxies almost universally show evidence of strong interactions or mergers (Heckman et al. 1986 ApJ 311, 586). Detailed studies of a few such cases show evidence that the galaxy recently acquired substantial gas (van Breugel et al. 1984 ApJ 277, 82; Heckman et al. 1982 ApJ 262, 529). This was suspected in the 1950s from Centaurus A. The HST snapshot survey of 3CR radio galaxies has shown a large fraction to show some kinds of morphological distortions (de Koff et al. 1996 ApJSuppl 107, 621).
QSOs: It was hard enough to tell that they were in galaxies, much less surrounded by others. Imaging from Mauna Kea has been extremely suggestive, with Hutchings and Campbell 1983 (Nature 303, 984) claiming that 30% of QSOs with z < 0.6 show evidence of interactions. Spectroscopy by Stockton (1979 IAU Symp. 92, 89) and Heckman et al. (1984 AJ 89, 958) confirms the association of these galaxies in redshift, and Stockton 1982 (ApJ 257, 33) has shown that many of the companions have their own low-luminosity active nuclei. Further individual systems have been studied by, for example, Shara et al 1985 (ApJ 246, 339; 4C 18.68), Yee and Green 1987 (AJ 94, 618; PG 1613+658), and Vader et al 1987 (AJ 94, 847; IRAS 00275-2359). Be careful in putting the statistical studies together; many of the "QSOs" in some studies are no more luminous than Markarian Seyferts, so that it is not clear which problem is being addressed. Calling the Sun a quasar doesn't answer the quasar-physics problem. Anyway, as was long expected, HST results have added considerably to our understanding. Most QSO host galaxies have compact companions within tens of kpc (Bahcall et al. 1995 ApJ 450, 486, Disney et al. 1995 Nature 376, 150), a result which was foreshadowed by Stockton's 1982 paper. This fraction is by now the most striking correlation of nuclear activity and galaxy interactions. Some of these companions are seen in this montage of HST images, from rather luminous normal companions to the very close, compact companions of PKS 1302-102 and PKS 2349-013.
Dynamical models show that galaxies are very sticky, and that a deeply penetrating encounter can dissipate so much orbital energy that a coalescence is inevitable. Simple estimates suggest that most bright galaxies must have undergone at least one merger of near-equals (see Toomre 1977, Yale conference p. 401); there have been many numerical studies of what happens here, so we have a good idea of what to look for in the real universe. In fact, there are several useful relics of mergers. Most commonly sought are tidal tails from a single main body; the dynamical evolution of the core proceeds so fast that tails from initial disks will still be visible for several billion years after the nuclei have merged. F. Schweizer 1982 (ApJ 252, 455) has shown that this in the case in NGC 7252, with a central body approaching a de Vaucouleurs light distribution while counter-rotating motions and tidal tails still exist farther out. Numerous such merger candidates have been identified from optical imaging; many are also strong IR sources. These have some of the most strongly enhanced far-IR levels observed, extending the notion of enhanced star formation to the most violent interactions possible; there has been some discussion of a role for violent cloud collisions between clouds starting in different galaxies, or emission directly produced by rapid shocks in dense gas disks (Harwit et al. 1987 ApJ 315, 28).
Mergers lead to an attractive notion about the formation of elliptical galaxies - do they all come from mergers of disk systems? In this case, one has only a single galaxy-formation problem (for disks) rather than two. Stronly dissipative processes are required, to avoid violating Liouville's theorem (but note that the maximum phase-space density in a disk may not be at the nucleus). Both observations (such as Graham et al 1984, Nature 310, 213) and modelling (Barnes and Hernquist 1991 ApJLett 370, L65) indicate that gas can collect very rapidly at the nucleus, and that the subsequent star formation can drive a powerful enough wind to sweep the galaxy free of gas. Voila! An elliptical! An attractive scheme, probably first clearly stated by Toomre in the 1977 Yale conference, but more evidence really should be collected. The current rate of mergers and luminosity function of ellipticals put interesting constraints on this (Keel & Wu 1995 AJ 110, 129), as do estimates of the history of the merger rate - at this point it appears that most ellipticals might be merger remnants, as long as rampant merging took place in the early Universe so that most ellipticals ceased star formation by z ~ 1. Current work includes tests for the number of pairs and mergers at high redshifts, which are connected since most merging occurs between bound pairs. The merger rate is often paramatrized to vary as (1+z)a, where a < 3 to avoid overproducing ellipticals today. In the local Universe, we find systems at all stages of merging - this image sequence shows a set of nearby mergers in the order in which they best match the order of things seen in numerical simulations. It is especially interesting that this same order makes sense for optical colors and far-infrared excess, both suggesting a transient burst of star formation associated with merging.
There are some additional post-merger signatures. These include shells in ellipticals, polar rings, counter-rotating stellar or gaseous subsystems, and external H I in ellipticals. Polar rings appear around some S0 or very early Sa galaxies; the connection to mergers arises from the fact that polar orbits are less vulnerable to smearing by differential precession than more equatorial ones, and thus longer lasting. An atlas has been presented by Whitmore et al. 1990 (AJ 100, 1489). Detailed modelling has been done by Steiman-Cameron and Durisen 1982 (ApJLett 263, L51),Schweizer at al. 1983 (AJ 88, 909), and Whitmore et al. 1987 (ApJ 314, 439). The Hubble Heritage team produced a stunning image of NGC 4650A showing young stars clusters and dust in the polar ring.
In contrast, counter-rotating subsystems attract attention because they should be very short-lived. Several cases have been reported in ellipticals (Franx and Illingworth 1988 APJLett 327, L55; Bertola and Bettoni 1988 ApJ 329, 102), S0's (NGC 4550, Rubin et al. 1992 ApJL 394, L9), and even the disk of the spiral NGC 4826=M64 (Braun et al. 1992 Nature 360, 442; 1994 ApJ 420, 558). Such motions cannot be primordial, and are thus evidence of recent addition of substantial stars or gas from outside. The H I detected in some ellipticals comes in patchy external rings, leading to the suspicion that it too was externally acquired (e.g. van Gorkom et al. 1986 AJ 91, 791).
All these processes should be more common in regions of higher galaxy density, like the whole universe long ago. What do we see at higher redshifts? This issue will be crucial in understanding galaxy evolution. Since mergers can trigger huge starbursts, and perhaps transform galaxy types, they may have been a controlling influence on galaxy evolution. In fact, galaxy formation is now thought to have been rather protracted, building up piece by piece from smaller constituents, so mergers might be our best present analogs to protogalaxies (see Djorgovski in Nearly Normal Galaxies, p. 290, for a statement of how rapidly the conventional wisdom can evolve). Most people who have inspected deep HST images have remarked on how many funny-looking galaxies they see, and quantitative studies back this up both as to number of statistically defensible pairs and number of "peculiar" systems, though one must be wary of passband and surface-brightness selection effects. Some of these oddities appear in this snippet from the Hubble Deep Field - North imagery.
The merger rate might appear to change strongly with time (in linear, and not comoving coordinates) simply as a collisional process, depending on the square of the galaxy density. There has been substantial analytic and numerical work on just when two galaxies will stick. Including gravitational focussing, Fang and Saslaw (1997 ApJ 476, 534) derive a merger cross-section:
where V0 is the initial (asymptotic) relative speed and r* is the disk radius (say of the larger one)i, including relevant halo material. Following Roos and Norman 1979 (A&A 76, 75), merging requires that v < 3.1 s for head-on encounters (the numerical factor may change for other kinds). Fang and Saslaw generalize this to include slower encounters,
where fast impulse encounters have m=0, n=2, and h = p leading to small S, while slow merging-friendly encounters have m=1, n=1, and m=1, n=1, 1 < h < 10. In general, approach velocities less than the internal velocities spell doom, and most encounters which lead to merging will spiral together over 6-10 crossing times. However, these considerations are not the ones relevant to asking how merging affects the entire galaxy population; demographics (Chatterjee 1987 Ap&S 135, 131) show that most merging today must occur betweeen members of pairs which are already bound, so that the history of which galaxies were formed in pairs (or small multiplets) dominates the whole question. Clusters, for example, are not fertile environments for merging per se, since most encounters will be strongly hyperbolic and transfer too little orbital energy to internal motions (though they can have interesting effects on the outer parts of galaxies, especially in the repeated applications forming harassment).
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