CONCLUSIONS

For the past two decades and more, interest in the structure and dynamics of systems of galaxies has not slackened. The main interest is in the presence of invisible (virial) mass, which gives this problem somewhat the character of a detective novel. Over the widest range of studies of the dark mass, a very important place is occupied by pairs as the very simplest systems of galaxies. The crucial role played by double galaxies has become more and more apparent in recent years.

The first step in this direction was the compilation of a sufficiently uniform and extensive sample of double systems in the `Catalogue of Isolated Pairs of Double Galaxies in the Northern Sky' (Karachentsev, 1972). In preparing this catalogue of 603 pairs, we searched principally charts of the Palomar Atlas in the neighbourhood of all galaxies brighter than a fixed photometric limit (15.7^m). The selection of isolated double systems was conducted on the basis of strict quantitative criteria from measurements of the separation and angular diameters of galaxies. Similar attempts were made later by Turner (1976a) and Peterson (1979a). Using objective isolation criteria allows one to calculate various selection effects which will strongly influence the characteristics of double systems.

With the goal of studying the kinematics and dynamics of double galaxies we began a massive survey of radial velocities for isolated pairs. A spectral study of objects in the catalogue was also conducted by Tifft and other observers. As a result of these simultaneous and intensive programs the radial velocities were all known by 1983. By comparison with the earlier, non-systematic observations of galaxies in pairs, we can attain much greater accuracy in the measurement of radial velocities, which allows greater precision in estimates of the mass of double galaxies.

The effectiveness and selectivity of our pair criteria were examined with the help of numerical Monte Carlo experiments. This modelling of the observed distribution of galaxies was conducted with regard to their location in systems of various scales and multiplicities. Applying the same inclusion criteria for double systems to the model distribution as in the real catalogue, we found the following result. Among catalogue objects 11% are optical pairs, incorporating galaxies which by chance lie close to one another along the line of sight but are not close in space. About 32% of the catalogue pairs are false double systems caused by projection along the line of sight of members of the same group or cluster. The role of false pairs (system members) was previously strongly underestimated, which led to anomalously high values of the mean orbital mass for double galaxies. The objective reason for the shortcomings of the selection criteria for pairs is the large dispersion in galaxy luminosities, so that the apparent magnitude or angular diameter of a galaxy is only a weak indicator of its actual distance.

The results of the modelling were used to recover the true spatial characteristics of double systems from their catalogue characteristics, including projection effects and the role of false pairs. After incorporating errors in the radial velocity measurements and the contribution of non-isolated pairs, the mean radial velocity difference for components of double systems is 120 km/s. Strong selection effects appear in the distribution of linear separations. For X > 100 kpc, more than 90% of pairs fail the isolation criteria. Combined with the increasing number of false pairs for larger X, this does not permit a meaningful estimate of the true number of wide double systems per unit volume of space. The majority of objects in the catalogue (~ 70%) are sufficently tight systems that the separation of the galaxies is less than the sum of their diameters. Correcting for the selection criteria the characteristic mean spatial separation is <r₁₂> = 83 kpc.

The same selection factor causes difficulties in estimating the spatial luminosity function (M₁, M₂). By comparison with field galaxies, components of pairs show a significant excess luminosity (M - 0.56^m). The observed strong correlation between the absolute magnitudes of double galaxy components comes not only from selection effects but also from physical properties of the objects in a given system. The excess luminosity and the (M₁, M₂) correlation probably relate to the simultaneous formation of double galaxies.

A central place in the study of double systems is undoubtedly occupied by the problem of unseen mass. It is frequently argued that pairs of galaxies are surrounded by invisible massive haloes and therefore that Keplerian dynamics is improper. To examine such a statement one often uses arguments both from `above' and from `below'. For many systems of galaxies at high levels of the structural hierarchy (groups, clusters and superclusters), the total masses of the components are not consistent with the large relative velocities of the galaxies. In order to have a balance between potential and kinetic energy in these systems, it is necessary to postulate the presence of dark (virial) mass, exceeding the visible mass of galaxies by an order of magnitude. On the other hand, for individual galaxies lower limits on the unseen mass may be set from observations of flat rotation curves. The observed departure from the decreasing Keplerian form V(R) ~ R^{- 1/2} demonstrates the diffuse character of the distribution of matter, i.e., extended massive haloes. Further support came from the excess mass in double systems with a high (~ 60 f) orbital mass-to-luminosity ratio, as found by Page (1952), Turner (1976b) and Peterson (1979b). The `anatomy' of this excess featured prominently in chapters 4 and 5. The data presented there show that the dominance of such high estimates of the orbital mass is due to the inclusion of a significant number of false pairs. After correction for such fictitious double systems, as well as for errors in the measurement of radial velocity, the mean orbital mass-to-luminosity ratio is in accord with the individual values f 8f needed to give flat rotation curves.

We emphasise that this comes not only from the coincidence of mean estimates. Due to projection effects the estimates of orbital mass and total luminosity give ratios spanning a range of [0, 30] f with a mean (7.8 ± 0.7) f and standard deviation 6.5f. Nearly the same range is spanned by individual estimates of the mass and luminosity for field galaxies. It is also important that the orbital and individual values of f for galaxies of various types along the Hubble sequence are in excellent agreement (see figure 34). Comparing the orbital masses of double galaxies with the sum of the individual masses, derived from rotation curves, from the 21-cm profile width, or from the nuclear stellar velocity dispersion, shows that the majority of the mass of galaxies lies within the standard optical radius (R₂₅). Although most of the catalogue objects are tight (contact) systems, wide pairs (X > 100 kpc) show no higher mean orbital mass-to-luminosity ratios than do the tight pairs, which does not agree with the hypothesis of very massive invisible haloes.

For this reason pairs of galaxies appear to conflict with the general trend of structures at different scales to show signs of virial mass excess. We cannot avoid some discussion of this strange situation.

Examining the observational data allows us to set limits on the possible character of the orbital motion in pairs. From various techniques we concluded that the orbits of double galaxies are close to circular. The best agreement with observations is found for a typical orbital eccentricity e = 0.25.

The exciting possibility of testing the conceptions of the origin and evolution of galaxies and systems of galaxies leads one to analyse correlations of the various parameters of double galaxies: morphological and spectral types, signs of interaction, colour indices, etc. So far only the `first cultural layer' has been reached.

By comparison with isolated galaxies double systems contain a much larger percentage of objects of early Hubble type, and the relative number of elliptical galaxies climbs with decreasing separation between pair components. The fraction of double systems in the catalogue with the same Hubble type for each component is significantly higher than expected for a random distribution of these properties.

More than half of the pairs in the catalogue show evidence of tidal interaction. The analysis shows that among the interacting systems one encounters all structural types with the same likelihood, but their distributions by type of interaction are highly non-uniform: linear structure (tails and bridges) are characteristic of objects with a significant stellar disk in circular rotation. For elliptical double galaxies where stellar orbits are strongly elongated, one usually observes amorphous, symmetrical atmospheres. This connection between the form of interaction and the character of stellar motions within pair members agrees with the results of numerical experiments.

Examining the spectral and morphological types of double galaxies shows that tidal interaction appears most prominent among galaxies with strong signs of emission. Activity in the nuclei of galaxies is apparently triggered by gas collisions and changes in the angular momentum of gas clouds due to tidal disturbances. The transfer of gas between components does not appear to play an important role, as shown by the spectra of elliptical galaxies apparently in contact with spirals.

In recent years much and varied evidence has shown that star formation processes in double systems are much more active than in field galaxies or members of rich clusters. There is evidence for this from the observed excess of infared and radio emission from double galaxies, the increased fraction of supernova hosts among such galaxies, and enhanced percentages of double systems among Seyfert objects and quasars. In pairs with small radial velocity differences and small separations, i.e., the ones in which tidal influences are most effective, there is an especially large chance of encountering a blue Markarian galaxy.

According to photoelectric data the components of double systems display a strong correlation in colour (the Holmberg effect). In pairs of spiral galaxies both their blue colour and this correlation may probably be explained by simultaneous bursts of star formation periodically induced by tidal effects. In pairs with elliptical components where gas resources for such bursts of star formation are insufficient, the similarity of the galaxies' colours may be due to a common chemical composition at the epoch of simultaneous formation of the components.

Considering double galaxies as a metagalactic population, we note the following properties of their distribution. The relative number of galaxies in the sample brighter than magnitude 15.7 is 0.042, leading to an estimate of their spatial density which is somewhat higher: 0.12 ± 0.02. The spatial distribution of pairs follows the general hierarchical clustering. About 90% of the closest pairs are in fact members of known clusters. No less than half of the double systems with radial velocity V₀ < 2400 km/s are located within the bounds of the Local Supercluster. The same situation is observed for much larger volumes. The two-point correlation function for the centers of pairs in the region D < 100 Mpc has an amplitude over the interval 0.7 to 20 Mpc systematically much higher than the standard Peebles function for galaxies. The maximum difference between these functions occurs on scales ~ 10 Mpc, which may be explained by an excess number of double systems on the edges of superclusters. The tendency of double galaxies to be located in the peripheral regions of systems of galaxies is also found in nearby groups and clusters.

The rms difference in radial velocities for double galaxies in the catalogue is 170 km/s. A value very close to this was found for neighbouring systems on the sky, from the large redshift survey to fixed limiting magnitude (194 km/s). From the dependence of mean velocity on separation for nearby pairs we estimate the peculiar motion of the centers of double systems to be (V_p) 80 km/s. In a picture of gravitational clustering (Turner et al., 1979), this estimate agrees with an open cosmological model with density parameter ₀ < 0.1.

To clarify the origin and dynamical evolution of double systems, the data of most interest are the magnitude and relative orientation of the angular momenta of the galaxies in pairs. This question has not received the proper attention. Because of their almost-circular motion, double galaxies have large orbital angular momenta. For 75% of the catalogue pairs the orbital angular momentum exceeds the rotational angular momentum of our Galaxy.

The ratio µ₁₂ of the value of the orbital angular momentum to the sum of the spin angular momenta for the components depends strongly on the structural type of the galaxy. Double systems of spiral galaxies have mean ratios µ₁₂ 1.3 - 2.5, pairs of type Sm are in the region µ₁₂ < 1, and for double elliptical systems the rotational angular momentum is swamped by the orbital motion, µ₁₂ 10.

Almost all scenarios for the origin of galaxies predict a significant ordering of the relative orientation of orbital and spin rotation vectors for double galaxies. The evidence for any such correlation is not strong. The distribution of pair components by position angles of the major axis and the angle of inclination is consistent with a random orientation of the rotation vectors. Reports by various authors of an excess number of pairs with anti-parallel spins require further observational confirmation. A primordial ordering of spins in double galaxies may have been disrupted by a change of mass and angular momentum in the non-equilibrium phase of protosystem formation, and an important role may later have been played by the precession and nutation of spiral galaxies in tight pairs.

We have noted many times that galaxies in double systems display correlations of numerous integrated properties: luminosity, linear diameter, structural type, mass-to-luminosity ratio, and rotational angular momentum. These correlations cannot be explained by observational selection but must have a physical origin. Because these properties characterize the global structure of galaxies it seems improbable that such correlations merely reflect the simultaneous coupled evolution of the components of pairs. It seems less risky to suppose that the structural properties have a relic nature, i.e., they reflect the original conditions under which the components were formed.

As well as the `sibling' relic properties, double galaxies display strong correlations of spectral type (emission properties) and colour indices. These similarities apparently have to do with active simultaneous evolution due to the action of tidal forces (the gaseous component of galaxies has less conservative dynamics than the stellar component).

Extensive numerical experiments recently conducted by numerous authors have stressed the dominant role played by dynamical friction in the evolution of double galaxies. This leads to a self-imposed evolutionary selection of pairs by orbital eccentricity. Those double systems for which the orbit is very elliptical and which have a small perigalactic distance will merge into single systems. Typical median orbital periods are 0.06 in units of the cosmological time H^-1. For the majority of catalogue pairs the characteristic merging time is only two or three times the orbital period. Therefore, on a time scale _m 0.1 - 0.3 many pairs should be transferred into the category of single objects.

The short time scale of this merging process implies that at time = 1 the fraction of single galaxies should be much higher than the observed relative number of isolated galaxies ₁ 0.05. However, this paradox is only apparent, because the distribution of double systems follows the general law of hierarchical clumping, and so after merging, pairs in groups and clusters do not produce isolated objects of the general galactic field.

For a relative number of double systems ₂ = 0.12 and characteristic time for merging _m 0.2 the expected number of mergers is <m> 1 at cosmological time = 1. If the rate of pair merging was much higher at earlier times then many galaxies may be viewed as the products of multiple mergers. Such a process may explain the numerous reports of excess numbers of blue objects among faint distant galaxies. During the merger double galaxies undergoing star formation become blue and at the same time more visible at large distances.

If many galaxies possess extended massive haloes the rate of mergers goes up, which provides another self-imposed evolutionary selection. We observe today only pairs without haloes because the merging time for these is much longer than for the galaxies that have disappeared.

These factors lead to a picture of rather violent dynamical evolution for galaxies and systems of galaxies, among which a most active, key role is played by double galaxies. Clarification of such a picture belongs to the near future.

Before bringing to a close this description of the observed properties of double galaxies we briefly describe several important questions needing further investigation.

1. We require the construction of a matching catalogue of objects in the southern hemisphere, incorporating the same isolation criteria and photometric limit m = 15.7^m.

2. In modelling the apparent distribution of galaxies we used a simple scheme of non-hierarchical clumping. For independent estimates of the effectiveness of the criteria, the role of projection factors, and the relative numbers of false pairs, it would be interesting to perform numerical experiments with another scheme - say, in place of the probability p_k in table 3 one could use a hierarchical matrix p_ij or even some sort of `my neighbour's neighbour is my neighbour' scheme, in determining the correlation function _g(r). Such an approach would allow studies of differences in the correlation functions _gg, _pp and _gp for galaxies and pair centers which are impossible to perform on the basis of the present models.

3. For 20% of the catalogue pairs the current accuracy of the radial velocity measurements is not high enough (_y > y) for the desired accuracy in estimating the orbital mass. It is especially important to increase the accuracy for wide pairs, since for X > 100 kpc a measurement error _y 15 km/s gives errors in the mass estimates ~ 10¹¹ M, making searches for massive haloes very difficult.

4. A currently important question is determining the bivariant luminosity function of double galaxies (M₁, M₂). The value of the luminosity excess for pair members by comparison with individual galaxies is very poorly known, as is the nature of the correlation of the absolute magnitudes M₁ and M₂.

5. Observations which obviously cannot be omitted are systematic measurements of the masses of double galaxies from rotation curves to the greatest possible distances from the center (R > R₂₅). Comparison of the sum of the individual component masses with estimates of the orbital mass is the most sensitive indicator of the character of orbital motion, as well as of the presence of dark mass around the system.

6. To clarify morphological classifications of double systems and make a more accurate analysis of interaction it is crucial to have large scale images of these systems. We presented a few photographs here, but these, together with illustrations from the Arp Atlas, cover only about a fifth of the objects in the catalogue.

7. The observed similarity of pair components in colour (the Holmberg effect) apparently has a different nature for spiral and elliptical double galaxies. Photoelectric observations of the integrated colour indices of pairs carried out with sufficiently high precision have the unique possibility of investigating the effects of synchronous evolution.

8. As well as measurements of the integrated colour of double galaxies there is considerable interest in measuring the colour indices of tidal structures at low surface brightness (extended atmospheres, bridges and tails). Such data are needed to clarify the roles of disk and spheroid stars in producing these tidal features.

9. The spin orientations of double galaxies with respect to their orbital direction appear overall to have an isotropic character. However, the various theories for the origin of galaxies predict a distinct ordering of the spin orientations. To search for any anisotropy it is necessary to have estimates of the spatial distribution of the rotation axis as determined by spectral data and large scale images.

10. Modelling dynamical processes in pairs of galaxies is usually rather simplified (parabolic orbits of the interacting companion, single component structures, galaxies of test particles). However, it is crucial to incorporate the kinematic properties of the dense and spheroidal subsystems as well as the gaseous subsystems. In many double galaxies the internal rotation period is close to the period of orbital motion, and the same time-scale characterises the bursts of star formation produced in the disks of galaxies by tidal effects. The coincidence of these three characteristic time-scales may be due to the amplification and inter-relation of various resonance effects. Under these circumstances the active coupled evolution of members of double systems may depart strongly from the evolutionary track of isolated galaxies. Finally, one might expect that a more complete incorporation of observational results in modelling the merging of double galaxies will lead to an understanding of their important role in the dynamical evolution of systems of galaxies.

NOTE: That's All Folks!.