Dynamics of galaxy groups: computer simulations versus observations

Vistas in Astronomy, Voi. 36, pp. 1-30, 1993 Printedin Gre~ Britain. All rightsreserved.

0083-6656/93$24.00 @ 1993PergamonPressLtd

DYNAMICS OF GALAXY GROUPS: COMPUTER SIMULATIONS VERSUS OBSERVATIONS L. G. Kiseleva* and V. V. Orlovi" *Institute of Astronomy, Cambridge CB3 0HA, U.K. tAstronomical Institute, St Petersburg State University, Bibliotchnaya pl. 2, St Petersburg, Petexhof 198904, Russia

Abstract A review of recent observations and computer simulations of galaxy groups is given. The most important aspects of the review, such as the main features and evolutionaxy status of compact and loose groups, dynamical mass estimations, hidden mass problem, galaxy merging, axe considered from the point of view of observational data and numerical studies. A short description of the basic N-body algorithms is also given. Contents 1. Introduction. 2. Main features of observed galaxy groups. 2.1 Methods of observations. 2.2 Criteria of selection and catalogues of groups. 2.3 Loose and compact groups. 2.4 Configurational properties. 2.5 Internal kinematics and discordant redshifts. 2.6 Dynamical mass estimations and hidden mass, 2.7 Morphological types of components. 2.8 Signs of tidal interaction and merging. 2.9 Galactic activity. 3. Methods of computer simulations. 3.1 General principles of numerical modelling. 3.2 Direct N-body codes. 3.3 Semi-analyticai approaches. 3.4 Modified N-body codes. 4. Results of computer simulations. 4.1 General features of evolution. 4.2 Dynamics and configurations. 4.3 Compact galaxy groups. 4.4 Tidal interactions and merging of components. 4.5 Dark mass estimations. 4.6 Groups within galaxy clusters. 5. Conclusions.

2

1

L G. Kiseleva and V. V. Orlov

Introduction

It is well known that galaxies form some structures of different multiplicity within different hierarchy levels. Nearly half of all galaxies are in groups of 3 to about 20 members (e.g., de Vancouleurs 1975; Tully 1987). In the last few decades a large number of studies, ' both observational and theoretical, have been devoted exclusively to groups of galaxies, which may be considered as tools for studying dynamical and evolutionary processes in the Universe. This review includes observational, theoretical, and numerical studies of galaxy groups carried out mainly during the last ten years. We are concerned here with the following main problems: 1) Recognition of groups within the fields of galaxies. 2) Nature of the compact groups. 3) Origin of discordant redshifts. 4) Presence of significant hidden mass and its role in group evolution. 5) Tidal interactions and merging: the influence to evolution and galactic activity. 6) Dynamical status and age of groups. 7) Galaxy groups as a part of the large scale structure. The aim of the review is to compare the data of observations with the results of theory and computer simulations and to generalize the various efforts with respect to the galaxy groups. In recent years a number of reviews on different topics connected with galaxy groups have been published. Among them may be mentioned the papers by Gouguenheim and Collin-Sonfrin (1980), GeUer (1984), BaUabh (1984), Gorbatsklj and Kritsuk (1987a,b), Giuricin (1989), Sandage (1990), Hickson (1990), Mamon (1990a).

2 2.1

M a i n features of o b s e r v e d galaxy groups Methods

of observation

Permanent improvement of observational devices and methods in all wave length regions creates some favourable conditions for successful studies of galaxy groups as one of the main elements of the large scale structure of the Universe. Using high-resolutlon CCD images in different colors allows us to study the structure and morphology of members of groups, in particular the faint galaxies. A preliminary identification of galaxies and selection of members is usually done from photographic surveys of the sky, like the Palomar Observatory Sky Survey (POSS) or the ESO/Uppsala Survey. The spectroscopy, especially with CCD and fibre multlobject detectors, gives the accurate redshifts (and corresponding radial velocities) of components, as well as some information about velocity fields in groups and internal galaxy kinematics. The infrared observations help us to study star bursts and nuclear activity of galaxies in groups. The structure and kinematics of the intergalactic and galactic gaseous medium is investigated using radio observations, in particular the 21 cm line of neutral hydrogen. Note that radio spectroscopy is also used for accurate determination of galaxy redshifts. The hot gas in groups is studied by the X-ray data obtained using space observations, e.g. GINGA, EINSTEIN, ROSAT etc. 2.2

Criteria

of selection

and catalogues

of groups

There is a number of catalogues of galaxy groups (e.g., Holmberg 1969, Karac.hentsev 1970, Shakhbazyan 1973 (see also the references in Hickson 1990), de Vaucouleurs 1975, Sandage 1975, Turner and Gott 1976, Rose 1977, Einasto et al. 1977, Materne 1978, 1979, Karachentseva et al.

Dynamics of Galaxy Groups

3

1979, Tully 1980, 1987, Huchra and Geller 1982, Hicksoa 1982, Geller and Huchra 1983, Vennik 1984, Ramella et al. 1989, Maia et al. 1989, Fouque et al. 1992, Allington-Smith et al. 1993, Nolthenius 1993). Different authors have used various criteria for selection of members of the groups. All suggested criteria are not completely objective, as they use some subjective critical values of selection parameters. Some of the groups were identified even when the redshifts (and corresponding radial velocities) of their members were not obtained (e.g., de Vancouleurs 1975, Turner and Gott 1976, Rose 1977, Karachentseva et al. 1979, Hickson 1982). These groups were defined using criteria of compactness (high surface density) and isolation of possible members from field galaxies. As example of such a criterion we may name the criterion by Rose (1977) n >_ 3 with m <_ 17.5,

a ~ _< 0.0035.

(1)

Here n is the number of members, m is the estimated blue magnitude of a galaxy, tr the average number of field galaxies per arcmin 2 with blue magnitude equal or brighter than the faintest galaxy enclosed in the area A a r c m i n 2 of sky covered by the group. The second condition corresponds to a group surface density contrast of about 1000 and more over the field. Hickson (1982) has visually inspected all the red POSS prints, covering about 67% of the sky; he used the following selection criterion: n >_ 4 with m > m s + 3 ,

RN > 3RG, #a _< 26.

(2)

Here mB is the estimated magnitude of the brightest group member, RG the radius of the smallest circle containing the group members, RN the distance from the center of this circle to the nearest nonmember satisfying the same magnitude condition, #a the mean surface brightness contained by this circle. Karachentseva et al. (1979) used a rather different criterion for selection of galaxy triplets with 6 > - 3 ° and b > 20° by POSS: = 3 with m < 15.7,

0.5al ~ ai <_ 2al, Z13/Zli ~--- 1/3.

(3)

Here al is the angular diameter of a chosen galaxy, ai the corresponding values of near neighbouts, z13 the angular separation between the galaxy a~ and a more distant neighbour in the triplet, xll the angular separations between aa and other galaxies - nonmembers of the triplet, for which the second condition in (3) is satisfied. Thus this criterion takes into account the angular diameters of galaxies and selects the triplets with components of comparable luminosities. The above criteria have two essential deficiencies: 1) only compact systems may be revealed, but the loose groups will not be identified; 2) a significant part of possible members may be a result of chance projection. Till the present time the radial velocities are obtained for all components of the groups by Hickson (1982) and triplets by Karachentseva et al. (1979). The redshifts for Hickson compact groups are available from Hickson; the radial velocities for the galaxy triplets were published by Karachentseva et al. (1987, 1988). It appeared that in many groups some components have discordant redshifts with respect to other members. The nature of discordant redshifts will be

4

L G. Kiseleva and V. V. Orlov

discussed below, however some additional criteria should be applied to eliminate the probable optical components. One example of such criteria was proposed by Anosova (1987) in order to recognize the random and non-random groups among stars and galaxies. The criterion is based on an estimation of (a) the probability P, that n objects from a whole sample of N objects, occupying the phase region E, could be located by chance within a phase subregion o 6 E and (b) the expectation E , of the number of such random groups in E . Anosova (1987) formulated this criterion for a uniform distribution Of N objects in E . In case of galaxies the region E is in the 3-dimensional phase space of angular coordinates and radial velocities. The criterion was applied to the Karachentseva et al. triplets (Anosova 1987), Vennik groups (Vennik and Anosova 1990), and Hickson compact groups (Anosova and Kiseleva 1993). As result, e.g., the Hickson 100 groups were classified as the confident accordant 3 groups ( En ~ 1 ), the probably accordant 51 groups ( 1 < En _~ 103 ), 33 groups with probable discordants ( 10s < En ~_ l0 s ), 13 groups with confident discordants ( E~ > i0s ).

However, amongst the groups with 1 < E. _< 10~ a population of 9 groups with large relative radial velocities ( Av > 1000 km/s ) was discovered. These groups are nearby and the discordant redshift components are usually the brightest ones. Anosova and Kiseleva (1993) concluded that this criterion should be used for an initial classification of galaxy groups. As the next step, it is necessary to take into account the additional information on the galaxies (the magnitudes, morphologies, signs of interactions, locations inside groups etc.). Another approach to an identification of physical galaxy groups in the redshift catalogues was made by Huchra and Geller (1982). They first choose a galaxy which has not been previously assigned to a group. Then they search around it for companions under the following criterion: D12 = 2 sin (xI2/2)V/Ho <_ D~(~I, ~2, m l , m2),

v~2 = I ~ - ~2 I_< v L ( ~ , ~ 2 , m ~ , ~ 2 ) .

(4)

Here D n and Vn are the relative linear projected separation and radial velocity of galaxies, z,2 their angular separation, V = (Vl + v2)/2 is the mean radial velocity of galaxies, m, and m2 the galaxy magnitudes, H0 the Hubble constant, DL and Vr. the critical values of relative separation and radial velocity. If no companions are found, the galaxy is considered as isolated. All companions found are added to the list of group members. The surroundings of each companion are then searched by the same way ('friends-of-friends' algorithm). This loop is repeated until no further members can be found. Huchra and Geller assumed that the luminosity function of galaxies is independent on distance and position. The values DL and VL are defined as DL = Doff, VL = V.0R',

(5)

where R' is a function that depends on luminosity function ~(M), limited m~gnitude of a galaxy sample and velocity V. Huchra and Geller have produced group catalogues for a range of the selection parameters Do and V0. The final versions of catalogues have Do = 0.63 Mpc and V0 = 400 kin/8 (Huchra and Geller 1982), D0 = 0.52 Mpc and Vo = 600 km/s (Geller and Huchra 1983) for the radial velocity 1000 kin~8. Mahtessian (1988) proposed an improvement of the above selection criterion: max(k~L,, k2L2)/Dn >_ Eo, Vn <_Vo.

(6)

Here Lt and L2 are the luminosities of galaxies, kt and k2 the coefficients dependent on the morphological types of galaxies, Eo and Vo the critical selection parameters. Mahtessian showed

Dynamics of Galaxy Groups

5

that the galaxy groups selected by his criterion have no dependence on internal velocity dispersion av on group kinematical distance < v > versus the Huchra and GeUer groups, for which the dispersion av increases with a growth of < v >. In order to find the neighbour for a given galaxy, Mahtessian used the parameter q = max(M1,M2)/r12,

(7)

where M1 and M2 are the galaxy masses, r12 the distance between galaxies. The parameter q defines the gravitational interaction between galaxies. According to Mahtessian (1988), the quantity q is a stronger criterion to reveal the physically connected groups as compared with the gravitational force parameter p = max(M~,M2)/r~2 (8) proposed and used by Tully (1980) and Vennik (1984) in their force hierarchy technique. The hierarchical clustering method was proposed and developed by Materne (1978) to study the spatial distribution of galaxies. The hierarchical structure of a sample is formed on the basis of maximization of the parameter p (eq.8) between alone galaxies or the galaxy groups at each step. The hierarchical clustering can be graphically illustrated by means of dendrograms (Vennik 1984). The density enhancement criterion is used to separate physical systems from field galaxies. Vennik and Anosova (1990) developed a combined approach using the hierarchical clustering technique and the criterion by Anosova (1987) in order to select possible additional members of the Vennik (1984) groups, as well as to divide the groups into the isolated and unisolated ones. Gourgoulhon et al. (1992) applied the hierarchical clustering algorithm for compiling the homogeneous group catalogue (Fouque et al. 1992). Nolthenius (1993) presented a new identification of groups and clusters in the CfA1 Catalog of Huchra et al. (1983), using a percolation algorithm to identify density enhancements. His new catalog includes 173 groups and clusters with multiplicity n E [3; 113]. The procedure of selection differs from that of the original Geller and Huchra (1983) catalog in several important respects, e.g. galaxy distances are calculated from the Virgo-Great Attractor flow model of Faber and Burstein (1988). It is shown that in the resulting catalog, contamination by interlopers is significantly reduced. In order to study the evolution of galaxies in small groups in a way unbiased by optical effects, Allington-Smith et al. (1993) observed the population of galaxies around a sample of 98 radio galaxies, 65 with redshifts less than 0.25, and 33 with redshifts between 0.25 and 0.50. They analyzed the properties of galaxies brighter than My = - 1 9 (assuming H0 = 50 km s -1 Mpc -1) within 0.5 Mpc of the radio galaxies and obtained that strong radio galaxies occur in groups whose range of richness is broad, but not as broad as that of groups in general: radio galaxies may tend to avoid very poor groups. There has been a slight decrease in richness of radio groups since the epoch observed at z = 0.4.

2.3

L o o s e a n d c o m p a c t groups

In dependence on the used criterion of selection, the compact galaxy groups (e.g., Shakhbazyan 1973, Rose 1977, Karachentseva et al. 1979, Hickson 1982), and the loose ones (e.g., Turner and Gott 1976, Materne 1978, Huchra and Geller 1982, Geller and Huchra 1983, Tully 1987, Main et al. 1989, Nolthenius 1993) may be identified. Compact galaxy groups are small isolated systems with projected separations comparable to the diameters of the galaxies. The visible densities of compact groups are comparable to those of the cores of rich clusters. Such groups may be the densest isolated systems of galaxies in the

6

L G. Kiseleva and V. V. Orlov

Universe. On the basis of the numerous signs of tidal interactions, a number of observers reached the conclusion that the Hickson compact groups are bound systems of four or more galaxies (e.g., Williams and Rood 1987, Sulentic 1987, Hickson and Rood 1988, Hickson 1990, Moles 1993, Palumbo 1993). There is another point of view on the status of the compact groups: Maroon (1986, 1987, 1990b, 1992), Walke and Mamon (1989) treated them as the chance alignments along the line-of-sight within loose groups. Hickson and Rood (1988), Walke and Maroon (1989) estimated the frequency of chance alignments inside loose g~oups, which satisfy Hickson's selection criterion (eq.2). Hickson and Rood considered this problem using static Monte-Carlo simulations. They showed that typical loose groups should yield less that 0.1% of chance alignments on average. Walke and Maroon derived semi-analytical expressions for the frequency of chance occurence of isolated subgroups within loose groups. Their analysis was checked with Monte-Carlo simulations. Unlike Hickson and Rood, Walke and Maroon took into account the influence of background galaxies, a contribution of small clusters, and an effect of bound binaries inside loose groups. The combination of the last two effects accounts for roughly half of the Hickson compact groups as chance alignments of galaxies within intermediate density groups and small clusters. We note that the results of Walke and Maroon agree with the N - body simulations by Mamon of dynamical evolution of loose groups. Thus the question on the nature of compact groups is still open. 2.4

Conflgurational

properties

The most reliable information on galaxy groups is the position of components in projection on the sky. The uncertainties of angular separations between components are connected with the deviations of galaxy forms from the symmetric ones. These uncertainties are about 0.1 ~ - 1~ (see, e.g., Karachentseva et al. 1979, Geller and Huchra 1983, Vennik 1984). The corresponding relative errors are about a few percent, as a rule. The configurations of the galaxy groups are important for the investigation of dynamical processes in these systems. A statistical connection could exist between the configurations and the evolutionary status of groups. However, the apparent configuration of a group is different from the actual one because of the projection effect. It seems essential to restore the distribution of actual configurations using that of the apparent ones. This problem was solved theoretically by Agekian (1954) in the general case for the triplets. He derived an integral equation connecting the two above distributions. No analytical solution of this equation has yet been found. Such a theoretical approach for the systems of larger multiplicity is too complicated. A more successful way to solve the above problem is by numerical approaches based on MonteCarlo methods. Two such means were applied to the galaxy triplets by Anosova et al. (1990, 1993), Kiseleva and Orlov (1989). The first method is based on dividing the region O (Figure I) of all possible configurations of triple systems into a set of subregions. For each subregion, the probabilities of transitions of the configurations to any other subregion and to the same one due to the projection effect are estimated. The matrix of transition probabilities and reverse matrix were derived by Anosova et al. (1993) using Monte-Carlo simulations for four subreglons corresponding to the hierarchical configurations, alignments, configurations close to the equilateral triangle, and intermediate configurations. The second method is based on some configurational parameters describing the alignment and

Dynamics of Galaxy Groups

2

I A (-0.5,0)

0

S~ . 5 ~

t

Figure h The region D of all possible configurations of triple systems. A, B and C are the positions of components.

hierarchy of triple systems. The examples of such parameters are the alignment parameter =

-

(9)

where ~o,,.= is the maximum angle in the configurational triangle; the hierarchy parameter • = 2,',,,.I(,',,, + ,',,..),

(10)

where r,~i., ri.t, and rmax are the minimum, intermediate, and maximum separations in the triplet. There is also a number of other parameters describing the alignment and hierarchy of triple systems. Kiseleva and Orlov (1989) compared actual and projected distributions of eight parameters and showed that amongst them/Y and A are the least sensitive ones with respect to the projection effects. Using the above methods, Anosova et al. (1990, 1993), Kiseleva and Orlov (1989) compared the distributions of confgurations for galaxy triplets of Karachentsew et al. (1979) and for the random configurations inside the circle. They showed that the confident and probably accordant galaxy triplets have a marked tendency to alignment. Any tendency to hierarchy was not observed. Malykh and Orlov (1986) studied the configurational properties of the Hickson compact groups with multiplicity n > 4. They used two structural parameters: 1) The variation B of square paired separations r~j in the group 2 " B = n(n - 1-------~y~(r,j - A)2/A ~, j
(11)

2

(12)

where A - n(n---

n r2 1) j<~ ~

is the dimensional parameter proposed by Agekian (1982). Note that B is the undimensional parameter which defines degree of the hierarchy in a group.

8

L G. Kiseleva and V. V. Orlov

2) The parameter C - the mean sum of square sines of angles in all possible triangles formed 5y members of a group. The value C defines an alignment of the group. Note that Kiseleva and Orlov (1989) also considered the parameters B and C for galaxy triplets and showed that those axe more sensitive to the projection effect than the characteristics/~ and

The average values < B > and < C > for 100 compact groups were compared with average values < B, > and < C, > in cases of distributions of simulated systems within the ellipses of different apparent sphericity ~. The observed < C > is closest to Co for the ellipse with sphericity = 0.4. Thus a tendency to alignment takes place. Any tendency to hierarchy was not observed in the compact groups. The compact groups have probably prolate forms which may be fitted by prolate spheroids with mean actual sphericity ~*-- 1/4. The observations contradict the hypothesis of the oblate spheroids. Hickson et al. (1984), using Monte-Carlo simulations, found that the compact groups may be fitted by triaxial ellipsoids with a mean ratio of axes 1.0:0.5:0.2. Thus the distributions of configurations for the compact galaxy groups provide evidence that these objects have rather recently formed inside some filamentary structures of matter. Hickson et al. (1984), as well as Malykh and Orlov (1986) concluded that the compact groups are elongated systems and cannot therefore be explained by a chance superposition of galaxies (see also Hickson 1990). 2.5

Internal

kinematics

and discordant

redshifts

The problem of internal kinematics in galaxy groups is not so popular as other aspects of study of the groups. However, there are a few papers devoted to this subject. Some of their authors investigated the kinematics of particular groups: IC 6S8 (Williams 1983); Marl~rian chain of galaxies in Virgo (Litzroth 1983); NGC 4005 (Williams 1986); M 31 system (Cera and Beckman 1988); Hickson 88 (Xu and Lu 1988); the Eridanus group (Willmer et al. 1989); NGC 128 (Jarvis 1990). Litzroth (1983), Williams (1986), Xu and Lu (1988) noted that the groups may have a general rotation. In these cases, the systematic trends in the radial velocities were found along the major axes of the groups. A short description of kinematical properties of galaxy groups was given by Puche and Carignan (1991). Cepa and Beckman (1988) estimated the orbital parameters of M 32 and NGC 205 about M 31, using some simple kinematic, dynamic and geometric assumptions. They found that both companions rotate in a retrograde sense compared to M 31 indicating a possible common origin independent of the main galaxy. These authors suggested either individual captures of satellites by M 31, or the capture and subsequent rupture of a single object. Litzroth (1983) considered the well-known Markarian chain consisting of eight galaxies in Virgo. Three double and two single galaxies are distinguished in the chain. The system radial velocities of double galaxies and one single galaxy NGC 4406 lie on a straight line in the velocity - angular separation diagram. Thus the system of seven galaxies forms a regular rigidly rotating chain system. It seems that the galaxy NGC 4374 at one end of the Markarian chain is not involved in this rotation. A statistical study of the internal motions in galaxy triplets was performed by Kiseleva and Orlov (1993a). They fixed in each triplet two components A and C with the largest projected separation. The sign of the product =

(VA

-- VB)(Vs

--

VC)

(13)

was defined. Here B is the 'intermediate' component; VA, Vs, and Vc the corresponding radial velocities. The Monte-Carlo simulations performed showed that in the case of pure radial too-

Dyno~n~s of Galaxy Groups

9

tions in triplets (infall or expansion of the group), the negative signs of a predominate; in the case of rotation of the triplet as a whole, the positive signs of a prevail; for isotropic velocity distribution, the positive signs are realized in about 1/3 of the cases under consideration. A comparison of simulations versus the data for 45 real and probably physical compact galaxy triplets by Karachentseva et al. (1988), as well as for 40 and 50 triplets from the lists of loose groups by Huchra and Geller (1982), Maia et al. (1989) was carried out. It was found that the hypothesis of general rotation of triplets is rejected at a high level of significance; the isotropic motions are the most probable ones for the triplets of Karachentseva et al. and Maia et al.; the radial motions (infall or expansion) are more probable for the triplets of Huchra and Geller (1982), nevertheless the hypothesis on isotropic motions cannot be rejected too. In principle such a method might be applied to galaxy groups of larger multiplicity. An unusual property of kinematical behaviour in the spiral-dominated groups was discovered by Sulentic (1984) for the Huchra and Geller (1982) catalogue. Sulentic found a statistically significant excess of positive redshifts z of companion galaxies relative to the brightest spiral groups members. A sample of 196 companion galaxies in 60 groups was considered. A sample of 62 companions in 21 E/SO-dominated groups shows no such excess. Sulentic (1984) gave a set of possible explanations of this phenomenon: a) the sample of groups is contaminated by interlopers; b) there are systematic errors in measuring z or/and selecting the dominant spiral galaxy; c) internal absorption in optically thick spiral galaxies results in a systematically low z ; d) non-Doppler redshifts in companions or blueshifts in dominant galaxies could exist; e) there are some kinematical effects in the groups, e.g. infall, expansion, or group rotation. Sulentic showed that the most probable conventional explanation for the excess of higher redshift companions to be contamination by interlopers is not in good agreement with observations: a reasonable assessment of this contamination falls far short of the observed excess. Sulentic favoured non-Doppler redshifts in the spiral groups. Byrd and Valtonen (1985) prefered another explanation. They carried out Monte-Carlo simulations of unbound expanding groups and noted a mistaken tendency to pick a galaxy of brighter apparent magnitude from the nearer portion of the expanding group population rather than the true primary. Their estimation of a number of companions redshifted with respect to the apparent primary (118 components from 196) is in agreement with the observed number (119 from 196) in the Huchra and Geller (1982) groups. Let us note that the unbound expanding components could be dynamically ejected from the bound groups (the corresponding computer N-body simulations will be discussed below). A tendency to expansion (or infall) was also found by Kiseleva and Orlov (1993a) for galaxy triplets from Huchra and Geller groups. One more aspect of the internal kinematics of galaxy groups is the presence of discordant redshift galaxies in some of the groups and the physical association of such components with their groups. A short review of previous studies of the discordant redshifts problem was given by Hickson (1990). The key question is whether discordant redshifts, especially in compact groups, can be explained by the chance projection of unrelated galaxies. Arguments against this hypothesis were advanced by Burbidge and Burbidge (1961), Arp and Lorre (1976), Arp (1982), Sulentic (1983), Sulentic and Lorre (1983) amongst others. Two basic arguments against the projection hypothesis are the following ones: 1) There is evidence of physical interaction between discordant and accordant redshift galaxies; 2) The required chance superpositions are unlikely. Studies supporting the above hypothesis were published by Rose (1977), Sharp (1985), and Hickson et al. (1988).

10

L G. Kiseleva and V. V. Orlov

Hickson et al. (1988) estimated the number of discordant redshift quintets expected by chance projection. They predicted that about 35% of all compact quintets should contain one galaxy with a discordant ( > 1000 km/s from the mean) redshift. This is in agreement with the observation that 4 of the 10 quintets with complete redshifts have one discordant redshift. The sample of 100 Hickson compact groups with complete sets of radial velocities was studied by Anosova and Kiseleva (1992). They considered the deviations DVof radial velocities from the median in each group. It appeared that in 42% of 26 quintets D V > l ( f k m / s . This estimation is in agreement with the above result by Hickson et al. (1988) and could support the hypothesis of chance superposition of discordant redshift galaxies. It may be noted that one case (the Hickson group No. 22) is a possible superposition of the unrelated binary and triplet. Hickson (1990) noted that the observed discordant-redshift galaxies show a preference for central location in their groups. A possible explanation of this effect could come from gravitational lensing (Hammer and Nottale 1986). In the last paper, the quintet VV 172, which contains a discrepant redshift member, was considered. Gravitational amplification by the gravitational potential of the foreground group would increase the probability of finding a superposed background galaxy near the center of the group mass distribution. However, Anosova and Kiseleva (1992) showed that there is no tendency for discordant redshift members to lie near the centers of the Hickson compact groups. There is an opposite tendency in fact for the discordants to be located in the periphery of the groups. 2.6

Dynamical

mass

estimations

and

hidden

mass

For many years astronomers have been trying to estimate the masses of galaxy groups, using the observational data (see the reviews by Davis 1982, 1987, Geller 1984, Trimble 1987 and references therein; Heisler et al. 1985; Vennik 1986; Karachentsev et al. 1989; Valtonen and Byrd 1990; Anosova et al. 1992). The data of these masses are important in the study of the dynamics of groups, as well as the large-scale distribution of matter in the Universe. The dynamical estimations of the mass of groups are directly connected with the problem of hidden mass and the mean mass density of the Universe. The masses of systems of galaxies are usually computed using the virial theorem. However, the conditions of the standard virial theorem are not fulfilled for small galaxy groups (see, e.g., Bahcall and Tremaine 1981, Heisler et al. 1985, Kiseleva and Chernin 1989, Anosova et al. 1991). These groups are non-stationary (see below) and sometimes physically unbound. In order to measure the virial stationarity of the bound gravitating system one uses a virial coefficient k = T / I U I,

(14)

where T and U are the kinetic and potential energies of the system. In the non-stationary case of galaxy groups, the value k E [0; 1] is a strongly variable function of time. The universal useful relation to estimate a dynamical mass of group is the following: Rv 2 M = a G ' (15) where R is a typical projected size, v is a typical relative rwlial velocity of the system, a is a parameter which depends on the system of units, the character of motions, and projection effects. The formula for the determination of R, v, and a depend on the used mass estimator. The standard virial estimator (see Heisler et al. 1985) gives the dynamical mass of the N-body system 31rN ~ i V~~ Mvr = 2---G~<~ R51 (16)

Dynamics of Galaxy Groups

11

where the Vi are the line-of-sight velocities relative to the centroid of the group, and the Rq are the projected separations between components. Bahcall and Tremaine (1981) found that the virial estimator is both inefficient and biased, especially because the presence of a close apparent pair in a group leads to an overestimation of the total mass. They proposed an alternative projected mass estimator

MPM

-

-

f PM ~ Vi21~, G(1V •'3/2)

(17)

where the P~ are the projected separations of galaxies from the centroid; fPM is the factor depending on the types of motions: fPM = 32/r for isotropic orbits and fPM = 64/~r for radial orbits. Heisler et al. (1985) recommended the first value fPM, since it gives a good agreement with numerical simulations. The projected mass estimator avoids some of the problems of the virial theorem. In particular, it is less sensitive to accidental projections of one component close to another. Heisler et al. (1985) also proposed two other mass estimators: the median mass one

f.~e

MM, = "--~-media[(V~ - Vj)2P~j];

(18)

and the average mass one

MA. -- G N ( N - 1) ~ ( V i - Vj)~P~j. (19) i
12

L G. £iseleva and V. %/.Orlov

The above estimations of M and f indicate the presence of significant dark matter inside the groups. The ratio of hidden to visible mass may be from 5 to 100 and even more. An additional analysis connected with computer simulations will be given in the Section 4 of this review. Vasanthi and Padmanabhan (1989) studied the mass M - radius R relationship for aggregates of galaxies: binaries, small groups, and galaxies. Their analysis showed that the data on groups and clusters fit a law M(R) = AR 3 + BR, (20) where A and B are the constants. This form suggests the existence of two components in dark matter: one is clustered around the galaxies (an isothermal halo M ,,, R) and another is distributed smoothly (a homogeneous background M ,,, Rs). The smooth distributions become significant at scales ;> 1 Mpc. It may be noted that there are many papers devoted to the dynamical mass estimates of individual groups (e.g., Einasto and Linden-Bell (1982) estimated the mass of the Local Group between as (3 - 6) × I012M®). These works are not included in this article.

2.7

Morphological types of components

The morphological properties of galaxies in groups may give important information on the formation, evolutionary state, and physical nature of the groups. The morphology of galaxies can be influenced both by internal and environmental processes. In his review Hickson (1990) described the morphology of components in his compact groups. The morphological types of galaxies in these groups show several trends: the fraction of spirals (about 50% or 60% according to Tikhonov 1986) correlates weakly with group density, more strongly with group luminosity, and most strongly with group velocity dispersion (Hickson et al. 1988b). Groups with high velocity dispersion contain few spirals. This seems to be opposite to what would be expected if elliptica~s are being produced by merging during dynamical evolution. Hickson et al. (1989) concluded that the morphology - velocity dispersion correlation is due to environmental effects at the time of galaxy formation. Bettoni and Fasano (1993) presented the first of a series of papers where they studied the morphology of early-type galaxies in Hickson's compact groups. 55 early-type galaxies belonging to 18 compact groups are considered and some morphological trends are suggested at this stage. In particular, an indication that boxy ellipticals are less frequent in compact groups than in different environments is found. Sulentic (1987), Hickson and Rood (1988) noted that galaxies within a group are more likely to have the same morphological type (spiral or non-spiral) than a random sample. Ramella et al. (1987) established that the GeUer and Huchra (1983) groups with the first-raaked elliptic member have a significantly higher fraction of elliptical galaxies (by a factor of ,,, 3) than the other groups, independently of the density. Hickson (1982) and Hickson et al. (1988b) found no significant differences between the morphological types of the first-ranked galaxies and the others. White (1990) explained this similarity as a by-product of the correlation of morphology and some other global group quantity. Tikhonov (1987, 1990) established a similarity of morphological contents for compact and loose groups. This could be an additional argument for Mamon's hypothesis on the compact groups being chance alignments within the loose groups. Thus the morphological content of galaxy groups does not depend on the density. This contradicts Dressler's (1980) dependence 'number of spirals space density', discovered for the rich galaxy clusters. Dressler showed that the number of spirals decreases when the density increases. Further, this dependence was continued up to the loose groups and isolated galaxies (see Bhavsar 1981, de Souza et al. 1982, Postman and Geller 1984,

Dynamicsof Galaxy Groups

13

Maia and da Costa 1990). However, the histograms in the papers by de Souza et al. (1982) and Bhavsar (1981) show a deviation from Dressler's dependence, just a stabilization of the fraction of spirals at the level 50 - 60%. This fraction is also conserved for the Hickson compact groups (Tikhonov 1987). At the same time, Maia and da Costa (1990) showed that in loose groups the morphology-density relation takes place. However, they noted that this relation is only fulfiled for late spirals. The population fraction of early spirals does not depend on the density. Mala and da Costa (1990) also considered the morphology - velocity dispersion correlation for loose groups and found no evidence for such significant independent correlation. This result contradicts one of Hickson et al. (1988b) for the compact groups. Whitmore (1993) studied the morphology-density relation for three environments: (1) compact groups; (2) loose groups; (3) the field. In all three cases he found that the relation is very weak or non-existent. Einasto and Einasto (1987) studied the morphology-density-luminosity relation of isolated, grouped, and clustered galaxies in three superclusters Virgo, Perseus, and Coma. They confirmed the universal morphology-density relation found by Dressier (1980) and extended to galaxy groups by de Souza et al. (1982) and Postman and Geller (1984). The samples of isolated galaxies contain no ellipticals and only a few lenticulars. The brightest isolated galaxies are by one magnitude fainter than the brightest galaxies in groups and clusters. The morphological and luminosity differences between grouped and isolated galaxies are probably intrinsic and due to differences during the formation. 2.8

Signs of tidal interaction

and

merging

It is becoming increasingly clear that gravitational interactions, collisions, and mergers continue to be important in the evolution of galaxy groups right to the present day. The observed signs of tidal interactions in the galaxy groups are various: the bridges, tails, rings, starbursts etc. (see, e.g., White 1982, Sulentic and Arp 1983, Gorbatskij and Kritsuk 1987a, Kollatschny and Fricke 1989a). Hickson (1990) noted that many galaxies in the compact groups are interacting. It was estimated that roughly one third of the galaxies in the compact groups show clear signs of interactions, such as morphological disturbances. In one-third of the groups there are three or more galaxies in interaction (Hickson 1990, in discussion). On the other hand, Tikhonov (1990) found that more than 50% of the 59 compact groups that he observed with the 6m telescope contain the interacting pairs of galaxies and only 12% contain three or more interacting galaxies, and roughly 40% of groups have zero interacting galaxies. Mamon (1992) separated the compact groups to two fractions depending on the presence of interaction signs. One may suppose that the compact groups without signs of interactions could be chance alignments within the loose groups. There are many papers in which the signs of gravitational interactions in some individual groups are described (see, e.g., Prugniel et al. 1987, Stocke and Burns 1987, Laurikainen and Moles 1988, van Moorsel 1988, Danks 1990, Brouillet et al. 1991, Hughes et al. 1991). For example, Laurikainen (1990) carried out a spectroscopic study of elliptical galaxies in eight small groups. He compared the properties of isolated and closely interacting eLUpticals. Isolated ellipticals have lower surface brightnesses and stronger metal lines, and are very red in comparison with interacting ones. He concluded that their origin is different from that of the majority of closely interacting eUipticals. As the computer simulations show (see below), the strong gravitational interactions in groups do often lead to merging of the components. Therefore the search for observational evidences of merging in galaxy groups is specially interesting. The degree of certainty about defining a galaxy merger depends strongly on the stage when we observe it (Keel 1990). The mergers axe

14

L G. Kiseleva and V. V. Orlov

easy to be identified at the early stages of merging when two or more nuclei may still be distinct. When the nuclei.can no longer be distinguished, some indirect tracers such as shells or H I in ellipticals or counter-rotating systems in E and S O galaxies may be used. A disturbance of the disk velocity field (or global H I profile) in early-type spirals may be observable when there is little morphological trace of the merger. The frequent associations of starbursts and mergers lead to the possibility of identifying disturbed galaxies with strong bursts with mergers. The elliptical mergers may have unusually blue colours resulting from a recent burst of star forrr~tion. This effect was discovered by Zepf and Whitemore (1990), Zepf et al. (1991) in the Hickson compact groups. The population of blue eliipticals in compact groups is consistent with the hypothesis that galaxies in these groups are merging and forming new eUipticais. Zepf and Whitemore (1990) found that optical spectroscopy may be able to distinguish a blue elliptical which is a result of the merger of two spirals from an already formed elliptical swallowing a gas rich system. It is generally assumed that mergers should produce ellipticalgalaxies, and so it was expected that the first-ranked galaxies in compact groups should have a lower spiral fraction than the other galaxies. However, Hickson (1982), Hickson et al. (1988b), and Tikhonov (1990) found no significant difference between the morphological type of the first-ranked galaxies and the others. According to Tikhonov (1990), among the brightest galaxies in the compact groups spiral galaxies constitute about 60%, which indicates that morphological type is preserved during merging. De Oliveira and Hickson (1991) considered the luminosity functions separately for the 38 spiral-rich and 30 spiral-poor compact groups. They have found that these two subsamples have the similar luminosity functions that do not provide significant evidence for previous mergings in spiral-poor groups. A similar result was obtained by Mardirossian et al. (1983) for a sample of the loose groups from the Huchra and Geller (1982) catalogue. Poor evidence was found of galactic cannibalism. In particular, the correlations of the magnitude difference between the two brightest members of each group with group compactness are insignificant. 2.9

Galactic

activity

Following Heckman (1990), by 'activity' we mean luminosities that are significantly larger and/or high energy phenomena that are significantly stronger than could be sustained by a normal population of stars. This definition includes the Seyfert galaxies, radio galaxies, quasars, starburst galaxies, and infrared-bright galaxies. The signs of galactic activity axe frequent in the galaxy groups. Petrossian (1985) compared the optical luminosities and relative intensities of some spectral lines for the saxnples of Seyfert galaxies which are isolated or the members of isolated pairs, groups, and clusters. He concluded that the values of physical characteristicsare on average the same and do not depend on the multiplicity of the systems. The spectrophotometric data for the Seyfert galaxies in groups are given by Kollatschny and Fricke (1989a), Fricke and Kollatschny (1989). Tovmassian and Shahbazian (1981) studied the radio emission of the galaxies in the groups by Turner and Gott (1976) and Einasto et al. (1977). They showed that the radio emission is most often observed from the first-ranked galaxies, independently of their absolute magnitudes. This is evidence in favour of a higher activity of the brightest galaxies in groups. A similar effect was discovered by Menon and Hickson (1985) for the Hickson compact groups. Besides, they found that in the spiral radio galaxies emission is seen predominantly from the circumnucleax regions, but in ellipticals,only nuclear emission is seen. Another feature of the radio observations is the almost total absence of extended radio emission (Hickson 1990). The observed flux is contained

Dynamics of Galaxy Groups

15

mostly within the visible galaxy. Menon (1992) studied the connection between the morphology of galaxies and their radio activity in the Hickson compact groups. As a rule, the E and SO radio galaxies are the firstranked galaxies of the groups; the spiral radio galaxies have an equal probability to be one of the three brightest members in a group. The activity of galactic nuclei is probably connected with their tidal interactions. Hickson et al. (1989b) considered the infrared properties of 54 IRAS galaxies in the compact groups and concluded that the far infrared emission of these galaxies is enhanced by about a factor of two compared to a sample of isolated galaxies by Keel et al. (1985) and comparable to that of the cluster galaxies by Bicay and Giovanelli (1987). The infrared luminosity function for the IRAS sources in the compact groups is comparable to that of the IRAS bright galaxy sample. Hickson et al. (1989b) concluded that of order 1% of all bright IRAS galaxies are in compact groups. The IR excess may signify an enhanced rate of star formation. There are a number of observed associations between the galaxy groups and quasars (see, e.g., Kritsuk 1989, Kollatschny and Fricke 1989b). The interactions of the quasars with their nearest companion galaxies axe often observed. Some examples of the quasars within the small galaxy groups may be found in the paper by Monk et al. (1986). Bahcall and Chokshi (1991) showed that the observed quasar correlation function is intermediate in strength between that of galaxies and of rich clusters. They interpreted that as an indirect evidence for the preferential location of quasars in small groups of galaxies. Optical QSOs are located in small groups (N ~ 10 galaxies, on average), probably requiring this environment in order to trigger their activity. R~dio-loud QSOs are located in a richer environment (N ~ 30) than optical QSOs.

3

Methods

3.1

of computer

simulations

General principles of numerical modelling

The galaxy groups can be treated in some approaches as systems of a few bodies interacting by Newton's law of gravitation. This allows an effective study by computer simulations. According to Marnon (1990a), the simulations published in the literature can be subdivided into two main categories: 1) "self-consistent" simulations, in which the galaxies in the groups are reproduced with as many particles as is computationally feasible; 2) "explicit-physics" methods, where each galaxy is represented as a single particle and the physical processes are explicitly included by hand. Self-consistent studies were performed, e.g. by Carnevalli et al. (1981), Ishizawa et al. (1983), Cavaliere et al. (1983), Barnes (1984, 1985, 1989), Ishizawa (1986), Governato et al. (1991), Kodalra et al. (1991). Explicit-physics investigations were carried out, e.g. by Roos and Norman (1979), Heisler et al. (1985), Navarro et al. (1986, 1987), Marnon (1987), Giuricin et al. (1988), Chernin et al. (1988), Kiseleva and Chernin (1988, 1989), Anosova et al. (1989, 1991, 1992), Chernin and Mikkola (1991). Diaferio et al. (1993) used the two sets of simulations of dynanfical properties of the galaxy groups from Ramella et al. (1989) catalog: self-consistent simulations as well as explicit-physics ones (A- and B-models). Neither of the two methods is superior to the other, but rather complementary (Marnon 1990a). The explicit-physics algorithms allow us to consider large sets of initial conditions and group parameters, requiring reasonable computer facilities. An interesting feature of this method is Jl~A 36t 1-B

16

L G. Kiseleva and V. E Orlov

that the importance of each dynamical process can be estimated for simulated groups by turning it off and comparing the results with those using the standard physics. The simulations of the self-consistent type are required to give meaningfulness for the results of the explicit-physics simulations.

3.2

Direct N-body m e t h o d s

Direct N-body simulations provide a useful tool for exploring a wide range of astronomical problems, in particular the galaxy groups. Any N-body code consists of the numerical integration of the equations of motion for each particle of index i: . --

-G

N y : mj( i=l,j~ ( T'i2 "~- ~.2~3/2',j/

(21)

where G is the gravitational constant, mj the masses, r~ and r: the coordinates of the bodies, rlj the mutual separations, e~j is a softening parameter. The last parameter prevents a force singularity as rij ~ 0, and its value depends on the sizes of galaxies. Widely used integrators are Runge-Kutta schemes of different orders and their modifications, predictor-corrector methods, the Bulirsch-Stoer algorithm, simplectic integrators etc. In all simulations an integration step is automatically chosen corresponding to assumed accuracy of calculations. A general description of the N-body codes is given by Aarseth (1985). For many years, Aarseth has developed his direct N-body algorithms. In application to galaxy groups and clusters, these algorithms are realized in the code N B O D Y 2 . This code includes the fourth-order fitting polynomial integrator, the individual time-step for each body, and the Ahmad-Cohen neighhour scheme (1973). This code is used by many explorers of dynamics of galaxy groups (e.g., Ishizawa et al. 1983, Ishizawa 1986, Navaxro et al. 1987, Governato et al. 1991, Diaferio et al. 1993). A necessary part of each N-body code is a system of units which the results of different simulations to be compared. The so-called "standard" units were recommended by I-Ieggie and Mathieu (1986), in which G=I, M0=l, E0=-1/4. (22) Here M0 is the total mass and E0 is the initial energy. These units are suitable for most types of bound systems, in particular for galaxy groups. This choice corresponds to a virial equilibrium r a d i u s / ~ = 1, and a mean crossing time r=

-

( 2 I E ° i)a/2 = 2v~.

(23)

In order to compare the results of computer simulations with the observational data, one should assign to the above dynamical units the appropriate physical values. The possibility of escapes due to gravitational interactions is usually taken into account in the N-body simulations. An escaping component is removed from the group when it is well enough isolated from other components and has positive individual energy. As a rule an effect of galaxy inelastic merging is also included in the N-body codes for galaxy groups, as a rule (for details see below). In standard simulations, an error checking is performed by the necessity of energy conservation. Even systems which include mergers, escape, and/or additional fixed external potentials may be treated in this way, since the total energy is adjusted accordingly. If the energy change exceeds the prescribed tolerance, the calculations may be repeated with reduced time-steps.

D ~ n i c s of Galaxy Grougs

3.3

17

Semioanalytical approaches

When realistic models of galaxy groups are investigated, one should take into account a number of effects, such as the gravitational field of diffuse intergalactic background, tidal stripping from the background mean field, dynamical friction on the background, collisional stripping etc. (see, e.g., Mamon 1987). All these effects were included by Mamon in his numerical code. The basic Mamon's scheme is a gravitational N-body code, in which galaxies and a diffuse background are all treated as single particles, with external parameters, such as mass, luminosity, internal energy, and tidal radius, but also with internal structure: the particles are assigned mass and luminosity profiles. This scheme requires only N + 1 particles, where N is the number of galaxies in the group, one particle representing the intergalactic background. With this method, the relative importance of a given physical mechanism can be assessed by simply turning it off. The particles representing galaxies are modelled as spherically symmetric mass distributions, with density p(r) = p(0)[(~) 2 + 1]-'~D, (24) where rc is the galaxy core radius. The index n = 2 for spiral or elliptical galaxies with massive halos ("halo" models) and n = 3 for ellipticals with constant M / L ratio ('modified Hubble' models). The mass distributions (24) are truncated at a tidal radius r = ft. The particle representing the intergalactic background is assigned a spherically symmetric modified Hubble mass distribution with rt = 15rc. The total force on each galaxy is the sum of three terms: the resultant force of the gravitational forces arising from each of the other galaxies, the gravitational force from the background, and the dynamical friction force that the background exerts on the galaxies. The force on the background is taken as the exact opposite of the sum of the forces felt by the galaxies (the 'recoil' effect). If the intergalactic background is treated as a smooth medium, one needs the collective effect of the encounters of galaxies with the much less massive particles (e.g., black holes, brown dwarfs, cold dark matter particles etc.), known as dynamical friction. The force of dynamical friction is described by the classical formula of Chandrasekhar (1943). In dense environments, tidal effects may significantly alter the member galaxies in the groups. Tidal processes come in two sorts (Maroon 1990a): collisional tides caused by the passage of another galaxy; the global background tide due to the non-uniform potential gradient of the background field. Due to the tidal processes, the galaxy is stretched, its morphology is disturbed, and the mass-loss may take place as some stars are accelerated beyond their escape velocity. With self-consistent simulations, collisional and background tides are implicit. In explicit-physics simulations, one must include the tidal processes by hand. More precisely, one must include a mass-loss, an internal energy-gain due to the stretching, a loss of orbital energy (tidal friction). This is usually done by analysing the results of self-consistent two-body encounters (see, e.g., the review by Athanassoula 1990 and references therein). An extreme case of tidal friction is such a great loss of orbital energy that an unbound galaxy pair can become bound, and even a bound pair can merge. Once again, this event occurs naturally in self-consistent simulations, but has to be introduced by hand in the explicit-physics models. In the last cases, one uses the merger criteria obtained from the numerical experiments of two galaxy collisions (see, e.g., van Albada and van Gorkom 1977, White 1978, Roos and Norman 1979, Aarseth and Fall 1980, Farouki and Shapiro 1982). The internal structure of galaxies is subject to change as the galaxies gain internal energy and lose mass, after tidal encounters with other galaxies and/or with the background. Maroon (1987) assumed the self-simnlar variations of the internal structure of galaxies due to the collisional

L G. Kiselevaand V. V. Orlov

18

stripping and merging. In his simulations, the background picks up mass tidally stripped off the galaxies, and acquires energy from the dissipation of galactic orbital by dynamical friction. The background is also assumed to evolve self-simulary. 3.4

Modified

N-body

codes

Using the self-consistent approach in the N-body simulations of the galaxy groups often requires a significant CPU time and memory for large N. This situation can be facilitated if one applies some modified N-body methods, such as tree codes (see, e.g., Barnes and Hut 1986), particle-mesh (PM) and particle-particle-particle-mesh (P3M) algorithms (e.g., Hockney and Eastwood 1981 and references therein; Efstathiou and Eastwood 1981; Efstathiou et al. 1985), vectorization of the N-body problem for supercomputers and connection machines (Hut and Makino 1988), using the specialized N-body computers of the GRAPE-type (Sugimoto et al. 1990). The basic idea of tree algorithms (Barnes and Hut 1986, 1989; Jernigan and Porter 1989 and references therein) is that, when computing the gravitational force at a given point, one can treat a distant localized region containing many particles as a single object. A tree-structure is used to partition the mass distribution of the system into a hierarchy of localized regions. Each node in the tree provides a concise description, in terms of total mass, center of mass position, and sometimes higher multipole moments, of the particles within the corresponding volume. If a more detailed description is needed, one looks at the descendents of the node. The leaves of the tree correspond to the particles. The number of levels in the tree is ~ logN, and construction of the tree takes ~ N log N operations. The number of operations can be reduced to ~ N using translation operators (Greengard and Rokhlin 1987). For comparison, direct-sum codes require N 2 operations in each time-step. Hernquist and Katz (1989) proposed a unification of smoothed particle hydrodynamics code and hierarchical tree method. A description of hybrid N-body-hydrodynamics code and its application to the study of galactic collisions is given by Hernquist (1991). In PM methods, Poisson's equation is solved on a fixed grid. The mass density is assigned to the grid from the particle distribution by an interpolation scheme. The potential is found from Poisson's equation. The force is either determined directly along with the potential or by finitedifferencing the mesh potential. The force on each particle is computed by interpolation from the grid values. The P3M codes combine the P M scheme for distant interactions and directsum algorithms for nearer particles. A new hierarchical P M three-dimansional N-body code was proposed by Villumsen (1989). This code is significantly faster than tree and P3M codes, and it has a much larger dynamic range in mass than these codes. The penalty is that only a small part of space could be treated at high resolution. In the last few years, supercomputers with pipeline architectures have become the most powerful tool for large scale scientific computations. The power of supercomputers derives from advances made in two different technologies: one is the increase in switching speed of elementary components; the other is the development of vector pipelines. Pipelined supercomputers have a SIMD (single instruction multiple data) architecture. A technological improvement is possible using multiple pipelines vazd/or multiple processors. There is yet another way to obtain a large computing power: using a large number of processors in parallel. This idea was realized in the Connection Machine (Hillis 1985). A comparison of gravitational N-body algorithms for supercomputers and Connection Machine was done by Hut and Makino (1988). The N-body problem is well constructed for vector/parailel decomposition. The force on any particle is evaluated independently of the forces on other particles. On vector processors, one can use very long vectors. On the Connection Machine, we can use a large number of processors.

Dynamicsof Galaxy Groups

19

Since the force calculation in the N-body problem is quite expensive, special-purpose hardware for gravity force calculation would be very useful (Sugimoto et al. 1990). Such a hardware, called GRAPE (GRAvity PipE), was built by Ito et al. (1990). GRAPE calculates the right-hand sides of equations of motion in the N-body problem. The system GRAPE is comprised of two following components: a host computer and a special-purpose pipeline. The development of special-purpose hardware in the form of Newton-force-accelerators is based on analogy to the idea of using floatpoint accelerators to speed up workstations. The detailed information about the GRAPE hardware design is given by Ito et al. (1990). For software aspects, see Makino et al. (1990). The above mentioned modern computer facilities may be successfully used in the self-consistent simulations of dynamics of the galaxy groups.

4 4.1

R e s u l t s of c o m p u t e r simulations General features of evolution

The galaxy groups are likely sites for strong interactions and merging between galaxies and may significantly evolve in a fraction of the Hubble time Ho 1 . Realistic dynamical theories for the evolution of small groups are difficult to construct, because an analytical approach is too complicated, and classical statistics does not work. Under such conditions, computer N-body simulations are the constructive tools to study this problem. The main features of dynamical evolution and state of galaxy groups were discovered in some computer simulations (see, e.g., Roos and Norman 1979; Carnevali et al. 1981; Ishizawa et al. 1983; Cavaliere et al. 1983; Giuricin et al. 1984; Barnes 1984, 1985, 1989; Ishizawa 1986; Maroon 1986, 1987, 1990a, 1992b; Navarro et al. 1986, 1987; Chernin et al. 1988; Kiseleva and Chernin 1988, 1989; Kiseleva 1989; Anosova et al. 1989, 1990b, 1991; Chernin and Ivanov 1990; Governato et al. 1991; Pech and Chung 1991; Chernin and Mikkola 1991). The first conclusion from statistical N-body simulations (Kiseleva and Chernin 1988; Anosova et al. 1989) is that small galaxy groups do not reach any stationary state similar to the equilibrium one of many-body gravitating systems. The typical evolutionary behaviour is that in which changes of dynamical structure take place from time to time. As a rule, a group 'forgots' its initial state during one or two crossing times and shows all typical features of evolution: close approaches of two or more galaxies, merging, formation and destruction of binary subsystems, ejections of components with return, escapes of bodies, intermediate states of simple interplay. A chaotic dynamics can develop in the small galaxy groups with a characteristic time scale less than the age of these systems. The main result of many simulations (see the review by Maroon 1990a) is rapid merging of galaxies leading to group coalescence. One would expect that the merging time should be much shorter in dense groups compared to loose ones. An orbital decay by dynamical friction of galaxies against an intergalactic background of dark matter is significant in speeding the merging process. During the evolution, a transition of orbital energy and angular momentum of galaxies to their internal energies and spins takes place. This mechanism could explain the origin of galaxy rotation (Chernin 1977, Kiseleva and Orlov 1987). Carnevali et al. (1981) showed that the exchange of energy from orbital to internal motions increases the merging instabilility which dominates the dynamics of galaxy groups and prolongs the collapse phase; this process allows the groups to be around for a long time before they produce a virialized remnant.

20

4.2

L G. Kisele~a and V. V. Orlov

Dynamics

and configurations

The dynamical status of galaxy groups may be statistically connected with the distributions of configurations (Kiseleva and Orlov 1989; Anosova et al. 1990a; Chernin and Ivanov 1990). Kiseleva and Orlov (1989) studied the dynamical evolution of simulated galaxy triplets by an explicit-physics method and compared the configurational parameters of simulated and observed triple galaxies. The configurations of simulated triplets were fixed in equal time intervals At -- 0.3T~ during 10T~ (T~ is the crossing time of a triplet). The actual configurations were projected to a few 'planes of sky' which were randomly inclined to the plane of triple system. The configurational parameters B, C (see formula (11) in Section 2 were fixed for projections. The average values of these parameters were compared with the corresponding ones for the observed galaxy triplets (Karachentseva et al. 1979, 1988), as well as the results of static Monte-Carlo simulations. For simulated triplets, there is a significant tendency to alignment, and any tendency to hierarchy is absent. The tendency to alignment is developed during the dynamical evolution. This trend is also observed for the systems with expanded hidden mass. Chernin and Ivanov (1990) considered a distribution of imaging points for simulated triplets within the region D (Figure 1). The imaging points were plotted during the dynamical evolution. The authors noted a tendency for points to fill the right lower subregion corresponding to hierarchical configurations and alignments. This trend was revealed only for models without dark Inass.

Diaferio et al. (1993) found that the distribitions of kinematic and dynamical quantities of the groups catalog by Ramella et al. (1989) selected from the CfA redshift survey can be reproduced by a single simulated group in the collapse phase 'observed' along different line of sights. This result shows that a) projection effects dominate the statistics of these systems, and b) observed groups of galaxies are probably young in the sense that they are still not virialized, The last result is consistent with the previous suggestions that groups are dynamicaly young (e.g. Rose 1979, Barnes 1985, 1989, Giuricin et al. 1988, Maia and da Costa 1990). 4.3

Compact

galaxy groups

The nature of compact galaxy groups was studied not only using the static Monte-Carlo models (see Section 2), but also by the dynamical N-body simulations (Maroon 1987, 1992b). Mmnon carried out a series of dynamical explicit physics simulations of loose groups in order to estimate two quantities: 1) the frequency of formation of bound dense subgroups within loose groups; 2) the frequency of compact subgroups as chance alignments. The simulations (Maroon 1993b) were run for 2.5 Hubble time Ho 1. The simulations were viewed (in projection along three orthogonal axes) 80 times per Hubble time. For each set of parameters (Maroon 1987), 100 simulations with different initial positions and velocities were run. Thus, the statistics (Maroon 1993b) was typically 100 times better than those of Maroon (1987). The standard runs involved loose groups of initially eight galaxies, sampled from a Schechter (1976) luminosity function. The dark matter was placed either mainly within galaxy halos, or in a common envelope. The most important result of these simulations is that one-dimensional chance alignments are typically 10 times more frequent than three-dimensional dense subgroups. The frequency of chance alignments increases with increasing number of galaxies and decreasing parent group size, as predicted by Wvlke and Maroon (1989) for static models. Chance alignments ought to be rich in binaries, which explains the numerous features of dynamical interaction in the Hickson compact

Dynamics of Galaxy Groups

21

groups. If the dark matter is in the individual halos, the dense subgroups are mostly bound, but if the dark matter is in the common envelope, the dense subgroups are usually unbound, because the galaxies react mainly to the potential of the full groups. The recent work of Athanassoula and Makino (1992) presented preliminary results of selfconsistent N-body simulations of the evolution of compact groups. The groups consist initially of five 'elliptical galaxies', modelled by isotropic Plummet spheres, and the final product of the simulation is one merger remnant. The median virial mass-to-light ratio 40h Mo/Lo is larger than the typical one of galaxies by an order of magnitude (Hickson 1990). Either the groups are unbound or they contain a significant hidden mass. The conventional picture (see, e.g., Barnes 1985 1989) is that compact groups evolve from looser groups and then are merged on a short time scale. A reasonable estimate of the typical life-time of compact groups is of order 0.1 Ho I (White 1990).

4.4

Tidal interactions and merging of components

In the dense galaxy groups, the tidal effects are strong enough to alter significantly the morphology of galaxies. This is illustrated in the self-consistent simulations by Barnes (1989), who considered the groups of six galaxies consisting of 8k - 16k particles. Barnes showed that tidal changes of morphology, as tails and bridges, take place due to gravitational interactions. A typical result of interactions is the merging of galaxies in a single object. Finally, the coalescence of all group members is observed, as a rule (see, e.g., Roos and Norman 1979; Barnes 1985, 1989; Maroon 1987). A review of the studies of merging process was performed by Maroon (1990a). The estimates of the mean time t,~ between mergers in the simulated groups are (0.2 - 4) tyi, where fly is the half-mass free-fall time of the group 3

r.l R~, ~1/2 t Y f = 2"GM" "

(25)

Here Rh is the half-mass radius of the group at maximum expansion; M the mass of the group. The collapsing groups merge at roughly the same rate as virialized groups. Maroon (1990a) noted that the merging rates in explicit-physics simulations (Roos and Norman 1979; Mamon 1987) are on average three to four times larger than the ones in the self-consistent models (Barnes 1985, 1989; Ishizawa 1986). These discrepancies may be explained as follows. The explicit-physics simulations use the merging criteria found from the studies of two-galaxy collisions. However, the other galaxies in a group come in and pump energy into the merging pair. This effect decreases the merger cross-sections in the groups compared to those in two-galaxy collisions. For the groups with a dominant intergalactic background, the above effect is not seen. A presence of dark matter in the groups significantly influences the merging processes. The lifetime of dense groups depend on where the dark matter is placed. Maroon (1992b) concluded that if the dark matter lies in galactic halos, the galaxies merge rapidly and, e.g., the groups of eight members survive for a typical time Hoa/30. If the dark matter is distributed in a common group envelope, the group survives longer: the lifetime of similar groups is roughly Hol/8. In the same time, Athanassoula and Makino (1992) found from their self-consistent simulations that compact groups of five elliptical galaxies with a common dark halo evolve (merge into one object) much faster than groups with individual halos. In the case of a common halo, the galaxies have smaller merger cross-sections, but the galaxy orbits decay towards the group center due to dynamical friction against the background matter. These results are also different from ones

22

L G. Kiseleva and V. V. Orlov

of Navarro et al. (1987). In the last simulations the common halo was modelled as a rigid potential and they didn't include the decelleration and subsequent inwards decay of galaxies due to the dynamical friction of the~common halo. This leads to larger relative velocities at the close approches of galaxies and, as result, to less merging according to their merging criterion. Governato et al. (1991) gave an example of the long-lasting dense group of five galaxies with dark matter halos. They used the self-consistent N-body simulations at a special choice of initial conditions: two most massive galaxies in the group had a circular relative orbit. Mamon's simulations (1987, 1990a) showed that no more than a few percent of dense groups can survive for over a Hubble time. Kiseleva and Orlov (1993b) studied the effect of distributed dark matter on the merging process in the galaxy triplets. These explicit-physics models used the Roos and Norman (1979) criterion of merging, the dynamical friction being neglected. The increasing of the dark mass density accelerates the merging rate. One of the interesting cosmogonic problems is the origin of galactic rotation. One of the possible explanations of this phenomenon is the tidal rolling due to the interactions with neighbour galaxies in the dense groups (Lambas et al. 1985). The other possibility is the transition of orbital angular momentum to spin momentum in the case of coalescence of two gaseous protogalaxies inside the small dense groups (Chernin 1977). This hypothesis was supported by numerical simulation of the triplets of gaseous protogalactic fragments (Kiseleva and Orlov 1987; Anosova et al. 1989). As the merging criterion, the results of hydrodynamical simulations (Barausov et al. 1988) were used. For the triplets without distributed dark matter, the frequency of merging at the first double approach of fragments is from 50% to 96% when the radii of fragments change from 0.001 to 0.1 of the mean size of triple system. The average spin momenta of mergers are in agreement with those of disk galaxies. The dark matter prevents the process of merging at the early stages of evolution of the protogalaxy triplets, different from the case of galaxy triplets, where the hidden mass helps the merging. There are other approaches, besides N-body simulations, to study the merging in cosmic structures, in particular in the galaxy groups. One of these ways was developed by Cavaliere et al. (1992), who considered a kinetic equation describing the mass distribution evolving under aggregations by merging. They obtained the numerical and analytical solutions of this equation. Two possible regimes of evolution of the galaxy groups were found: self-similar evolution and a gravitational phase transition over a few crossing times. Such phase transition in the groups leads to the formation of a giant elliptical or cD-like galaxy. These results are not contradictory to observations of those groups dominated by a cD-like galaxy and to the N-body simulations. 4.5

Dark

mass

estimations

A numerical experiment is a constructive method to study different problems connected with the presence of hidden mass in the galaxy groups. It concerns, in particular, the amount of dark matter and its distribution within groups. An application of mass estimators described in the Section 2 (formulae (16)-(19)) to the individual observed groups gives art uncertainty of actual mass estimations up to 4 orders of magnitude (Kiseleva and Chernin 1988; Anosova et al. 1991). Such a large uncertainty is caused by two main reasons: 1) the standard virial theorem is not valid for the small galaxy groups because of their non-stationarity; 2) the projection effects may introduce a strong additional error in the dynamical mass estimations. The first item is illustrated by the time-dependencies of the virial coefficient k (eq.14). These

Dynamics of Gala~ Groups

23

dependencies (Kiseleva and Chernin 1988; Anosova et al. 1989, 1991) for the bound galaxy triplets and quintets show the large variations of k from 0.01 to 0.99 in the absence of hidden mass. These variations may lead to errors of up to two orders of magnitude in the individual mass estimations. The projection effect is that the mass estimators (16)-(19) use the positions of galaxies on the sky and their radial velocities instead of the three-dimensional coordinates and velocities. In order to measure the last effect for galaxy triplets, the following procedure was carried out (Kiseleva and Chernin 1988; Kiseleva 1989; Anosova et al. 1991). During the dynamical evolution of simulated triplets with known (visible and hidden) total mass, the positions of components were projected to 200 'planes of sky' distributed randomly and the three-dimensional velocities were transformed to the corresponding 'radial velocities' orthogonal to the 'plane of sky'. The dynamical masses (16)-(19) were calculated using the above mentioned projected values. The more than 100 histograms constructed of these masses showed the error in the estimation of individual mass of a triplet may achieve more than 3 orders of magnitude. The above two types of uncertainties render impossible a reliable individual mass estimate for observed small galaxy groups. Another way to evaluate the individual triplet masses was examined by Kiseleva (1989), Chernin and Mikkola (1991), Anosova et al. (1992). In computer simulations of galaxy triplets with dark matter, a database of about 3 x 104 projected models was compiled. From this database, the examples to be in agreement with actual galaxy triplets (Karachentseva et al. 1979, 1988) were selected. The biggest numbers (100 and 84 cases) of similar examples were found for two galaxy triplets. However, a dispersion of mass estimations about 1.5 orders of magnitude is observed even in these cases. Thus, this algorithm does not allow us to estimate with certainty the total mass of individual galaxy triplets. A statistical method of mass estimation for a homogeneous sample of galaxy groups was proposed by Kiseleva and Cheruin (1988), Kiseleva (1989), Anosova et al. (1992). The first step consists in the determination of medians for projected mean harmonic mutual separation R and r.ra.s, peculiar radial velocity V of the sample of galaxy groups under consideration. The second step is the modelling of galaxy groups with different mass ratio, value of hidden mass, and initial conditions, and compiling of the simulated samples with the same number of objects as in the observed sample, taking into account the projection effects. The third step is a choice amongst the simulated samples whose R and V are the same as in the observed sample within 10%. For the selected samples, the average hidden mass within the group volume is calculated. Then the mean dark mass is defined by all selected samples. The estimation M0 is assumed to be the most probable one for the observed ensemble of galaxy groups. The authors have applied the above method to the sample of 46 probably accordant galaxy triplets from the list by Kara~:hentseva et al. (1979, 1988). They found the value Mo = (4.3 d: 1.2) Mr, where Mt is the visible mass of the triplet. Diaferio et al. (1993) gave the median mass of Ramella et al. (1989) galaxy groups indicated by the N-body simulations as (0.5 - 1.0) × 1014M~. The median of MVT for observed groups is 0.2 × 1014M®, so there is underestimate by an additional factor of ,,~ 1.8.

4.6

Groups within galaxy

clustering

The galaxy groups are often the parts of larger structures, as the galaxy clusters, superclusters, filaments etc. (see, e.g., Williams 1984; Focardi et al. 1984; West 1989; Kalloglyan and Unanyan 1990). The dynamical evolution of galaxy groups within the galaxy clustering was investigated by Bhavsar et al. (1980, 1981), Evrard (1986, 1987) by cosmological N-body simulations for N ,,~ 103. These authors considered the evolution of the large-scale distribution of galaxies and distinguished the groups as

24

L G. Kiseleva and V. V. Orlov

the regions of enhanced density. Bhavsar et al. (1980) estimated the fraction fg of galaxies in groups as a function of surface density enhancement 8:

f0(fl) =/~-a.

(26)

Values of/~ were considered from 1.5 to 10000. In this interval, the dependence (26) has a universal character at a ~ 0.5 for different initial conditions and cosmological models. The fg(/~) curves and the mean number of galaxies per group are similar for the models and observations. The multiplicity functions of the galaxy groups are also in good agreement with and support the gravitational instability picture (Bhavsar et al. 1981). Evrard (1986, 1987) simulated the evolution of cosmological N = 800-body models with hidden mass. Each galaxy consists of one luminous and 25 dark particles. Hidden mass is 90% of the total mass. At the end of the calculations, the modelled catalogues of groups with different multiplicities were compiled. The relative propagation of small galaxy groups is similar to the observed one (Huchra and Geller 1982). However, the typical sizes and velocity dispersions axe in disagreement with observations. Some segregation of luminous and dark matter takes place. The constructed profiles of mass-to-light ratios in the groups are as follows: M / L ( < r) ~ rl/2.

(27)

This profile does not depend on the multiplicity. About 2/3 of the toted mass connected with groups is outside the visible part of the groups.

5

Conclusions

This review contains the results of observations and computer simulations of loose and compact small galaxy groups during approximately the last decade. The main results described in the review may be summarised as follows: 1) A number of objective selection criteriaallow us to construct a few catalogues of galaxy groups with known redshifts. 2) The probably accordant and discordant redshift components were revealed in some groups. 3) A number of dynamical mass estimators was proposed; the obtained estimations support the presence of significanthidden mass in the groups. 4) The merging and tidal interactions are the dominant processes in the evolution of galaxy groups; these processes may trigger the starbursts and nuclear activity in the interacting galaxies and merger remnants. 5) Some groups may be parts of larger galaxy aggregations and can be used as the tracers of the large-scale structures of t h e Universe.

6

Acknowledgments

The authors are very grateful to S.J.Aarseth for useful discussions as well as to Vistas editor A,E.Roy for his correction of the manuscript. This work was partially supported by a grant from the Royal Society.

7

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30

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