A, B o k s e n b e r g , Mon. N o t . R. A s t r o n . S o c . , 1 9 3 , 415 ( 1 9 8 0 ) . J . A. C o o k e , D. E. E m e r s o n , B. D. K e l l y , a n d H. T. ~ a c G i l l i v r a y , S o c . , 196, 397 ( 1 9 3 1 ) . 4. J . S. Bowen a n d A. H. V a u g h a n , P. A. S. P . , 85, 174 ( 1 9 7 3 ) . 5. N. A. T i k h o n o v , S o o b s h c h . SAO AN SSSR, 3_99, 40 ( 1 9 8 3 ) . 3.

Mon. N o t .

~. Astron.

REVIEWS

MULTIPLE TRAPEZIUM TYPE SYSTEMS L. V. Mirzoyan and G. N. Salukvadze

Investigations of multiple Trapezium type systems are reviewed and discussed. It i s s h o w n that the existing observational and theoretical investigations confirm the fundamental feature of these systems -- their dynamical instability.

i. Introduction Before the discovery by Ambartsumyan [I] of stellar associations -- loci of stellar formation in the Galaxy, where the generation of stars continues into our own time -- all stellar systems were regarded as being dynamically stable both in stellar dynamics and in astronomy in general. The discovery of stellar associations showed, however, that there may also be in the Galaxy systems which were dynamically unstable during the period of their formation and are at the present time expanding. The theoretical prediction that stellar associations expand [2], confirmed for the first time from observations by Blaauw [3], was of immense significance for the problem of the origin and evolution of stars and stellar systems. Subsequently morphological study of the stellar associations showed that among the associations are found multiple star systems which must possess a still greater degree of dynamic instability than the associations themselves as a whole. On the basis of this a new type of multiple star was distinguished (see, for example, [4]) which is characterized by an extraordinarily high degree of dynamic instability. The arguments ran as follows. In systems consisting of two stars (binaries) both components of the system revolve around its center of gravity and the motions take place in accordance with Kepler's laws. They are periodic and may continue for a very long time. In this case the system must be dynamically stable. In systems with a large number of stars, in the overwhelming majority of cases, a structure is observed which is also linked with the Keplerian or almost Keplerian motions; for example, a triple star equals a binary plus a comparatively distant third component: a quadruple star equals a binary plus a binary at a distance many times exceeding the mutual separations of the components of the binary, etc. It is obvious that these systems also must be dynamically stable. All systems having this type of structure were termed multiple systems of the o!dinary type [4]. There also exists however stellar systems whose structure differs greatly from the structure of the systems mentioned above. In these systems there are at least three components such that the mutual spatial separations between them are of the same order. It can be shown that the motions in such systems must be of a different type, so that they m u s t be dynamically unstable. It turns out that a multiple system which has this type of spatial configuration must disintegrate fairly rapidly. The convention may be adopted that the mutual separations of the components are of the same order if they Byurakan Astrophysical Observatory; Abastumani Astrophysical Observatory. Translated from Astrofizika, Vol. 21, No. 5, pp. 399-417, September-October, 1984. Original article submitted April 26, 1984.

0571-7132/84/2105--0567508.50

9 1985 Plenum Publishing Corporation

567

differ by not more than a factor of three. One such multiple system of stars is the wellknown Trapezium around the star G' in Orion, after which multiple systems of the new type have been given the name multiple systems of the Trapezium of Orion type or simply Tra~ pezium type [4], and their configurations are Trapezium type configurations. The present review gives an exposition of the main results from studies of Trapezium type multiple systems during the period since they were recognized as a special type. 2. The Youth of Trapezium Type Multiple Systems General theoretical considerations permit us to assume that a system having a Trapezium type configuration cannot exist for longer than the time necessary for some revolutions of its components about the common center of gravity. Moreover the time taken for a Trapezium type system to disintegrate must, naturally, be dependent on the sign of the total energy of the system, that is, on the original velocity distribution of its components. Calculations show [4] that the disintegration time for Trapezium type multiple systems is of the order of 2-106 yr if the system has a negative total energy, and of the order of 105 and less if the total energy of the system is positive (see following section). So whatever the sign of the total energy it must be reckoned that Trapezium type multiple systems are among the youngest objects in associations~ Thus the first indication of the youth of Trapezium type systems was obtained theoretically from the concept of their dynamic instability. However subsequently this conclusion, which is central for the problem of the origin and evolution of stars, received many confirmations based directly upon the observational data about these systems. We shall now consider some of these confirmations. At the start of the fifties Ambartsumyan [4] used the data from Aitken's New General Catalog of Binaries (ADS) [5], which contains 17180 binaries and multiple stars, to show that among the multiple systems whose main (that is,brightest) stars belong to the spectral classes O--B there is a considerable percentage of real Trapezia. The point is that not all systems observed as Trapezia are real. Some multiple systems which do not in reality have Trapezium type configurations may be observed on the celestial sphere as Trapezium type systems as a result of projection. Such systems have been given the name of ~geudotrapezia. Ambartsumyan [6] calculated the probability that a multiple system which does not have a Trapezium type configuration would turn into an observed Trapezium as a result of projection. It turned out to be 0.08 for a triple system and greater for systems of higher multiplicity. After allowance for the comparative frequency of incidence of triple and quadruple stars and also the possible effect of systems of higher multiplicity, the weighted mean probability that a multiple star of the ordinary type would turn into a pseudotrapezium was taken as P = 0.09. After taking into account the proportion of pseudotrapezia among observed Trapezia, the important result already mentioned was obtained, that real Trapezia are encountered in the main among the multiple systems with main stars in the spectral classes O--B. If we bear in mind that OB-stars are the characteristic population of OBassociations, and consequently are very young, we can reach the conclusion that Trapezium type systems are also very young formations. In other words, the life of real Trapezia must be shorter than the life of OB-stars. In this short time a Trapezium type multiple system succeeds in distingrating either completely or partly, losing some of its members, and in turning into a multiple system of the ordinary type, with a smaller number of members. This is confirmed by Table I, which was compiled by one of the authors [7] on the basis of the Index Catalog of Visual Binaries [8], Which contains 64247 binaries and multiple stars. The second column in Table 1 gives the number of multiple systems whose main stars belong to the spectral classes shown in the first column; the

568

TABLE I. Statistics of Hultiple Stars According of the Index Catalog of Visual Binaries.

Spectral class o f main s t a r

Total number of mult. stars

Number of observed Trapezia

Calculated numberof pseudotrapezia

Probable number of real Trapezia

to the Data

Relative number of Trapezia (%)

O --B2

39

5

34

58

B3-BS--B

23

6

17

24

B8--B9

25

11

14

12

A

60

35

25

6

F

41

28

13

4

G

33

20

13

6

K

37

14

23

15

8

1

7

64

146

47

99

19

M Unknown

spectrum

526

next two columns give the number of observed Trapezia and the (calculated) number of pseudotrapezia, and the last two columns give the probable number of real Trapezia and the relative number of Trapezium type systems in all the multiple stars [9]. The data in the last column of Table 1 are convincing evidence in favor of the conclusion [6] that real Trapezia are encountered in the main among multiple systems whose main stars belong to the spectral classes O--B. Original evidence of the use of Trapezium type multiple systems is contained in Agekyan's study [I0]. On the basis of the visible distribution of triple star configurations he obtained the actual distribution of the latter. The distribution so obtained shows that the proportion of unstable (Trapezium type) systems is greatest for the spectral classes 0 and B. This means, from the conclusion of [6], that Trapezium type systems consist predominantly of young stars, that is, they are young formations. The conclusion that Trapezia have a tendency to be found in systems consisting of young stars was reached also by Sharpless [ii] through using data on Trapezium type multiple systems which are found in emission nebulae. These data show that a strong tendency is observed on the part of the brightest (main) components of these systems to have spectral classes which are earlier than 09. We note that Sharpless's list of Trapezium type multiple systems [Ii] contained 25 multiple stars. An observational confirmation that Trapezium type systems are young which is closely connected with what has already been mentioned, is their abundance in stellar associations and young clusters (see, for example, [12-15]). At the same time an abundance of Trapezium type systems is observed not only in associations where the characteristic stellar population consists of hot giant and supergiant stars (OBassociations), but also in T-associations, whose characteristic population consists of stars like T Tau. In recent years 120 Trapezium type systems containing stars like T Tau have been discovered in T associations by one of the authors [16, 17]. Before that Zakirov [18], using a less strict criterion for selecting Trapezium type multiple systems, distinguished 46 systems of that type in T-associations. Another piece of evidence for the youth of Trapezium type multiple systems is the existence of systems with a Trapezium type configuration among known young objects. For example, some infrared radiation sources at a wavelength of 2.2 ~m coincide in their coordinates with known Trapezium type systems [19], which cannot be regarded as accidental. Quite recently Gyul'budagyan [20] discovered eight close Trapezium type systems consisting of infrared sources and compact radio sources. It should be added that after the existence of real Tr~nezium type systems was discovered, Ambartsumyan [4] in 1954 compiled the f i r s t catalog of Trapezium type multiple systems, which contains I08 systems; he used in the main data from the Aitken catalog [5]. In all these systems except one, the main stars, in known cases, have spectral classes 0 or B. In 50 cases the spectral class of the main stars is 569

unknown. As the author himself notes [4], this catalog is not complete even in relation to the multiple stars contained in the Aitken catalog. The object of compiling the first Trapezium type system catalog was to distinguish those Trapezia which are of primary interest for further research. Later, in 1978, one of the authors [7], using the richer and more accurate data of the Index Catalog of Visual Binaries [8], published the new Abastumani catalog of Trapezium type multiple systems, which contains 412 systems. Comparison of the Abastumani catalog of Trapezium type multiple systems with Ambartsumyan's catalog showed [7] that of the latter catalog 41 Trapezia were not in %he Ahastumani catalog; on the other hand the Abastums/li catalog contained 33 new Trapezia from the Aitken catalog [5] which did not figure in the first Trapezium type system catalog [4]. Here two circumstances should be noted. In the first place, the criterion for distinguishing Trapezia used in compiling the Ambastumani catalog is somewhat stricter. By this criterion [7] a multiple star is a Trapezium type system i f the greatest of the three mutual separations of the components, taken as separation of the same order, is greater than the least of them by a factor not greater than 2.6. At the same time 3.0 was taken as the limiting value of this ratio in the catalog [4]. However this difference is insignificant, and in both cases a system should be regarded as Trapezium type system if it satisfies one of these criteria. Secondly, unlike the catalog [4] the Ambastumani catalog [7] contained also Trapezium type multiple system's of which the main stars belong to the spectral classes A, F, G, and K. As can be seen from the data in Table i, the existence of such Trapezium type systems is not probable, however it is not excluded. It is these two circumstances which cause the differences mentioned between the catalogs of Trapezium type multiple systems compiled at Byurakan [4] and Abastumani [7]. As regards Trapezium type mutiple systems of which the main stars belong to the spectral class M, their relative number is not less than the relative number of Trapezia with main stars of the spectral classes O and B, as can be seen from Table I~ The same result was obtained earlier in [6]. This is definitely evidence Of the existence among them of real Trapezium type systems. However the total number of Trapezium type multiple systems with main stars of the type M is very small for statistical conclusions. It is essential to add that among the systems contained in the catalogs mentioned there may be a considerable number (up to 10%) of pseudotrapezia, as was no%ed above. ~'~ether actual systems belong to the pseudotrapezium type we shall only be able to discover in the future on the basis of a study of them from all angles (proper motions, spectral classes, and separations of the individual components of the system)~ We must finally mention the catalog of Trapezium type systems compiled in Mexico on the basis of the Index Catalog of Visual Binaries [8] which was used in the work done by Allen and Tapia [21] on the statistical investigation of Trapezium type multiple systems. This catalog, which contains more than 900 Trapezium type systems, has unfortunately not been published so far, and it is as yet not possible to judge the criteria used in compiling it. 3. The Dynamic Instability of Trapezium Type Systems Ambartsumyan [4] was the first to show that the nature of the motion of stars in Trapezium type multiple systems must differ greatly from the nature of the motion in multiple systems of the ordinary type. In ordinary multiple systems the motion of the components is Keplerian or almost Keplerian. It is clear that motions such as this may continue throughout a very 1one period, and so such systems must be dynamically stable. In t h i s r e s p e c t multiple systems of the ordinary type differ greatly from galactic clusters, where as a result of the close passage of individual stars past one another processes must occur in which kinetic energies are exchanged, and that in the last analysis leads to the establishment of a Maxwellian distribution of stellar velocities.

570

As a result stars which have attained velocities sufficient to overcome the force of attraction in the system gradually leave the cluster. A hew batch of stars leaves the cluster when after the relaxation time of the system has elapsed a ~{axwellian distribution of stellar velocities is again established in it. Multiple repetition of this process leads with time to the gradual breakup of the cluster [22]. Trapezium type multiple systems are similar to galactic clusters, differing from them only in that the number of stars in them is considerably less. So in order to determine the relaxation time T we may use the familiar equation derived for stellar clusters (see [23]):

T = 8.8-105 [/'

SNR ~ m

where N is the number of stars in the system, and m is the mean mass of the stars.

1 lg N - - 0.45

years,

R is the radius of the system in parsec,

By using this equation in the limiting case, when N is equal to several units, R is of the order of lO 000 a.u., and m is of the order of the Sun's mass, Ambartsumyan obtained [4]: T = 2-106 years. This means that a Trapezium type multiple system succeeds in disintegrating while each star in it completes in all only a few revolutions around the system's center of gravity. Clearly this estimate relates to Trapezium type multiple stars which have negative total energy. On the basis of general theoretical considerations it may however be admitted that many Trapezium type systems may have positive total energy. In this case the age of a Trapezium type multiple system must amount to only 105 years and less [4]. The firs% study devoted to investigating the motion in Trapezium type multiple systems on the basis of observational data, and which was concerned with the prototype of this class of multiple stars, the Orion Trapezium, was carried out in 1953 by Parenago [24]. The results of a more detailed study of that system were published in his article [25]. Since the final results of both these articles coincide fully, we shall consider only the latter article, which contains the details of this study. Parenago [25] considered six components (A, B, C, D, E, and F) of the Orion Trapezium for which there are numerous m i c r o m e t r i c measurements of their mutual separations and their positional angles. He used all the available micrometric measurements (a total of 1212 measurements in various combinations) carried out in the course of 120 years (1820-1940). Thanks to a special method which he carefully developed, Parenago [25] succeeded in using all this material and to a satisfactory degree of accuracy obtained data on the positions and proper motions at various epochs of the six components listed above of the Orion Trapezium. The results of Parenago's study [25] point unequivocally Orion Trapezium in its projection on the celestial sphere (Fig. also in space.

to an expansion of the ]), and consequently

Less reliable results based on the proper motions of the stars and also providing evidence of the expansion of the Orion Trapezium were obtained by Franz [26] and Strand [27], who determined the ki~nematic age of this multiple system as I04 years and 1.4-104 years, respectively. Unfortunately, the studies carried out by these authors and containing the results indicated have not yet been published. In 1957 the question of the stability of the Orion Trapezium was investigated by Akhundova [28], who used the photographic observations of S. K. Kostinskii made in ~he period 1909-1933. Comparing these observations with her own, she arrived at the conclusion that this system is stable. However if it is borne in mind that the proper motions of the components of the Orion Trapezium are in all cases small, as is shown by the results of Parenago's study [25] , it may be thought the Akhundova's results [28], which were obtained on the basis of photographic material whose quality was not high, cannot serve as the basis for such a decisive conclusion (because of the brightness of the components of the Trapezium their images on the plates obtained

571

-4.9,, n

B -5"27'10"

E/ A..~

§

1.6

~-4.5

/D 20"

F IIoC

[-

4 km/sec

|

!

5h30m22 s

21 s

Fig. I. Expansion of the Orion Trapezium with respect the component C according to [25]. The arrows indicate the relative proper radial velocities in km/sec. by Kostinskii blend together). The kinematics of Trapezium type multiple systems were considered in 1974 in the exhaustive study by the Mexican astronomers Allen, Poveda, and Worly [29]. For all components of Trapezium type systems in Ambartsumyan's catalog [4] the authors gathered together from known catalogs and lists of binaries the available measurements of the mutual separations and positional angles. Then from these systems those Trapezia were chosen in which at least three stars are observed and there are for them a minimum of four different measurements of the relative positions. As a result it emerged that of the 108 Trapezium type systems in the catalog [4] only 42 satisfy the requirements given above. Then for each of these remaining 42 "well-observed" Trapezia graphs were drawn showing the dependence of the m e a s u r e d s e p a r a t i o n s of the components on the time of observation. After analyzing the appearance of the graphs so obtained the authors concluded that complete contraction or expansion is not observed in any of the Trapezia considered. It is only in 16 Trapezia that one or two components of the system display a marked separation from the main star. In particular in the Orion Trapezium the marked separation of the component E was established and a barely noticeable separation of the components B and C from the main star A. In connection with the work by Allen, Poveda, and Worly [29] it should be noted that the results obtained in it have a negative conclusion reached by the authors on the basis of those results are not in accordance with each other. The point is that the mutual separations of the components in the system from the main star as dfscovered by the authors are in 16 cases, including the Orion Trapezium, evidence that in the corresponding systems motions are taking place which are directed away from their center of gravity, that is there are indications of expansion.* The kinematics of Trapezium type multiple systems was considered in detail in studies by one of the authors (see, for example, [SO]). This research relates to Trapezium type systems which have main stars belonging to the spectral classes O--B2, and among these there must be many real Trapezia. The systems studied were chosen from the Abastumani Trapezium Catalog [7], which turns o~t to include Sg Trapezia like this. The Orion Trapezium was excluded from consideration, vestigation into it having been given above.

the results of the in-

For the remaining 38 Trapezium type multiple systems the results were collected *The eight Trapezium type systems in which Allen, Poveda, and Worly [29] did not find any changes in the mutual separations of the components also exhibit clear signs of expansion according to [30].

572

1'.'5

AB ,,,IL ~

1.3

~

~ ''

I

9

I

AC

!

I

I

!

9

,B

/"

/

3.9

/

/

/ / / /

/

/

3.7 I

t

I

I

I

I

AO 9.3

j t ..~ ....-

8.5

I

1880

@ I

I

i

,

I

I

1960

1920

F i g . 2. R e l a t i o n s indicating expansion of the multiple Trapezium type system ADS 719 a c c o r d i n g t o [ 3 0 ] . The a b s c i s s a is the time of observation t and t h e ordinate the angular distance p (in arc seconds) of the component from the m a i n star.

of measurements of the relative positions of the components published in various binary catalogs, as w e r e d a t a from t h e b i n a r y c a r d c a t a l o g s o f t h e o b s e r v a t o r y at Nice (France) and at the Naval Observatory (USA), a n d a l s o d a t a d e t e r m i n e d b y t h e a u t h o r f r o m p h o t o graphic observations carried out at the Abastumani Astrophysical Observatory. Of t h e s e 38 T r a p e z i u m t y p e m u l t i p l e systems only the be sufficiently v o u c h e d f o r by o b s e r v a t i o n s (the majority of and n o t l e s s t h a n f i v e o b s e r v a t i o n s a r e made o f t h e m ) : ADS 4728, 5322, 5977, 13374, 13626, 14526, 14831, 15184, 16095,

following !5 turned out to the components are observed 719, 2783, 2843, 3709, 4241, 16381.

The o b s e r v a t i o n a l material used, which contains the mutual separations of the components of the Trapezium type systems mentioned above, covers in most cases a time interval o f m o r e t h a n 100 y e a r s . The e a r l i e s t observations are in the main the work o f V. S t m u v e , a n d t h e l a t e r o n e s w e r e f o r t h e m o s t p a r t o b t a i n e d f r o m p h o t o g r a p h i c observations carried out at the Naval Observatory i n t h e USA a n d a t t h e A b a s t u m a n i Astrophysical Observatory a n d a l s o f r o m m i c r o m e t r i c m e a s u r e m e n t s made b y C. W o r l y . On t h e b a s i s o f t h i s a s t r o m e t r i c material graphs were drawn of the mutual separat i o n o f t h e c o m p o n e n t s as a f u n c t i o n of the time (the epoch of observation). Consideration of these graphs showed that observations indicate e x p a n s i o n i n 14 T r a p e z i u m t y p e s y s t e m s o u t o f t h e 15 s t u d i e d . By way o f e x a m p l e F i g . 2 g i v e s g r a p h s o f t h e r e l a t i o n ship mentioned for the four components of the Trapezium type multiple s y s t e m ADS 719. This instability

result i s new and w e i g h t y e v i d e n c e of real Trapezium type systems.

in

favor

of

the

concept

of the

dynamic

The r e l a t i v e p r o p e r m o t i o n s o f t h e c o m p o n e n t s o f t h e 16 T r a p e z i u m t y p e s y s t e m s from the catalog [4] w e r e d e t e r m i n e d i n t h e a r t i c l e by Y a t s e n k o [31] o n t h e b a s i s o f photographic observations. However there is in that article no d i s c u s s i o n of the results obtained from the point of view of the internal motions in these Trapezium

573

type systems. The high tangential velocities d i s c o v e r e d for individual components of some of these systems are considered by the author merely to be an i n d i c a t i o n that these Trapezia are optical. Of p a r t i c u l a r interest from the point of view of the q u e s t i o n ol the dynamic s~ability of T r a p e z i u m type systems are the studies on the dynamic evolution of these systems carried out by numerical i n t e g r a t i o n of the equations of motion for the components of the system using a computer. In the articles of Duboshin, e~ al. (see, for example, [32]) on the Orion T r a p e z i u m itself they used familiar o b s e r v a t i o n a l data to calculate the dynamic evolution of this system on various assumptions about the initial conditions of the ambient medium. It is natural that the data o b t a i n e d in this are completely different. For example, w h e n the Orion T r a p e z i u m is assumed to be an isolated system, it turns out that it is extremely unstable, and the time for it to d i s i n t e g r a t e is e s t i m a t e d at lO 5 years. On the Other hand, w h e n it is assumed that the components o2 the T r a p e z i u m move in a sphere uniformly filled with stars, then, d e p e n d i n g on the assumptions made in regard to the dimensions of that sphere and the d i s t r i b u t i o n of the density of matter in it, the calculations lead to a disintegrating, pulsating, or stable system, respectively'. Thus the results of c a l c u l a t i o n of the dynamic e v o l u t i o n of the Orion T r a p e z i u m are determined completely by the choice of the initial conditions, as was to be expected, and 'this choice i s extremely arbitrary, so it cannot be considered to be decisive when c o n s i d e r i n g the q u e s t i o n of the dynamic s t a b i l i t y of the system. A study which is more i n t e r e s t i n g in this sense is that of Allen and P o v e d a on the dynamic evolution of T r a p e z i u m type systems in general.

[33]

On the a s s u m p t i o n that the system has negative total energy, this article studies the motions of stellar components in 30 T r a p e z i u m type systems each of which consists of six components and has different structure parameters. It was assumed that the total mass of each T r a p e z i u m amounted to 1 7 0 M ~ It was further assumed that each T r a p e z i u m has three pairs of stars with masses 5 0 M | 20M| and 15~,~., respectively, contained w i t h i n a sphere of radius 5000 a.u. The results o b t a i n e d in c a l c u l a t i n g the dynamic e v o l u t i o n showed that over lO 6 years of their subsequent life two thirds of the T r a p e z i u m type systems considered still continue to be T r a p e z i u m type systems. In this result Allen and P o v e d a [33] saw a c o n t r a d i c tion to the concept of the dynamic i n s t a b i l i t y of T r a p e z i u m type systems. It turned out, however, tion of the result obtained.

that this c o n c l u s i o n was based on an incorrect

interpreta-

In fact, as is shown in [34], the result o b t a i n e d by Allen and P o v e d a [33] shows that the p r o b a b i l i t y that a T r a p e z i u m type system w o u l d keep its c o n f i g u r a t i o n in the course of 106 years is two thirds. This means that over a total of 2.106 years more than half ef all the T r a p e z i u m type systems in the s e l e c t i o n studied, or more a c c u r a t e l y 1 -(2/3) 2 = 5/9 of them, will lose their c h a r a c t e r i s t i c c o n f i g u r a t i o n and cease to be Trap e z i u m type systems. In other words, the half life of T r a p e z i u m type systems with n e g a t i v e total energy is less than 2.106 years. It follows from this that T r a p e z i u m type systems with a n e g a t i v e total energy lose their c h a r a c t e r i s t i c c o n f i g u r a t i o n on average in about 2-106 years. From t h e p o i n t o f v i e w o f t h e d y n a m i c i n s t a b i l i t y o f T r a p e z i u m t y p e s y s t e m s some very characteristic results are those from the calculations o f A l l e n and P o v e d a ~33~ on t h e s t r u c t u r e o f t h e s y s t e m s s t u d i e d o v e r 106 y e a r s o f t h e i r d y n a m i c e v o l u t i o n ~ They show t h a t o f 30 o r i g i n a l T r a p e z i u m t y p e s y s t e m s 11 i n t h a t t i m e l o s t t h e i r T r a p e z i u m type configuration, of which three disintegrated leaving binaries and e i g h t t u r n e d i n t o systems of the ordinary type. Of t h e r e m a i n i n g 19 s y s t e m s w h i c h p r e s e r v e d their Trapezium type configurations, o n l y i n s i x d i d t h e n u m b e r o f members n o t c h a n g e , w h i l e s i x s y s t e m s e j e c t e d o n e member e a c h a n d s e v e n s y s t e m s two members e a c h . In fact, 1 3 systems also partly o v e r t h e 10 6 y e a r s t h e l a t t e r disintegrated~ The s i x s y s t e m s which preserved a l l t h e i r members o v e r t h i s t i m e u n d e r w e n t a c o m p a r a t i v e l y slight evolution: namely, five of them increased somewhat in their dimensions. The r e s u l t s

574

of Allen

and Poveda's

study

[33~

are

therefore

a new and a l t o g e t h e r

surprisin~ piece o f evidence in favor o f the theoretically important concept o f the dynamic instability of Trapezium type systems. These systems if they have negative total energy must over a period of the order of 2"106 years either disintegrate completely or, losing some of their members, change their initial configuration and turn into systems of the ordinary type with a smaller number of members. It should be added that from the point of view of the dynamic evolution of Trapezium type systems great interest attaches to the search for and study of such systems which are at earlier and later stages of development than those which are contained in the catalogs [4, 7]. When one bears in mind that Trapezium type systems are expanding systems, that is, their mean dimensions increase as they develop, it is natural to suppose that these must be very close and very wide systems, respectively. The question,of wide and close Trapezium type systems was considered in greater detail by Ambartsumyan [4], who investigated some systems of both classes. Unfortunately, after his thorough study [4] this question was not considered by anybody in the case of Trapezia containing stars of the spectral classes O--B. It was only quite recently that Gyul'budagyan [20] discovered ll wide Trapezium type systems consisting of B stars in the constellation Puppis. He found another 10 wide Trapezium type systems among the objects in the catalogs [35, 36], which contain stars connected with reflection nebulae. We may note as a matter of interest in this connection that, since wide Trapezium type systems must be comparatively older formations than close systems of that type, it follows that stars of the type 0 and early B should hardly be encountered in them at all. The systems discovered by Gyul'budagyan [20] satisfy this condition. Close Trapezium type systems in T-associations were considered in an article by one of the authors [17]. Of the total 120 Trapezium type systems discovered by him eight turned out to be very close. Thus the r e s u l t s both of an observational and of a theoretical character which have been gained from the study of Trapezium type systems provide a foundation for concluding that these systems, which have an unusual spatial confi~uration, are dynamically unstable and are at the present time disintegrating either completely or partially (forming systems of the ordinary type with fewer members). At the same time the disintegration period for Trapezium type systems depends on their total energy, as one might expect. If the system has negative total energy, its disintegration time is of the order of 2-100 years. But if the total energy of a Trapezium type system is positive, then its disintegration time is considerably shorter: 105 years or less. The probability of total disintegration in the second case is a good deal greater. 4. The Group Formation of Stars Immediately after distinguishing Trapezium type multiple stellar systems as a distinct type, Ambartsumyan [37] showed that real Trapezia almost always have as their brightest member stars of the spectral classes O--B. This observational fact is illustrated by the data of Table 1 and shows that Trapezium type multiple systems must be predominantly members of OB-associations.

Confirmation of this conclusion was obtained in the studies of Ambartsumyan and Markaryan [38], Markaryan [12, 13], Sharpless [ii], and Salukvadze [14, 15]. These contain numerous examples indicating that real Trapezium type multiple systems belong overwhelmingly to known OB-associations. This conclusion is confirmed in the case of T-associations by studies carried by one of the authors _[16, 17]. This important result has great significance for the development of the concept of the group origin of stars. In fact, a consideration of the processes of formation and disintegration of pairs of stars, that is binaries, as a result of random close approaches on the part of stars during their motions in the Galaxy enabled Ambartsumyan [i] to conclude that in our stellar system the processes of disintegration of binaries are taking place at the present time millions of times more frequently than the processes of formation of new pairs. This means that the set of stellar pairs existing in the Galaxy cannot be the product of random approaches by stars. From thls was obtained a conclusion which is

575

extremely important for the problem of stellar evolution, of e a c h pair have a common origin.

namely,

that the components

This conclusion is also true for systems of stars with a ~reater number of members. In particular, it can be stated that all the members of a Trapezium type multiple system have a common origin -- they originated together. So it must be assumed that the existence of a large number of Trapezium type multiple systems in regions of stellar formation an the Galaxy, in stellar associations, is a weighty piece of evidence in favor of the idea that stars are formed in groups, that is~ the process of formation of stars is of a group nature (see, for example, [39] and also

[91 ). T h e e x i s t e n c e of real Trapezia consisting of stars which have recently come into being point to an important property of the process of stellar formation: stars are formed in associations by groups, and in this process there are formed not only dynamically stable groups (binaries, multiple stellar systems of the ordinary type, and clusters consisting of many stars), but also dynamically unstable groups (Trapezium type systems, associations and, possibly, unstable stellar clusters). In this context it can be assumed that in the formation of stars in associations the number of unstable multiple stars which are being formed is considerably greater than that of stable ones. However with the passage of time dynamically unstable groups of stars break up either wholly or partially, turning into multiple systems of the ordinary type. But dynamically stable multiple systems hardly break u~ at all. As a result of this their number gradually increases in the Galaxy on account of the accumulation of more and more fresh generations of stable systems. S o we see in it at the present time an incomparably greater number of stable systems than of unstable ones. The recognition and study of Trapezium type multiple systems has thus enabled us to reach a better understanding of the process of stellar formation in the galaxy, and in particular of its group nature, which was first established by Ambartsumyan (sees for example, [39]). 5. Trapezium Type Systems Among Multiple Galaxies The morphological investigation of multiple galaxies carried out by Ambartsumyan [40] showed an unusual abundance among them of systems with Trapezium type configurations~ Of 132 multiple! galaxies which appear in Holmberg's catalog [41], 87 (65%) have Trapezium type configurations and only 27 (20%) systems are systems of t h e ordinary type. The remaining 18 (15%) multiple galaxies may also be included among the Trapezium type systems, since it is possible to find in them three galaxies for which the ratio of the greatest to the least of the mutual separations lies between 2.5 and 3.0. From the point of view under consideration the set of multiple galaxies differs sharply from the set of multiple stars, in w h i c h the overwhelming majority of the multiple systems are systems of the ordinary type. This sharp difference between the characteristic configurations of multiple stars and multiple galaxies is illustrated clearly by Figs. S and Fig. 4. The first of them shows the observed configurations of the six brightest visual multiple stars from Aitken~s catalog [5], and the second shows the configurations of the six brightest multiple gala x l e s from Holmberg's catalog [42]. These figures show that of the multiple stars represented all have configurations of the ordinary type, while all the multiple galaxies have Trapezium type configurations. The existence among the muti21e galaxies of a considerable number of Trapezium type systems is evidence in favor of the concept of the group origin of galaxies. By analogy with Trapezium type multiple stellar systems it .may be assumed that multiple galaxies also which have Trapezium type configurations are systems which are dynamically unstable, and which are at the present time in the process of decay~ This enables us to assert that multiple galaxies are arising also an our time in the Metagalaxy. The study of multiple galaxies with Trapezium type configurations led Ambartsumyan (see, for example, [43]) to important conclusions on the origin and evolution of ~alaxies,

576

p Or J

cc L e o

a Gem

IIIII

s

.

i UMa

.2

I~ SccR

9

# F i g . 3. C o n f i g u r a t i o n s of the brizhtest multiple stars in Aitken's catalog according to [41]. The s c a l e i s d i f f e r e n t for the different examples.

17

212

45 @

@

246

348

468

@

Fig. 4. Configurations of the six brightest multiple galaxies in Holmber~'s catalog according to [41]. The numbers of the corresponding systems in this catalog are indicated in the figure. and in particular it made it possible to develop the essentially new idea of activity on the part of their central condensations, the nuclei of the galaxies.

6.

Conclusions

The discovery that there are in existence in the Galaxy stellar systems which are dynamically unstable played a fundamental part in the workin G out of new ideas on the origin and evolution of stars and stellar systems. As a result of this discovery it appeared to be for the first time possible to study the phenomena connected with star formation directly on the basis of astronomical observations. In particular, important results in this area were obtained after multiple systems of a new type, Trapezium type systems, were distinguished and investigated. It turned out that these systems consist of very young stars, are dynamically unstable, and are at the present time disintegrating. Moreover the disintegration time is many orders of magnitude less than the life of the component stars. As a result, after Trapezia disintegrate the stars of which they are composed gradually enrich the general stellar field of the Galaxy. This fact is important evidence in favor of the concept of the group origin of stars. The understanding of Trapezium type multiple systems has turned out to be very fruitful also in the problem of the origin and development of galaxies, although the

577

study of individual been begun.

multiple

galaxies

with Trapezium

In conclusion we shall note some problems systems which are the most important for us.

type configurations

has still not

in the study of Trapezium

type stellar

1. The search for Trapezium type laultiple stars which contain stars of the spectral classes O--B2, including very close ones. 2. The determination of the proper motions and radial velocities of stars in Trapezium type systems which have a higher probability of being real (the Tr~nezia connected with stars of the spectral classes O--B). 3. The physical taining OB-stars. 4. ~esearch

study of the components

(physical

and statistical)

of individual Trapezium into Trapezium

type systems

type systems

con-

in T-associa-

tions. In order to solve these problems, in addition to terrestrial astronomical observations it is extremely desirable that Trapezium type systems should be observed from outside the atmosphere. In particular, observations from outside 'the atmosphere should be extremely effective in determining the proper motions of stars composing Trapezium type systems. It is to be hoped that these investigations will in the last analysis help the solution of problems connected with the study of the earliest states of stars following immediately after their formation. These researches may be effective also in the study of stellar dynamic properties of Trapezium type systems, in particular for final establishment that there are in the Galaxy stellar systems with positive total energy. LITERATURE

CITED

i. V. A. Ambartsumyan, The Evolution of Stars and Astrophysics [in Russian], Izdo ~ Arm. SS~, Erevan (1947). 2. V. A. Ambartsumyan, Astron. Zh., 26, 3 (1949). 3. A. Blaauw, Bull. Astron. Inst. Neth., I I, 405 (1952). 4. V. A. Ambartsumyan, Soobshch. Byurak. Obs., 15, 3 (IS54). 5. R. G. Aitken, New General Catalog of Double Stars, Carnegie Institution, Washington (1932). 6. V. A. Ambartsumyan, Dokl. Akad. Nauk Arm. SSR, i_33, 97 (1951). 7. G. N. Salukvadze, Byull. Abastumanskoi Ohs., 499, 39 (1978). 8. H. M. Jeffers, W. H. van den Boss, and F. M. Greeby, Index Catalog of Visual Double Stars, Vol. 21, Publ. Lick Obs. (1963). 9. L. V. Mirzoyan, Binary and Multiple Stars as Tracers of Stellar Evolution, IAU Colloquium No. 69 (eds. Z. Kopal and J. Rahe), Reidel, Dordrecht (1982), p. Sl. I0. T. A. Agekyan, Astron. Zh., 3_!i, 544 (1954). II. S. Sharpless, Astrophys. J., 119, 334 (1954). 1 2 . B. E. Markaryan, Soobshch. Byurak. Obs., 5, 3 (1950). 13. B. E. Markaryan, Soobshch. Byurak. Obs., 9, 3 (1951). 14. G. N. Salukvadze, Soobshch. Akad. Nauk Gruz. SSR, 93, 329 (1979). 15. G. N. Salukvadze, Astrofizika, i_55, 311 (1979). 16. G. N. Salukvadze, Astrofizika, i_66, 505 (1980). 17. G. N. Salukvadze, Astrofizika, 16, 687 (1980). 18. M. M. Zakirov, in: The Study of Extremely Young Stellar Complexes [in Russian]~ Izd. Fan, Tashkent (1975), p. 95. 19. M. Roth, I. Echevarria, I. Franco, and I. Warman, Rev. ~ex. Aston. Astrofisica, 4, 209 (1979). 2 0 . A. L. G y u l ' b u d a g y a n , Astrofizika, 19, 747 ( 1 9 8 3 ) . 2 1 . C. A l l e n a n d M. T a p i a , R e v . Mex. A s t r o n . A s t r o f i s i c a , 3 , 119 ( 1 9 7 7 ) . 2 2 . V. A. A m b a r t s u m y a n , Uch. Z a p . L e n i n g r . G o s . U n i v . , No. 2 2 , S e r . M a t . Nauk ( A s t r o n o m i y a ) ~ No. 4, 19 ( 1 9 3 8 ) . 2 3 . V. A. A m b a r t s u m y a n , D o k l . A k a d . Nauk Arm. SSR, 1-6, 97 ( 1 9 5 3 ) . 2 4 . P . P. P a r e n a g o , A s t r o n . Z h . , 3-6, 249 ( 1 9 5 3 ) . 2 5 . P . P . P a r e n a g o , T r . G A I S h . , 2_55, 3 ( 1 9 5 4 ) . 2 6 . S. S h a r p l e s s , Vistas Astron., 8 , 127 ( 1 9 6 6 ) .

578

27. 28. 29. 30. 31. 32. 33. 34, 35. 36. 37. 38. 39. 40. 41. ~2. 43.

K. h a . S t r a n d , J . R. A s t r o n . S o c . C a n . , 6 7 , 67 ( 1 9 7 3 ) . G. V. A k h u n d o v a , I z v . GAO AN SSSR, 2 1 , 83 ( 1 9 5 7 ) . C. Allen, h. Poveda, and C. Worly, Rev. Max. Astron. Astrofisica, i, i01 (1974). G. N. Salukvadze, Astrofizika (in press). A. I. Yatsenko, Stellar Clusters and Associations [in Russian] (ads. J. Ruprechl and J. Palous), Publ. Astron. Inst. Czechoslovak, Ac. Sci., No. 56, Praha (1983), p. 212. G. N. Duboshin, A. I. Rybakov, E. P. Kalinina, and P. N. Kholopov, Soobshch. GAISh.~ No. 175, 3 (1971). C. Allen and A. Poveda, The Stability of the Solar System and Small Stellar Systems, IAU Symposium No. 62 (ed. Y. Kozai), Reidel, Dordrecht-Boston (1974), p. 239. L. V. Mirzoyan and M. A. Mnatsakanyan, Astrofizika, 1-1, 551 (1975). S. Van den Bergh, Astron. J., 71, 990 (1966). S. Van den Bergh and W. Herbst, Astron. J., 800, 208 (1975). V. A. Ambartsumyan, Dokl. Akad. Nauk Arm. SSR, 13, 19.9 (1951). V. A. Ambartsumyan and B. E. Markaryan, Soobshch. Byurak. Obs., 2, 3 (1949). V. A. Ambartsumian, [AU Transactions, Vol. 8, University Press, Cambridge (1954), p. 665. V. A. Ambartsumyan, Communication at a Symposium of IAU in Dublin [in Russian], Izd. AN Arm. SSR, Erevan (1955). V. A. Ambartsumyan, Izv. Akad. Nauk Arm. SSR, Ser. FMET Nauk, 9, 23 (1956). E. B. Holmberg, Ann. Obs. Lund, 6 (1937). V. A. Ambartsumian, La Structure et l'Evolution d e l'Univers, Edition Stoops, Brussels (1958), p. 241.

579