TRAPEZIUM-TYPE
WIDE SYSTEMS
G. N. SALUKVADZE and G. SH. JAVAKHISHVILI* Abastumani Astrophysical Observatory. Georgia, U.S.S.R.
Summary. On the basis of the SmithsonianObservatoryCatalogues 15 Trapezium-typesystems are found. Photometric distances are determinedfor the Trapeziumcomponents.A conclusionis drawn on physical relations of the componentsin the systems. The fact of existence of Trapezium-typelarge stellar systems confirms the existence of Trapezia with positive total energy.
The idea on Trapezium-type multiple systems was introduced by Prof. V.A. Ambartsumian as a particular class of multiple stars in which the space distances between the components are of the same order of magnitude (Ambartsumian, 1954). The first list of Trapezia was compiled by Ambartsumian (1954) and a more complete list by one of the present authors (Salukvadze, 1978). These two ists contain such Trapezia, the distances between whose components are 0.02-0.20 pc (4 x 103-4 x 104 AU) i.e., only close systems. All the basic conclusions on the Trapezia properties were drawn by Prof. V. A. Ambartsumian in terms of general theory assumptions just after this interesting class of multiple systems was separated. At present an exceedingly small age of Trapezia is taken for granted. Its study enables a better understanding of star formation process in the Galaxy, in particular its group character. So far Prof. V. A. Ambartsumian's important suggestion on a positive total energy of Trapezium-type multiple systems is expected to be corroborated. Recently, however, on the basis of a thorough treatment of observational material for 15 Trapezia from the catalogue of Salukvadze (1978) available at present, a conclusion was drawn on the expansion of a certain number of Trapezia (Salukvadze, 1985). From the standpoint of a dynamical evolution of Trapezium-type systems it is of interest to search and study such objects which are at earlier or later stages of evolution than those listed in the above-mentioned catalogues. Considering that Trapezium type systems are expanding - i.e., their average sizes increase with evolution - it is natural to believe that there are very close and wide systems accordingly. Theoretical estimations show that with positive total energy the lifetime of a Trapezium is no more than 10 6 yr. If 5 km s - 1 is adopted to be the expansion velocity, then the Trapezia keep their configuration until their sizes become of the order of 5 pc. The problem of existing very wide systems was studied by Prof. V. A. Ambartsumian (1954). The first list, consisting of 5 wide Trapezium-type systems, was also compiled by him. Here it should be noted that the spectral-type in these systems is known for primary stars only. Unfortunately, nobody has dealt with this problem. Quite recently Gyolbudaghian (1983) has found 11 wide systems in Puppis. * Presented by G. N. Salukvadze. Astrophysics and Space Science 142 (1988) 79-83. 9 1988by Kluwer Academic Publishers.
80
G. N, SALUKVADZEAND G. SH, JAVAKHISVIL| TABLE I
No.
BD
a~gso
62950
d (kpc)
mo
Sp.
r I (pc)
r 2 (pc)
1
+ 60 ~502 +60 504 +60 507
2h28m53s 2 29 01 2 29 31
+ 61 ~14' +61 09 +61 18
1.4 1,3 2,1
7.m83 8.11 8.42
05 04 O5
2.6
5.7
2
--05 --05 --05 -05
1319 1315 1320 1325
5 5 5 5
32 32 32 33
55 48 58 03
--05 --05 --05 -05
27 25 27 18
0.6 0.8 0,7 0.6
5.08 5.13 6.39 6.83
O9,5 06 B1 B1
0.4
1.7
3
-04 -04 -04 -04
1184 1186 1183 1190
5 5 5 5
32 33 32 33
53 02 53 37
-04 -04 -04 -04
27 224 31 27
0,4 0,6 0.7 0.7
6.22 6.31 6.56 7.14
B2.5 B2.5 BI,5 B2
0.7
2.1
4
+1331124 + 1331120 + 13 1123
6 05 40 6 05 27 6 05 37
+13 59 + 13 59 + 13 56
1.0 0.8 1.4
6.94 8.13 8.78
B1 B2,5 B2
0,8
1.1
5
+05 + 04 +05 +05 +04 +05 +04 +05
6 6 6 6 6 6 6 6
+04 + 04 +05 +05 +04 +05 +04 +04
59 52 04 04 52 00 53 58
1.4 1,7 1.5 1.1 1.9 1.9 1.2 1,3
6.73 7.26 7.59 7.91 8.17 8.18 9.29 9.36
06 05 08.5 B1 O8 09 B2 B2
1.6
4.7
6
+04 1361 +04 1360 +04 1363
6 35 49 6 35 43 6 35 57
+04 39 +04 40 +04 40
1.4 1.4 1.8
7.14 8.19 8.70
BOIII B0.9 B1
0.8
1.6
7
- 5 7 3508 - 5 7 3499 - 5 7 3502
10 33 54 10 33 47 10 33 48
- 5 7 58 - 5 7 56 - 5 7 59
2.1 2.2 2.0
6.51 6.71 7.30
BOII B0.51 BIII
1.3
1.7
8
- 5 7 3533 - 5 7 3540 - 5 7 3516
10 34 13 10 34 21 10 33 59
- 5 7 57 - 5 8 01 - 5 8 00
(1.9) 2,7 2,4
8.2 8.3 8.6
BIIII B0.5II-III BIIlI
2.8
3.8
9
-60 -60 -60 -60 -60
11 11 11 11 11
-61 -61 -61 -61 -61
1.4 1.5 1.7 1.6 1.9
8.05 8.46 8.54 8.57 9,07
B2Iy B2Iy B2III B2Iy B21y
1.8
5.2
8.01 8.35 9.07
B0.5 BIIII B2III
1.5
3.0
4.1
4,5
1283 1302 1282 1279 1291 1286 1295 1281
3102 3128 3157 3136 3145
29 29 29 28 28 29 28 29
33 33 34 33 34
16 29 12 58 41 30 54 12
35 51 ll 56 00
19 37 ~ 19 17 11 22
10
- 5 9 4551 - 5 9 4552 - 5 9 4564
12 50 47 12 50 46 12 50 57
- 6 0 03 - 6 0 07 - 6 0 08
1,4 2,0 2,1
11
- 6 2 3096 - 6 2 3079 - 6 2 3090
13 11 28 13 10 30 13 10 56
- 6 3 19 - 6 3 19 - 6 3 07
1.2 1.8 0.8
12
- 3 3 11875 - 3 3 11887 - 3 3 11867
17 12 02 I7 12 33 17 11 42
- 3 3 29 - 3 3 40 - 3 3 41
0.8 1,2 1.4
09 09 B2 5.53 6.55 7.92
O8 09 B1
TRAPEZIUM-TYPE WIDE SYSTEMS
81
Table I (continued)
~1950
d (kpc)
m~
Sp.
r 1(pc)
r2 (pc)
- 32~12574 17~15m04s -32 12593 17 15 39 - 32 12576 17 15 08
-- 32~16' -32 17 - 32 21
0.9 1.1 i.1
8'P.15 8.73 8.74
B2 B2 B2
1.4
2.7
14
+61 2364 +61 2365 +61 2366
22 51 57 22 52 21 22 52 39
+62 19 +62 23 +62 20
1.0 1.2 1.1
9.07 9.20 9.72
B1 B1 B1
1.7
3.3
15
+61 2373 +61 2136 +61 2372
22 54 48 22 54 33 22 54 44
+62 27 +62 36 +62 21
0.9 1.1 0.8
7.65 7.74 8.78
07 B0 B1
1.6
3.9
No.
BD
13
51950
We intended to search for wide Trapezium-type multiple systems in which all the components are of O - B 2 spectral-type since a large percent of Trapezium-type real systems are encountered among this spectral-type. The SAO catalogues sample of O - B 2 spectral-types with astrophysical data was performed at the Soviet Stellar Data Center on our request. Altogether 2601 such objects are found. Further the stars were arranged on the computer Nairi-2 according to increasing right ascentions and in the square of + 15' around each star all stars were picked out. On the whole this procedure was done for all 2601 stars from our list. Then the listings were carefully examined and all the sample groups were extracted. Finally 60 groupings were revealed. The distances between the components and position angles were computed. Consequently, the ratios of the greatest distances to the smallest ones were estimated. It was found that many groupings do not suffice the definition of Trapeziumtype multiple systems and they are called e Lyrae; some others consisting of several components involve the groupings of young O - B 2 stars. Hence, the data on 15 Trapezia left in the final list, given in Table I, are as follows: stellar numbers according to BD, coordinates of the stars making the Trapezia, their distances, a visual magnitude, their spectra, minimum and maximum distances between the Trapezia components. The distance moduli to the stars forming the Trapezia were determined by a known formula m - M = 5 lgr - 5 + A(r), where A(r) is the interstellar extinction. In order to compute A(r) the relation A(r) = R ( N - V)o was used. For R the value of 3.1 was adopted. M v and (B - V)o values for known spectral types in the M K system were adopted from Schmidt-Kaler (1985). For stars forming System No. 8 (Table I) the distances are taken from papers by Rubin (1982) and Neckel (1967). As the errors in distance estimates by the photometric method amount to 3 0 ~ , it can be thought that the dispersions in distances of the stars in each wide system (Table I) is not high and they are almost at the same distance. It follows from the above assumption that in general Trapezium-type multiple systems
82
O . N . SALUKVADZE AND G-. SH. JAVAKHISVILI
represent groups of stars formed together. Very likely most of wide systems found by us are real Trapezia. The fact that wide systems exist favours the suggestion of a positive total energy of Trapezium-type multiple systems. It is clear that, with a negative total energy, the configuration of multiple stars conforming to the Trapezium definition would not be satisfied. References Ambartsumian, V. A.: 1954, Bull. Bjurakan Obs. 15, 3. Salukvadze, G. N.: 1978, Bull. Abastumani Astrophys. Obs., No. 49, 39. Salukvadze, G. N.: 1985, Astrophysics (Astrofizika) 22, 97. Gyolbudaghian, A. L.: 1983, Astrophysics 19, 747. Ochsenbein, F.: 1980, Inf. Bull. Strasbourg Stellar Data Center 19, 74. Schmidt-Kaler, Th.: 1965, 'Zustandgr6ssen und Zustanddiagramme der Sterne', in Landolt-BSrnstein, Zahlenwerte und Functionen aus Wissenschaft und Technik, Berlin, p. 251. Rubin, V. C., Burley, I., Kiasatpoor, A., Klock, B., Pease, G., Ruschheidt, E., and Smith, C.: 1982, Astron. J., 67, 491. Neckel, Th.: 1967, Landessternwarte Heidelberg-KSnigstuhl Ver6ffentl. 19, 1.
POVEDA - I think it is appropriate to recall that some years ago in collaboration with C. Allen and C. Worley we made a study of the separations among pairs of stars in as many Trapezia as we could find reliable data in a long base time. In that study modeling about 40 Trapezia with sufficient data we did not find a single case of expansion. We found, however, that occasionally one star will move out of the Trapezia as for instance was the case of star E in Orion Trapezium. We concluded, therefore, that there is no evidence of positive energy in Trapezia, not even for the best documented case, the Trapezium in Orion. SALUKVADZE - We have studied the kinematics of 15 Trapezium,type multiple stars with O-B2 spectral-type primary stars. Besides our own photographic observations we have used the measurement results of relative positions of the multiple stars published in different catalogues of double stars. In most cases the time interval of the observational material is more than 100 years. The results of calculations and the plots of dependence of distances from the epoch of observation indicate that out of 15 Trapezia investigated by us, 14 show the expansion. A similar work is done by Allen, Poveda, and Worley. They have considered 44 Trapezia from Prof. Ambartsumian's list and a full expansion was found in none of them. Only in 16 Trapezia one or a few components showed systematic removal from the primary star. Out of 15 Trapezia picked out by us, in common with C. Allen et al., relative motions were found in three Trapezia ADS 2843 (component B), ADS 13374 (component C), and ADS 14831 (component C). In our opinion the reason of divergence in the results consists in the following: (1) Allen et al., considered the Trapezia of all spectral types and, what really matters, out of 44 Trapezia studied, 133ones are not included in our Catalogue, i.e., they are not Trapezium type systems, 6 ones are Trapezia of late and unknown spectral types. From the remaining 25 Trapezia 15 ones are the Trapezia under investigation. (2) The plots of the paper by Allen et aL, show that the observational data obtained by 1965 were used to construct them. We used the published observations up to 1980. It is clear that the final observations are of a decisive value in drawing conclusions on the relative motions of the Trapezia components. The results ofosur investigations of the Trapezia kinematics have led us to a main conclusion as follows: Investigations of Trapezia based on the treatment of the observational data confirm the suggestion on the instability of certain parts of the Trapezium type multiple stars. At the same time it should be noted that at present for the majority of stars the observational precision is not enough in order that the relative motions of their components be determined.
TRAPEZIUM-TYPE WIDE SYSTEMS
83
ABT - What is the difference between a large trapezium system and an early-type duster with very few members? Does it depend on the geometry of the stellar positions, as assumed by Poveda et al. and Ambartsumian? SALUKVADZE - If there are such galactic clusters with ~ 10 members, then the difference between such clusters and Trapezium-type wide systems depend on their geometric configuration. As I have mentioned the term of Trapezium-type multiple systems was first introduced by V. A. Ambartsumian as a particular class of multiple stars in which the ratio of the greatest distances to the smallest ones between the components is less than 3. However, when we consider the internal motion of stars in multiple systems with negative total energies, we say that they are similar to galactic clusters and differ from them only by that the number of stars in them is much less. Consequently in determining the relaxation time for Trapezium type systems, we use a formula deduced by V. A, Ambartsumian for stellar clusters.