Astrophysics, Vol. 42, No. 4, 1999

NEW

MULTIPLE

SYSTEMS

OF THE

TRAPEZIUM

TYPE

G. N. Salukvadze and G. Sh. Javakhishvili

UDC 524.388

In the Guide Star Catalog (GSC) 223 new trapezia have been found. A new, more complete list of trapezia, including 637 objects, has been compiled on the basis of the GSC and the Washington Double Star Catalog.

I. Introduction

In his multifaceted scientific activity Academician V. A. Ambartsumian gave a special place to the study of multiple stellar systems of the Trapezium type. In investigating trapezia, he stimulated work in this direction in every way. His constant interest in the dynamics of unstable objects and, in particular, trapezia is now understandable, but then few could forsee that the study of these systems would play an enormous role in the investigation of the problem of the origin and development of stars. Before Ambartsumian's discovery [1] of stellar associations - - centers of star formation in the Galaxy - - all stellar systems were assumed to be dynamically stable in astronomy in general and in stellar dynamics in particular. The discovery of stellar associations showed that systems also exist in the Galaxy that were dynamically unstable in the period of their formation and are now expanding. This theoretical prediction of Ambartsumian, first confirmed on the basis of Blaauw's observations [2], was of enormous importance for the problem of the origin and evolution of stars and stellar systems. The morphological investigation of stellar associations later showed that in the composition of associations one encounters multiple star systems, which have a greater degree of dynamical instability than the associations as a whole. This enabled Ambartsumian [3] to single out among multiple stars a new type: multiple systems of the Orion Trapezium type, characterized by a high dynamical instability. The laws of celestial mechanics enable us to assume that a system having a configuration of the Trapezium type cannot continue to exist longer than the time required for several revolutions of its components about the common center of mass. And the decay time of a system of the Trapezium type depends on the sign of the system's total energy, i.e., on the original velocity distribution of its components and the distances between them. Calculations showed [3] that the decay time of multiple systems of the Trapezium type is on the order of 2x106 years if the system has a negative total energy and on the order of t0 ~ years or tess if the system's total energy is positive. The discovery that there are dynamically unstable stellar systems in the Galaxy has played a fundamental role in the development of flew concepts of the origin and evolution of stars and stellar systems. Thanks to this discovery, it became possible for the first time to study phenomena associated with star formation directly on the basis of astronomical observations.

Abastumani Astrophysical Observatory, Georgia. Translated from Astrofizika, Vol. 42, No. 4, pp. 571-578, OctoberDecember, 1999. Original article submitted July 25, 1999; accepted for publication August 20, 1999. 0571-7256/99/4204-0431 $22.00

9

Kluwer Academic/Plenum Publishers

431

Since multiple stellar systems of the Trapezium type are new stellar systems in the Galaxy to some extent, to study them, naturally, one must first set up a catalog of these systems. It is clear that a catalog of multiple stellar systems of the Trapezium type, as Ambartsumian has repeatedly indicated, "must be cleaned of optical and spurious trapezia." Because of the great importance of the latter, one of the authors of the present paper, studying the statistical, kinematic, and physical characteristics of trapezia, has constantly sought an opportunity to compile a complete catalog of trapezia that would contain a high percentage of actual trapezia.

2. Catalogs and Lists of Multiple Stellar Systems of the Trapezium Type The first list of multiple stellar systems of the Trapezium type was compiled by Ambartsumian [3] on the basis of Aitken's New General Catalog of Double Stars [4]. Ambartsumian used the following criterion to assign a multiple star to the Trapezium type. In the case of a triple system, a multiple star was considered to be a system of the Trapezium type if the ratio of the largest distance to the smallest in it is less than three. In order to exclude optical systems, he introduced upper limits on the distances of the faint components from the primary star, while components fainter than 12".5 were excluded altogether. This criterion of Ambartsumian is given in [3]. As noted in [3], this list is incomplete and contains 108 multiple systems of the Trapezium type, the study of which is of primary interest. Investigators of multiple systems of the Trapezium type have long used Ambartsumian's list, and since it contains a high percentage of spurious trapezia, some results based on a statistical investigation of trapezia proved to be not entirely correct. In this connection, at the end of the 1970s G. N. Salukvadze, on Ambartsumian's suggestion, set out to compile a new, more complete catalog of trapezia. For this it was necessary to reconsider the criteria for selecting trapezia from among multiple stars contained in the catalogs of binary and multiple stars. Aitken's catalog (ADS), published in 1932, contains 17,180 binary and multiple stars from the North Pole down to declination 6 = - 2 0 ~ measurements of which had been published by the end of 1927. In 1963 the Index Catalog of Visual Double Stars [5], on which measurements had been published up to the end of 1960, came out. This catalog was the most complete at that time, not only with respect to stars but also with respect to the data characterizing the double stars. The Index Catalog contains stars over the entire sky and their total number is 64,247. On the basis of the Index Catalog of Visual Double stars, Salukvadze compiled the new Catalog of Multiple Systems of the Trapezium Type [6]. In compiling the fmal version of the Catalog of Multiple Systems of the Trapezium Type, Salukvadze took a value of 2.6 for K 0 and excluded optical systems using the solid curve in Fig. 1. The final version of the Catalog of Multiple Systems of the Trapezium Type contains 412 trapezia. S. Sharpless [7] discovered 11 trapezia in emission nebulae. Finally, we must mention a catalog of systems of the Trapezium type compiled in Mexico on the basis of the Index Catalog of Visual Double Stars [8]. This catalog, containing over 900 systems of the Trapezium type, has not yet been published, and it is not yet possible to judge the criteria used in compiling it. Multiple systems of the Trapezium type have also been found in T associations. In four T associations, Tan T1, Tan T2, Tan T3, and Ori T2, M. M. Zakirov [9] identified 46 systems, calling them multiple star systems of the Trapezium type. Salukvadze found 120 multiple systems of the Trapezium type in 13 T associations [10, 11]. In [12] V. Hambarian gives a list of 27 multiple systems of the Trapezium type, 20 of which consist of variable stars of the T Tauri type and 7 of which are flare stars.

432

100

80

60

40

20

_7 ~ - , , , , , , , ' , , ~ 8.0

....... 9.0

, .... ..,,.,,,,,..,,.,.,.,,,~.. 100

11.0

120

130

Fig. 1. Criteria for choosing multiple systems of the Trapezium type.

3. Search for New Multiple Stellar Systems of the Trapezium Type Based on the GSC (Guide Star Catalog) and WDS (Washington Double Star Catalog) In the process of compiling the Abastumani catalog of trapezia and as a result of a detailed familiarity with catalogs of double stars and observational data on relative positions, it was found that in compiling a catalog of double stars, observers have not payed enough attention to the search for and observation of multiple systems, since they have given preference to observations of close double stars with the aim of determining their orbits and other characteristics. The impression is therefore created that the presently existing catalogs of double stars are far from complete with respect to multiple stars. It is then natural to assume that the Abastumani catalog of Trapezia is also incomplete. In this connection, we decided to create a complete catalog of trapezia having primary stars of spectral types O-B2, since physical trapezia are often encountered among multiple stars with primary stars of these spectral types. The sample of stars of spectral types O-B2 was made from the SAt:) catalog. There were 2601 such stars. For them about 1000 negatives in the form of photographic plates and films were obtained over several years on a 125-cm reflector with a Ritchey-Chr6tien optical system. We planned to search for southern stars on maps of the European Southern Observatory's southern survey atlas. But the observatory recently obtained the GSC, written on laser disks, and it became possible to analyze it. We changed our earlier plan and attempted to search for multiple stellar systems of the Trapezium type not only around stars of spectral types O-B2 but around stars of all spectral types. The Guide Star Catalog was specially created for the Hubble Space Telescope (HST). It contains 19 million stars and other nonsteUar objects, 15 million of which are stars of from sixth to fifteenth magnitude. The original version of the GSC has been described by B. M. Lasker et al. [13], J. L. Russell et al. [14], and H. Jenkner et al. [15]. To search for multiple systems of the Trapezium type, from the catalogs, written on two laser disks, we first selected stars down to 12".5 and written in separate files by zones. After this, the next subroutine compared each star with other stars. If the distance between two stars was less than 80", such a pair was written in a separate file. Since the resolving power of the catalog is fairly low, we decided to limit the minimum distance between pairs to 5".

433

A special subroutine tested the repetition of the appearance of stars. If a star was encountered at least twice, this meant that the distance between the given stars produced pairs having at least two stars and a distance of less than 80". Another subroutine identified individual groups of stars within a diameter of 80". The next routine isolated the brightest star from each group, which we call the primary star. The distances from the primary star to the other components were then calculated. From this sample, using criteria for determining multiple systems of the Trapezium type and excluding optical systems, we compiled lists of new trapezia. We used the criteria described by Salukvadze [6]. We used a continuous curve (Fig. 1). This curve was first expressed empirically and has the form Pm~. = 2"5m2 - 78m + 594.875. This formula was obtained by a second-order approximation. We thus obtained a list of multiple stars that was compared with the Washington Double Star Catalog [16]. As a result of the comparison, we excluded from the list the multiple stars that figure in the WDS. For the remaining multiple stars, applying the criterion K 0 = 2.6, we obtained a list of new trapezia containing 223 objects. Since the WDS was published in 1984 and contains more accurate data both on the relative positions and on the magnitudes of the components of 73,610 double and multiple stars, we thought it appropriate to also compile a list of multiple stellar systems of the Trapezium type on the basis of the WDS. Such a list was indeed compiled and contains 414 trapezia. It is interesting to note that a comparison of the Abastumani Catalog of Multiple Systems of the Trapezium Type with the list compiled on the basis of the WDS showed that the latter did not contain 77 trapezia from the Abastumani catalog. This was due to the following circumstances: 1) the program excluded all trapezium components for which no magnitudes were given in the WDS; 2) the magnitudes of trapezium components and the distances between components given in the WDS differ considerably from the corresponding IDS data. To determine the spectral types more accurately, the two lists of trapezia were compared with the principal known spectroscopic catalogs. To exclude optical pairs formed as a result of background stars failing within a circle with a radius equal to the distance of the faint components of the corresponding magnitudes, we made counts in the GSC around each system within a diameter of one degree. The probabilities of background stars falling within these circles were calculated from the Poisson formula for each trapezium. As a result of the calculation, we determined the number of residual optical systems as a function of spectral type. For the list of trapezia compiled on the basis of the WDS, we also calculated the number of pseudotrapezia. The results of the calculations with the improved spectral types are given in Table 1. An examination of the first three rows of this table fully confirms the earlier conclusion that among multiple stars for which the primary component belongs to the spectral interval 0-B2 there is a considerable percentage of actual trapezia. After compiling the lists of trapezia based on the GSC and WDS, we combined these two lists and thus obtained a new version of the catalog of multiple stellar systems of the Trapezium type, containing 637 objects. The results of the counts are given in Table 2. As seen from Table 2, the total number of trapezia increased mainly due to systems for which the spectral type of the primary star was unknown. They comprise 151 out of the 223 new objects, while the other 72 trapezia are distributed as follows: 7 O-B2, 7 B3-B5 + B, 10 B8-B9, 13 A, 12 F, 4 G, 18 K, and 1 M. A catalog of multiple stellar systems of the Trapezium type will be published in the near future. We wish to thank Prof. Pfau, Mr. Strobel, and Ms. Walter (Germany), who presented as a gift to one of the authors of this paper a computer on which the present work was carded out.

434

T A B L E 1. Statistics on Trapezia Based on W D S Data Spectral type

Total number of multiples

O-B2

87

B3-B5+B

Calculated number of pseudoof optical trapezia systems 8

Number of observed a'apezia

Percentage of trapezia

1

47

54

78

7

1

22

28

B8-B9

101

10

0

19

19

A

324

30

1

45

14

F

237

21

1

40

17

G

185

17

1

37

20

K

115

10

1

32

28

14

1

0

7

5O

465

38

4

165

36

1606

142

10

414

M

Unknown Total

T A B L E 2. Statistics on Trapezia Based o n the C o m b i n e d Catalog of Trapezia Spectral type

Calculated number

Number of

of optical systems

observed trapezia

O-B2

54

B3-B5+B

29

B8-B9

29

A

58

F

52

G

41

K

50

M

8

Unknown Total

316 15

637

435

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.

436

V. A. Ambartsumian, Aso'on. Zh., 26, 3 (1949). A. Blaauw, Bull. Astron. Inst. Neth., 11, 405 (1952). V. A. Ambartsumian, Soobshch. Byurakan. Obs., 15, 3 (1954). R. G. Aitken, New General Catalog of Double Stars, Vol. 1, p. 707, Vol. 2, p. 781, Carnegie Institution, Washington (1932). H. M. Jeffers, W. H. van den Bos, and F. M. Greeby, Index Catalog of Visual Double Stars, Publ. Lick Obs., 21, Part I, 280, Part II, 804 (1963). G. N. Salukvadze, Byull. Abastuman. Aso'ofiz. Obs., 49, 40 (1978). S. Sharpless, Vistas Astron., 8, 127 (1966). C. Allen, A. Poveda, and C. E. Worley, Rev. Mex. Aso'on. Astrofis., 1, 101 (1974). M. M. Zakirov, in: Investigation of Exo'emely Young Stellar Complexes [in Russianl, Fan, Tashkent (1975), p. 95. G. N. Salukvadze, Astrofizika, 16, 505 (1980). G. N. Salukvadze, Astrofizika, 16, 687 (1980). V. V. Hambarian, Astrofizika, 28, 149 (1988). V. M. Lasker, C. R. Sturch, B. J. McLean, J. L. Russell, H. Jenkner, and M. S. Shara, Astron. J., 99, 2019 (1990). J. L. Russell, B. M. Lasker, B. J. McLean, C. R. Sturch, and H. Jenkner, Astron. J., 99, 2059 (1990). H. Jenkner, B. M. Lasker, C. R. Sturch, B. J. McLean, M. S. Shara, and J. L. Russell, Astron. J., 99, 2019 (1990). C. E. Worley and G. G. Douglass, The Washington Visual Double Stars Catalog, U.S. Naval Observatory, Washington (1984).