Orientation of the Orbital Planes of Visual Binary Systems R. Gł˛Ebocki

ACTA ASTRONOMICA Vol. 50 (2000) pp. 211–220

Orientation of the Orbital Planes of Visual Binary Systems

by R. Gł˛ebocki

Institute of Theoretical Physics and Astrophysics, University of Gdansk,´ ul. Wita Stwosza 57, 80-952 Gdansk,´ Poland e-mail: ﬁ[email protected]

Received April 19, 2000

ABSTRACT

The space distribution of orbital poles for 252 visual binaries is analyzed to check a possible tendency towards parallelism. It is conﬁrmed that orbital planes do not show any trend to be parallel to the Galactic plane. No strong evidence is found for a preferential orientation of the orbital planes for subgroups of binaries with similar periods and eccentricities. Asymmetry in the distribution of orbital poles is seen only for a subgroup of 19 binaries lying closer than 10 pc. Small differences in the distribution of orbital poles are also detected for subgroups with different location on HR diagram. Key words: binaries: visual – Stars: formation

1. Introduction

Several studies of the distribution of the lines of poles of the orbits of visual binaries have been made. It is clear that any pronounced trend for these lines to exhibit a preferred direction would be of the utmost signiﬁcance for concepts of the origin of binary stars. As the capture theory postulates the close approach of stars, stellar motion and star streams become the controlling factor in determining the orientation of the orbital planes. According to this theory, we should expect some parallelism to exist among the binary orbits, unless the disturbing gra- vitational force has entirely masked the original orderlines so that it is no longer recognizable. The random distribution of orbital planes agrees better with the frag- mentation theory where rotation of protostellar cloud is the determining factor on the orientation. Batten (1967) analyzed positions of the orbital poles for 52 visual binaries, emphasizing that for half of them the reliability of orbital parameters is low. He concluded that his data yield no strong evidence for a preferential orientation of orbital planes.The distribution of poles is random, although there is a large area in the northern hemisphere (in Galactic coordinates) in which few poles are found. 212 A. A.

Therefore he concluded that his ”investigation should be repeated when a substan- tial number of new orbital planes can be determined. A sample twice or even four times the size of the present one is needed.” The latest studies of this problem are those of Gillet (1988) and Dommanget (1988). Gillet analyzed 61 visual binaries from Worley and Heintz (1983) catalog using accurate statistical procedures. He concluded that the orientation of orbital planes for this sample is random, although he notes that the tests applied in the investigation would yield erroneous results for dataset consisting of equal numbers of antipodal directions. Dommanget (1988)

came to the conclusion that for systems nearer than 10 pc (10 systems) the poles

Æ Æ

were assembled around a position near: l 100 , b 15 . He analyzed about 140 systems, but he admitted that for only two thirds of them unambiguous determination of the ascending node was available. It seems desirable to re-open the question of randomness as new, more accurate data become available. In the last few years two catalogs of high quality orbital parameters for visual binaries has been published: ”Double and Multiple Systems Annex: Orbital Solutions” in the Hipparcos Catalogue (ESA 1997), hereinafter abbreviated as HIPO, and ”Visual Binary Orbits and Masses post Hipparcos” Söderh- jelm (1999), hereinafter abbreviated as VBO. These catalogs increase the number of visual binaries with reliable orbital parameters to more than four hundred systems. We analyze the orbital poles distribution in the Galactic coordinates for this sample, and discuss possible preferential orientation within smaller subgroups cha- racterized by different orbital periods – Porb , eccentricities – e, and positions on HR diagram.

2. Observational Data and Method of Analysis

2.1. Orbital Parameters

HIPO catalog of orbital elements contains data for six elements together with their standard errors for 235 visual binary systems. The determination of orbital pole position is based on two orbital elements: the inclination – i, and the position

of ascending node – Ω. The following convention is used in HIPO: for the ap-

Æ Æ

parent direct motion (counter-clockwise) 0 i 90 , for retrograde (clockwise)

Æ Æ apparent motion 90 < i 180 . The distribution of i values for HIPO sample is

shown in Fig. 3.2.118 of ESA (1997). There is an obvious deﬁcit of binaries with

j j Ω cosi 1. The position angle of the node – is measured counter-clockwise. If the radial velocity of the component is known, then Ω gives the position an-

gle of the ascending node. In the absence of spectroscopic information there is an Æ

ambiguity of ¦180 in the position angle of the ascending node, in which case the Æ catalog gives the value between 0 Æ and 180 (which actually may be the descending node). This ambiguity explains why in Fig. 3.2.119 of ESA (1997) there are more entries in the ﬁrst two quadrants than in the other two. Vol. 50 213

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V H L U QD L E I

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P X 1

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Fig. 1. Frequency histograms for orbital inclination (upper diagram, 20 Æ bins) and ascending node

(lower diagram, 30 Æ bins).

VBO catalog (Söderhjelm 1999) contains data for 204 visual binaries for which speckle interferometric measurements are available. Orbital elements are given for the systems for which parallax error is below 5% and a reliable orbit can be ﬁt to both: modern speckle interferometry and Hipparcos observations. There is no individual error evaluation of orbital parameters. Inclination and ascending node convention in VBO is the same as in HIPO. Eleven binaries are common in HIPO and VBO. Apart from 180 Æ difference in Ω for HD 26690 and HD 27176, the remaining data are in a very good mutual agreement in both catalogs. It justiﬁes the assumption that individual errors of i and Ω are the same in VBO as in HIPO. The

214 A. A.

Æ Æ δΩ average errors for HIPO data: δi 10 and 13 are assumed as individual errors for VBO orbital elements. For eleven systems present in both catalogs VBO values are used in our further analysis.

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(91 06+1 06&1

9, Fig. 2. HR diagram for 252 analyzed binaries. Straight lines arbitrarily divide binaries into three subgroups: MSH – hot main sequence stars, MSC – cool main sequence stars and EV – evolved

stars. Æ

The mentioned above ambiguity of ¦180 for some binary systems prevents the determination of their orbital pole positions for the entire sample of 428 stars. Further analysis is limited to 252 stars (131 from HIPO and 121 from VBO) for

which Ω is uniquely deﬁned from radial velocity measurements. For obvious re-

Æ Æ > asons there is a deficit of systems with i < 15 and i 165 in this sample. In Fig. 1 the frequency histograms are presented to illustrate the absence of signifi- cant systematic effects in the final sample. The HR diagram for the primaries is

presented in Fig. 2, with arbitrary division into three subgroups of stars discussed

< :

in the next Section, namely: MSH – hot main sequence stars (V I 0 6), MSC

: – cool main sequence stars (V I 0 6), EV – evolved stars situated above and to the right of main sequence. Vol. 50 215

2.2. Method of Analysis The analysis of space orientation of orbital planes relative to the Galactic plane is performed using a position of orbital ”north” pole as deﬁned by Batten (1967). Because of an obvious misprint in formulas given in the Batten’s paper, the equ-

atorial coordinates (A; D) of the orbital pole are found using the below presented

procedure (see Fig. 3 for explanation and names of angles):

δ ¢ α

cos φ cos cos 1

α= φ

sinβ sin sin 2

δ ¢ δ ¢ ¢ β ε

sinD sin cosi cos sini cos 3

α ¢ β ε=

sin A sini sin cosD 4

α ¢ δ ¢ δ ¢ β ε℄=

cos A cosi cos sini sin cos cosD 5

Æ Ω

where: α and δ is right assension and declination of binary star, ε 90 , Æ and by deﬁnition β assumes values between 0 Æ and 180 while φ is in the same quadrant as α.

L 36 Ν ε = Ω − 90 α φ = 26

6 β

δ ε

2 φ 3 '

δ Fig. 3. Celestial sphere showing relations between equatorial coordinates of a star (α; ) and orbital Ω parameters (i; ). S is position of visual binary, P is position of binary ”north” pole.

The pole position given by the above formulas is that which would be derived by applying a left hand rule to the orbital motion. The equatorial coordinates of

the ”north” orbital pole are changed to the Galactic longitude and latitude using the

Æ Æ Æ Æ

; ; same notation as in (ESA 1997): l 180 180 , b 90 90 . 216 A. A.

3. Results

The positions of the poles of orbits were calculated for 252 visual binary sys-

tems. Errors of the orbital inclinations, i, and of the positions of ascending node Æ

Ω, lead to an average error of pole position of ¦14 . Therefore any fluctuations on a scale less than about fifteen degrees should be regarded as spurious. The results are presented on all-sky plots using Aitoff (i.e., equal area) projection as described in ESA (1997) p. 311. Any selection effects in the distribution of positions of the analyzed binaries with respect to the Galactic coordinate system would influence statistical analysis of the orientation of orbital planes. The distribution of the positions of binaries for our sample is indeed uniform over the sky as shown in Fig. 4a. A lack of any dependence of the star density on Galactic latitude reflects the fact

that almost all stars in the sample are nearby (215 systems are closer than 100 pc).

Æ Æ A slight increase in density for l 80 ¤ 90 could be related to the Orion arm of our Galaxy.

D 3RVLWLRQVRIELQDULHV

E 3RVLWLRQVRIRUELWDOSROHV

Fig. 4. The positions of binaries (a), and orbital poles (b), in the Galactic coordinates presented in Aitoff (equal area) projection.

The positions of binary poles are presented in Fig. 4b. It is evident that there is no pronounced concentration of pole positions. The result is similar to that of Vol. 50 217

3ROHSRVLWLRQV 3RUE \ 3RUE!\

Fig. 5. The positions of orbital poles in the Galactic coordinates using Aitoff (equal area) projection. =

Filled circles represent binaries with Porb < 3 years (N 102), open circles represent binaries with = Porb > 3 years (N 150).

3ROHSRVLWLRQV H H!

Fig. 6. The positions of orbital poles in the Galactic coordinates using Aitoff (equal area) projection.

: = > : Filled circles represent binaries with e < 0 3 (N 88), open circles represent binaries with e 0 3

(N = 164).

Batten (1967), and conﬁrms the expectation of no general tendency for parallelism

of orbital planes among visual binaries. A slight asymmetry in the pole distri-

bution between the northern and southern Galactic hemispheres (N bpole 0

132, N bpole 0 120) is not signiﬁcant statistically. The reality of some other

ﬂuctuations of density seen in Fig. 4b (e.g., higher concentrations at: l 150 ,

Æ Æ Æ Æ Æ

¤ ¤

b 30 and l 90 120 , b 0 20 and lower concentration at l

Æ Æ Æ Æ

0 ¤ 80 , b 0 20 should be checked on a more numerous sample. There is no

j j clear preference for values of b pole 90 corresponding to orbital planes parallel to the Galactic plane. There is also no indication of preference for perpendicular orientation of the orbital planes relative to the Galactic plane as mentioned by Dommanget (1988). 218 A. A.

The uniform distribution of orbital pole positions for the whole sample does not exclude any possible preferences for parallelism of orbital planes within more homogeneous subgroups of binaries. Because our sample contains only 252 binary systems we cannot divide them into more than three groups to avoid spurious ef-

fects. In Fig. 5 we present orbital pole distributions for two subgroups: short-period > binaries (Porb < 3 y) and long-period binaries (Porb 3 y). In both cases the distributions are random. In close binaries evolution forces circularization of orbits with time. In visual binaries one can rather expect that eccentricities reﬂect conditions at

the epoch of the system formation. In Fig.6 we show distributions of orbital poles :

for two subgroups with different eccentricities: 91 binaries with e 0 3 and 161 : binaries with e > 0 3. Again, no trace of preferential orientation is present.

06+ D 1

E 06& 1

(9 F 1

j j Fig. 7. One hemisphere presentation of orbital pole positions in l ; b Galactic coordinates. a) hot main sequence stars, b) cool main sequence stars, c) evolved stars.

Small number of objects in the analyzed sample can lead to an apparent de- tection of high or low density areas on all-sky plots (see e.g., Chang 1929, Heintz 1969). Small density of points per square degree can be artiﬁcially increased by disregarding the direction of orbital motion (clockwise or anticlockwise). In order Vol. 50 219

06+

06& GHJ

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Fig. 8. Density (number of poles per 10 square degrees) distribution as a function of Galactic latitude j jb , for three subgroups of binaries: MSH – hot main sequence stars, MSC – cool main sequence stars, EV – evolved stars.

to accommodate the points in one projected hemisphere we use presentation with

j j

l ; b coordinates. To have the same position of a pole for orbits with the same or-

j j bital plane orientation but opposite motion of stars, changes of bpole < 0 into b must be associated with 180 Æ shift in l . Such presentation is useful for analysis of less numerous samples (see e.g., similar ”one-hemisphere” presentation in Fig. 1 of Batten 1967).

Using HR diagram for primaries (Fig. 2) we divide our sample into three sub-

< :

groups: MSH – main sequence hot stars with V I 0 6, i.e., more massive than

about 3 M , MSC – main sequence stars cool with V I 0 6, EV – evolved stars above and to the right of main sequence. The dividing lines are shown in Fig. 2. Massive MSH stars are the youngest, EV group represents the oldest binaries (except possible pre-main-sequence stars) while age cannot be well deﬁned among MSC. The distribution of pole positions for these three subgroups is pre-

sented in Fig. 7 using ”one-hemisphere” presentation. No evident concentrations j or ”avoided areas” are seen for any subgroup. However, some dependences on jb can be traced in Fig. 8 where the number of binaries with orbital poles of similar

Galactic latitude is presented for these three subgroups. MSH binaries show no j dependence on jb , while MSC poles are mainly close to Galactic plane, i.e., more orbital planes are perpendicular than parallel to the Galactic plane (for 65% MSC 220 A. A.

Fig. 9. The positions of orbital poles in the Galactic coordinates using Aitoff (equal area) projection

for 19 binaries less distant than 10 parsecs from the Sun.

j j j

poles jb is less than 30 ). Evolved binaries display a maximum at b between Æ 20 Æ and 45 . Both effects should be checked on larger samples.

Dommanget (1988) found a concentration of orbital poles of 10 nearby bina-

Æ Æ

³ ries at l ³ 100 , b 15 . A possible parallelism of the orbital planes of nearby visual binaries is checked in Fig. 9. Indeed, a subgroup of 19 binaries from our sam-

ple located at distance r 10 pc, shows asymmetry in the distribution of their orbi-

Æ Æ

tal poles. The poles are assembled around positions near l ³ 110 , b 10 and

Æ Æ Æ Æ Æ

º ³ º j j ² l ³ 115 , b 5 . In two large regions, namely: 80 l 80 and b 50 there are no orbital poles. The scarcity of the material does not permit to draw de- ﬁnite conclusions, but Dommanget’s suggestion that space might be divided into elements of the order of 20 parsecs where visual systems show similar orbital plane orientation seems to be strengthened.

Acknowledgements. This paper was supported by KBN grant 2 P03D 009 12.

REFERENCES

Batten, A.H. 1967, I.A.U. Symp., 30, 199. Chang, Y.C. 1929, Astron. J., 40, 11. Dommanget, J. 1988, Astrophys. and Space Sci., 142, 171. ESA 1997, The Hipparcos and Tycho Catalogues, ESA SP-1200. Gillet, S.L. 1988, Astron. J., 96, 1967. Heintz, W.D. 1969, J. R. Astron. Soc. Can., 63, 275. Söderhjelm, S. 1999, Astron. Astrophys., 341, 121. Worley, C.E., and Heintz, W.D. 1983, Publ. U.S. Naval Obs., XXIV, Part VII.