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

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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 deter- mining 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 deter- mination 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 ab- breviated 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 sys- tems. 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 +,32 9%2 V H L U QD L E I R U H E P X 1 2UELWDOLQFOLQDWLRQL V H L U QD L E I R U H E P X 1 $VFHQGLQJQRGHΩ 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. @ Q J D P > Y 0 (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 ´ µ cos φ cos cos 1 α= φ ´ µ sinβ sin sin 2 δ ¢ · δ ¢ ¢ ´β · εµ ´ µ sinD sin cosi cos sini cos 3 α µ ¢ ´β · εµ= ´ µ sin ´ A sini sin cosD 4 α µ ¢ δ ¢ δ ¢ ´β · ε℄= ´ µ 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 ; µ ; µ ´ 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.
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