Orbital elements are determined using a three- 1. INTRODUCTION 2. NEW SPECKLE INTERFEROMETRIC DATA 3. METHOD OF ORBIT CALCULATION

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1 THE ASTRONOMICAL JOURNAL, 117:1023È1036, 1999 February ( The American Astronomical Society. All rights reserved. Printed in U.S.A. BINARY STAR ORBITS FROM SPECKLE INTERFEROMETRY. I. IMPROVED ORBITAL ELEMENTS OF 22 VISUAL SYSTEMS BRIAN D. MASON1,2,3 AND GEOFFREY G. DOUGLASS US Naval Observatory, 3450 Massachusetts Avenue, NW, Washington, DC AND WILLIAM I. HARTKOPF1,2 Center for High Angular Resolution Astronomy, Georgia State University, 38 Peachtree Avenue, Atlanta, GA Received 1998 October 5; accepted 1998 October 29 ABSTRACT Improved orbital elements for 22 binary systems are presented. For 12 systems, masses are calculated using available trigonometric parallaxes and making certain assumptions regarding the mass ratio. For the other 10 systems, provisional elements are provided that should provide relatively accurate ephemerides for the next decade. Key words: binaries: close È binaries: visual È stars: fundamental parameters È techniques: interferometric 1. INTRODUCTION The most well-known beneðt of speckle interferometry is probably its ability to resolve binary stars at or near the di raction limit of telescopes. This has resulted in a powerful synergy between short-period visual and long-period spectroscopic binaries, leading to stellar masses and more e ective characterization of the empirical mass-luminosity relation for stars. In addition to the ability to reach the di raction limit of a telescope, interferometry has provided the possibility of signiðcant improvement of precision of measurement, yielding typical errors of 0.5 in position angle and 0.5% in separation. The time base of routine speckle interferometric observations of binary stars is now in excess of 20 years. As a result of this long series of observations, which are of exceptional accuracy and precision, binary star orbits once considered deðnitive when based on classical techniques (typically, Ðlar micrometry), are now being further reðned, often resulting in signiðcant changes in the orbital elements. Improvements to the orbital elements based on these data, coupled with the parallaxes (primarily from the Hipparcos program), are yielding masses for these binaries with smaller errors. Orbital elements, ephemerides, predicted radial velocity curves, and model-dependent masses are calculated and presented for 12 binary systems. Also presented are elements and ephemerides for an additional 10 systems. These 10 orbits, while better than previously published determinations, must still be regarded as provisional. 2. NEW SPECKLE INTERFEROMETRIC DATA Most of the data used in these calculations are tabulated in the Washington Double Star Catalog (WDS; Worley & Douglass 1997) Database and the Third Catalog of Inter- ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ 1 Visiting Astronomer, Kitt Peak National Observatory and Cerro Tololo Interamerican Observatory, National Optical Astronomy Observatories, operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation. 2 Visiting Astronomer, Mount Wilson Observatory, operated under a collaborative agreement between the Carnegie Institution of Washington and the Mount Wilson Institute. 3 Guest Observer, McDonald Observatory, University of Texas at Austin ferometric Measures of Binary Stars (Hartkopf, McAlister, & Mason 1997). Additional measures obtained on a variety of telescopes are presented in Table 1. The US Naval Observatory (USNO) speckle camera, initially described by Douglass, Hindsley, & Worley (1997), has been upgraded with a new intensiðed CCD and reduction software package as described by Germain et al. (1999a, 1999b). All data taken with the 0.7 m telescope at the USNO produced realtime directed vector autocorrelations (DVA; see Bagnuolo et al. 1992) and were reduced in the manner described in Douglass et al. Speckle data from CHARA taken with the 4.0, 3.8, and 2.5 m telescopes (listed in Table 1) have been taken with the CHARA speckle camera (McAlister et al. 1987); these data were postprocessed using the DVA algorithm. USNO speckle data from the McDonald 2.1 m telescope were taken with the USNO speckle camera and also postprocessed with the DVA algorithm. In Table 1, the Ðrst column gives the epoch J coordinate, which is the primary identiðer from the WDS. The discoverer designation is provided in the second column with the Henry Draper catalog number in the third column. The fourth column lists the epoch of the observation expressed as a fractional Besselian year. The Ðfth and sixth columns give the measured position angle (h) and angular separation (o), respectively. While equinox J coordinates are provided, position angles have not been corrected for precession and are thus based upon the equinox for the epoch of observation. Colons following h and o values indicate measurements of somewhat reduced accuracy, usually the result of observing fainter systems or systems of larger magnitude di erence. The seventh column provides the characteristics of the Ðlter used in the observation expressed in nanometers (central wavelength/fwhm). The Ðnal column gives the aperture of the telescope in meters where the observation was obtained, which also uniquely deðnes the telescope. The telescopes include the 4.0 m Blanco telescope on Cerro Tololo, the 3.8 m Mayall telescope on Kitt Peak, the 2.5 m Hooker telescope on Mount Wilson, the 2.1 m Struve telescope at McDonald Observatory, or the 0.7 m USNO refractor in Washington, D.C. 3. METHOD OF ORBIT CALCULATION Orbital elements are determined using a three-

2 TABLE 1 NEW SPECKLE INTERFEROMETRIC MEASURES WDS or Discoverer j/*j Telescope a, d (J2000.0) Designation HD Date (BY) h o (nm) (m) 00596[0112 A 1903 AB A / ]7054 Bu 513 AB : 0.806: 549/ / ]2640 A 1844 AB / ]0158 Stt 517 AB / [2718 Fin / [5429 I / ]3953 StF / / ]1044 Bu 612 AB : 0.303: 549/ / / ]0939 StF 1879 AB / / / / / / / / / [1947 B 2351 Aa,b / / ]3018 StF 1937 AB / / / / / / / / / / / / / / / / / / / / / / / / / / / / [1122 StF 1998 AB / / / / / / / / / / / / / /24 0.7

3 BINARY STAR ORBITS. I TABLE 1ÈContinued WDS or Discoverer j/*j Telescope a, d (J2000.0) Designation HD Date (BY) h o (nm) (m) / ]2753 Kui 83 AB : 0.233: 549/ : 0.288: 538/ / / / / / [2953 HdO 150 AB : 0.390: 549/ [1951 Fin / / [0637 A : 0.125: 538/ dimensional adaptive grid search ÏÏ technique, as described in Hartkopf et al. (1989). The routine for the determination of formal errors has been changed to one adapted from the analysis programs of Tokovinin (1992) and yields more reliable errors. Many of the systems presented here have extensive histories of visual observation that, although of lower accuracy than the interferometric data, provide crucial information in the determination of the orbital period. Given a set of elements P, T, and e, the four Thiele-Innes elements (A, F, B, and G)Èhence the four remaining geometric elements (aa, i, ), and u)ècan be determined by the method of least squares. What follows are the steps used in the grid search technique. 1. An initial set of values for P, T, and e is chosen as well as grid step sizes for these elements. 2. Other elements are determined for each point in the grid, then these elements are used to derive overall weighted O[C residuals (see weighting method below). 3. The grid is recentered on the (P, T, e) set giving smallest residuals, and the process repeated. 4. Grid step sizes are reduced and the process repeated until step sizes decrease below 0.01 year in P and T, in e. 5. The rms residuals are determined separately for visual and interferometric data. Observations whose residuals exceed 3 times their rms errors are given zero weight. 6. The grid search is now repeated, until steps fall below year in P and T, in e. 7. Formal errors are determined for all elements. Relative weights are assigned to each astrometric observation based on the telescope aperture and observing technique. Visual observations made with larger telescopes are found to be more accurate than those made using smaller instruments. C. Worley (1987, private communication) noted roughly a factor of 2 di erence in variance between visual observations made with telescopes of greater than 18 inch (46 cm) versus less than 18 inch apertures. A weight of 1.0 is assigned to a visual observation made with a large ÏÏ (aperture 18 inch) telescope, while a weight of 0.5 is given to visual observations made with a small ÏÏ (aperture \18 inch) telescope. Relative weights of interferometric versus visual measures were initially determined by Hartkopf et al. (1989) based on rms residuals for eight very well-observed binaries. These relative weights have been born out in subsequent orbital analyses as well. A Center for High Angular Resolution Astronomy (CHARA) interferometric measure made using a4mclass telescope is therefore given an initial weight of 20, while CHARA or USNO measures made with 2 m class telescopes and Hipparcos measures are given onehalf this weight. Other interferometric measures are given weights of 5 (a more multidimensional weighting scheme is currently under consideration). Weights for measures averaged from several nightsï data are scaled by Jn, and weights for measures noted as being of poor quality are reduced by 50%. In most cases, all data were used in the Ðnal orbital solution. However, in the case of six systems (B 2351, Bu 513, HdO 150, Kui 83, StF 1937, and StF 1998) the close approach or wealth of measures from high angular resolution techniques allowed for an alternate method of computation. In each of these cases, all data were utilized for the determination of the orbital period. Then, with the period Ðxed at this value, the remaining six elements were calculated using only measures from high-resolution techniques (in the systems listed here, the techniques are speckle interferometry and measures from Hipparcos). For these systems, the error in the period is adopted from the Ðrst orbit calculation, while the errors to the remaining elements are adopted from the second orbit calculation. 4. NEW ORBITS Following the manner of Hartkopf, Mason, & McAlister (1996) and Mason (1997), the new sets of orbital elements are presented below in Figures 1È6, in which we have combined the tabular information with the orbit plots for each star in an atlas ÏÏ format. For each system, the top left of the Ðgure shows the relative visual orbit of the system; the x and y scales are in arcseconds. The solid curve represents the newly determined orbital elements, while the dashed curve represents previously published orbital elements, as referenced in the notes for each system. The dot-dashed line indicates the line of nodes. Speckle measures from the USNO, CHARA, and other groups are shown as stars, Ðlled circles, and open circles, respectively. Visual measures made with small ÏÏ or large ÏÏ (aperture less or more than 18 inch) telescopes are shown as plus signs or hash marks, respectively. Measures from the ESA Hipparcos satellite are indicated by an HÏÏ. All measures are connected to their predicted positions on the new orbit by O[C ÏÏ lines, where dotted O[C lines indicate measures given zero weight in the Ðnal solution. For purposes of scaling, some zero-weighted measures far outside the extent of the orbit are not plotted.

4 1026 MASON, DOUGLASS, & HARTKOPF Vol. 117 FIG. 1.ÈOrbital information for 02019]7054 \ Bu 513 AB (top) and 05017]2640 \ A 1844 (bottom). The scale is in arcseconds The top right portion of the Ðgures gives predicted radial velocity curves based on these elements, together with published trigonometric parallaxes (unless otherwise stated, from Hipparcos; ESA 1997) and estimated mass ratios. The published *m from the WDS (or other sources as indicated in the notes) can be used along with the tables from Lang (1992) or Gray (1992) to obtain an estimate of the mass ratio assuming the objects are of the same luminosity class. If they are of di erent luminosity classes (a hot dwarf and a cool giant, for example), a drastically di erent *m at some other color could be expected. Of the 12 systems presented in Figures 1È6, seven of the systems (Fin 47, Hu 644, Bu 612, B 2351, StF 1937, StF 1998, and HdO 150) have predicted radial velocity di erences of at least 10 km s~1 at periastron and thus could possibly be detected by a concerted radial velocity program. The middle and bottom right of each Ðgure give the orbital elements, along with the formal errors and an ephemerides covering the next 10 years. Worley & Heintz (1983) provided grades to published orbits ranging from grade 1 ÏÏ (deðnitive) to grade 5 ÏÏ (indeterminate). The systems presented in Figures 1È6 would probably all be qualiðed as at least grade 2 ÏÏ (good). While a new quantitative grading scheme is currently in development at USNO, for the present we adopt the criteria Ðrst discussed in Hartkopf et al. (1996) for quantifying deðnitive orbits (formal errors ¹0.5% for P and a; ¹1% for e, ¹0.5% of P for T ; and ¹1 for i, ), and u). By these

5 No. 2, 1999 BINARY STAR ORBITS. I FIG. 2.ÈOrbital information for 11053[2718 \ Fin 47 (top) and 13198]4747 \ Hu 644 (bottom). The scale is in arcseconds restrictive qualiðcations, Bu 612 AB (\13396]1044) would be considered deðnitive, although others (Hu 644 and StF 1937) are quite close to this grade. 5. MODEL-DEPENDENT MASSES The *m limit of speckle of approximately 3 mag (Mason 1996) also imposes some restrictions on the mass ratio. Systems that have large mass ratios would not be detected by speckle interferometry, as systems of this type also have large magnitude di erences. In most cases in which the *m limit is relatively small, the two stars will be of the same luminosity class, although there are known cases of hot dwarf ] cool giant binaries (e.g., Mason et al for three examples of this). A binary composed of a hot giant and a cool dwarf will tend to show a large di erence in the *m values measured at di erent wavelengths. Furthermore, systems of these types can often be recognized as having composite spectra due to the great di erences in the visible spectral lines for the two components. Unless noted otherwise, spectral types are taken from SIMBAD. The tables of Lang (1992) or Gray (1992) allow for a spectral type to be assigned to the secondary based on the type of the primary, the magnitude di erence from the WDS, and the determination of luminosity class. After spectral types are assigned the bolometric magnitude can be calculated using the parallax and bolometric correction for that spectral type. Table 2 and Figure 7 present the results for these 12 systems. The solid line in Figure 7 is calculated

6 1028 MASON, DOUGLASS, & HARTKOPF Vol. 117 FIG. 3.ÈOrbital information for 13396]1044 \ Bu 612 AB (top) and 15123[1947 \ B 2351 Aa, b (bottom). The scale is in arcseconds from the mass-luminosity equation of Heintz (1978). Error bars are based on the parallax errors for the magnitudes and errors from the parallaxes and orbits for the masses Notes on Individual Systems 02019]7054 \ Bu 513 AB \ 48 Cas.ÈWhile the spectroscopic orbit of Abt (1965) was graded as very poor and unreliable ÏÏ in the catalog of Batten, Fletcher, & Mac- Carthy (1989), it has not yet been improved upon. The spectral type of the primary is provided by Gray & Garrison (1989). A M of 3.11 ^ 0.57 M is calculated for Bu 513 AB, 13% smaller A`B than the 3.51 M _ based on the Heintz _ (1969) orbit. This system was originally intended to be used as a scale calibrator for USNO data taken with the McDonald 2.1 m telescope. On closer inspection, it was noted that residuals were increasing with time, and so correction is now applied to this grade 1 (Worley & Heintz 1983) orbit. The largest contributor to the error in the mass is the uncertainty in the semimajor axis. This error will decrease if measures of high accuracy continue to be taken while this system moves toward closest approach in late ]2640 \ A 1844.ÈUnfortunately, this wellknown pair has not been observed often by either visual or speckle techniques. The existing data cover more than three full revolutions since its discovery, and the rather high *m

7 No. 2, 1999 BINARY STAR ORBITS. I FIG. 4.ÈOrbital information for 15232]3018 \ StF 1937 AB (top) and 16044[1122 \ StF 1998 AB (bottom). The scale is in arcseconds results in little chance of an incorrect quadrant assignment by observers. The Hipparcos *m of 1.93 ^ 0.14 (ESA 1997) agrees well with that determined by lunar occultation (2.03 ^ 0.05; Schmidtke, Africano, & Quigley 1989) observed in a similar passband. The grade 2 orbit of Baize (1959a) is shown in Figure 1 (bottom). Two speckle measures and that of Hipparcos have been made since the orbit determination of Mason (1994). While the elements have not changed signiðcantly, the errors are smaller. This orbit replaces that earlier calculation. This M of 1.72 ^ 0.77M is calculated for A 1844, 41% larger A`B than the A`B based on the Baize (1959a) orbit. The errors in 1.13MA`B both aa and n are larger than desirable. Regular observing by speckle interferometry should decrease the error in aa signiðcantly over the next decade as this system approaches and passes through periastron. While the inclination is small, the sharp lines associated with G stars make this an attractive target for radial velocity study [2718 \ Fin 47 \ s1 Hya.ÈThis system has gone through nine full orbital revolutions since it was Ðrst resolved by Finsen (1928), leading to a period error of only 56 hours. The high inclination (96.5), relatively late spectral type (F3IV according to Abt 1981), and short period (7.55 yr) would seem to make this target well suited to spectroscopic investigation. For purposes of scaling, some zeroweighted measures are not plotted. The of M A`B

8 1030 MASON, DOUGLASS, & HARTKOPF Vol. 117 FIG. 5.ÈOrbital information for 17370]2753 \ Kui 83 (top) and 19026[2953 \ HdO 150 AB (bottom). The scale is in arcseconds 3.86 ^ 0.51 calculated for this system is only 7% smaller than the 4.13 M based on the grade 2 orbit of van den Bos (1957). The largest _ contributor to the error in this determination is the parallax ]4747 \ Hu 644.ÈThe parallax of this system from the Hipparcos satellite (ESA 1997) seems suspect. The separation of this pair closed from 1A.0 to 0A.5 during the lifetime of the Hipparcos program, which could result in a signiðcant problem in the parallax determination (about 20% of the data were rejected in calculating their published parallax; C. Martin 1998, private communication). Consequently, the parallax is taken from the Yale Parallax Catalogue (van Altena, Lee, & HoÑeit 1995). Using this value, a mass sum of 1.24 ^ 0.24 M is calculated. This value agrees well with the determination _ of Henry & McCarthy (1993; M \ 1.20 ^ 0.18 M ). The orbit of Soulie (1986) shown in A`B the diagram seems to _ underestimate the value of aa. The M seems a bit low. However, this is approaching the lower A`B limit of the mass-luminosity relation of Heintz (1978; set at 0.5 M ) and the parallax error may be larger than the value quoted. _ The orbit seems very well characterized ]1044 \ Bu 612 AB.ÈFor purposes of scaling some zero-weighted measures are not plotted. Two orbits (Danjon 1956: Churms 1954) are listed in the literature for this system; both are given grades of 3 by Worley & Heintz (1983). The Danjon (1956) orbit had smaller O[C values

9 No. 2, 1999 BINARY STAR ORBITS. I FIG. 6.ÈOrbital information for 21044[1951 \ Fin 328 (top) and 23517[0637 \ A 2700 (bottom). The scale is in arcseconds and is plotted in Figure 3a. A long-time base of visual measures (Ðrst measured in Burnham 1879) covering over Ðve orbital periods and speckle measures (Ðrst measure in McAlister 1977) of one orbital period allow for a very accurate determination of the orbital elements. As a result, this system could serve as a secondary spatial scale calibrator. While it has an expected *V of about 18 km s~1 at periastron, this early F star is likely r to have very broad lines making it less suitable than others for radial velocity studies. A M of 2.43 ^ 0.38 M is calculated 14% (29%) smaller than A`B the value based on _ the elements of Danjon (Churms). Both of these are outside the 1 p error bars. These points seem a bit o the mass-luminosity curve in Figure 7; however, Abt (1981) has classiðed these as subgiants, which would explain the deviation [1947 \ B 2351 Aa, b \ Lib.ÈThe collection of speckle data for this system is almost as rich as that for Bu 612. However, the visual data for this very close system are scant. The grade 3 orbit of Heintz (1982) is shown in Figure 3b. The *m from visual estimates of 0.4 ^ 0.2 barely falls within the 1 p error bars from the lunar occultation measure of 1.25 ^ 1.01 at 445 nm (Eitter & Beavers 1979; a *m of 1.40 ^ 0.88 at 720 nm was also determined). Heintz (1966) also provided spectroscopic elements; however, he found them difficult to reconcile with the visual elements. The parallax error is primarily responsible for the large error

10 1032 MASON, DOUGLASS, & HARTKOPF Vol. 117 B 2351 A Bolometric Magnitude HDO 150 A B 2351 B HDO 150 B FIN 328 A BU 513 A FIN 47 A & B BU 612 A BU 612 B STF 1998 A STF 1998 B BU 513 BFIN 328 B A 1844 A STF 1937 A STF 1937 B A 1844 B A 2700 A A 2700 B KUI 83 A KUI 83 B 8 HU 644 A 10 HU 644 B Mass (solar masses) FIG. 7.ÈModel-dependent mass luminosity values. The solid line is calculated from the mass-luminosity equation of Heintz (1978) bars associated with the calculated mass sum of this system: 6.05 ^ 2.23 M, compared with the M of 4.38 M _ A`B _ using elements from Heintz (1982) ]3018 \ StF 1937 AB \ g CrB.ÈThere are over 850 published means for this system. For the sake of clarity, only high angular resolution data are plotted in Figure 4a. For this system a M of 2.44 ^ 0.18 M is calculated, 14% smaller than the A`B 2.78 M based on _ the Silbernagel (1929) orbit. The Silbernagel orbit _ was given a grade of 1 ( deðnitive ÏÏ), and it does not appear that a correction to the elements would be necessary if all measures are plotted. However, the precision and accuracy of speckle interferometry allows a correction to be made. While complete orbital coverage will allow the elements to be even more accurately determined, the largest contributor to the error in M is the Hipparcos parallax error of 1.24 mas. The spectroscopic A`B orbit of Chang (1929) was graded as very poor and unreliable ÏÏ in the catalog of Batten et al. (1989) [1122 \ StF1998 AB \ m Sco.ÈFor considerations of scale some zero-weighted measures are not plotted in Figure 4 (bottom). The published orbit is from Harrington (1987). This system has some of the oldest interferometric measures of binary stars, obtained by Schwarzschild (1896). A M of 1.84 ^ 0.58 M is calculated for this system, A`B _ 41% smaller than the value based on the elements of Harrington (1987). SigniÐcant improvement can be made to the elements at the next periastron passage. However, this is not predicted to occur until It is uncertain why this system with a *m of only 0.3 was not resolved by Hipparcos. At the Hipparcos mean epoch, a separation of 0A.623 is predicted. No parallax was determined for this system by Hipparcos, and the n value used is from the Yale Parallax Catalogue (van Altena 1995). These subgiants appear o the main-sequence mass-luminosity curve, as expected ]2753 \ Kui 83.ÈA M of 1.27 ^ 0.30 M is calculated for this pair of M dwarfs, A`B 17% larger than _ the 1.07 M based on the grade 1 orbit of Baize (1972). Like many of _ these systems, the largest source of error contributing to the mass sum is the parallax. Originally intended as a scale calibrator for the McDonald 2.1 m telescope, comparison of O[C values with the published orbit led to this calculation. This is yet another case of an orbit, previously characterized as deðnitive, ÏÏ which has been improved by speckle interferometry [2953 \ HdO 150 AB \ f Sgr.ÈThis is another case of a previously published grade 1 orbit (van den Bos 1960a) that has been improved. A mass sum of 5.37 ^ 0.69 M is determined here, 25% smaller than the 6.87 M value _ based on the elements of van den Bos (1960a). A _ complete orbital cycle has been observed by speckle inter-

11 No. 2, 1999 BINARY STAR ORBITS. I TABLE 2 MASS AND LUMINOSITY DETERMINATIONS Mass Component (M ) _ Bolometric Magnitude Bu 513 A 1.92 ^ ^ 0.04 Bu 513 B 1.19 ^ ^ 0.04 A 1844 A 1.00 ^ ^ 0.16 A 1844 B 0.72 ^ ^ 0.16 Fin 47 A 1.93 ^ ^ 0.07 Fin 47 B 1.93 ^ ^ 0.07 Hu 644 A 0.66 ^ ^ 0.13 Hu 644 B 0.58 ^ ^ 0.13 Bu 612 A 1.24 ^ ^ 0.11 Bu 612 B 1.19 ^ ^ 0.11 B 2351 Aa 3.54 ^ 1.12 [0.58 ^ 0.13 B 2351 Ab 2.51 ^ 1.12 [0.08 ^ 0.13 StF 1937 A 1.26 ^ ^ 0.05 StF 1937 B 1.18 ^ ^ 0.05 StF 1998 A 0.92 ^ ^ 0.11 StF 1998 B 0.92 ^ ^ 0.11 Kui 83 A 0.64 ^ ^ 0.16 Kui 83 B 0.63 ^ ^ 0.16 HdO 150 A 2.97 ^ ^ 0.08 HdO 150 B 2.40 ^ ^ 0.08 Fin 328 A 1.67 ^ ^ 0.08 Fin 328 B 1.00 ^ ^ 0.08 A 2700 A 0.60 ^ ^ 0.10 A 2700 B 0.58 ^ ^ 0.10 ferometry for this system. The luminosities of these stars seem uncertain, with classiðcations ranging from subgiant (Abt 1981) to class IVÈV (Gray & Garrison 1987) [1951 \ Fin 328 \ g Cap.ÈDespite having a large *m determined variously as 2.37 ^ 0.06 according to Hipparcos (ESA 1997) and 1.67 ^ 0.72 from lunar occultation (Evans & Edwards 1983), older speckle data carried an inherent 180 ambiguity and many quadrant Ñips were necessary to arrive at the correct solution for this system. The orbit of Olevic & Jovanovic (1997) is plotted in Figure 6 (top), while that of Zulevic (1993) is not. The Zulevic orbit has much larger O[C values due to incorrect quadrant assignments. The calculated values of M give some indication of the importance of the correct identiðcation of the quadrant with the DVA. The elements of Olevic A`B & Jovanovic (1997) result in a mass sum of 19.6 M, while those of Zulevic (1993) lead to a mass sum of 21.3 _ M. Those based on the new elements are 2.67 ^ 0.87 M _. These elements also replace the older calculation _ of Mason (1994), which would have resulted in a mass sum of 2.75 M [0637 _ \ A 2700.ÈNew orbital elements were published simultaneously by both Mason & Hartkopf (1998) and Docobo & Ling (1998). While these elements replace those earlier values of Mason & Hartkopf (1998), all three of these are within 1 p of each other, and it will take more data and time to determine deðnitive elements for this TABLE 3 ORBITAL ELEMENTS FOR BINARIES WITH INCOMPLETE PHASE COVERAGE P a i ) T 0 u a, d (J2000.0) Name (yr) (arcsec) (deg) (deg) (yr) e (deg) 00596[0111 A 1903 AB 153 ^ ^ ^ ^ ^ ^ ^ [6943 I ^ ^ ^ ^ ^ ^ ^ ]0158 Stt 517 AB 530 ^ ^ ^ ^ ^ ^ ^ ]0942 StF ^ ^ ^ ^ ^ ^ ^ ]3302 Stt ^ ^ ^ ^ ^ ^ ^ [5245 B ^ ^ ^ ^ ^ ^ ^ [5429 I ^ ^ ^ ^ ^ ^ ^ ]3953 StF ^ ^ ^ ^ ^ ^ ^ ]0939 StF 1879 AB 243 ^ ^ ^ ^ ^ ^ ^ [6625 HJ ^ ^ ^ ^ ^ ^ ^ 2.0 TABLE 4 EPHEMERIDES FOR BINARIES WITH INCOMPLETE PHASE COVERAGE h o h o h o h o h o a, d (J2000.0) NAME (deg) (arcsec) (deg) (arcsec) (deg) (arcsec) (deg) (arcsec) (deg) (arcsec) 00596[0111 A 1903 AB [6943 I ]0158 Stt 517 AB ]0942 StF ]3302 Stt [5245 B [5429 I ]3953 StF ]0939 StF 1879 AB [6625 HJ

12 1034 MASON, DOUGLASS, & HARTKOPF Vol. 117 FIG. 8.ÈOrbital plots of (clockwise from top left) 00596[0111 \ A 1903 AB, 01220[6943 \ I 263, 07417]0942 \ StF 1130, 08421[5245 \ B 1624, 08041]3302 \ Stt 187, and 05135]0158 \ Stt 517 AB. The scale is in arcseconds. system. For comparison, the grade 3 orbit of Baize (1959b) is plotted in Figure 6 (bottom). The mass sums resulting from these various calculations are: 1.18 M (Mason & Hartkopf 1998), 1.32 M (Docobo & Ling 1998), _ 1.38M (Baize 1959b), and 1.12 ^ _ 0.41 M for this calculation. The _ parallax is the largest source of _ error here. More high angular resolution data should be able to reðne this orbit over time. 6. ORBITAL ELEMENTS OF BINARIES WITH INCOMPLETE PHASE COVERAGE The following 10 systems have improved orbital elements but are still subject to signiðcant changes of their elements with new observations. Many of these systems have very long calculated orbital periods that may be o signiðcantly from the true value. However, the calculated orbits are better than the previously published orbits shown in Figures 8 and 9, and the resulting ephemerides should be reasonably well behaved over the next 10 years. Figures 8 and 9 present orbit plots of these 10 systems. The previously published orbits and grades (when available) are as follows: 00596[0111 \ A 1903 AB (Heintz 1990), 01220[6943 \ I 263 (Klerk 1973; grade 5), 05135]0158 \ Stt 517 AB (van den Bos 1960b; grade 5), 07417]0942 \ StF 1130 (Baize 1984), 08041]3302 \ Stt 187 (Morel 1970; grade 3), 08421[5245 \ B 1624 (Heintz 1969; grade 4)

13 No. 2, 1999 BINARY STAR ORBITS. I FIG. 9.ÈOrbital plots of (clockwise from top left) 11210[5429 \ I 879, 12108]3953 \ StF 1606, 14542[6625 \ HJ 4707, and 14463]0939 \ StF 1879 AB. The scale is in arcseconds [5429 \ I 879 (Newburg 1967; grade 2), 12108] 3953 \ StF 1606 (van der Wiele 1973; grade 4), 14463]0939 \ StF 1879 AB (Wierzbinski 1957; grade 4), and 14542[6625 \ HJ 4707 (Woolley & Mason 1948; grade 4). The symbols used are the same as for the relative orbit plots of Figures 1È6. Table 3 presents the orbital elements and associated errors for these systems, while Table 4 provides ephemerides covering the next 10 years (in two-year increments) for these 10 systems. The orbit of 11210[5429 (\I 879) is the best of these 10 systems. However, at this declination the prospect of future measures is uncertain. Southern hemisphere double star observers are encouraged to place this star on their program. Thanks are provided to the US Naval Observatory for its continued support of the Double Star Program. The speckle interferometry program at Georgia State University has been supported by the National Science Foundation, most recently through grant AST , by the Office of the Dean of the College of Arts and Sciences, and by the ChancellorÏs Initiative Fund administered by the Office of the Vice President for Research and Sponsored Programs at GSU. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France. Abt, H. A. 1965, ApJS, 11, 429 ÈÈÈ. 1981, ApJS, 45, 437 van Altena, W. F., Lee, J. T.-L., & Hoffleit, E. D. 1995, The General Catalogue of Trigonometric Stellar Parallaxes (4th ed.; New Haven: Yale Univ. Obs.) Bagnuolo, W. G., Jr., Mason, B. D., Barry, D. J., Hartkopf, W. I., & McAlister, H. A. 1992, AJ, 103, 1399 Baize, P. 1959a, J. Obs., 42, 115 ÈÈÈ. 1959b, J. Obs., 42, 111 ÈÈÈ. 1972, A&AS, 6, 147 ÈÈÈ. 1984, A&AS, 56, 103 Batten, A. H., Fletcher, J. M., & MacCarthy, D. G. 1989, Publ. Dom. Astrophys. Obs. Victoria, 17, 1 van den Bos, W. H. 1957, Union Obs. Circ., 6, 290 ÈÈÈ. 1960a, Union Obs. Circ., 6, 342 ÈÈÈ. 1960b, Union Obs. Circ., 6, 339 Burnham, S. W. 1879, MmRAS, 44, 141 Chang, Y. C. 1929, ApJ, 70, 185 REFERENCES Churms, J. 1954, Union Obs. Circ., 6, 232 Danjon, A. 1956, Ann. Obs. Strasbourg, 5, 6 Docobo, J. A., & Ling, J. F. 1998, Circ. dïinf., No. 135 Douglass, G. G., Hindsley, R. B., & Worley, C. E. 1997, ApJS, 111, 289 ESA, 1997, The Hipparcos and Tycho Catalogues (ESA SP-1200) (Noordwijk: ESA) Eitter, J. J., & Beavers, W. I. 1979, ApJS, 40, 475 Evans, D. S., & Edwards, D. A. 1983, AJ, 88, 1845 Finsen, W. S. 1928, Union Obs. Circ., 3, 35 Germain, M. E., Douglass, G. G., & Worley, C. E. 1999a, AJ, in press ÈÈÈ. 1999b, AJ, in press Gray, D. F. 1992, The Observation and Analysis of Stellar Photospheres (2d ed.; Cambridge: Cambridge Univ. Press) Gray, R. O., & Garrison, R. F. 1987, ApJS, 65, 581 ÈÈÈ. 1989, ApJS, 70, 623 Harrington, R. S. 1987, Circ. dïinf., No. 101 Hartkopf, W. I., Mason, B. D., & McAlister, H. A. 1996, AJ, 111, 370 Hartkopf, W. I., McAlister, H. A., & Franz, O. G. 1989, AJ, 98, 1014

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