SPECKLE INTERFEROMETRY AT SOAR IN 2014*

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Published 2015 July 17 © 2015. The American Astronomical Society. All rights reserved.
, , Citation Andrei Tokovinin et al 2015 AJ 150 50 DOI 10.1088/0004-6256/150/2/50

1538-3881/150/2/50

ABSTRACT

The results of speckle interferometric observations at the Southern Astrophysical Research Telescope (SOAR) telescope in 2014 are given. A total of 1641 observations were taken, yielding 1636 measurements of 1218 resolved binary and multiple stars and 577 non-resolutions of 441 targets. We resolved for the first time 56 pairs, including some nearby astrometric or spectroscopic binaries and ten new subsystems in previously known visual binaries. The calibration of the data is checked by linear fits to the positions of 41 wide binaries observed at SOAR over several seasons. The typical calibration accuracy is 0fdg1 in angle and 0.3% in pixel scale, while the measurement errors are on the order of 3 mas. The new data are used here to compute 194 binary star orbits, 148 of which are improvements on previous orbital solutions and 46 are first-time orbits.

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1. INTRODUCTION

Binary stars matter in astronomy in many different ways: as calibrators of various stellar properties, as tracers of star formation, and as hosts to diverse astrophysical phenomena such as mass transfer, circumstellar and circumbinary disks, or dynamical resonances, to name a few. Knowledge of orbital elements is needed in these applications. However, only a small fraction of known visual binaries have known orbits, mostly because of orbital periods being much longer than the time covered by observations. Even known orbits are not always reliable for the same reason: lack of sufficient data.

We report here a large set of binary star measurements made at the 4.1 m Southern Astrophysical Research Telescope (SOAR) with the speckle camera. This paper continues the previous series published by Tokovinin et al. (2010b, hereafter TMH10), Tokovinin et al. (2010a), Hartkopf et al. (2012), Tokovinin (2012), and Tokovinin et al. (2014, hereafter TMH14). Our primary goal is improvement of known orbital elements and determination of new orbits. The emphasis is placed on close and nearby pairs resolvable at SOAR, where orbital periods are measured in years rather than decades or centuries. The orbits of these fast binaries can be computed or improved only after a few years of speckle interferometry monitoring. Many orbits were already computed for the first time or improved using data obtained during previous speckle runs. An "orbit optimizer" was used to select binaries where observations in the coming three years could potentially yield noticeable orbit improvement.

The second, overlapping program is the characterization of multiplicity of solar-type stars within 67 pc (the FG-67 sample, Tokovinin 2014a). By resolving known binaries with astrometric acceleration (Makarov & Kaplan 2005) or variable radial velocity (RV), we obtain estimates of their periods and mass ratios and lay a foundation for future orbit determination. The spectroscopic discoveries are mostly furnished by the Geneva-Copenhagen Survey of Nordström et al. (2004, hereafter GCS). On the other hand, by observing relatively wide binaries with separations up to 3'' we constrain the existence of subsystems around their components. Several such subsystems are discovered here. In addition, we have now specially targeted distant physical secondary components to the main FG-67 stars, looking for subsystems. This work (Tokovinin 2014b) complements the large survey of the northern sky done with Robo-AO (Riddle et al. 2015) and shows that subsystems in the secondary components are as frequent as in the main components.

In this paper we also observed Hipparcos binaries within 200 pc with southern declinations, so far largely neglected. These observations allow us to evaluate orbital motion and to find a subset of "fast movers" for further monitoring. Some nearby tight binaries from Hipparcos were monitored from the outset of the SOAR speckle program. This strategy of focusing on fast binaries has resulted in several new orbits, with more still to come. Our approach for this program was therefore similar and complementary to that of the speckle program active at the WIYN 3.5 m telescope at Kitt Peak in recent years (e.g., Horch et al. 2011a, 2011b, 2012). To date, that program has resolved over 150 close companions from the Hipparcos list.

We re-observed some close (hopefully, fast) pairs resolved at the Blanco telescope in 2008. Some of them moved substantially in 6 years, and may yield first orbits. As a "filler," several neglected pairs were also measured or found unresolved.

This paper is structured as follows. Section 2 describes briefly the instrument and data processing and gives an estimate of data consistency for the whole series of measurements at SOAR. The results are presented in Section 3 in the form of data tables with comments on the newly resolved pairs and multiple systems. In Section 4, the new and revised orbits are given, and Section 5 concludes the paper.

2. OBSERVATIONS

2.1. Instrument and Observing Method

The observations reported here were obtained with the high-resolution camera (HRCam)—a fast imager designed to work at the 4.1 m SOAR telescope (Tokovinin & Cantarutti 2008). For practical reasons, the camera was mounted on the SOAR Adaptive Module (SAM, Tokovinin et al. 2008). However, the laser guide star of SAM was not used; the deformable mirror of SAM was passively flattened and the images are seeing-limited. The SAM module corrects for atmospheric dispersion and helps to calibrate the pixel scale and orientation of HRCam, as explained in TMH14. The transmission curves of HRCam filters are given in the instrument manual.5 We used mostly the Strömgren y filter (543/22 nm) and the near-infrared I filter (788/132 nm). The response curve of the latter was re-defined as a product of the filter transmission and detector response furnished by the respective manufacturers.

The electron multiplication CCD (EM CCD) Luca-S used in HRCam failed in 2014 July. It was sent to its manufacturer (Andor) for repair and received back in 2014 December. For the two runs in the fall of 2014, we used the EM CCD Luca-R, kindly loaned by G. Cecil. It has a larger format of 1004 × 1002 pixels, with smaller pixels of 8 μm compared to Luca-S (658 × 496, 10 μm pixels). The second lens in HRCam was replaced by the achromatic doublet of 75 mm focal length to get the pixel scale of 14.33 mas. The detector software driver was also upgraded on this occasion.

Although the two Luca cameras look exactly the same and come from the same manufacturer, their CCDs are radically different. Luca-S uses a line-transfer CCD, while Luca-R has a frame-transfer CCD. We found that Luca-R had poor charge transfer efficiency (CTE) in the vertical direction. Weak signals such as cosmic-ray hits and dark current from hot pixels are smeared vertically over ∼5 pixels, while strong signals are transferred with less spread. This results in the signal-dependent loss of resolution in the vertical direction (along CCD columns), which was accounted for in the data processing by an additional adjustable parameter. This problem was revealed unexpectedly during the 2014 October run. In the next run, we placed stars closer to the line register, improving slightly the vertical CTE by reducing the number of charge transfers.

We studied the distribution of the bias signal of both cameras. It is very well modeled by the sum of a Gaussian component (readout noise) and a negative exponent that corresponds to the single-electron events amplified stochastically by the gain register. Most events are generated by the CCD clocking (clock-induced charge, CIC) typical for EM CCDs. The width (decrement) of the exponential term depends on the EM gain. The rate of CIC events is found as the ratio of the areas below these two terms. For Luca-R, the readout noise is 4.5 ADU and the CIC rate is 0.03. The CIC events are not smeared vertically because no charge transfer is involved. For Luca-S, the readout noise is 9 ADU, the exponential decrement is 30 ADU (for the gain setting of 200 used here), and the rate of CIC events is 0.13 per pixel. About half of the CIC events are removed by the threshold of 17 ADU applied in the power spectrum calculation.

The SOAR telescope suffers from 50 Hz vibration (see TMH14). The vibrations are non-stationary, causing variable loss of resolution if the 20 ms exposure time is used. Most data were taken with an exposure of 5 ms, sampling 1/4 of the vibration period. The resolution is then recovered and the effect of vibrations becomes less dramatic. It disappears completely at an exposure time of 2 ms, used on the brightest targets. With such short exposures, the power spectra extend to the cut-off frequency and are very symmetric. The Luca-R detector suffering from the CTE problem was used mostly with a 10 ms exposure as a compromise between vibrations and poor CTE at low signal levels.

The observations consist of taking a cube of 400 images of 200 × 200 pixels each. For binaries wider than 1farcs5, the 400 × 400 format was used. Each object and filter combination is normally recorded twice, these data are processed independently, and the result is averaged. We used 2 × 2 detector binning on the faintest targets observed in the I filter, with a minor under-sampling and loss of resolution. Measurements of binaries made with and without binning agree well mutually. Faint red dwarfs with I ∼ 12 still produced useful data.

2.2. Observing Runs

The observing time for this program was allocated through NOAO (proposals 2013B-0172, 2014A-0038, 2014B-0019, eight nights total) and by the Chilean National TAC (proposal CN2014B-27, four nights).

Table 1 lists the observing runs, the calibration parameters (position angle offset θ0 and pixel scale in mas), and the number of objects covered in each run. The calibration of angle and scale was done by referencing to the SAM imager, as described in TMH14.

Table 1.  Observing Runs

Run Dates θ0 Pixel Nobj
    (degree) (mas)  
1 2014 Jan 15–16, 22 1.26 15.23 309
2 2014 Mar 7–8 −1.30 15.23 201
3 2014 Apr 19–20 −1.40 15.23 385
4 2014 Oct 5–7 −0.69 14.33 553
5 2014 Nov 7–8 0.66 14.33 253
6 2015 Jan 10–11 –0.20 15.23 248

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Run 1 was affected by transparent clouds. Two hours on 2014 January 22 were added as a backup program. During this run, the Nasmyth rotator of SOAR had a large offset of +2fdg8. The seeing was mediocre to poor. The instrument was not dismounted between runs 1 and 2, but the Nasmyth rotator was re-initialized, explaining the difference in θ0. The sky was clear, and two hours were added on March 7 as a backup from other program. The sky was also clear on the two nights of run 3, with seeing good to excellent.

Runs 4 and 5 used the substitute detector Luca-R and were affected by the CTE problem. For this reason the observations were performed mostly in the I filter with 10 ms exposure. All three nights of run 4 were clear, and mostly with good seeing (the median full width at half maximum, FWHM, of re-centered average images was 0farcs60, the best FWHM was around 0farcs45). The detector was removed between runs 4 and 5 in an attempt to improve the CTE by tuning the electronic parameters; however, this turned out to be impossible. During run 5, the seeing varied from average to poor. In the worst case, the star did not fit in the 3'' field, illuminating all pixels. In such cases, the image is truncated, the power spectrum contains bright vertical and horizontal lines, and the detection limits are poor. Under poor seeing, data obtained with the 400 pixel field and 2 × 2 binning are of better quality, without image truncation.

The two nights of run 6 were clear, with seeing average to poor. The HRCAM was returned to its original configuration with the Luca-S detector. Measurements with the SAM internal light source confirmed that the pixel scale did not change compared to runs 1–3.

2.3. Data Processing

The data processing is described in TMH10. As a first step, power spectra and average re-centered images are calculated from the data cubes. The auto-correlation functions (ACFs) are computed from the power spectra. They are used to detect companions and to evaluate the detection limits. The parameters of binary and triple stars are determined by fitting the power spectrum to its model, which is a product of the binary (or triple) star spectrum and the reference spectrum. We used as a reference the azimuthally averaged spectrum of the target itself in the case of binaries wider than 0farcs1. For closer pairs, the "synthetic" reference was used (see TMH10).

The signal-dependent vertical smearing of the image caused by the CTE problem required a modification of the reference spectrum. We model the smearing by an additional Gaussian term in the reference spectrum $P({f}_{x},{f}_{y})$:

Equation (1)

where fx and fy are spatial frequency coordinates along CCD lines and columns respectively, TDL is the diffraction-limited transfer function, fc is the cut-off frequency, $\kappa =| f| /{f}_{c}$, p0 and p1 describe the speckle signal attenuation (both are negative, p0 is related to seeing), and the new parameter ${\rm{\Delta }}y$ is the FWHM of the CTE smear in the column direction in pixels. This "elliptical" synthetic reference was used for all binaries, both wide and close, observed in runs 4 and 5. The parameters of the reference $({p}_{0},{p}_{1},{\rm{\Delta }}y)$ were fitted to the power spectrum jointly with the binary parameters (θ, ρ, ${\rm{\Delta }}m$).

In the case of close binaries, the parameters of the elliptical reference and of the binary itself are mutually correlated, so the resulting measures could be biased. The close binary star B 430 (19155–2515) was observed with position angles of the instrument differing by 90°. The "fringes" in the power spectrum had different orientations relative to the CCD. However, the binary parameters (θ, ρ, ${\rm{\Delta }}$m) fitted to these power spectra are mutually consistent, (283fdg7, 0farcs0673, 0.785) and (285fdg0, 0farcs0690, 0.722). Therefore, the CTE effect is, to first order, accounted for by the modified reference model. Still, measurements of close binaries from runs 4 and 5 (2014.77 and 2014.86) should be taken with some caution.

Wide binaries resolvable in the re-centered long-exposure images are processed by another code that fits only the magnitude difference ${\rm{\Delta }}$m, using the binary position from speckle processing. This procedure corrects the bias on ${\rm{\Delta }}$m caused by speckle anisoplanatism and establishes the correct quadrant (flag * in the data table).

For run 5, we also calculated shift-and-add (SAA or "lucky") images, centered on the brightest pixel in each frame and weighted proportionally to the intensity of that pixel. All frames without rejection were co-added. Binary companions, except the closest and the faintest ones, are detectable in these SAA images, helping to identify the correct quadrant. Such cases are marked by the flag q in the data table. Quadrants of the remaining binary stars are guessed based on prior data or orbits, not measured directly.

2.4. Recalibration

Calibration of scale and angular offset in speckle interferometry is challenging because the accuracy of modern measurements with 4 m telescopes exceeds the accuracy of even the best orbits. Comparison with ephemerides is useful only as a sanity check. Recognizing this problem, we observed several wide binaries during each run. Their motions are slow and can be modeled by linear functions of time. These models can then be used to check the calibration of the archival data. This approach tests only the mutual consistency of speckle runs, rather than absolute calibration of the whole data set.

We selected 41 binaries wider than 0farcs5 that do not contain resolved subsystems and were observed during at least 4 runs each. The angle and separation of each binary is approximated by linear functions of time. If the fitted slope is less than twice its rms error, a zero slope is assumed. Deviations from these models are interpreted as calibration corrections. For each run, they are median-averaged. We then iterate by fitting new linear models corrected for the run's systematics, determining new calibration parameters of the runs, etc.

Figure 1 shows the offsets in angle and scale determined by this procedure for those of 26 runs where at least N = 2 calibrators were observed. Run 0 refers to observations at the Blanco telescope in 2008.5 (TMH10). Runs 1–6 in this paper correspond to numbers 21–26 in the plot. Vertical bars show the rms scatter between calibrators (not errors of the mean, which are smaller by $\sqrt{N}$). A typical rms scatter is 0fdg1 in angle and 0.3% in scale.

Figure 1.

Figure 1. Systematic offsets in angle (in degrees) and relative scale determined from wide binaries. The beginning date of each run is shown in the lower plot.

Standard image High-resolution image

This analysis reveals good mutual consistency of ∼5000 speckle measurements produced by HRCam to date. The largest systematics are found in runs 10 and 11 (2011.9 and 2012.1). The published data can be corrected by subtracting the angular offsets found here and dividing the separations by the new scale factors. We plan to observe more calibrators and publish improved systematic corrections in the future. The data of this paper rely only on the original instrument calibrations and are not corrected for the offsets found so far.

This study gives an estimate of the accuracy of speckle measurements. After correction for run systematics, the median rms deviations from the models for the 41 calibrator binaries are 0fdg1 in angle and 1.9 mas in separation. The actual errors should be a factor of ∼1.5 larger (∼3 mas), considering that the number of independent measurements is about twice the number of fitted parameters. This study will be repeated in the future with additional speckle runs and calibrators.

3. RESULTS

3.1. Data Tables

The data tables have almost the same format as in the previous papers of this series. They are available in full only electronically. Table 2 lists 1636 measures of 1218 resolved binary stars and subsystems, including 56 newly resolved pairs. The columns of Table 2 contain (1) the WDS (Mason et al. 2001) designation, (2) the "discoverer designation" as adopted in the WDS, (3) an alternative name, mostly from the Hipparcos catalog, (4) Besselian epoch of observation, (5) filter, (6) number of averaged individual data cubes, (7, 8) position angle θ in degrees and internal measurement error in tangential direction ρσθ in mas, (9, 10) separation ρ in arcseconds and its internal error σρ in mas, and (11) magnitude difference ${\rm{\Delta }}$m. An asterisk follows if ${\rm{\Delta }}$m and the true quadrant are determined from the resolved long-exposure image; a colon indicates that the data are noisy and ${\rm{\Delta }}$m is likely over-estimated (see TMH10 for details); the flag "q" means the quadrant is determined from the SAA image. Note that in the cases of multiple stars, the positions and photometry refer to the pairings between individual stars, not the photo-centers of subsystems.

Table 2.  Measurements of Double Stars at SOAR (Fragment)

WDS Discoverer Other Epoch Filt N θ ρσθ ρ σρ Δm [O–C]θ [O–C]ρ Reference
(2000) Designation Name +2000     (degree) (mas) ('') (mas) (mag) (degree) ('') Code*
00026–0829 A 428 HIP 210 14.7632 I 2 317.6 0.3 0.1197 0.9 0.4 : −1.0 0.003 This work
      14.8535 I 2 315.6 1.4 0.1165 0.8 0.3 −2.5 0.000 This work
00028+0208 BU 281 AB HIP 223 14.8561 I 2 160.3 0.2 1.5938 0.2 1.4 *
00058–6833 HDS 4 HIP 488 14.7661 I 2 229.3 4.8 0.1971 1.9 1.9
00115–5545 HDS 25 HIP 927 14.7661 I 3 75.3 0.7 0.1546 0.6 0.8
00135–3650 HDS 32 HIP 1083 14.7662 I 2 226.3 1.0 0.2565 0.6 0.8
00143–2732 HDS 33 HIP 1144 14.8534 I 2 55.5 0.3 0.1117 0.3 0.9 0.6 −0.002 This work
      14.8534 y 1 55.4 0.6 0.1115 0.6 1.0 0.4 −0.002 This work

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VOT) versions of the full table are available.

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For stars with known orbital elements, columns (12)–(14) of Table 2 list the residuals to the ephemeris position and code of reference to the orbit adopted in the Sixth Catalog (Hartkopf et al. 2001, hereafter VB6).6 New and revised orbits computed in this work (Section 4) are referenced as "This work."

We did not use image reconstruction, and measured the position angles modulo 180° (except the SAA images in run 5). Plausible quadrants are assigned on the basis of orbits or prior observations, but they can be changed if required by orbit calculation. For triple stars, however, both quadrants of inner and outer binaries have to be changed simultaneously; usually the slowly moving outer pair defines the quadrant of the inner subsystem without ambiguity.

Table 3 contains the data of 441 unresolved stars, some of which are listed as binaries in the WDS or resolved here in other filters. Columns (1) through (6) are the same as in Table 2, although Column (2) also includes other names for objects without discoverer designations. For stars that do not have entries in the WDS, fictitious WDS-style codes based on the position are listed in Column (1). Column (8) is the estimated resolution limit, the largest of the diffraction radius λ/D and the vertical CTE smear ${\rm{\Delta }}$y (applicable to runs 4 and 5 only). Columns (8, 9) give the 5 σ detection limits ${\rm{\Delta }}$m5 at 0farcs15 and 1'' separations determined by the procedure described in TMH10 (please note that this is not the resolution of the observations). When two or more data cubes are processed, the largest ${\rm{\Delta }}$m value is listed. The last column marks by colons noisy data mostly associated with faint stars. In such cases, the quoted ${\rm{\Delta }}$m might be too large (optimistic); however, the information that these stars were observed and no companions were found is still useful for statistics (Tokovinin 2014b).

Table 3.  Unresolved Stars (Fragment)

WDS (2000) Discoverer Hipparcos Epoch Filter N ρmin 5σ Detection Limit Δm
α, δ (J2000) Designation or Other +2000       Δm (0farcs15) Δm (1'') Flag
  or Other Name Name       (arcsec) (mag) (mag)  
00006–6641 GLI 289 HIP 55 14.7661 I 2 0.039 1.95 3.07
00052–6251 HIP 425 HIP 425 14.7661 I 2 0.039 2.78 4.10
00174–5131 HDS 40 HIP 1393 14.7662 I 2 0.039 2.56 3.97
00250–3042 HIP 1976 HIP 1976 14.8534 I 2 0.039 3.42 4.82
00301+0452 HIP 2358 HIP 2358 14.8561 I 2 0.039 2.28 3.69
00310–3138 HDS 69 HIP 2433 14.7662 I 2 0.039 1.69 4.01
00324+0657 MCA 1 Aa,Ab HIP 2548 14.7632 I 2 0.039 3.01 4.25

Only a portion of this table is shown here to demonstrate its form and content. Machine-readable and Virtual Observatory (VOT) versions of the full table are available.

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3.2. Newly Resolved Pairs

Table 4 lists 56 newly resolved pairs. The last two columns of Table 4 contain the spectral type (as given in SIMBAD or estimated from absolute magnitude) and the Hipparcos parallax (van Leeuwen 2007, hereafter HIP2). Fragments of ACFs of newly resolved triple systems are shown in Figure 2. We comment on the newly resolved binaries below. The following abbreviations are used: PM—proper motion, CPM—common proper motion, RV—radial velocity, SB1 and SB2—single- and double-lined spectroscopic binaries, INT4—4th Interferometric Catalog (Hartkopf et al. 2001).

Figure 2.

Figure 2. Fragments of ACFs of newly resolved triple systems (north up, east left, arbitrary scale). The peaks in the ACFs are labeled by component designations. Angular separations in the wide and close pairs are listed in the images.

Standard image High-resolution image

Table 4.  Newly Resolved Pairs

WDS Discoverer Other Epoch Filt θ ρ Δm Sp. πHIP2
(2000) Designation Name +2000   (degree) ('') (mag) Type (mas)
01379–8259 TOK 426 HIP 7601 14.7661 I 112.8 0.0640 0.5 G1V 36.5
02098–4052 TOK 427 HIP 10096 14.7689 I 218.3 0.0397 1.4 F3V 14.1
03046–5119 TOK 428 Ba,Bb HIP 14313 14.7635 I 107.9 0.1911 0.5 : G6V? 18.7
04386–0921 TOK 387 HIP 21625 14.0457 I 47.0 0.0557 0.6 F8? 16.1
04469–6036 TOK 388 HIP 22229 14.0456 I 266.2 0.0431 1.2 F8V 16.1
05354–0450 TOK 430 Aa,Ab HIP 26237 14.8567 I 6.2 0.1589 0.2 B1V 3.7
06303–5252 TOK 435 Aa,Ab HIP 30995 15.0288 I 176.1 0.2134 4.1 q G4V 14.0
06497–7433 TOK 389 HIP 32735 14.0597 I 330.7 0.3343 3.1 K0IV 15.7
06499–2806 HDS 947 AC HIP 32767 15.0289 I 231.3 0.4237 3.2 q K1V 14.6
07038–4334 TOK 390 Ca,Cb HIP 34052 14.0431 I 10.8 0.2268 4.4 K6V 57.4
07294–1500 TOK 391 Ca,Cb HIP 36395 14.1853 I 121.2 0.0902 1.2 M0V 28.5
07304+1352 TOK 392 Da,Db HIP 36497 14.0596 I 67.6 0.1143 2.5 F8 22.0
07312+0210 TOK 393 HIP 36557 14.0433 I 168.6 0.0572 2.0 G0 15.7
08021–1710 TOK 394 AC HIP 39293 14.0460 I 332.5 1.8351 3.0 M1.5 33.3
08447–2126 TOK 395 BC HIP 42910 14.0460 I 184.6 0.1645 0.1 K7V 27.5
09299–3629 TOK 440 BC HIP 46572 15.0317 I 90.4 0.1126 1.4 q sdF2 5.0
09586–2420 TOK 437 HIP 48906 15.0317 I 292.6 0.0640 1.3 q F3V 8.9
10056–8405 TOK 396 Aa,Ab HIP 49442 14.0436 I 192.6 0.1760 1.4 F8V 15.6
10070–7129 TOK 397 HIP 49546 14.3027 y 345.5 0.0263 1.7 F5V 16.7
10223–1032 TOK 398 HIP 50796 14.3002 I 147.7 1.6626 2.8 K4V 25.8
10530+0458 TOK 438 HIP 53212 15.0292 y 194.9 0.0486 0.8 q G5 11.9
12176+1427 TOK 399 Aa,Ab HIP 59933 14.3004 I 95.2 0.0429 1.0 F8 17.5
12250–0414 TOK 400 HIP 60574 14.1855 I 71.2 0.2194 2.6 G5 21.5
12528+1225 TOK 401 HIP 62933 14.3004 y 141.3 0.0598 1.6 A7III 16.4
13132–0501 TOK 402 HIP 64499 14.1858 I 314.8 0.1062 1.8 G5 19.2
13321–1115 TOK 291 Aa,Ab HIP 66018 14.1858 I 159.4 0.8947 4.6 G0 18.0
13344–5931 TOK 403 HIP 66230 14.1857 I 314.3 0.1037 2.5 G0V 18.6
13382–2341 TOK 404 Aa,Ab HIP 66530 14.1857 I 63.4 0.1570 3.9 G4V 20.6
13401–6033 TOK 292 B,Ca HIP 66676B 14.1857 I 293.3 0.9178 3.7 G6V 16.9
13401–6033 TOK 292 Ca,Cb HIP 66676B 14.1857 I 5.2 0.1614 0.0 G6V 16.9
13495–2621 TOK 405 HIP 67458 14.1858 I 15.0 0.7306 4.4 G9V 24.3
14014–3137 TOK 159 Aa,Ab HIP 68507 14.3031 I 101.6 0.0652 2.1 F5 16.2
14382+1402 TOK 406 HIP 71572 14.1859 I 153.9 0.0900 1.5 G5 21.2
14464–3346 TOK 407 Ba,Bb HIP 72235B 14.3031 I 41.3 0.4116 4.1 K4 24.0
15362–0623 TOK 301 Aa,Ab HIP 76400 14.1860 I 78.1 0.1908 3.9 G5 15.7
15367–4208 TOK 408 Ca,Cb HIP 76435C 14.3007 I 97.2 0.0562 0.4 K4 20.6
16142–5047 TOK 409 HIP 79576 14.1833 I 145.4 0.0791 3.0 G8V 24.2
16195–3054 TOK 410 Ba,Bb HIP 79979 14.1833 I 85.0 0.0396 1.4 G1/G2 20.7
16454–7150 TOK 411 Aa,Ab HIP 82032 14.3034 I 267.2 1.3373 4.1 F8V 18.3
16563–4040 TOK 412 AC HIP 82876 14.3034 y 144.0 1.4585 5.1 O7V –0.7
17054–3346 TOK 413 Aa,Ab HIP 83612 14.3035 y 82.3 0.0303 1.7 : G1V 18.4
17098–1031 TOK 414 HIP 83962 14.1833 y 59.1 0.0325 1.8 : F5IV 24.2
17264–4837 TOK 415 Ba,Bb HIP 85326 14.3035 I 118.6 1.0059 2.4 * K1V 20.7
17266–3258 TOK 416 HIP 85360 14.3035 I 26.9 1.1597 5.9 * G3V 26.4
17341–0303 TOK 417 HIP 85963 14.3010 I 88.9 0.0907 2.6 F8 15.3
17342–1910 TOK 418 AC HIP 85965 14.3036 I 133.6 0.2163 3.3 F2V 2.5
17342–5454 TOK 419 HIP 85969 14.1833 I 72.1 0.5544 3.4 G4V 23.7
18243–0405 TOK 420 Aa,Ab HIP 90198 14.3037 I 83.6 0.0477 0.8 A3 8.7
18267–3024 TOK 421 HIP 90397 14.3036 I 100.4 0.0690 2.5 G0V 21.4
18346–2734 TOK 422 Aa,Ab HIP 91075 14.3037 I 101.7 0.0864 1.7 G5V 15.0
19206–0645 TOK 432 AC HIP 95068 14.3011 I 56.4 0.9751 6.4 * K0 3.0
19209–3303 TOK 433 Aa,Ab HIP 95106 14.7683 I 160.0 0.2721 2.5 G0.5 V 21.2
19221–2931 TOK 423 Aa,Ab HIP 95203 14.3010 y 36.4 0.7672 5.8 * G0IV 19.6
19409–0152 TOK 424 HIP 96834 14.3011 I 102.2 0.0355 1.3 : F8 20.8
19453–6823 TOK 425 Ba,Bb HIP 97196 14.3038 I 312.1 0.0829 1.4 K3 21.3
22259–7501 TOK 434 Ba,Bb HIP 110719 14.7657 I 58.1 0.1917 1.4 : K5 43.4

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01379–8259. HIP 7601 is a nearby (27 pc) dwarf also known as GJ 67.1 or HR 512. According to Wichman et al. (2003), it is a young spectroscopic triple detected in X-rays (1RXS J013755.4–825838). GCS also recognized the star as SB2. Spectroscopic monitoring (A. Tokovinin 2015, in preparation) shows that all three components are similar stars of approximately one solar mass. Here we resolved the outer subsystem AB and observed its fast motion. In fact it was already resolved at SOAR on 2011.036 at 221fdg0 and 0farcs044, but this low-quality observation has not been published. The available data indicate that the period of AB is 1.7 years; the pair completed nearly two revolutions since its first resolution in 2011.

02098–4052. HIP 10096 is SB2 according to GCS. The separation corresponds to a period of ∼5 years.

03046–5119. HIP 14307 and 14313 form the 38'' pair DUN 10 AB belonging to the FG-67 sample. The component B is resolved here at 0farcs19. The estimated period of Ba,Bb is ∼25 years. No motion is seen in 2 months. The subsystem Ba,Bb is also manifested by asymmetric line profiles (A. Tokovinin 2015, in preparation). The A component has never been observed at high angular resolution.

04386–0921. HIP 21265 is an X-ray source and an SB2 according to GCS (one observation only). It is resolved here at 56 mas, which corresponds to a period of ∼5 years.

04469–6036. First resolution of HIP 22229 at 0farcs043, ${\rm{\Delta }}$I = 1.2. The measure is uncertain, but the elongation is confirmed with 2 ms exposure and is not seen in other observed stars, so it is not caused by vibration. This is a triple system containing an eclipsing binary AL Dor of Algol type with an eccentric orbit (Bulut & Demirkan 2007). The separation implies an orbital period of the outer system on the order of 5 years.

05354–0450. This is HIP 26237, HD 37018, HR 1892, 42 Ori, a young star in Orion which has not been observed at high angular resolution so far, according to INT4. We resolved the known binary AB = DA 4 and discovered the spectacular subsystem Aa,Ab at 0farcs16 (Figure 2).

06303–5252. HIP 30995 is an SB2 according to GCS. The new companion at 0farcs2 with ${\rm{\Delta }}$I = 4.1 mag is unlikely to correspond to the SB2, so the system is probably triple.

06497–7433. HIP 32735 has an acceleration detected in HIP2, but no RV data. The resolved 0farcs3 pair implies a period of ∼80 years. The spectral type K0IV given in SIMBAD may be inaccurate because the luminosity and color of the components correspond to main sequence stars with masses of 1.0 and 0.6 ${{\mathcal{M}}}_{\odot }$.

06499–2806. The 0farcs2 pair HDS 947 had not been observed since its discovery by Hipparcos. Here it is revealed as a triple system (Figure 2) with comparable separations between components. HDS 947 probably corresponds to AB, while the fainter C component is new.

07038–4334. HIP 34052 = HD 53680 = HIP 34065C = GJ 264 is a spectroscopic and astrometric binary for which Sahlmann et al. (2011) give an orbit with P = 1688 days = 4.62 years and an estimated semi-major axis of 0farcs15. There is also an astrometric orbit (Makarov et al. 2008) with P = 4.11 years that predicts θ = 327° for the moment of our first observation. The binary is resolved at 0farcs23, ${\rm{\Delta }}$I = 4.4 mag and shows some orbital motion. The binary makes a quadruple system together with components A and B (GJ 264.1 and 264) that form a 20farcs5 pair at 185'' from C. The B component was also observed here and found unresolved.

07294–1500 is another nearby multiple system. The main component HIP 36395 is a visual binary with a known 728-year orbit, also measured here. The C component (NLTT 17952) at 20farcs4 is physical, and yet another CPM component F is found at 1072'' (Tokovinin & Lépine 2012), while the WDS components D and E are optical. We observed C and resolved it at 0farcs09. The orbital period of Ca,Cb is on the order of 6 years, estimated masses are 0.6 and 0.4 ${{\mathcal{M}}}_{\odot }$. We also targeted F and did not resolve it. The magnitudes and colors of C and F are quite similar.

07304+1352 is a quadruple system. The 7farcs7 pair AB (STF 1102) is HIP 36485, the CPM component D = HIP 36497 = HD 59450 is located at 112'' from it, while the WDS components C and E are optical. The physical nature of AD is established by common PM, distance, and RV. D is a known SB1 with P = 2708 days = 7.4 years (Halbwachs et al. 2012) and an estimated semi-major axis of 93 mas, also an acceleration binary. We resolved the Da,Db pair at 0farcs11, ${\rm{\Delta }}$I = 2.6. The minimum mass of Db derived from its SB orbit is 0.27 ${{\mathcal{M}}}_{\odot }$, while we estimate the masses of Da and Db as 1.05 and 0.6 ${{\mathcal{M}}}_{\odot }$ from their luminosity. A previous non-resolution of D is reported in INT4; it was also unresolved with Robo-AO (Riddle et al. 2015).

07312+0210, HIP 36557 = HD 59688. According to observations by D. Latham (2012, private communication), this is a spectroscopic triple with an inner period of 70 days (double-lined, also detected by GCS, mass ratio 0.7) and an outer period of 2007 days or 5.5 years. The outer system is also detected by astrometric acceleration (Makarov & Kaplan 2005). We resolve it here at 0farcs057, ${\rm{\Delta }}$I = 2.0, ${\rm{\Delta }}$y = 2.5 mag, and see the orbital motion. The estimated mass of Ab is 0.88 ${{\mathcal{M}}}_{\odot }$. The semi-major axis of the 70 days inner binary Aa,Ab is 7 mas, so accurate measurements of AB can detect the sub-motion to determine the orientation of the inner orbit.

08021–1710. This is the high-PM M-dwarf LP 784–12 (HIP 39293) at 30 pc from the Sun. A new distant component C was found at 1farcs8 in addition to the known pair HDS 1140 which closed from 0farcs4 in 1991.25 to 0farcs33 now (Figure 2). It is confirmed as physical by its fixed position during one year, the quadrant of the triple was determined in run 5.

08447–2126. Like the previous object, the late-type nearby binary HDS 1260 was discovered by Hipparcos and is expected to move rapidly (HIP 42910, $\mathrm{BD}-20^\circ $ 2665). It was targeted at SOAR for the first time. To our surprise, the object turned out to be a resolved triple, with the secondary being a 0farcs16 pair of equal stars (Figure 2). Hipparcos failed to recognize the triple nature of this star. The estimated period of BC is 15 years. The outer pair AB has closed from 0farcs8 to 0farcs5 and moved in position angle since its discovery. The separations between components are comparable, so this triple system may be interesting dynamically.

09299–3629. HIP 46572 is called a "high proper motion star" in SIMBAD, although its PM and RV are actually quite moderate. The binary AB has moved little in the 24 years since its resolution by Hipparcos. We discover the subsystem BC (Figure 2) with an estimated period of ∼100 years.

09586–2420. HIP 48906 is a double-lined binary according to the GCS, first resolved here at 64 mas. The period should be ∼20 years.

10056–8405. HIP 49442 = HD 88948 is a nearby dwarf in the 3farcs9 visual binary HJ 4310 AB. According to GCS, the RV of the main component A varies by 3.5 km s−1. Here it is resolved into a 0farcs18 Aa,Ab pair with an estimated orbital period of 25 years. No astrometric acceleration was detected, however. The visual secondary B was targeted separately and found unresolved.

10070–7129. HIP 49546 is an astrometric binary of 1.5 year period (Goldin & Makarov 2006) with variable RV. The period corresponds to a semi-major axis of 25 mas. The star is resolved here tentatively at 26 mas (with 2 ms exposure). This resolution is below the diffraction limit and needs confirmation. The measured position angle of 346° is close to 342° predicted by the astrometric orbit.

10223–1032. HIP 50796 is a single-lined and astrometric binary according to Torres (2006), with a period of 570.98 days (1.56 years), K1 = 20.76 km s−1, e = 0.611. The Hipparcos parallax corrected for the binary motion is 20.6 ± 1.9 mas. The spectroscopic secondary companion is over-massive, most likely a close pair of M-dwarfs. If so, the new speckle companion at 1farcs66 with a period on the order of 500 years makes the system quadruple. The speckle companion might contribute to the IR excess found by Torres. The system is an X-ray source, and is possibly young.

10530+0458. D. Latham (2012, private communication) identified HIP 53212 = HD 94292 as SB2 with a period of 8.3 years and a highly eccentric orbit. It is resolved here securely at 50 mas.

12176+1427. HIP 59933 has a variable RV according to GCS. The 32 mas separation corresponds to an orbital period of ∼2 years. However, the separations in the y and I filters are somewhat discordant; further confirmation is needed.

12250–0414. HIP 60574 is a spectroscopic triple with periods 14 days and 22 years (D. Latham 2012, private communication), also an acceleration binary. We resolved the outer pair at 0farcs22 separation, matching the spectroscopic period. The lines of the visual secondary Ab could potentially be detected in the spectrum by cross-correlation, leading eventually to a full 3D orbit.

12528+1225. HIP 62933 (41 Vir) was observed on request by F. Fekel who studies its spectroscopic orbit. Apparently it is resolved for the first time.

13132–0501. HIP 64499 has a variable RV, with a preliminary spectroscopic orbit of 17 years period (D. Latham 2012, private communication). It is resolved at 0farcs1 and shows no motion in one month.

13321–1115. No previous indication of binarity was available for HIP 66018, apart from the CPM companion B at 84''. We discovered another faint component Ab at 0farcs89, ${\rm{\Delta }}$I = 4.6, likely to be physical (low background density). The B component (V = 14.8) was targeted, but its speckle signal was weak and no obvious close companions to B were found.

13344–5931. HIP 66230 has a variable RV in the GCS and an astrometric acceleration. We resolved it at 0farcs1, ${\rm{\Delta }}$I = 2.5, estimated period ∼10 years. The pair moved by 4° in one month.

13382–2341. HIP 66530 has a variable RV according to the GCS. It is resolved at 0farcs16 in the I band only, estimated period ∼20 years. This is a triple system, considering the CPM companion B at 28'' (LDS 4385 AB).

13401–6033. HIP 66676 (A) and HD 118735 (B, G6V, V = 9.17) at 77'' share common PM (although it is small, 58 mas yr−1) which, together with photometry, indicates with high probability that it is a physical pair AB (Tokovinin & Lépine 2012). We targeted the secondary component B and found it to be a resolved triple. The faint star C, at 0farcs92 from B, is itself a close 0farcs16 pair Ca,Cb (Figure 2). Note that this is a region of the sky with very high stellar density, raising suspicion that the Ca,Cb pair might be a random background object. Re-observation of the triple in 2015 (to be published) shows, however, that it is physical because the center of C = (Ca,Cb) moves relative to B with a speed of 11 mas yr−1 (or 3 km s−1), compatible with the expected orbital motion of BC and much less than the system's PM of 58 mas yr−1. The estimated period of Ca,Cb is ∼30 years, the period of BC is ∼300 years.

13495–2621. HIP 67458 is a double-lined chromospherically active binary with orbital period of 7.2 days (D. Latham 2012, private communication). We found a faint tertiary companion at 0farcs73 with an estimated orbital period on the order of 100 years. The speckle survey of chromospherically active stars by Mason et al. (1998) did not detect this tertiary, lacking the dynamic range of HRCam.

14014–3137. HIP 68507 is an acceleration binary with a variable RV resolved here at 0farcs06. The period of Aa,Ab is on the order of 5 years. There is a faint physical companion B at 6farcs7 found in 2MASS (Tokovinin 2011). Another visual companion at 14'', SEE 195, is optical, as revealed by its fast relative motion.

14382+1402. HIP 71572 is an acceleration binary without RV data. It is found to be a tight 90 mas pair with a small ${\rm{\Delta }}$m and an estimated period under 10 years (some motion is seen in one month). Very likely it can be studied as a double-lined SB.

14464–3346. HIP 72235B is located at 9'' from the primary star and shares its proper motion (AB = HDS 2082). Pre-discovery measurements of this Hipparcos pair were published by Wycoff et al. (2006). The RV of A may be variable (D. Latham 2012, private communication). The star B turns out to be a 0farcs4 binary Ba,Bb with masses of 0.70 and 0.17 ${{\mathcal{M}}}_{\odot }$ estimated from the luminosity. Its period is on the order of 100 years. The whole system could thus be quadruple.

15362–0623. HIP 76400 is identified by the GCS as an SB2 with a mass ratio q = 0.93, but there is no spectroscopic orbit available. We resolved the 0farcs19 pair with ${\rm{\Delta }}$I = 3.9, indicating a mass ratio of ∼0.5 and an orbital period of ∼30 years. Very likely the resolved binary does not match the spectroscopic double-lined system. Considering the CPM component B at 80'' (Tokovinin & Lépine 2012), this system could be a quadruple with a 3-tier "3+1" hierarchy.

15367–4208. HIP 76435 is a G5V star from the FG-67 sample. Its companion C (AC = FAL 78) at 13farcs5 is physical, while the Hipparcos companion B at 4farcs3 is not seen in the 2MASS images and has not been confirmed otherwise. We targeted C and resolved it into a close binary. Estimated masses of Ca and Cb are 0.70 and 0.66 ${{\mathcal{M}}}_{\odot }$, period ∼4 years.

16142–5047. HIP 79576 has a variable RV (GCS). The 79 mas separation implies an orbital period of ∼5 years. This is the high-PM star LTT 6467 with a low metallicity [Fe/H] = −0.78. Ivanov et al. (2013) found no CPM companions.

16195–3054. HIP 79980 and HIP 79979 form a 23'' CPM pair AB where the F6III primary is slightly evolved, while the G1/G2 secondary is closer to the main sequence, but still above it. The Hipparcos parallax of B, −4.7 mas, is obviously wrong, so we assume the parallax of the primary, 20.7 mas. The RV(B) is variable (GCS), and we resolve it into a 40 mas pair with an estimated period on the order of 1 year. The pair moved by 10° in a month. Binary motion is the likely cause of the incorrect Hipparcos parallax.

16454–7150. HIP 82032 is located in a crowded field, so the new faint Ab companion found here at 1farcs3 could be optical. The star was observed because of its suspected variable RV (GCS), but the newly found companion, even if physical, is too distant to explain this variability. Another visual companion B at 11farcs5 (AB = B 2392) is optical, as evidenced by its fast relative motion. The star is on the HARPS exo-planet program.

16563–4040. HIP 82876 is a distant O7V star. The 0farcs26 pair AB (HDS 2394) was measured among other neglected binaries. We found another faint companion C at 1farcs46 (Figure 2). The star has an extensive literature, including multiplicity surveys with speckle interferometry and RV (Chini et al. 2012). Owing to the large distance, no detectable orbital motion is expected. Indeed, the AB pair was measured with HRCam in 2008.5 at the same position as it is now. Those observations in the y band did not detect the companion C owing to a lower signal-to-noise ratio.

17054–3346. The RV of HIP 83612 varies by 52 km s−1 (GCS). It is a very close pair with an estimated period of ∼1.5 years, and the measure near the diffraction limit derived from the elongated power spectrum is tentative. The Hipparcos parallax is likely biased by the binary. The visual component B = HIP 83609 (AB = WNO 5) at 25'' is optical.

17098–1031. HIP 83962 = HR 6375 has a variable RV according to the GCS, while N. Gorynya (2013, private communication) detected double lines. It is resolved tentatively at 33 mas with ${\rm{\Delta }}$y = 1.8 mag (the 5 ms exposure makes it unlikely that the asymmetry is caused by vibrations). The separation corresponds to an orbital period on the order of 1 year, which could bias the Hipparcos parallax. However, Eggleton & Tokovinin (2008) consider the star as single. The new pair was not resolved in 2014.3; presumably it became closer.

17264–4837. HIP 85342 and HIP 85326 form a physical pair AB at 127'' separation (common PM, RV, and parallax). The B component = HIP 85326 has a variable RV and an astrometric acceleration which could hardly be produced by the 1'' speckle companion Bb found here, owing to its long estimated period of ∼300 years. It seems that B is triple and the whole system is quadruple. This companion Bb was not detected in the previous speckle observations because it is red: ${\rm{\Delta }}$I = 2.4, ${\rm{\Delta }}$y = 4 mag; its color matches a dwarf star at the same distance as the system. However, the field is crowded and the newly found companion could still be optical.

17266–3258. HIP 85360 is an acceleration and spectroscopic binary. Its preliminary spectroscopic period (D. Latham 2012, private communication) corresponds to a semi-major axis of 80 mas. The star is chromospherically active and possibly young. The faint companion found here at 1farcs16 is most likely optical, as the field is extremely crowded. Re-observation within a year will resolve its status.

17341–0303. HIP 85963 has a variable RV and is an acceleration binary. The 91 mas separation implies an orbital period of ∼10 years; the estimated masses are 1.37 and 0.81 ${{\mathcal{M}}}_{\odot }$. Despite extensive literature (51 references in SIMBAD), there is no published spectroscopic orbit, while several high-resolution spectroscopic studies addressed the abundance.

17342–1910. B 1863 is a known close binary which has been unexpectedly found to be a triple (Figure 2). The new distant component C is detectable also in the y filter, but we measured only the inner binary in y. The star was observed at the Blanco telescope in 2008.5397, and the pair actually measured then was AC, at 133fdg8, 0farcs217, ${\rm{\Delta }}$y = 3.7 (same as now, see Table 2). The inner pair AB with a smaller ${\rm{\Delta }}$m was unresolved in 2008.5, while it is clearly resolved now. Owing to the large distance from the Sun, we expect only a slow motion, so even the inner pair observed since 1929 may not yet be ready for computing its first orbit.

17342–5454. HIP 85969 has a variable RV according to the GCS and confirmed by Jones et al. (2002). The 0farcs55 separation implies a period on the order of 80 years. The star is on the exo-planet program at the Anglo-Australian Telescope.

18243–0405. The neglected pair YSC 67 turned out to be a new triple (Figure 2). The outer 0farcs35 binary AB was known previously, now we detect elongation that implies an inner subsystem Aa,Ab. We compared with stars in the same area of the sky observed before and after to assure that the elongation is not of instrumental origin; it is seen in two filters.

18267–3024. HIP 90397 is an acceleration binary with a variable RV (GCS), resolved here at 69 mas (estimated period ∼4 years). The star is targeted by exo-planet programs.

18346–2734. HIP 91075 was noted as a double-lined binary by the GCS (one observation only). The separation of 86 mas implies a period of ∼10 years, while the double-lined observation matches the moderate magnitude difference (estimated masses 1.04 and 0.77 ${{\mathcal{M}}}_{\odot }$). The star is an X-ray source, so a future combined orbit could determine masses for testing evolutionary models of young stars. The sky around the object is quite crowded; the 9'' companion I 1026 is optical (it moves too fast).

19206–0645. HIP 95068 is the neglected Hipparcos binary HDS 2735 AB, a distant K-type giant. We did not resolve this 0farcs1 binary, which remains unconfirmed, but detected instead another faint star at 1''. The stellar background is crowded, the PM is small, and the status of the new companion remains uncertain.

19209–3303. HIP 95106 and 95110 form the 13farcs7 pair HJ 5107 AB. The RV variability of A was suspected by the GCS, it is now resolved as a 0farcs27 binary with estimated period of ∼35 years. The component B was also observed and found unresolved. It contains a spectroscopic pair (A. Tokovinin 2015, in preparation), the whole system is quadruple.

19221–2931. HIP 95203 is another acceleration binary with variable RV resolved here. The relatively large separation of 0farcs77 corresponds to a period of ∼180 years. The actual period can be as short as 60 years if the pair is seen now near its maximum separation (it would then have been closer at the time of the Hipparcos mission). Most likely, however, the faint visual companion found here and the spectroscopic/acceleration pair make a triple system. There is another companion HIP 95164 at 435''. The status of this wide pair (is it a real binary or just two members of a moving group?) is not clear, but the association of those stars leaves no doubt (common RV, PM, and parallax).

19409–0152. HIP 96834 has a spectroscopic orbit with a period of 1 year and expected semi-major axis of 27 mas (D. Latham 2012, private communication). We resolved this pair, although the measurement near the diffraction limit is uncertain. However, there are some unsolved questions. Why, despite the small magnitude difference ${\rm{\Delta }}$y = 1.2 mag, were double lines not seen? Why, despite the 1 year period, was the Hipparcos parallax not strongly affected and the star appears to be on the main sequence?

19453–6823. We resolved the secondary component of HDS 2806 AB into a close pair Ba,Bb (Figure 2). This is a K3 dwarf within 50 pc from the Sun. The pair Ba,Bb should be fast and turn around in about 10 years.

22259–7501. HIP 110712 and 110719 form the 20farcs6 pair DUN 238 AB. We observed both components. The A component has a variable RV according to the GCS, but not confirmed by Jones et al. (2002); it was unresolved. The newly found pair Ba,Bb has a period on the order of 10 years. Considering the distant companion C found by Caballero (2012), the system contains at least 4 stars.

4. NEW AND IMPROVED ORBITS

The measurements reported here served to improve or compute anew orbits of 194 binary stars. The orbital elements in standard notation and their formal errors are given in Table 5. Its last column lists the VB6 code to a prior orbit if it exists (astrometric orbits in brackets). Errors of the elements (except provisional orbits of grade 5) are given in the following line. For the elements that were fixed (from, for example, a spectroscopic orbit), an asterisk replaces the error. As discussed in TMH14, orbit improvements range from minor "cosmetic" upgrades to some quite drastic revisions. Blanks in the last column indicate the 43 first-time orbit solutions (plus three with prior astrometric orbits). The grades are assigned according to the general grading rules adopted in VB6 (Hartkopf et al. 2001). Most orbital elements are derived using the USNO orbit code.

Table 5.  Orbital Elements

WDS Discoverer P T0 e Ω a i ω Gr Orbit
(Figure) Designation (year) (year)   (°) ('') (°) (°)   Reference
00026–0829 A 428 414.95 2005.35 0.503 192.2 0.505 111.9 226.8 4 Zul1984b
    ±20.96 ±2.47 ±0.013 ±2.0 ±0.021 ±1.2 ±4.2    
00143–2732 HDS 33 10.22 2013.47 0.609 215.3 0.124 28.4 80.0 2 Cve2012
    ±0.07 ±0.04 ±0.009 ±5.3 ±0.002 ±2.5 ±4.3    
00155–1608 HEI 299 4.550 1995.363 0.360 60.8 0.306 145.6 344.5 2 Hry1998
    ±0.002 ±0.016 ±0.005 ±1.4 ±0.002 ±1.3 ±2.2    
00315–6257 I 260 CD 44.73 2011.62 0.810 241.6 0.495 124.7 112.2 3 Msn2001c
    ±0.34 ±0.01 ±0.001 ±0.2 ±0.001 ±0.3 ±0.2    
00321–0511 A 111 AB 10.64 2015.19 0.538 206.5 0.122 155.7 101.6 2 Sta1978b
    ±0.02 ±0.19 ±0.014 ±18.5 ±0.003 ±4.2 ±14.9    
00533+0405 A 2307 57.78 2012.51 0.419 222.4 0.233 74.3 357.9 2 USN1999b
    ±3.87 ±1.25 ±0.029 ±1.4 ±0.005 ±1.6 ±13.2    
01024+0504 HDS 135 AB 28.23 2002.69 0.671 268.6 0.461 144.8 22.1 2 Bag2006
    ±0.17 ±0.01 ±0.002 ±1.0 ±0.002 ±0.7 ±1.2    
01028+0214 A 2308 141.80 1958.95 0.124 306.6 0.367 62.9 10.5 3 Baz1984a
    ±5.52 ±4.96 ±0.025 ±1.7 ±0.006 ±2.2 ±13.9    
01104–6727 GKI 3 1.778 1986.193 0.112 68.2 0.147 133.3 73.0 3 (Gln2007)
    ±0.006 ±0.176 ±0.033 ±9.8 ±0.009 ±7.0 ±30.8    
01196–0520 A 313 128.51 2014.72 0.161 171.5 0.274 133.7 245.5 2 USN1999a
    ±2.24 ±1.42 ±0.009 ±2.4 ±0.004 ±0.9 ±4.5    
01220–6943 I 263 272.15 1936.56 0.374 231.3 0.791 68.6 297.3 4 Msn1999a
    ±47.48 ±5.30 ±0.059 ±2.8 ±0.075 ±1.9 ±14.1    
01308–5940 TOK 183 4.66 2012.83 0.462 349.5 0.0458 75.0 13.9 4
    ±0.23 ±0.23 ±0.067 ±3.4 ±0.0030 ±0.0 ±16.2    
01350–2955 DAW 31 AB 4.562 1932.600 0.317 224.3 0.174 19.5 244.6 1 Msn1999c
    ±0.002 ±0.034 ±0.007 ±9.9 ±0.003 ±2.9 ±9.4    
01424–0645 A 1 637.62 1888.34 0.454 232.1 0.844 42.0 264.7 5 Sca2008c
01528–0447 RST 4188 618.71 2619.26 0.553 22.7 1.048 72.1 10.9 5 Hei1996a
02158–1814 HTG 1 295.93 1681.32 0.151 187.1 2.184 35.5 270.2 5 Sod1999
02166–5026 TOK 185 16.00 2011.32 0.467 243.6 0.132 63.2 312.4 5
02374–5233 TOK 186 3.22 2011.31 0.083 52.0 0.0785 115.5 17.0 3
    ±0.06 ±0.23 ±0.020 ±3.0 ±0.0031 ±2.5 ±25.4    
02405–2408 SEE 19 310.26 2016.80 0.839 225.6 0.393 147.2 73.2 4 Lin2010c
    ±146.13 ±0.32 ±0.009 ±39.0 ±0.098 ±3.3 ±22.9    
02415–7128 B 1923 101.50 2011.42 0.376 222.9 0.522 116.3 252.3 4 Hrt2012a
    ±2.77 ±0.33 ±0.015 ±2.8 ±0.010 ±0.9 ±2.0    
02517–5234 HU 1562 65.00 2021.92 0.876 237.4 0.264 111.7 6.1 4 Hei1979b
    ±6.18 ±0.35 ±0.029 ±3.1 ±0.005 ±5.2 ±10.4    
02572–2458 BEU 4 Ca,Cb 1.518 2007.088 0.540 2.0 0.062 160.4 341.8 2 Tok2014a
    ±0.001 ±0.021 ±0.024 ±9.1 ±0.002 ±12.0 ±11.0    
03014+0615 HDS 385 15.27 2012.90 0.397 347.4 0.117 52.5 2.7 2 Bag2005
    ±0.09 ±0.07 ±0.004 ±1.0 ±0.001 ±0.7 ±2.4    
03236–4005 I 468 237.68 1971.45 0.505 319.5 2.548 41.6 30.9 5 Sod1999
03272+0944 HDS 433 50.81 2008.43 0.571 109.4 0.439 26.7 8.0 3 Cve2010c
    ±0.62 ±0.04 ±0.004 ±2.9 ±0.004 ±1.2 ±2.9    
03339–3105 B 52 19.36 1997.19 0.363 140.8 0.224 85.7 11.1 2 Hei1996c
    ±0.05 ±0.17 ±0.011 ±0.7 ±0.003 ±0.8 ±4.1    
03544–4021 FIN 344 AB 14.03 2008.05 0.579 247.4 0.0614 32.4 49.7 2 Hrt2012a
    ±0.04 ±0.04 ±0.008 ±2.0 ±0.0005 ±1.5 ±2.3    
03545+0510 A 1831 BC 216.02 1986.20 0.099 231.8 0.187 56.0 300.1 4 Ole1998a
    ±42.23 ±25.43 ±0.144 ±5.3 ±0.013 ±5.4 ±47.3    
04008+0505 A 1937 42.93 2014.94 0.550 25.9 0.1000 47.1 14.7 2 Tok2014a
    ±1.13 ±0.15 ±0.019 ±4.4 ±0.0012 ±3.1 ±8.0    
04070–1000 HDS 521 AB 21.42 1996.78 0.687 219.0 0.225 122.9 76.4 3 Msn2011a
    ±0.37 ±0.06 ±0.009 ±1.8 ±0.005 ±1.0 ±0.5    
04163+0710 WSI 97 5.6805 1997.088 0.808 358.1 0.1011 148.0 47.6 3 RAO2014
    ±0.0058 ±0.011 ±0.005 ±1.7 ±0.0009 * ±1.7    
04368–1733 A 2915 109.99 2012.35 0.470 151.8 0.305 62.0 94.1 3 Baz1986a
    ±7.99 ±1.14 ±0.053 ±4.1 ±0.025 ±5.0 ±12.9    
04374–0951 RST 3401 126.18 1967.68 0.366 98.9 0.325 146.2 52.9 3 Nov2007d
    ±6.11 ±1.47 ±0.026 ±10.9 ±0.011 ±5.2 ±14.5    
04389–1207 HDS 599 48.48 2003.67 0.828 152.5 0.333 78.4 281.2 4 Cve2014
    ±4.70 ±0.22 ±0.032 ±0.9 ±0.006 ±1.0 ±0.8    
04422+0259 A 2424 55.79 2011.46 0.348 228.8 0.147 85.0 90.8 3 WRH1976a
    ±4.07 ±0.64 ±0.012 ±0.6 ±0.009 ±0.5 ±9.0    
04505+0103 A 2622 403.34 1956.27 0.477 259.9 0.345 127.1 270.1 4 Sca2003a
    ±62.54 ±5.59 ±0.046 ±10.2 ±0.044 ±4.9 ±23.0    
04506+1505 CHR 20 5.734 2003.829 0.058 130.1 0.0904 114.4 92.8 3 Sod1999
    ±0.005 ±0.096 ±0.007 ±0.7 ±0.0010 ±1.7 ±6.0    
04515–3454 FIN 320 42.92 2006.48 0.826 198.4 0.227 111.6 292.1 3 Doc2013d
    ±0.39 ±0.13 ±0.004 ±0.6 ±0.001 ±0.3 ±0.2    
04545–0314 RST 5501 84.66 2004.32 0.515 219.1 0.243 120.8 310.3 3 Msn2011c
    ±1.42 ±0.39 ±0.011 ±1.0 ±0.003 ±1.4 ±1.9    
05025–2115 DON 91 AB 43.55 1997.46 0.720 246.5 1.062 60.7 280.6 4 Sod1999
    ±0.27 ±0.86 ±0.028 ±3.9 ±0.049 ±2.1 ±1.2    
05073–8352 HDS 669 26.45 2014.41 0.669 6.1 0.272 61.0 71.3 4
    ±1.01 ±0.03 ±0.016 ±2.8 ±0.009 ±1.4 ±2.8    
05245–0224 MCA 18 Aa,Ab 9.399 2011.613 0.435 129.0 0.0462 103.5 34.7 3 Bag1999b
    ±0.040 ±0.000 ±0.432 ±6.4 ±0.0195 ±15.3 ±27.1    
05289–0318 DA 6 1491.21 1995.70 0.846 247.1 1.021 48.3 349.7 4 Lin2010c
    ±672.53 ±1.14 ±0.045 ±4.3 ±0.287 ±2.3 ±1.1    
05484+2052 STT 118 AB 227.52 1986.06 0.869 137.9 0.792 89.7 290.8 4 Pal2005b
    ±15.48 ±0.09 ±0.026 ±2.0 ±0.037 ±0.8 ±1.4    
05532–6150 SLR 15 1251.74 1970.32 0.824 138.4 1.303 122.1 292.2 4 Hei1993d
    ±78.90 ±0.75 ±0.008 ±1.7 ±0.061 ±2.2 ±3.6    
05542–2909 FIN 382 20.16 2014.80 0.473 169.2 0.154 129.5 110.8 3 Hrt2012a
    ±0.03 ±0.08 ±0.018 ±4.0 ±0.003 ±2.4 ±5.1    
06293–0248 B 2601 AB 16.53 1999.33 0.387 209.6 1.072 53.3 42.0 3 Sgr2000
    ±0.01 ±0.01 ±0.002 ±0.3 ±0.002 ±0.2 ±0.4    
06314+0749 A 2817 31.55 2015.34 0.281 57.3 0.192 37.3 320.8 2 Pop1969b
    ±1.41 ±0.28 ±0.015 ±4.4 ±0.007 ±1.9 ±11.7    
06359–3605 RST 4816 Ba,Bb 14.03 2004.09 0.577 288.8 0.182 111.9 296.2 2 Tok2012b
    ±0.02 ±0.03 ±0.005 ±0.3 ±0.001 ±0.2 ±0.4    
06439–5434 HDS 934 12.37 2014.21 0.216 93.4 0.132 18.5 70.3 3 Hrt2012a
    ±0.02 ±0.04 ±0.004 ±4.6 ±0.001 ±1.9 ±4.2    
06454–3148 EHR 9 Ba,Bb 6.865 2014.728 0.224 189.7 0.126 138.9 5.6 4
    ±0.137 ±0.318 ±0.038 ±13.6 ±0.010 ±8.3 ±15.5    
06481–0948 A 1056 616.86 1962.17 0.522 256.0 0.501 56.7 280.6 4 Sca1983f
    ±513.30 ±10.30 ±0.282 ±13.7 ±0.255 ±7.0 ±32.6    
06490–1509 AC 4 581.32 2031.70 0.761 157.5 0.957 52.6 280.6 5
06493–0216 FIN 322 58.69 1969.56 0.293 241.6 0.148 112.2 68.0 3 Hrt2011d
    ±1.61 ±0.78 ±0.015 ±0.9 ±0.006 ±1.2 ±6.0    
07026+1558 A 2462 AB 44.45 2012.79 0.661 67.3 0.204 134.4 45.5 3 Baz1976
    ±0.44 ±0.02 ±0.002 ±0.7 ±0.001 ±0.5 ±0.8    
07043–0303 A 519 AB 90.40 2012.50 0.260 93.6 0.397 96.6 283.0 3 Tok2014a
    ±1.44 ±0.42 ±0.026 ±0.7 ±0.006 ±0.7 ±3.4    
07113–1032 A 2122 169.68 2021.25 0.712 150.3 0.203 120.2 228.6 4 USN2002
    ±13.75 ±2.39 ±0.021 ±5.1 ±0.007 ±3.7 ±2.5    
07143–2621 FIN 323 118.54 1971.01 0.747 131.3 0.178 80.2 85.0 4 Ole2004b
    ±11.14 ±0.74 ±0.094 ±3.0 ±0.012 ±1.0 ±3.6    
07155–7552 I 312 847.09 2012.33 0.859 152.9 2.308 97.5 86.1 5
07175–4659 I 7 85.01 1958.70 0.955 236.0 0.891 104.4 244.8 3 Msn2011c
    ±1.22 ±0.44 ±0.014 ±5.1 ±0.048 ±2.3 ±2.5    
07374–3458 FIN 324 AC 80.68 2016.58 0.648 262.1 0.323 158.6 32.7 3 Hrt2012a
    ±1.63 ±0.37 ±0.014 ±8.4 ±0.004 ±4.9 ±8.2    
07435–2711 B 737 290.20 1967.59 0.566 86.2 0.335 105.7 324.4 4
    ±14.74 ±1.93 ±0.014 ±2.1 ±0.016 ±1.2 ±4.3    
07456–3410 TOK 193 15.00 2010.83 0.305 58.4 0.473 67.7 342.5 4
    * ±0.15 ±0.032 ±0.8 ±0.016 ±1.4 ±6.8    
07490–2455 TOK 194 2.422 2011.557 0.408 212. 0.0374 29.5 295.3 3
    ±0.075 ±0.084 s ±0.072 ±32. ±0.0031 ±13.9 ±28.8    
07522–4035 TOK 195 7.388 2012.067 0.380 90.3 0.0624 86.2 170.0 4 (Jnc2005)
    ±0.657 ±0.206 ±0.000 ±6.8 ±0.0071 ±7.0 ±0.0    
08061–0047 A 1971 572.52 1910.43 0.409 202.8 1.070 125.6 99.1 5 Ole1993
08125–4616 CHR 143 Aa,Ab 31.42 2017.49 0.339 173.6 0.0738 71.7 257.6 3 Msn2010c
    ±0.33 ±0.21 ±0.020 ±1.0 ±0.0012 ±1.7 ±2.0    
08144–4550 FIN 113 AB 385.48 1973.09 0.700 103.4 0.566 81.6 346.0 5 Cve2010e
08251–4910 RST 321 25.78 2000.85 0.219 128.6 0.310 40.9 232.1 2 Hrt2012a
    ±0.41 ±0.15 ±0.005 ±0.8 ±0.004 ±0.7 ±4.1    
08270–5242 B 1606 14.66 2011.84 0.353 277.0 0.152 61.7 11.9 2 Tok2012b
    ±0.08 ±0.01 ±0.002 ±0.2 ±0.000 ±0.1 ±0.2    
08317–2601 I 807 720.66 1936.16 0.370 134.2 0.631 129.4 244.5 5
08345–3236 FIN 335 17.36 2014.08 0.572 268.9 0.139 30.6 43.8 2 Doc2013d
    ±0.03 ±0.03 ±0.004 ±1.9 ±0.001 ±1.3 ±2.0    
08380–0844 HDS 1242 41.66 2014.55 0.392 198.2 0.249 24.9 254.0 4 Hrt2012a
    ±4.50 ±0.53 ±0.011 ±14.8 ±0.020 ±6.3 ±5.1    
08391–5557 HU 1443 AB 876.85 1860.89 0.644 104.3 1.400 128.1 314.0 5
08421–5245 B 1624 74.05 1995.69 0.240 89.7 0.474 71.4 0.1 3 Hrt2012a
    ±0.43 ±0.31 ±0.003 ±0.2 ±0.002 ±0.2 ±2.1    
08431–1225 RST 3603 98.92 1964.70 0.393 155.5 0.268 154.5 14.1 3 Hrt2010a
    ±3.48 ±1.39 ±0.031 ±13.1 ±0.007 ±10.0 ±17.8    
08447–4238 CHR 238 2.257 2012.557 0.615 42.4 0.0785 145.8 332.8 3 Hrt2012a
    ±0.004 ±0.056 ±0.042 ±7.1 ±0.0046 ±14.0 ±7.9    
08474–1703 BU 586 442.24 2009.74 0.529 239.7 0.538 63.9 317.3 5 Msn2009
08538–4731 FIN 316 7.209 2007.601 0.253 108.5 0.0781 11.1 106.8 2 Hrt2012a
    ±0.004 ±0.009 ±0.002 ±8.8 ±0.0003 ±1.6 ±8.7    
08539+0149 A 2554 43.86 2021.18 0.502 112.4 0.210 162.4 339.7 3 Zir2007
    ±0.80 ±0.30 ±0.030 ±16.7 ±0.005 ±11.4 ±17.3    
08589+0829 DEL 2 5.566 2006.445 0.778 281.8 0.398 122.2 23.7 3 Hrt2012a
    ±0.024 ±0.039 ±0.019 ±1.7 ±0.008 ±3.1 ±3.2    
09149+0427 HEI 350 198.56 2000.40 0.574 84.6 1.856 122.2 344.7 5 (Hei1994a)
09173–6841 FIN 363 AB 3.445 2013.376 0.455 154.6 0.0888 140.7 117.2 2 Doc2013d
    ±0.002 ±0.007 ±0.003 ±0.8 ±0.0004 ±0.6 ±0.7    
09194–7739 KOH 83 Aa,Ab 19.84 1999.00 0.795 20.2 0.146 65.0 276.2 5
09228–0950 A 1342 AB 52.98 2020.20 0.074 202.4 0.169 68.5 58.7 2 Msn2011a
    ±0.37 ±0.45 ±0.008 ±0.4 ±0.001 ±0.6 ±3.3    
09252–1258 WSI 73 27.3 2014.80 0.860 101.1 0.235 86.0 283.4 5
09275–5806 CHR 240 2.621 2014.453 0.173 267.4 0.0478 111.4 125.6 3
    ±0.025 ±0.049 ±0.029 ±2.3 ±0.0018 ±2.3 ±6.6    
09278–0604 B 2530 34.80 2010.11 0.270 330.8 0.428 85.4 341.9 2 Sod1999
    ±0.06 ±0.10 ±0.003 ±0.1 ±0.001 ±0.1 ±1.1    
09313–1329 KUI 41 18.38 2002.17 0.335 230.8 0.647 139.9 105.3 3 Sod1999
    ±0.11 ±0.03 ±0.004 ±0.9 ±0.002 ±0.2 ±0.6    
09327+0152 FIN 349 40.57 1972.12 0.420 138.6 0.154 54.7 72.6 2 Msn2011a
    ±0.19 ±0.16 ±0.009 ±0.6 ±0.001 ±0.6 ±0.8    
09387–3937 I 202 163.69 2005.49 0.414 178.6 0.932 111.4 203.4 4 Hrt2012a
    ±3.53 ±0.67 ±0.012 ±1.1 ±0.017 ±0.9 ±2.2    
09407–5759 B 780 10.63 2005.86 0.338 86.1 0.123 128.6 17.6 2 DRs2012
    ±0.01 ±0.02 ±0.002 ±0.3 ±0.000 ±0.3 ±0.8    
09495–1033 A 1344 260.75 1991.89 0.781 119.5 0.355 116.2 90.9 4 Hei1986b
    ±25.54 ±1.16 ±0.030 ±2.4 ±0.009 ±2.6 ±1.8    
10050–5119 HU 1594 134.51 2028.97 0.629 87.3 0.281 64.4 21.0 3 USN2002
    ±3.76 ±2.28 ±0.033 ±1.6 ±0.009 ±3.3 ±4.6    
10120–2836 B 194 91.89 2003.58 0.676 198.3 0.226 76.0 59.7 3 USN2002
    ±0.85 ±0.22 ±0.012 ±0.5 ±0.003 ±0.7 ±1.1    
10161–2837 TOK 199 2.507 2014.734 0.353 278.5 0.0450 114.5 51.8 4
    ±0.022 ±0.020 ±0.017 ±1.7 ±0.0013 ±1.8 ±3.0    
10282–2548 FIN 308 AB 32.76 2018.13 0.739 155.4 0.144 48.6 270.6 3 Hrt2012a
    ±2.67 ±1.28 ±0.135 ±4.5 ±0.033 ±16.2 ±2.7    
10375–0932 RST 3708 154.81 1971.26 0.457 183.9 0.416 54.6 24.4 4 Hei1991
    ±55.88 ±11.57 ±0.197 ±17.0 ±0.026 ±19.7 ±37.9    
10419–7811 HDS 1530 43.48 2007.33 0.637 114.9 0.277 55.2 121.2 5
10426+0335 A 2768 81.66 1976.39 0.550 57.8 0.401 140.1 354.9 2 Hrt2010a
    ±2.05 ±0.21 ±0.005 ±1.0 ±0.002 ±1.7 ±2.9    
10465–6416 FIN 364 AB 13.25 2020.60 0.025 316.7 0.0805 115.2 17.6 2 Hrt2012a
    ±0.20 ±2.49 ±0.022 ±1.7 ±0.0014 ±2.2 ±64.8    
10529–1717 HDS 1556 14.93 2002.74 0.544 110.5 0.173 99.2 51.4 3 Hrt2012a
    ±0.26 ±1.39 ±0.056 ±2.1 ±0.028 ±3.6 ±17.3    
10557+0044 BU 1076 138.90 1921.62 0.714 219.3 0.750 125.7 323.4 4 Hrt2010a
    ±3.02 ±5.07 ±0.036 ±4.0 ±0.069 ±9.5 ±10.8    
11009–4030 FIN 365 26.86 1990.21 0.087 107.4 0.168 100.5 50.5 3 Tok2012b
    ±0.23 ±1.14 ±0.029 ±1.1 ±0.004 ±0.9 ±16.3    
11014–1204 HDS 1572 18.64 2013.69 0.686 142.4 0.173 98.7 133.8 3
    ±0.72 ±0.03 ±0.013 ±0.4 ±0.003 ±0.8 ±1.5    
11102–1122 HDS 1590 20.63 1995.82 0.698 255.8 0.136 129.4 72.2 3 Hrt2012a
    ±1.62 ±1.68 ±0.011 ±5.4 ±0.006 ±0.9 ±1.5    
11125–1830 BU 220 365.68 1983.93 0.434 325.3 0.553 99.8 337.3 4 Hei1995
    ±8.02 ±3.59 ±0.014 ±0.6 ±0.022 ±0.8 ±6.7    
11272–1539 HU 462 48.40 2008.46 0.087 127.6 0.445 166.5 347.7 2 WSI2006b
    ±0.11 ±0.49 ±0.004 ±11.7 ±0.003 ±2.9 ±10.5    
11297–0619 A 7 204.32 2050.54 0.656 93.3 0.447 105.1 59.8 4 USN2002
    ±11.20 ±19.37 ±0.017 ±4.9 ±0.077 ±5.8 ±13.4    
11544–3745 HWE 71 248.80 2008.48 0.720 276.3 1.004 99.6 162.0 5
12396–3717 DAW 63 56.85 2021.02 0.287 194.5 0.387 21.6 3.7 3 Hrt2010a
    ±0.32 ±0.55 ±0.015 ±13.8 ±0.004 ±5.3 ±16.4    
13145–2417 FIN 297 AB 60.81 1957.92 0.691 188.3 0.233 66.0 295.0 2 Msn2010c
    ±3.27 ±3.17 ±0.041 ±2.7 ±0.010 ±1.7 ±2.2    
13169–3436 I 1567 40.88 2006.40 0.457 145.5 0.326 121.6 274.0 2 Tok2012b
    ±0.18 ±0.01 ±0.002 ±0.2 ±0.000 ±0.1 ±0.4    
13310–3924 SEE 179 83.14 1956.12 0.521 146.5 0.161 145.2 244.4 2 Fin1964b
    ±1.26 ±1.91 ±0.013 ±8.6 ±0.004 ±4.0 ±3.6    
13342–1623 RST 3844 121.85 2010.94 0.432 264.5 0.255 117.6 19.4 3 USN2002
    ±2.70 ±0.49 ±0.007 ±1.1 ±0.003 ±0.7 ±2.4    
13472–0943 KUI 65 155.21 2014.17 0.854 99.0 0.268 144.2 22.7 3 Zir2012
    ±20.85 ±0.11 ±0.006 ±4.5 ±0.012 ±6.1 ±7.6    
13571–2731 I 234 200.72 2057.91 0.725 165.9 0.773 117.3 83.9 4 Mro1966b
    ±17.44 ±10.04 ±0.023 ±8.6 ±0.043 ±1.3 ±1.1    
14020–2108 WSI 79 30.00 2015.16 0.746 123.3 0.239 135.3 119.4 4
    * ±0.17 ±0.037 ±9.9 ±0.011 ±2.7 ±9.2    
14025–2440 B 263 161.43 2014.56 0.499 20.4 0.480 38.8 81.7 4
    ±28.68 ±1.92 ±0.019 ±9.9 ±0.072 ±9.0 ±10.0    
14190–0636 HDS2016 AB 18.67 2003.74 0.302 285.0 0.348 107.9 71.0 3
    ±0.33 ±0.03 ±0.011 ±0.8 ±0.001 ±0.5 ±2.2    
14295–3702 HDS 2045 Aa,Ab 18.39 2008.92 0.468 160.0 0.137 126.9 137.3 3
    ±0.74 ±0.06 ±0.018 ±2.6 ±0.006 ±2.0 ±2.2    
14375+0217 CHR 42 Aa,Ab 21.54 1994.64 0.844 312.4 0.143 53.7 41.9 3 Hrt2000a
    ±0.10 ±0.20 ±0.016 ±3.6 ±0.007 ±3.0 ±5.6    
14581–4852 WSI 80 23.40 1998.44 0.724 267.3 0.342 113.1 297.0 4
    ±0.94 ±2.07 ±0.020 ±4.9 ±0.050 ±6.6 ±8.6    
15047–5625 RST 2937 146.05 2006.50 0.809 173.6 0.214 105.9 113.4 4
    ±24.74 ±0.03 ±0.054 ±2.0 ±0.028 ±4.3 ±6.0    
15226–4755 SLR 20 429.60 1972.88 0.469 56.0 1.899 109.7 344.6 4 Hei1993d
    ±4.57 ±1.56 ±0.004 ±0.9 ±0.019 ±0.5 ±2.0    
15227–4441 COP 2 AB 736.69 2009.83 0.808 125.1 1.409 117.6 19.6 5 Zir2007
15246–4835 B 1288 AB 449.82 2013.70 0.742 143.4 0.326 67.5 284.9 4 USN2002
    ±50.91 ±0.60 ±0.019 ±1.7 ±0.028 ±2.3 ±6.1    
15252–4659 RST 767 249.27 1921.63 0.504 116.6 0.525 136.0 335.4 5 Csa1975c
15262–2819 RST 769 201.47 1977.28 0.379 163.2 0.392 141.9 238.0 5 Doc1996b
15355–4751 HDS 2191 62.52 2005.25 0.315 201.9 0.302 88.6 267.1 4
    ±14.96 ±1.10 ±0.243 ±1.1 ±0.037 ±0.9 ±14.6    
15420+0027 A 2176 52.68 1987.16 0.653 97.7 0.148 27.2 279.3 2 USN2006b
    ±2.04 ±0.38 ±0.027 ±12.9 ±0.008 ±7.4 ±9.9    
16035–5747 SEE 258 AB 26.84 1990.87 0.515 42.0 0.328 168.7 320.0 2 Sod1999
    ±0.09 ±0.21 ±0.012 ±43.2 ±0.006 ±9.9 ±44.1    
16065–4027 RST 1876 96.95 2037.31 0.006 97.5 0.303 97.5 338.1 4
    ±2.07 ±1.54 ±0.027 ±0.8 ±0.011 ±0.9 ±6.2    
16085–1006 BU 949 56.33 2018.34 0.774 198.1 0.289 82.3 157.8 2 Hrt2009
    ±0.20 ±0.35 ±0.016 ±0.5 ±0.003 ±0.5 ±2.9    
16170–5342 I 987 102.47 1952.08 0.262 59.3 0.384 15.9 12.2 3 Hei1986a
    ±1.77 ±1.72 ±0.021 ±39.9 ±0.012 ±10.8 ±43.4    
16224–3220 JSP 691 264.96 1958.53 0.590 101.9 0.870 122.0 307.2 4 Hei1981a
    ±43.30 ±0.81 ±0.046 ±2.9 ±0.102 ±2.2 ±4.7    
16229–1701 CHR 54 39.89 2011.76 0.634 236.6 0.183 101.9 306.0 3 Lin2011c
    ±1.21 ±1.14 ±0.049 ±2.7 ±0.008 ±2.1 ±2.8    
16318–0216 A 693 96.18 1991.33 0.278 220.9 0.195 129.3 344.2 2 Hrt2010a
    ±0.89 ±0.68 ±0.011 ±2.2 ±0.003 ±1.7 ±3.8    
16391–3713 FIN 340 AB 23.99 2013.87 0.621 149.6 0.102 55.4 143.3 2 Hrt2012a
    ±0.06 ±0.02 ±0.004 ±0.4 ±0.000 ±0.4 ±0.8    
16544–3806 HDS 2392 37.25 2010.49 0.325 166.5 0.187 60.2 321.9 5
16589–3737 SEE 315 38.73 1984.63 0.154 243.9 0.186 39.4 102.4 2 Sta1981a
    ±4.48 ±1.11 ±0.106 ±1.7 ±0.006 ±8.6 ±11.2    
17156–1018 BU 957 90.33 1934.61 0.554 23.0 0.296 102.0 7.0 3 Hei1984b
    ±1.52 ±2.41 ±0.067 ±2.1 ±0.013 ±4.6 ±11.3    
17156–3836 FIN 355 14.23 1985.97 0.476 191.9 0.249 115.3 137.2 2 Msn2010c
    ±0.03 ±0.06 ±0.010 ±0.6 ±0.002 ±0.6 ±1.0    
17157–0949 TOK 53 Ba,Bb 5.10 2010.25 0.416 349.0 0.0305 150.0 326.3 2
    ±0.18 ±0.52 ±0.076 ±556 ±0.0056 ±35.0 ±78.0    
17157–0949 A 2592 AB 157.60 2013.20 0.330 31.7 0.381 133.6 267.0 3 Tok2014a
    ±9.0 ±1.56 ±0.017 ±1.4 ±0.017 ±1.6 ±7.5    
17166–0027 A 2984 140.76 1890.53 0.866 220.5 0.959 65.1 287.5 4 Ole1993
    ±0.23 ±0.36 ±0.003 ±0.0 ±0.008 ±0.0 ±0.0    
17181–3810 SEE 324 300.00 1997.49 0.484 249.6 0.439 106.5 42.2 5
17283–2058 A 2244 AB 44.52 2015.23 0.578 265.5 0.168 40.2 25.0 2 Msn1999c
    ±2.18 ±0.26 ±0.044 ±9.7 ±0.003 ±3.9 ±15.3    
17305–1006 RST 3978 49.24 1981.10 0.343 96.8 0.547 83.0 79.5 3
    ±1.19 ±1.52 ±0.090 ±1.8 ±0.044 ±2.2 ±7.4    
17471–3807 I 1336 36.06 2017.29 0.578 15.8 0.132 45.0 11.3 3 Hei1986b
    ±2.08 ±0.19 ±0.050 ±8.4 ±0.001 ±0.1 ±14.2    
18018+0118 BU 1125 AB 213.97 2028.73 0.601 161.3 0.787 55.1 66.0 4 Hrt2009
    ±23.83 ±1.62 ±0.074 ±4.4 ±0.033 ±5.1 ±5.1    
18044–5953 RST 5099 45.64 2009.10 0.513 114.4 0.259 68.2 107.1 4 Hrt2010a
    ±2.10 ±0.10 ±0.010 ±1.0 ±0.004 ±1.0 ±2.7    
18092–2211 RST 3157 9.325 2015.286 0.423 250.8 0.154 49.6 54.5 3 Hei1990c
    ±0.021 ±0.175 ±0.042 ±6.5 ±0.005 ±5.2 ±6.3    
18171–4336 HDS 2583 153.90 2016.88 0.724 58.5 0.153 129.9 24.2 4
    ±308.47 ±2.38 ±0.025 ±15.5 ±0.082 ±44.0 ±81.0    
18281–2645 HDS 2615 150.28 1990.48 0.609 166.6 0.897 96.4 328.7 4
    ±211.19 ±6.64 ±0.004 ±3.2 ±0.366 ±4.2 ±76.5    
18305–2848 HDS 2624 42.93 2007.53 0.531 42.3 0.0979 144.5 14.0 3
    ±10.94 ±1.05 ±0.104 ±22.1 ±0.0211 ±33.2 ±24.7    
18323–1439 CHR 73 2.774 2012.600 0.602 213.9 0.0365 135.6 2.0 3 Ole2005d
    ±0.002 ±0.189 ±0.166 ±10.6 ±0.0053 ±23.2 ±22.7    
18439–0649 YSC 133 13.52 2002.36 0.124 97.6 0.0787 112.1 290.2 3
    ±2.60 ±4.77 ±0.023 ±2.4 ±0.0117 ±3.2 ±77.4    
18465–0058 MCA 53 Aa,Ab 42.48 2012.42 0.665 163.7 0.102 131.1 355.5 3 Msn2010c
    ±2.20 ±1.12 ±0.057 ±21.8 ±0.008 ±11.3 ±39.0    
18516–6054 RST 5126 54.16 2011.97 0.492 195.0 0.130 21.7 12.8 3
    ±3.17 ±0.36 ±0.020 ±34.5 ±0.005 ±13.8 ±36.1   USN2002
19029–5413 I 1390 47.36 2009.65 0.682 241.2 0.198 56.0 51.0 3
    ±0.80 ±0.60 ±0.052 ±7.8 ±0.012 ±4.2 ±7.5    
19040–3804 I 1391 47.38 2006.14 0.641 271.3 0.178 35.8 56.4 4 Hei1973b
    ±0.22 ±0.23 ±0.019 ±5.2 ±0.003 ±1.3 ±5.7    
19105–5813 B 2468 182.29 2013.45 0.891 168.5 0.655 140.0 5.0 5
19155–2515 B 430 19.95 2014.98 0.506 285.1 0.132 82.1 7.5 2 Hrt2001b
    ±0.09 ±0.41 ±0.042 ±0.5 ±0.004 ±1.0 ±5.7    
19164+1433 CHR 85 Aa,Ab 13.673 2008.572 0.022 242.3 0.0583 131.3 262.7 2 McA1993
    ±0.069 ±1.101 ±0.010 ±4.5 ±0.0014 ±3.7 ±28.7    
19194–0136 HDS 2734 Aa,Ab 41.19 2021.53 0.506 27.8 0.321 30.4 348.2 4
    ±5.46 ±2.07 ±0.068 ±39.7 ±0.018 ±7.2 ±57.6    
19296–1239 HU 75 129.67 2009.47 0.652 183.1 0.496 31.5 245.3 3 Sca2003d
    ±2.70 ±0.29 ±0.012 ±5.9 ±0.013 ±3.4 ±4.7    
19398–2326 SEE 389 46.20 1976.63 0.088 327.9 0.221 93.5 0.4 2 Doc1994a
    ±0.10 ±0.60 ±0.007 ±0.3 ±0.001 ±0.2 ±4.7    
19407–0037 CHR 88 Aa,Ab 20.56 1996.01 0.058 185.7 0.0854 150.8 328.1 3 Msn2010c
    ±0.14 ±1.04 ±0.030 ±12.6 ±0.0024 ±7.0 ±27.5    
19573+0513 A 604 228.15 1935.43 0.268 94.7 0.291 108.0 306.0 3 Hei1991
    ±17.63 ±5.63 ±0.019 ±1.9 ±0.016 ±1.2 ±12.2    
19581–4808 HDS 2842 32.04 2015.65 0.807 254.7 0.273 74.1 67.2 4
    ±7.08 ±0.23 ±0.061 ±7.9 ±0.031 ±0.9 ±6.0    
20210–1447 BLA 7 Aa,Ab 3.765 2015.704 0.043 34.3 0.0665 80.9 120.0 3 Msn1994
    * ±0.035 * ±2.1 ±0.0023 ±3.2 *    
20347–6319 HU 1615 357.17 1999.08 0.851 257.5 0.387 46.0 263.0 5 USN2002
20507–3116 B 997 63.67 2014.34 0.179 281.1 0.207 41.5 306.4 3 Hrt2010a
    ±34.66 ±14.29 ±0.142 ±27.2 ±0.053 ±8.1 ±141.1    
20562–3146 B 1001 265.93 1969.51 0.369 187.0 0.322 131.2 219.0 4 USN2002
    ±10.98 ±2.93 ±0.021 ±5.1 ±0.016 ±3.7 ±9.4    
21051+0757 HDS 3004 AB 80.42 2016.78 0.691 88.1 0.463 58.0 48.7 4 Lin2012a
    ±163.73 ±1.39 ±0.062 ±32.2 ±0.326 ±21.2 ±63.5    
21058–5744 HU 1625 560.04 2072.29 0.000 222.1 0.657 81.6 118.5 5
21074–0814 BU 368 AB 345.28 1954.64 0.665 270.1 0.576 87.6 304.2 3 Pal2005b
    ±15.75 ±1.11 ±0.020 ±0.5 ±0.013 ±0.6 ±1.9    
21158–5316 FIN 329 36.04 1997.91 0.115 260.5 0.179 107.1 284.8 3 Doc2013d
    ±0.59 ±3.77 ±0.035 ±3.3 ±0.006 ±0.7 ±29.5    
21243+0343 A 2288 122.72 1950.41 0.659 135.4 0.300 139.4 86.1 3 Sca2003e
    ±2.29 ±0.50 ±0.011 ±4.3 ±0.007 ±1.8 ±3.3    
21255+0203 A 2289 AB 159.45 2008.15 0.652 141.1 0.207 111.0 51.1 4 USN2002
    ±21.43 ±1.85 ±0.025 ±4.2 ±0.013 ±3.1 ±7.1    
21274–0701 HDS 3053 20.93 2015.86 0.349 152.8 0.166 51.1 148.5 2 Msn2010c
    ±0.84 ±0.35 ±0.043 ±2.2 ±0.005 ±1.7 ±3.3    
21436–1108 LV 10 1219.17 2038.43 0.494 9.1 2.039 36.2 4.2 5 USN2002
21477–1813 CHR 223 113.86 2018.85 0.748 284.3 0.365 99.8 71.5 5  
21536–1019 FIN 358 49.38 1976.32 0.770 289.4 0.0791 30.5 9.2 3 Msn2001c
    ±1.98 ±1.86 ±0.054 ±40.9 ±0.0025 ±11.4 ±49.2    
21552–6153 HDO 296 AB 27.94 1997.59 0.420 282.0 0.276 83.2 41.4 2 Doc2011f
    ±0.32 ±0.41 ±0.031 ±0.4 ±0.009 ±0.5 ±5.0    
22029+1547 HDS 3129 20.57 2005.43 0.777 230.1 0.100 124.9 273.1 3 Hor2010
    ±0.07 ±0.02 ±0.002 ±0.5 ±0.000 ±0.2 ±0.3    
22156–4121 CHR 187 25.87 2014.92 0.386 91.6 0.201 68.8 66.7 3
    ±0.13 ±0.05 ±0.006 ±0.4 ±0.004 ±0.7 ±0.6    
22241–0450 BU 172 AB 145.07 1987.66 0.702 113.5 0.402 161.4 296.9 2 Doc2007d
    ±1.85 ±0.05 ±0.003 ±3.0 ±0.003 ±0.7 ±3.0    
22384–0754 A 2695 132.45 2027.46 0.576 285.5 0.252 76.8 47.9 3 Hrt2010a
    ±4.91 ±6.74 ±0.039 ±1.4 ±0.022 ±2.8 ±7.8    
22500–3248 HDO 301 26.46 2015.07 0.516 194.6 0.184 162.9 255.8 2 Hrt2010a
    ±0.04 ±0.04 ±0.003 ±5.2 ±0.001 ±1.5 ±4.9    
22546+1054 HDS 3257 249.14 2007.00 0.415 51.2 0.344 67.1 20.9 4
    ±99.01 ±45.27 ±0.361 ±18.4 ±0.255 ±26.0 ±122.6    
23227–1502 HU 295 64.33 2006.96 0.148 276.3 0.406 77.8 1.6 2 USN1999b
    ±0.31 ±0.45 ±0.003 ±0.3 ±0.002 ±0.5 ±2.9    
23374+0737 FOX 102 AB 127.12 2006.75 0.292 139.1 0.263 22.2 259.4 3 Hrt2014b
    ±3.20 ±0.64 ±0.010 ±6.6 ±0.005 ±2.8 ±7.8    

Download table as:  ASCIITypeset images: 1 2 3 4 5 6

We do not publish figures for all new orbits here, as they will be available online in VB6.7 Figure 3 illustrates orbit revisions ranging from dramatic to minor. Three first-time orbits are presented in Figure 4. Below we comment on some pairs.

Figure 3.

Figure 3. Examples of revised orbits. New orbits are plotted with solid lines, previous orbits in dashed lines. The position of the primary at the coordinate center is marked by a large cross, the line of nodes is traced by a dash–dotted line. The scale is in arcseconds. Interferometric (solid blue), Hipparcos (red), and micrometer (green crosses) measures are connected to their expected positions on the new orbit. A dotted "O–C" line indicates a measure given zero weight in the orbit solution. Left: a dramatic orbit revision for 01143–2732 (HDS 33, period 10.2 years). Center: the long-period system 01528–0447 (RST 4188, 619 years), where new interferometric observations caused a substantial orbit revision; two more centuries of data are still needed to cover the extremity of the ellipse and to constrain period and semi-major axis. Right: a minor revision of 08251–4910 (RST 321, 25.8 years) demonstrating systematic errors of the historic micrometer measures.

Standard image High-resolution image
Figure 4.

Figure 4. Examples of new orbits (see the caption to Figure 3). Left: the Hipparcos binary 05073–8352 (HDS 699, period 26.5 years). Center: "fast" spectroscopic binary 10161–2837 (TOK 199, 2.5 years). Right: visual binary 11544–3745 (HWE 71, 249 years) that passed recently through periastron.

Standard image High-resolution image

04163–0710. WSI 97 is a single-lined nearby binary. Using the radial velocities measured by D. Latham (2012, private communication), we computed a combined orbit (the previous visual orbit reported by Riddle et al. (2015) had a wrong period). The inclination is close to 180° and had to be fixed in order to match the RV amplitude. The complete orbit including RVs will be published later.

04506–1505. CHR 20 is a Hyades binary for which Griffin (2012) published an SB2 orbit. We combined his RVs with the speckle data, resulting in a very accurate period. The combined orbit corresponds to a mass sum of 2.1 ${{\mathcal{M}}}_{\odot }$ and an orbital parallax of 22 mas, in good agreement with the HIP2 parallax of 23.69 ± 0.87 mas.

05245–0224. MCA 18 Aa,Ab has an SB1 orbit with P = 9.44 years. The orbit given here uses only the speckle data, however.

07490–2455. The period of TOK 194 matches the astrometric orbit of Goldin & Makarov (2007). The mass sum in this pair composed of a giant primary and possibly an A-type secondary is 5.9 ${{\mathcal{M}}}_{\odot }$. The measure on 2011.93 was ignored as spurious (it was affected by vibrations).

07522–4035. TOK 195 is the bright star a Pup (HD 64440, HR 3080) known as a spectroscopic binary. However, examination of the RV data reveals that the orbit by Parsons (1983) is only approximate. The binary is difficult to measure, always close to the diffraction limit and with ${\rm{\Delta }}$m ∼ 3. Instead of the spectroscopic period of 6.99 years, our orbit has P = 7.4 years and is still preliminary. More RV coverage is obviously needed.

08391–5557. HU 1443 A,BC is a triple system. We provide the first very tentative orbit for the outer binary, but note its large residuals from the recent measures of AB. Strictly speaking, the orbit should describe the motion of the center-of-gravity of BC around A, rather than the measures of AB. Such refinement was made for the orbit of A 2592 AB (17156–0949), but it is not warranted for this preliminary orbit.

10161–2837. TOK 199 is marked as an SB2 in the GCS, while D. Latham (2012, private communication) derived an orbital period of 916 days, now independently confirmed by our orbit (Figure 4).

17157–0949. This is the triple system HIP 84430. We computed the first orbit of the secondary subsystem Ba,Bb which was discovered at SOAR in 2009 and has just completed one full revolution since. Its separation is always close to the diffraction limit. Adopting a mass sum of 2.6 ${{\mathcal{M}}}_{\odot }$ for Ba,Bb, the resulting dynamical parallax is 7.6 ± 1.5 mas, while the HIP2 parallax is 4.9 ± 0.9 mas. The latest orbit of the outer pair A 2592 AB published in TMH14 does not account for the fact that the speckle measurements at SOAR refer to A,Ba and not to AB. Here we give a more accurate solution that uses the positions of AB computed from the measures of A,Ba under the assumption that Ba and Bb have equal masses. After this correction and orbit adjustment, the weighted residuals are 4.3 mas in separation and 1fdg3 in angle. Interestingly, there were a considerable number of speckle interferometry measures of this pair obtained in the 1980s and 1990s at 4 m telescopes, but none of them recognized the subsystem Ba,Bb, despite its small ${\rm{\Delta }}$m.

Ignoring the multiplicity, the spectroscopic survey of Guillo ut et al. (2009) determined a moderate axial rotation $V\mathrm{sin}i=10.8$ km s−1 and detected the lithium line of 52.8 mÅ equivalent width which, together with the X-ray detection by ROSAT (RasTyc 1715-0948), normally indicates youth. These authors do not mention this star in particular, but discuss a group of active lithium-rich giants in their sample, to which this system apparently belongs. Even with the larger dynamical parallax (instead of the HIP2 parallax), all three resolved components of HIP 84430 are located above the main sequence in the color–magnitude diagram. This multiple system is peculiar and merits further study.

5. SUMMARY

We present here a large set of new speckle interferometry measurements of close binary stars, mostly with southern declinations. The total number of measurements made with HRCam since 2008 now exceeds 5000. This unique data set is used for calculation of 46 new orbits and for improvement of 148 known orbits. For comparison, the data in TMH14 resulted in 13 new orbits and in the improvement (sometimes drastic) of 45 previously known orbits. We demonstrate the good internal consistency of speckle astrometry with HRCam by repeated measurements of relatively wide binaries. Typical errors are on the order of 3 mas even for these wide pairs.

The high angular resolution and dynamic range of HRCam give access to close binaries never resolved before. Some of those objects had prior indication of binarity from variable RV or astrometric acceleration. In such cases, direct resolution allows us to estimate statistically orbital periods (which are typically short) and to evaluate masses. This clarifies the statistics of binary and multiple stars in the solar neighborhood. We also resolved a number of components in previously known nearby wide binaries, converting them into triple or higher-order hierarchies.

A total of 56 newly resolved pairs are reported here, ten of those being inner or outer subsystems in visual binaries (Figure 2). Most of those subsystems are totally unexpected. Some of the newly resolved binaries or subsystems are interesting for various reasons, such as being young (e.g., X-ray sources), having comparable separations and approaching the dynamical stability limit, such as HIP 9497 with periods of 138 and 13.9 years (TMH14), or being targets of exo-planet programs.

We thank the operators of SOAR D. Maturana, P. Ugarte, S. Pizarro, and J. Espinoza for efficient support of our program. G. Cecil has kindly loaned us his Luca-R detector which was used for five nights instead of our own broken camera. R.A.M. acknowledges support from the Chilean Centro de Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL PFB/06, and the Project IC120009 Millennium Institute of Astrophysics (MAS) of the Iniciativa Científica Milenio del Ministerio de Economía, Fomento y Turismo de Chile. R.A.M also acknowledges ESO/Chile for hosting him during his sabbatical leave throughout 2014. This work used the SIMBAD service operated by Centre des Données Stellaires (Strasbourg, France), bibliographic references from the Astrophysics Data System maintained by SAO/NASA, and the Washington Double Star Catalog maintained at USNO.

Facilities: SOAR - The Southern Astrophysical Research Telescope.

Note added in proof

The component C in 16563–4040 (TOK 412 AC) was independently discovered by Sana et al. (2014) and is designated in the WDS as SNA 60 AC. By error, the newly discovered close companion in 04308–5727 (TOK 429 Aa,Ab) was omitted from Table 4, Figure 2, and Section 3.2, but its measurements are found in Table 2. The total number of newly resolved companions is still 56.

Footnotes

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10.1088/0004-6256/150/2/50