# Spectroscopic Orbits of Subsystems in Multiple Stars. IX

Andrei Tokovinin  Cerro Tololo Inter-American Observatory — NSF’s NOIRLab
Casilla 603, La Serena, Chile<EMAIL_ADDRESS>
###### Abstract

New spectroscopic orbits of inner subsystems in 14 hierarchies are determined
from long-term monitoring with the optical echelle spectrometer, CHIRON. Their
main components are nearby solar-type stars belonging to nine triple systems
(HIP 3645, 14307, 36165, 79980, 103735, 103814, 104440, 105879, 109443) and
five quadruples of 2+2 hierarchy (HIP 41171, 49336, 75663, 78163, and 117666).
The inner periods range from 254 days to 18 yr. Inner subsystems in HIP 3645,
14313, 79979, 103735, 104440, and 105879 are resolved by speckle
interferometry, and their combined spectro-interferometric orbits are derived
here. Astrometric orbits of HIP 49336 Aa,Ab and HIP 117666 Aa,Ab are
determined from wobble in the observed motion of the outer pairs. Comparison
with three spectroscopic orbits found in the Gaia DR3 archive reveals that
Gaia under-estimated the amplitudes (except for HIP 109443), while the periods
match approximately. This work contributes new data on the architecture of
nearby hierarchical systems, complementing their statistics.

binaries:spectroscopic — binaries:visual

##  1 Introduction

Observations of spectroscopic subsystems in nearby solar-type stars are
motivated by the desire to determine their periods and mass ratios,
complementing statistics of hierachies in the solar neighborhood (Tokovinin,
2014). Many subsystems discovered by, e.g., Nordström et al. (2004) or by
astrometric acceleration lack orbits and therefore confuse the statistics. A
long-term program at the 1.5 m telescope at Cerro Tololo with the CHIRON high-
resolution optical echelle spectrograph has been conducted to determine the
missing periods, with the goal to reach relative completeness for periods
shorter than $\sim$1000 days. The results obtained so far were reported in
eight papers; the last paper 8 (Tokovinin, 2022) contains references to the
full series. The total number of spectroscopic orbits determined throughout
this program is 102. Summary and statistical analysis of this material are
presented in the accompanying paper 10 (2022, submitted). The first papers
resulting from this project featured short-period orbits, but longer periods
became accessible as the time coverage increased. Most orbits presented here
have periods longer than a year. Some of them are preliminary, lacking
adequate phase coverage, but they are still useful for statistical purposes,
justfying their publication here. Six inner subsystems are wide enough to be
resolved by speckle interferometry, allowing calculation of the combined
spectro-interferometric orbits.

In 2022 June, the third release of the Gaia catalog (GDR3) has changed the
landscape by publishing $\sim 10^{5}$ spectroscopic orbits and a comparable
number of astrometric orbits in their non-single star catalog, NSS (Gaia
Collaboration et al., 2022). However, stars with close visual companions were
removed from the Gaia SB sample. Comparison of the NSS with the CHIRON orbits,
presented in paper 10, shows an overlap of only about 30%, so the NSS
completeness with respect to multiple stars remains low. Some NSS orbits in
common with CHIRON have substantially different parameters (examples are found
below). Although the NSS orbits contribute significantly to the statistics of
nearby hierarchies, they do not yet replace the ground-based monitoring and do
not render the CHIRON survey obsolete.

This paper is organized similarly to the previous ones. The data and methods
are outlined in Section 2, where the orbital elements are also given. The
hierarchical systems are discussed in Section 3. A short summary in Section 4
concludes the paper.

##  2 New Spectroscopic Orbits

Table 1: Basic Parameters of Observed Multiple Systems

WDS | Comp. | HIP | HD | Spectral | $V$ | $V-K_{s}$ | $\mu^{*}_{\alpha}$ | $\mu_{\delta}$ | RV |  $\varpi$aafootnotemark:
---|---|---|---|---|---|---|---|---|---|---
(J2000) |  |  |  | Type | (mag) | (mag) | (mas yr-1) | (km s-1) | (mas)
00467$-$0426 | A | 3645 | 4449 | G5 | 7.58 | 2.00 | 24* |  $-$261* | 9.7 | 30.08:
| B | … | … | M4V | 15.20 | 4.92 | 21 |  $-$260 | … | 30.51
03046$-$5119 | A | 14307 | 19330 | F8V | 7.54 | 1.25 | 88 | 71 | 20.4 | 18.36
| B | 14313 | … | K1V | 8.59 | 1.91 | 85 | 72 | 20.2 | 18.42:
07270$-$3419 | A | 36165 | 59099 | F6V | 7.03 | 1.23 |  $-$305* | 96* | 65.4 | 20.32:
| B | 36160 | 59100 | G1.5V | 8.19 | 1.59 |  $-$307 | 91 | 64.9 | 20.71
08240$-$1548 | AB | 41171 | 70904 | F2/F3V | 8.55 | 1.06 |  $-$28* |  $-$16* |  $-$1.4 | 4.94:
10043$-$2823 | A | 49336 | 87416 | F6V | 7.82 | 1.19 |  $-$27 |  $-$23 |  $-$13.4 | 10.67:
| B | … | … | … | 8.19 | … |  $-$49 |  $-$36 |  $-$11.8 | 10.94:
15275$-$1058 | A | 75663 | 137613 | G0 | 8.14 | 1.35 |  $-$62* |  $-$36* |  $-$56.3 | 7.73
| B | … | … | … | 9.21 | 1.50 |  $-$61 |  $-$35 |  $-$56.8 | 7.78
15577$-$3915 | A | 78163 | 142728 | G3/5V | 9.04 | 1.54 | 17 | 7 | 9.4 | 10.49
| B | … | … | … | 10.30 | 2.08 | 18 | 7 | 10.5 | 10.65
16195$-$3054 | A | 79980 | 146836 | F5IV | 5.51 | 1.14 | 82 | 23 | 0.3 | 22.71
| B | 79979 | 146835 | F9V | 6.82 | 1.11 | 76 | 27 |  $-$0.9 | 25.53:
21012$-$3511 | A | 103735 | 1999918 | G3V | 7.66 | 1.61 |  $-$176 |  $-$63 | 61.6 | 22.10:
| B | … | … | … | 17.14 | 1.64 |  $-$176 |  $-$67 | … | 22.09
21022$-$4300 | A | 103814 | 200011 | G3IV+K0IV | 6.64 | 1.62 | 71* |  $-$112* |  $-$33.5 | 11.25
| B | 103819 | 200026 | K0III | 6.90 | 2.27 | 70 |  $-$111 |  $-$35.6 | 11.25
21094$-$7310 | AB | 104440 | 200525 | F9.5V | 5.68 | 1.49 | 445* |  $-$330* |  $-$11.1 | 46.99:
| C | … | … | … | 13.50 | 6.16 | 433 |  $-$303 |  $-$8.3 | 50.6
21266$-$4604 | A | 105879 | 203934 | F7V | 7.18 | 1.28 | 29* |  $-$112* | 35.5 | 12.44:
| D | … | … | … | 9.96 | 1.76 | 31 |  $-$112 | 35.7 | 13.10
22104$-$5158 | A | 109443 | 210236 | F8V | 7.63 | 1.32 | 220* |  $-$104* |  $-$3.8 | 15.33:
| B | … | … | … | 13.25 | … | 225 |  $-$104 | … | 15.58
23518$-$0637 | AB | 117666 | 223688 | G5V | 8.73 | 1.69 | 85* |  $-$12* | 14.3 | 13.4:

††footnotetext: Proper motions and parallaxes are from Gaia DR3 (Gaia
Collaboration et al., 2021). Colons mark parallaxes biased by subsystems,
asterisks mark PMs from Brandt (2021).

The hierarchical systems studied here are listed in Table 1. The data are
collected from Simbad and GDR3 (Gaia Collaboration et al., 2021), the radial
velocities (RVs) are mostly determined in this work. The first column gives
the Washington Double Star (WDS, Mason et al., 2001) code based on the J2000
coordinates. The HIP and HD identifiers, spectral types, photometric and
astrometric data refer either to the individual stars or to the unresolved
subsystems. Parallaxes potentially biased by unresolved subsystems are marked
by colons, and asterisks indicate proper motions from Brandt (2021).

###  2.1 Spectroscopic Observations

Observations, data reduction, and orbit calculations were described in
previous papers of this series (e.g. Tokovinin, 2022). To avoid repetition,
only a brief outline is given here.

The spectra used here were taken with the 1.5 m telescope sited at the Cerro
Tololo Inter-American Observatory (CTIO) in Chile and operated by the Small
and Medium Aperture Telescopes Research System (SMARTS) Consortium.111
http://www.astro.yale.edu/smarts/ Fifteen hours of observing time were
allocated to this program per semester, starting from 2017B. Observations were
made with the fiber-fed CHIRON optical echelle spectrograph (Tokovinin et al.,
2013; Paredes et al., 2021) by the telescope operators in service mode. The
spectra taken with the image slicer have a resolution of 85 000. They are
reduced by the standard CHIRON pipeline. The wavelength calibration is based
on the thorium-argon lamp spectra taken after each object.

The RVs are determined from Gaussian fits to the cross-correlation function
(CCF) of echelle orders with the binary mask constructed from the solar
spectrum, as detailed in Tokovinin (2016a). The RV errors depend on several
factors such as the width and contrast of the CCF dip, blending with other
dips, and signal-to-noise ratio. The rms residuals from the orbits can be as
low as 0.02 km s-1 , but typically are between 0.1 and 0.5 km s-1 for the
systems studied here. I assign the RV errors (hence weights) to match roughly
the residuals, with larger errors for blended or noisy dips. Some blended CCFs
are fitted by fixing the width or amplitude of individual components
determined from other spectra with better-separated dips. Otherwise, a heavily
blended dip is fitted by a single Gaussian, and the resulting biased RV is
assigned a large error and a low weight in the orbit fit.

The width of the CCF dip is related to the projected rotation velocity $V\sin
i$, while its area depends on the spectral type, metallicity, and, for blended
spectra of several stars, on the relative fluxes. Table 2 lists average
parameters of the Gaussian curves fitted to the CCF dips. It gives the number
of averaged measurements $N$ (blended CCFs of double-lined binaries are
ignored), the dip amplitude $a$, its dispersion $\sigma$, the product
$a\sigma$ proportional to the dip area (hence to the relative flux), and the
projected rotation velocity $V\sin i$, estimated from $\sigma$ by the
approximate formula given in (Tokovinin, 2016a) and valid for $\sigma<12$ km
s-1 . The last column indicates the presence or absence of the lithium 6708 Å
line in individual components.

Table 2: CCF Parameters  HIP | Comp. | $N$ | $a$ | $\sigma$ | $a\sigma$ | $V\sin i$ | Li
---|---|---|---|---|---|---|---
|  |  |  | (km s-1) | (km s-1) | (km s-1) | 6708Å
3645 | Aa | 10 | 0.403 | 3.66 | 1.47 | 2.4 | N
3645 | Ab | 10 | 0.115 | 3.93 | 0.45 | 3.5 | N
14313 | Ba | 8 | 0.297 | 3.99 | 1.19 | 3.8 | N
14313 | Bb | 8 | 0.232 | 4.30 | 1.00 | 4.7 | N
36165 | Aa | 9 | 0.208 | 5.19 | 1.08 | 7.0 | N
36160 | B | 4 | 0.403 | 3.49 | 1.41 | 1.4 | N
41171 | Aa | 12 | 0.030 | 18.08 | 0.46 | 32.0 | N
41171 | Ab | 12 | 0.062 | 5.63 | 0.35 | 8.1 | N
41171 | Ba | 12 | 0.030 | 4.35 | 0.13 | 4.9 | N
41171 | Bb | 12 | 0.017 | 3.80 | 0.07 | 3.1 | N
49336 | Aa | 19 | 0.116 | 4.06 | 0.47 | 4.0 | N
49336 | Ab | 19 | 0.082 | 5.96 | 0.49 | 8.8 | N
49336 | B | 19 | 0.028 | 6.97 | 0.19 | 10.9 | N
75663 | Aa | 19 | 0.218 | 6.85 | 1.50 | 10.7 | Y
78163 | Ba | 12 | 0.355 | 4.26 | 1.51 | 4.6 | N?
79979 | Ba | 5 | 0.194 | 4.30 | 0.83 | 4.7 | Y
79979 | Bb | 5 | 0.115 | 3.71 | 0.43 | 2.7 | N
103735 | Aa | 4 | 0.320 | 3.59 | 1.15 | 2.1 | Y
103735 | Ab | 4 | 0.058 | 3.83 | 0.22 | 3.2 | N
104440 | Aa | 3 | 0.274 | 5.03 | 1.38 | 6.7 | Y
104440 | Ab | 3 | 0.025 | 4.96 | 0.13 | 6.5 | N
103814 | Aa | 8 | 0.297 | 3.92 | 1.16 | 3.5 | N
105879 | Aa | 1 | 0.193 | 5.69 | 1.10 | 6.9? | N
105879 | Ab | 1 | 0.045 | 3.19 | 0.14 | 1.0? | N
109443 | Aa | 6 | 0.266 | 4.97 | 1.32 | 6.5 | Y
117666 | Aa | 10 | 0.209 | 3.81 | 0.80 | 3.1 | N?
117666 | Ba | 10 | 0.194 | 3.69 | 0.71 | 2.6 | N?
Table 3: Spectroscopic Orbits  HIP | System | $P$ | $T$ | $e$ | $\omega_{\rm A}$ | $K_{1}$ | $K_{2}$ | $\gamma$ | rms1,2 | $M_{1,2}\sin^{3}i$
---|---|---|---|---|---|---|---|---|---|---
|  | (d) | (JD -2,400,000) |  | (deg) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (${\cal M}_{\odot}$)
3645 | Aa,Ab | 1529.6 | 59055.5 | 0.240 | 176.3 | 9.985 | 11.423 | 9.597 | 0.037 | 0.78
|  |  $\pm$3.7 |  $\pm$9.5 |  $\pm$0.012 |  $\pm$2.3 |  $\pm$0.271 |  $\pm$0.275 |  $\pm$0.132 | 0.145 | 0.68
14313 | Ba,Bb | 6648.1 | 53347.9 | 0.488 | 318.1 | 8.048 | 8.228 | 21.540 | 0.184 | 1.01
|  |  $\pm$96.6 |  $\pm$105.7 |  $\pm$0.008 |  $\pm$1.5 |  $\pm$0.153 |  $\pm$0.155 |  $\pm$0.049 | 0.191 | 0.99
36165 | Aa,Ab | 2300.4 | 57921.4 | 0.610 | 64.4 | 5.69 | … | 65.52 | 0.037 | 1.28:
|  |  $\pm$16.1 |  $\pm$37.9 |  $\pm$0.075 |  $\pm$4.9 |  $\pm$1.16 | … |  $\pm$0.34 | … | 0.39
41171 | Ba,Bb | 963.1 | 58913.2 | 0.607 | 273.4 | 15.61 | 18.70 |  $-$3.32 | 0.30 | 1.10
|  |  $\pm$1.7 |  $\pm$1.7 |  $\pm$0.007 |  $\pm$0.8 |  $\pm$0.16 |  $\pm$0.25 |  $\pm$0.07 | 0.46 | 0.92
41171 | Aa,Ab | 25.4133 | 58449.999 | 0.5320 | 308.25 | 47.18 | 48.27 |  $-$1.41 | 1.84 | 0.70
|  |  $\pm$0.0001 |  $\pm$0.005 |  $\pm$0.0005 |  $\pm$0.09 |  $\pm$0.23 |  $\pm$0.03 |  $\pm$0.03 | 0.13 | 0.69
49336 | Ba,Bb | 1307.4 | 58895.8 | 0.163 | 132.5 | 4.55 | … |  $-$11.73 | 0.19 | 1.35:
|  |  $\pm$8.4 |  $\pm$38.4 |  $\pm$0.021 |  $\pm$11.4 |  $\pm$0.15 | … |  $\pm$0.09 | … | 0.50
75663 | Aa,Ab | 623.76 | 59098.35 | 0.653 | 269.9 | 10.045 | … |  $-$56.352 | 0.041 | 1.47:
|  |  $\pm$0.21 |  $\pm$0.47 |  $\pm$0.002 |  $\pm$0.6 |  $\pm$0.053 | … |  $\pm$0.029 | … | 0.48
78163 | Ba,Bb | 2083.2 | 59208.6 | 0.619 | 27.7 | 10.84 | … | 10.55 | 0.080 | 0.93:
|  |  $\pm$20.4 |  $\pm$20.0 |  $\pm$0.025 |  $\pm$4.9 |  $\pm$1.63 | … |  $\pm$0.45 | … | 0.71
79979 | Ba,Bb | 1083.16 | 57635.32 | 0.610 | 349.8 | 15.31 | 18.01 | 0.00 | 0.121 | 1.14
|  |  $\pm$1.84 |  $\pm$4.81 |  $\pm$0.003 |  $\pm$1.3 |  $\pm$0.16 |  $\pm$0.21 |  $\pm$0.06 | 0.204 | 0.97
103735 | Aa,Ab | 4251.8 | 59433.5 | 0.368 | 152.4 | 7.29 | 10.13 | 61.69 | 0.020 | 1.09
|  |  $\pm$12.1 |  $\pm$11.3 |  $\pm$0.003 |  $\pm$1.2 |  $\pm$0.04 |  $\pm$0.23 |  $\pm$0.05 | 0.375 | 0.79
103814 | Aa,Ab | 1089.8 | 58393.5 | 0.601 | 331.0 | 4.48 | … |  $-$33.62 | 0.010 | 1.78:
|  |  $\pm$9.4 |  $\pm$16.1 |  $\pm$0.079 |  $\pm$9.1 |  $\pm$1.44 | … |  $\pm$0.23 | … | 0.28
104440 | A,B | 1947.5 | 57909.2 | 0.631 | 178.5 | 10.202 | 16.759 |  $-$11.211 | 0.020 | 1.15
|  |  $\pm$0.9 |  $\pm$1.7 |  $\pm$0.002 |  $\pm$0.8 |  $\pm$0.044 |  $\pm$0.180 |  $\pm$0.046 | 0.494 | 0.70
105879 | Aa,Ab | 2935.6 | 60032.2 | 0.631 | 359.7 | 11.07 | 13.83 | 35.44 | 0.418 | 1.24
|  |  $\pm$9.4 |  $\pm$13.0 |  $\pm$0.019 |  $\pm$2.5 |  $\pm$0.66 |  $\pm$0.91 |  $\pm$0.14 | 0.843 | 1.00
109443 | Aa,Ab | 978.5 | 58715.3 | 0.214 | 24.3 | 3.02 | … |  $-$3.80 | 0.008 | 1.30:
|  |  $\pm$37.4 |  $\pm$210.9 |  $\pm$0.084 |  $\pm$67.7 |  $\pm$0.34 | … |  $\pm$0.27 | … | 0.18
117666 | Aa,Ab | 781.2 | 59353.7 | 0.105 | 128.4 | 4.944 | … | 14.336 | 0.089 | 0.97:
|  |  $\pm$1.6 |  $\pm$62.8 |  $\pm$0.042 |  $\pm$29.4 |  $\pm$0.135 | … |  $\pm$0.128 | … | 0.95:
117666 | Ba,Bb | 253.9 | 59204.8 | 0.269 | 113.9 | 9.28 | … | 14.264 | 0.128 | 0.42
|  |  $\pm$0.145 |  $\pm$2.5 |  $\pm$0.018 |  $\pm$3/3 |  $\pm$0.16 | … |  $\pm$0.132 | … | 0.31
Table 4: Radial Velocities and Residuals (fragment)

HIP | System | Date | RV | $\sigma$ | (O$-$C) | Comp.
---|---|---|---|---|---|---
HD |  | (JD -2,400,000) | (km s-1) | Instr.
3645 | Aa,Ab | 54781.5350 | 8.94 | 2.00 | 0.22 | a
3645 | Aa,Ab | 57985.7810 | 13.38 | 0.50 | 0.05 | a
3645 | Aa,Ab | 57985.7810 | 4.95 | 0.70 | -0.40 | b
3645 | Aa,Ab | 58130.5330 | 16.01 | 0.05 | -0.01 | a
3645 | Aa,Ab | 58130.5330 | 2.33 | 0.25 | 0.08 | b

††footnotetext: (This table is available in its entirety in machine-readable
form). Instrument codes: B – Butler et al. (2017); E – Fiber echelle
(Tokovinin, 2015); F – Frasca et al. (2018) G – Gaia DR2; L – DuPont echelle
(Tokovinin et al., 2015); N – Nidever et al. (2002)

Table 5: Visual and Astrometric Orbits  HIP | System | $P$ | $T$ | $e$ | $a$ | $\Omega_{\rm A}$ | $\omega_{\rm A}$ | $i$
---|---|---|---|---|---|---|---|---
|  | (yr) | (yr) |  | (arcsec) | (deg) | (deg) | (deg)
3645 | Aa,Ab | 4.188 | 2020.563 | 0.240 | 0.0967 | 314.0 | 176.3 | 97.6
|  |  $\pm$0.010 |  $\pm$0.026 |  $\pm$0.012 |  $\pm$0.0014 |  $\pm$0.7 |  $\pm$1.7 |  $\pm$1.0
14313 | Ba,Bb | 18.20 | 2004.94 | 0.488 | 0.1591 | 292.6 | 318.1 | 84.2
|  |  $\pm$0.68 |  $\pm$0.29 |  $\pm$0.008 |  $\pm$0.0017 |  $\pm$0.3 |  $\pm$1.6 |  $\pm$0.5
49336 | Ba,Bb | 3.580 | 2020.127 | 0.163 | 0.0071 | 9.3 | 132.5 | 140.4
|  |  $\pm$0.023 |  $\pm$0.105 |  $\pm$0.021 |  $\pm$0.0009 |  $\pm$6.0 |  $\pm$11.4 |  $\pm$13.5
49336 | A,B | 397.8 | 1971.24 | 0.729 | 0.886 | 321.5 | 253.5 | 142.3
|  |  $\pm$17.9 |  $\pm$0.32 |  $\pm$0.010 |  $\pm$0.021 |  $\pm$1.6 |  $\pm$1.9 |  $\pm$1.5
79979 | Ba,Bb | 2.966 | 2016.674 | 0.610 | 0.0601 | 103.8 | 349.8 | 82.9
|  |  $\pm$0.005 |  $\pm$0.013 |  $\pm$0.003 |  $\pm$0.0007 |  $\pm$0.7 |  $\pm$1.3 |  $\pm$1.0
103735 | Aa,Ab | 11.64 | 2021.598 | 0.368 | 0.1363 | 168.1 | 152.4 | 87.4
|  |  $\pm$0.03 |  $\pm$0.031 |  $\pm$0.003 |  $\pm$0.0009 |  $\pm$0.4 |  $\pm$1.2 |  $\pm$0.7
104440 | A,B | 5.332 | 2017.424 | 0.631 | 0.1905 | 194.3 | 178.5 | 93.0
|  |  $\pm$0.003 |  $\pm$0.005 |  $\pm$0.002 |  $\pm$0.0013 |  $\pm$0.4 |  $\pm$0.8 |  $\pm$1.0
105879 | Aa,Ab | 8.037 | 2023.237 | 0.631 | 0.0669 | 231.5 | 359.7 | 97.0
|  |  $\pm$0.026 |  $\pm$0.036 |  $\pm$0.019 |  $\pm$0.0018 |  $\pm$1.0 |  $\pm$2.5 |  $\pm$1.6
117666 | Aa,Ab | 2.138 | 2021.33 | 0.105 | 0.0079 | 26.1 | 128.4 | 148.0
|  |  $\pm$0.004 |  $\pm$0.17 |  $\pm$0.043 |  $\pm$0.0007 |  $\pm$5.3 |  $\pm$29.4 | fixed
117666 | A,B | 30.073 | 2020.392 | 0.309 | 0.1809 | 24.3 | 356.5 | 147.5
|  |  $\pm$0.071 |  $\pm$0.044 |  $\pm$0.004 |  $\pm$0.0009 |  $\pm$1.4 |  $\pm$1.5 | fixed
Table 6: Radial Velocities of Other Components  HIP | Comp. | Date | RV
---|---|---|---
|  | (JD -2,400,000) | (km s-1)
14257 | C | 57986.8700 | 28.496
36160 | B | 56940.8450 | 64.859
36160 | B | 57266.9055 | 64.884
36160 | B | 58121.7557 | 64.889
36160 | B | 58193.5556 | 64.881
36160 | B | 58546.5656 | 64.873
36160 | B | 59168.7635 | 64.899
105879 | D | 55477.5014 | 36.077
105879 | D | 56885.7159 | 35.714
Table 7: Positional Measurements and Residuals

HIP | System | $T$ | $\theta$ | $\rho$ | $\sigma$ | O$-$Cθ | O$-$Cρ
---|---|---|---|---|---|---|---
|  | (yr) | (°) | (′′) | (′′) | (°) | (′′)
3645 | Aa,Ab | 2011.6850 | 159.8 | 0.0300 | 0.002 | 5.4 | 0.000
3645 | Aa,Ab | 2011.9417 | 139.9 | 0.0598 | 0.002 |  $-$0.1 |  $-$0.000
3645 | Aa,Ab | 2014.7537 | 311.2 | 0.1076 | 0.002 | 0.3 |  $-$0.000
3645 | Aa,Ab | 2021.8909 | 320.5 | 0.0742 | 0.002 |  $-$1.9 |  $-$0.001
3645 | Aa,Ab | 2022.4447 | 316.3 | 0.1153 | 0.002 | 0.2 | 0.000
14313 | Ba,Bb | 2014.7635 | 107.9 | 0.1911 | 0.002 |  $-$0.4 | 0.001
14313 | Ba,Bb | 2014.7635 | 108.3 | 0.1908 | 0.002 |  $-$0.0 | 0.000

††footnotetext: (This table is available in its entirety in machine-readable
form)

###  2.2 Orbit Calculation

The orbital elements and their errors are determined by the least-squares fits
with weights inversely proportional to the adopted RV errors. The IDL code
ORBIT222Codebase: http://www.ctio.noirlab.edu/ãtokovin/orbit/ and
https://doi.org/10.5281/zenodo.61119 was used (Tokovinin, 2016b). Several
double-lined pairs studied here were resolved by speckle interferometry, and
in such case the combined orbits are fitted jointly to the RVs and position
measurements. In some triple systems, the orbits of the outer and inner
subsystems are fitted jointly to the RVs and, where available, position
measurements using a modification of the same code ORBIT3 (Tokovinin, 2017)
described by Tokovinin & Latham (2017). Both codes allow to fix some orbital
elements to avoid degeneracies (e.g. for circular or face-on orbits) or to
cope with insufficient data (e.g. an incomplete coverage of the outer orbit).

Table 3 gives elements of the spectroscopic orbits in standard notation. Its
last column contains the masses $M\sin^{3}i$ for double-lined binaries. For
single-lined systems, the mass of the primary star (listed with colons) is
estimated from its absolute $V$ magnitude, and the minimum mass of the
secondary that corresponds to the 90° inclination is derived from the orbit.
Table 4, published in full electronically, provides individual RVs and
residuals to orbits. The Hipparcos number of the primary star and the system
identifier (components joined by comma) in the first two columns define the
pair. Then follow the Julian date, the RV, its adopted error $\sigma$ (blended
CCF dips are assigned larger errors), and the residual to the orbit (O$-$C).
The last column specifies to which component this RV refers (’a’ for the
primary, ’b’ for the secondary). The RVs of some other visual components are
provided, for completeness, in Table 6. It contains the HIP number, the
component letter, the Julian date, and the RV. The less accurate RVs derived
from blended dips are marked by colons.

The elements of visual orbits are given in Table 5. For combined spectro-
interferometric orbits, it repeats common elements, but the period $P$ and
epoch $T$ are given in Julian years rather than days. This table also contains
elements of the outer visual orbits fitted jointly with the inner subsystems
using ORBIT3. The positional measurements used in these orbits are published
(except the latest observations at SOAR); they are listed together with the
adopted errors and residuals in Table 7.

###  2.3 Complementary Data

I use here astrometry and photometry from the GDR3 (Gaia Collaboration et al.,
2021) and from the earlier data releases where needed. For multiple systems,
the standard astrometry is compromised by acceleration and/or unresolved
companions (this bias is reduced for the stars with astrometric solutions in
the NSS). The RUWE parameter (Reduced Unit Weight Error) captures the
excessive astrometric noise, helping to identify biased astrometry in GDR3.
Most (but not all) stars with subsystems studied here have RUWE$>2$. Uncertain
Gaia parallaxes are marked by colons in Table 1. Astrometric subsystems are
detected by the increased RUWE or by the difference $\Delta\mu$ between the
short-term proper motion (PM) measured by Gaia and the long-term PM $\mu_{\rm
mean}$ deduced from the Gaia and Hipparcos positions Brandt (2021). For stars
with a large RUWE, I use the long-term PMs determined by Brandt in place of
the PMs measured by Gaia.

For some systems, spectroscopy is complemented by speckle interferometry of
the outer pairs. Most speckle observations used here were made at the Southern
Astrophysical Research Telescope (SOAR) and are referred to in the text simply
as ’SOAR data’. The latest observations and references to older publications
are found in Tokovinin et al. (2022). Apart from the position measurements,
speckle interferometry provides differential photometry of close visual pairs.

##  3 Individual Objects

Figures in this section show the RV curves and the matching visual orbits for
resolved subsystems. In the RV plots, green squares denote the primary
component, blue triangles denote the secondary component, while the full and
dashed lines plot the orbit. Typical error bars are smaller than the symbols.
In the visual orbit plots, squares denote the measured positions, connected by
short lines to the ephemeris positions on the orbital ellipse (solid line).
Masses of stars are estimated from absolute magnitudes using standard main-
sequence relations from Pecaut & Mamajek (2013). Orbital periods of wide pairs
are evaluated statistically from their projected separations (see Tokovinin,
2018a). Semimajor axes of spectroscopic subsystems are computed using the
third Kepler’s law, and the photocenter amplitudes are evaluated based on the
estimated masses and fluxes.

###  3.1 HIP 3645 (Triple)

Figure 1: Visual orbit and RV curve of HIP 3645 Aa,Ab.

This solar-type triple system belongs to the 67-pc sample. The outer 60″
common proper motion (CPM) pair A,B (LDS 9100) has been discovered by Luyten
(1979). Star B is an M4V dwarf of $V=15.2$ mag known as LP 646-9 with an
accurate GDR3 parallax of 30.51 mas. The parallax of A is biased by the inner
subsystem, first discovered as a 3.5 yr astrometric binary in Hipparcos
(Goldin & Makarov, 2007). This pair has been resolved in 2011 by Horch et al.
(2017) at a separation of 30 mas (LSC 10 Aa,Ab). Its speckle monitoring at
SOAR started in 2015\. The three first observations did not resolve the pair,
but the measurements in 2021 and 2022 are good, indicating a magnitude
difference of $\Delta I=1.1$ mag and a separation of up to 0$\farcs$11.

Double lines were noted by Nordström et al. (2004), and the star is called
“Spectroscopic binary” in Simbad. Most CHIRON spectra of A are also double-
lined. The RVs of Aa and Ab are used here jointly with the position
measurements to derive a combined orbit (Figure 1). The period is 4.2 yr,
longer than the Goldin’s one. The orbit is oriented edge-on, and the RV
amplitudes translate into Aa and Ab masses of 0.78 and 0.68 $M_{\odot}$ ,
somewhat smaller than 0.94 and 0.80 $M_{\odot}$ estimated from the absolute
magnitudes. The visual orbit, unbiased parallax of B, and the spectroscopic
mass ratio correspond to the masses of 0.97 and 0.85 $M_{\odot}$ that agree
better with the photometric estimates. The masses imply RV amplitudes 7%
larger than measured, and this minor discrepancy could be caused by line
blending. The ratio of dip areas corresponds to $\Delta m_{\rm Aa,Ab}=1.29$
mag, slightly larger than measured by speckle in the $I$ band. Both components
rotate slowly.

###  3.2 HIP 14307+14313 (Triple)

Figure 2: Visual orbit and RV curve of HIP 14313 Ba,Bb.

This system has some similarity to the previous one: a wide binary within 67
pc that hosts a subsystem. The 38″ pair A,B (DUN 10) has been known since
1826. The WDS lists another pair A,C at 510″ separation (TOK 428). Star C (HIP
14257, HD 19254, F7V) has a PM of (98.8, 67.6) mas s-1 , similar to the PMs of
A and B, and for this reason it was listed in the survey of CPM pairs
(Tokovinin & Lépine, 2012). However, the difference of the PM, parallax (14.70
mas according to GDR3), and RV (28.5 km s-1 , see Table 6) of star C with
respect to A and B rule out its physical association. There is no excessive
astrometric noise in A and C (RUWE close to 1) in GDR3, and no parallax for B
because it is a close binary.

Star B has been resolved by speckle interferometry at SOAR in 2014 and bears
the name TOK 428 Ba,Bb in the WDS. The pair slowly opened up from 0$\farcs$19
to 0$\farcs$21 by 2016, closed down to 33 mas in 2021.96, and was resolved
again in 2022.68 after passing through the conjunction. Double lines in the
CHIRON spectra show only a slow evolution, as can be seen in the RV curve
(Figure 2). The preliminary combined 18 yr orbit fitted to the RVs and
position measurements predicts periastron in 2023 March, when the largest RV
difference between Ba and Bb will occur. Continued observations are needed to
improve our first orbit.

Speckle interferometry at SOAR established the magnitude difference of $\Delta
I_{\rm Ba,Bb}=0.42\pm 0.06$ mag, while the ratio of dip areas gives $\Delta
m_{\rm Ba,Bb}=0.19$ mag. The latter leads to the visual magnitudes of 9.25 and
9.44 for Ba and Bb, respectively, and the “photometric” masses of 0.90 and
0.87 $M_{\odot}$ . The “spectroscopic” masses are slightly larger, 1.01 and
0.99 $M_{\odot}$ , and the orbital parallax of 18.26 mas matches well the GDR3
parallax of A, 18.36 mas. Stars Ba and Bb rotate slowly and have no lithium
line.

###  3.3 HIP 36165+36160 (Triple)

Figure 3: The RV curve of HIP 36165 Aa,Ab.

The wide 17″ pair of HIP 36165 (star A, $V=7.03$ mag, F6V) and HIP 36160 (star
B, $V=8.19$ mag, G1.5V) has been discovered by John Herschel in 1835 (HJ
3969). The fast and common PM, matching parallaxes and RVs prove the bound
nature of this pair with an estimated period of 15 kyr. Nordström et al.
(2004) noted that the RVs of both A and B were variable. However, CHIRON and
other sources indicate that B has a constant RV of 64.9 km s-1 and is most
likely a single star (RUWE 1.0 in GDR3). The RV of A, on the other hand,
varies with a small amplitude; this motion produces astrometric noise in Gaia
(RUWE 11.9) and a large acceleration detected by Brandt (2021).

The spectroscopic orbit with a period of 6.3 yr derived from the CHIRON RVs is
illustrated in Figure 3. The descending part of the RV curve is not yet
covered, so the orbit is preliminary. The period is well constrained, but the
eccentricity can be larger. The estimated mass of Aa, 1.28 $M_{\odot}$ ,
matches its spectral type F6V. The minimum mass of Ab is 0.39 $M_{\odot}$ ; no
spectral lines of Ab are detectable, while speckle and adaptive optics imaging
(Tokovinin et al., 2010) has not resolved any subsystems around stars A and B.

###  3.4 HIP 41171 (Quadruple)

Figure 4: The RV curve of HIP 41171 Ba,Bb (top) and the CCF with four well-
separated dips recorded on JD 2,459,900 (bottom, solid line). The plus signs
show the sum of four Gaussian curves, plotted individually by dotted lines.

This is a rare case of a quadruple-lined object (SB4). The system has been
presented and discussed in paper 6 of this series (Tokovinin, 2019), where a
25-day SB2 orbit of Aa,Ab (main component in the 0$\farcs$9 visual pair RST
4396) was determined. The lines of Ba and Bb are clearly separated from the
lines of Aa and Ab only in certain phases of the 25-day orbit. Systematic
monitoring at these moments during several years has led eventually to the
determination of the 2.6 yr orbit of Ba,Bb (Figure 4). The RVs of Aa and Ab
match the published orbit; slightly refined elements of Aa,Ab derived with
additional data are given in Table 3.

The visual magnitudes of Ba and Bb (10.95 and 11.38 mag, respectively) were
estimated from the areas of the four CCF dips. They correspond to the masses
of 1.09 and 1.00 $M_{\odot}$ (mass ratio $q_{\rm Ba,Bb}=0.92$), similar to the
spectroscopic masses $M\sin^{3}i$ of 1.10 and 0.92 $M_{\odot}$ ($q_{\rm
Ba,Bb}=0.83$). This means that the orbit of Ba,Bb has a large inclination. It
is oriented unfavorably ($\omega=273\arcdeg$), so despite the estimated
semimajor axis of 12 mas the pair Ba,Bb has never been resolved by speckle
interferometry at SOAR, not even partially, in 9 visits. The prospect of its
resolution with larger telescopes or interferometers is good, though. The
outer pair A,B has an estimated period of 1.2 kyr and moves very slowly in
retrograde sense. It has covered a 22° arc since its discovery in 1940\. The
0$\farcs$9 pair is recognized as two sources in GDR3, which gives a parallax
of 4.93$\pm$0.03 mas (RUWE 1.6) for A and no parallax for B.

###  3.5 HIP 49336 (Quadruple)

Figure 5: The RV curve of HIP 49336 Ba,Bb (top, the plus sign marks uncertain
measurement) and a fragment of the outer orbit with wobble (bottom). The black
solid and blue dashed lines represent the outer orbit with and without wobble,
respectively. The green squares are the measured positions of B relative to A.

Like the previous object, this quadruple system is a left-over from the
previous work (paper 7, Tokovinin, 2020), where the 44.5-day orbit of the main
subsystem Aa,Ab was established. The outer pair I 292 (ADS 7629) has a visual
orbit with $P=380$ yr and $a=0\farcs 869$. It is not resolved by CHIRON, and
the spectra are triple-lined. The lines of Ba, free from blending when the
lines of Aa and Ab are well separated, show a slow RV variation detected in
paper 7. Monitoring with CHIRON at favorable phases of Aa,Ab has continued for
a few more years (with an interrupt for COVID-19) and now the orbit of Ba,Bb
with a period of 3.6 yr is sufficiently well constrained.

When the existence of a long-period subsystem was established, more frequent
speckle observations at SOAR were scheduled in hope of detecting the wobble.
Indeed, as shown in the lower panel of Figure 5, the apparent motion of A,B
deviates from the smooth blue line describing the outer orbit. The elements of
A,B and Ba,Bb were fitted jointly with ORBIT3 using both position measurements
and RVs. This helps to better constrain the period of Ba,Bb and defines the
orientation of its orbit. The RV difference between A and B identifies the
correct ascending node of the outer orbit and the mutual inclination, 33°. The
small eccentricity $e_{\rm Ba,Bb}=0.16$ indicates absence of the Lidov-Kozai
cycles, in agreement with moderate mutual inclination.

The inclination of Ba,Bb determined from the wobble and the RV amplitude lead
to the Bb mass of 0.50 $M_{\odot}$ , assuming that Ba is a 1.35 $M_{\odot}$
star. The resulting mass ratio $q_{\rm Ba,Bb}=0.37$ and the semimajor axis of
31.4 mas imply a wobble with an amplitude of 8.5 mas, similar to 7.1 mas found
from fitting the A,B positions.

###  3.6 HIP 75663 (Quadruple)

Figure 6: The RV curve of HIP 75663 Aa,Ab. Dashed line is the RV curve of the
GDR3 orbit with corrected $\omega$.

Components A and B of the 9$\farcs$4 visual binary STF 1939 (ADS 9640) are
resolved by the CHIRON 2$\farcs$7 fiber aperture, so their RVs are measured
separately. As established in paper 4 (Tokovinin, 2018b), star B is a double-
lined twin binary with a period of 22.9 days and $e_{\rm Ba,Bb}=0.61$, while
the RV of A varies with a long period. Continued CHIRON monitoring leads to an
orbital period of 623.8 days (1.7 yr), see Figure 6. The periastron in 2020.68
was missed because of the telescope closure to COVID-19, but the following
periastron of this eccentric ($e_{\rm Aa,Ab}=0.65$) orbit in 2022.39 has been
well covered. I also used six RVs from Butler et al. (2017) with an offset of
$-56.85$ km s-1 chosen to fit the orbit (the published RVs have arbitrary zero
point).

Gaia DR3 independently determined a spectro-astrometric orbit of HIP 75663A
with a period of 626.6758 days and amplitude $K_{1}=5.80$ km s-1 . The general
character of this orbit is similar to the one presented here, although the
argument of periastron $\omega=94\fdg 5$ is inverted. The dashed line in
Figure 6 shows the GDR3 orbit with $\omega$ corrected by 180°. Fitting an
astrometric orbit removes the bias of parallax and PM, leading to a good
agreement between parallaxes of A (7.73 mas) and B (7.78 mas); the biased
parallax of A in GDR3 is 8.97 mas with a RUWE of 5.45. Note that the short
period of Ba,Bb and the equality of its components make its GDR3 astrometry
bias-free (RUWE 1.05).

As noted in paper 4, star A is located slightly above the main sequence
(estimated age $\sim$4 Gyr), and the lithium line is detectable in the spectra
of both A and B. The Aa mass of 1.47 $M_{\odot}$ estimated from the standard
relation for dwarfs is only approximate. The corresponding minimum mass of Ab
derived from our orbit is 0.48 $M_{\odot}$ . If the orbital inclination of
69$\fdg$1 measured by Gaia is adopted, the mass of Ab becomes 0.52 $M_{\odot}$
. On the other hand, the Ab mass derived from the GDR3 astrometric orbit is
0.46 $M_{\odot}$ , less than the minimum spectroscopic mass, while the small
RV amplitude in the GDR3 orbit leads to a minimum mass of 0.09 $M_{\odot}$ .
The actual mass of Ab should therefore be close to 0.5 $M_{\odot}$ and the
semimajor axis of the Aa,Ab orbit is 14 mas.

###  3.7 HIP 78163 (Quadruple)

Figure 7: The RV curve of HIP 78163 Ba,Bb.

The 2+2 quadruplet HIP 78163 resembles the previous one, but with inverted
roles of the components. The double-lined twin pair Aa,Ab with $P=21.8$ days
and $e_{\rm Aa,Ab}=0.58$ is very similar to star B in HIP 75663 (22.9 days,
$e=0.61$); its orbit has been determined in paper 4 of this series (Tokovinin,
2018b). Star B of HIP 78163 is located at 5$\farcs$9 from A (WG 185 pair in
the WDS, estimated period 7.4 kyr). The RV of B varies slowly, and, as for the
previous object, Gaia determined an orbit with a period of 1532 days, this
time only an astrometric one. The period found here is longer, 2083 days (5.7
yr). The Gaia astrometric orbital fit gives a parallax of 10.65 mas for B
which agrees much better with the 10.49 mas parallax of A (unbiased, RUWE
0.86). In contrast, the raw (biased, RUWE 6.22) GDR3 parallax of B is 11.28
mas, while DR2 measured an even more discrepant parallax of 13.57 mas. The
duration of the GDR3 mission is only 34 months, so a more accurate orbit of
Ba,Bb is expected in the future releases.

The spectroscopic orbit of Ba,Bb shown in Figure 7 is eccentric, $e_{\rm
Ba,Bb}=0.62$. The RV maximum is not fully covered, but the next periastron is
expected only in 2026. I use with a low weight the RV measured in 2015.5 by
Gaia because the CHIRON data cover only 1690 days. Adopting a mass of 0.93
$M_{\odot}$ for Ba, the minimum mass of Bb is 0.71 $M_{\odot}$ . Lines of Bb
might be detectable in the spectra, unless it is a white dwarf. However, the
spectra can be partially contaminated by the light of A, depending on the
seeing and guiding (the separation is only 5$\farcs$9), so accurate modeling
of the CCFs needed to extract the RVs of Bb is problematic.

###  3.8 HIP 79979+79980 (Triple)

Figure 8: Visual orbit and RV curve of HIP 79979 Ba,Bb.

The outer 23$\farcs$4 pair A,B (BSO 12) has been known since 1837. Its
brighter component A ($V=5.51$ mag, F5IV) is listed in the bright star catalog
as HR 6077. The fainter ($V=6.82$ mag, F9V) star B has its own designations
HIP 79979 and HD 146835. The RV variability of B was suspected by Nordström et
al. (2004). The RVs of A and B were found equal in (Tokovinin et al., 2015),
casting doubt on the existence of a subsystem, but the first CHIRON spectrum
taken in 2017 produced a double CCF. By that time, B has been resolved at SOAR
as a tight visual pair TOK 410. The preliminary orbit with $P=3$ yr predicted
periastron in 2022.6, as actually observed (Figure 8).

Using the unbiased parallax of 22.71 mas measured in GDR3 for A, the Ba,Bb
orbit gives the mass sum of 2.11 $M_{\odot}$ . This matches the spectroscopic
masses of 1.14 and 0.97 $M_{\odot}$ (the inclination $i_{\rm Ba,Bb}=82\fdg 9$
is known) and the absolute magnitudes of Ba and Bb. So, despite the modest
number of RVs, the orbit of Ba,Bb is reasonably well defined.

Stars A and B have almost identical $V-K$ colors (see table 1), but differ by
1.3 mag in the $V$ band. Star A is obviously evolved; it is located above the
main sequence. In contrast, star B, despite being a binary, is located on the
standard main sequence.

###  3.9 HIP 103735 (Triple)

Figure 9: Visual orbit and RV curve of HIP 103735 Aa,Ab.

The primary component A ($V=7.66$ mag, G3V) of the wide 186″ pair is a visual
and spectroscopic binary. The secondary star B (2MASS J21012669-3509333,
$V=17.14$ mag) is a white dwarf identified by Tokovinin & Lépine (2012) in the
large PM survey and confirmed by Gaia.

Both Nidever et al. (2002) and Nordström et al. (2004) noted that RV of A was
variable. The first CHIRON spectrum taken in 2017 revealed an asymmetric
(blended) CCF. The same year the 0$\farcs$14 pair Aa,Ab has been resolved at
SOAR (TOK 344 Aa,Ab). In the following five years, the pair passed though the
periastron: the separation decreased and increased again, the CCF dips
separated apart. These data allow calculation of a combined orbit with
$P=11.6$ yr presented in Figure 9. One RV published by Nidever et al. (2002)
is used, it refers to the brighter star Aa.

The combined orbit yields masses of 1.00 and 0.72 $M_{\odot}$ for Aa and Ab,
respectively, and an orbital parallax of 21.5 mas, in rough agreement with the
accurate GDR3 parallax of star B, 22.09 mas. The GDR3 parallax of A is
inaccurate and biased, 23.55$\pm$0.47 mas. The astrometric acceleration is
reflected by the large RUWE of 15.6, as well as by the PM anomaly (Brandt,
2021).

###  3.10 HIP 103814 (Triple)

Figure 10: RV curve of HIP 103814 Aa,Ab. The GDR3 orbit is traced by the
dashed line.

The 57″ pair of bright stars HIP 103814 (HR 8042, $V=6.64$ mag, G3IV+K0IV) and
HIP 103839 ($V=6.90$ mag, K0III) has been known since 1826 (DUN 236 in the
WDS). B is redder than A and brighter in the $K$ band. This is a rare pair
composed of two giants, and it does not belong to the 67-pc sample of solar-
type stars.

The fact that star A is a binary follows from its astrometric acceleration
detected by Hipparcos, RUWE of 23.0 in GDR3, and, possibly, composite
spectrum. The eight CHIRON RVs do not fully constrain the orbit shown in
Figure 10. However, the GDR3 spectro-astrometric orbit with $P=1119.65$ days
confirms the period independently. The shape of the Gaia RV curve is similar
(after correcting $\omega$ by 180°), although its amplitude is substantially
smaller (2.41 km s-1 ) compared to the CHIRON orbit (4.48 km s-1 ).

Assuming that the mass of Aa is 1.78 $M_{\odot}$ , the GDR3 astrometric orbit
with an amplitude of 7.7 mas corresponds to the Ab mass of 0.53 $M_{\odot}$
(the full semimajor axis is 33.3 mas). This implies a early-M dwarf companion
which contributes negligible light, so the spectrum of A cannot be composite.
The minimum Ab mass derived from the CHIRON orbit is 0.28 $M_{\odot}$ , and
the actual mass is 0.62 $M_{\odot}$ , considering the inclination of the
astrometric orbit. The width and contrast of the CCF dip do not change with
orbital phase, proving that Ab is much fainter than Aa.

###  3.11 HIP 104440 (Triple)

Figure 11: Visual orbit and RV curve of HIP 104440 A,B.

This is a resolved visual triple located at 20 pc from the Sun (GJ 818.1). The
outer 6$\farcs$4 pair AB,C has been known since 1894 (HDO 305). Star C is
faint ($V=13.5$ mag) and red, likely an M4V dwarf. AB,C is in slow retrograde
motion with an estimated period of 1 kyr. The PM difference between AB and C
is caused by motion in the outer orbit.

The bright ($V=5.68$ mag, F9.5V) visual pair A,B known as I 379 has been
presumably discovered by R. Innes in 1898, although we know now that the
separations on the order of 1″ measured by him were totally wrong (this pair
is never wider than 0$\farcs$3). Apart from the three spurious measurements by
Innes, only W. Finsen reported a resolution of this pair in 1932 which also
does not match the orbit. The magnitude difference measured at SOAR is
substantial, $\Delta y=3.15$ mag, and such close pairs are beyond the capacity
of visual observers. In this case, the WDS name I 379 corresponds to the
spurious discovery, despite several “confirming” visual resolutions.

Goldin & Makarov (2007) published two possible astrometric orbits of this star
with periods of 6.65 and 5.87 yr based on Hipparcos transits. The true period
is even shorter, 5.3 yr. The first visual orbit of A,B which also used the
CHIRON RVs has been published in (Tokovinin et al., 2020); it is updated here
(Figure 11). The pair goes though the periastron in 2022.9, and the previous
periastron in 2017.4 has been also covered. The orbit ignores spurious
historic micrometer measurements and is based entirely on the SOAR and CHIRON
data.

The absolute magnitudes of A and B correspond to the masses of 1.13 and 0.72
$M_{\odot}$ and a dynamic parallax of 49.7 mas which compares well with the
GDR3 parallax of star C, 50.6 mas; the GRD3 parallax of A, 47.0 mas, is
biased. Masses derived from the combined orbit are 1.15 and 0.74 $M_{\odot}$ ,
and the orbital parallax is 51.0 mas.

###  3.12 HIP 105879 (Triple)

Figure 12: Visual orbit and RV curve of HIP 105879 Aa,Ab. The insert shows the
CCF recorded on JD 24 57218 when the dips were well separated.

This is yet another typical solar-type triple system composed of wide and
tight visual pairs. Star A ($V=7.18$ mag, F7V) has been identified as a
double-lined binary with CHIRON in 2015.5, first resolved at SOAR in 2017.6,
and designated in the WDS as HJ 5267 Aa,Ab. The variable RV was noted
previously by Nordström et al. (2004), astrometric acceleration was detected
by Hipparcos and by its comparison with Gaia. The wide companion D (CD$-$46
13953, $V=9.96$ mag) at 44″ has a matching PM and RV. Its GDR3 parallax of
13.102$\pm$0.014 mas defines accurate distance to the system. The companion B,
seen only once by J. Herschel in 1834 at 5″, is spurious, and the companion C
at 238″ listed in the WDS is optical. So, to the best of our knowledge, this
is a triple system.

The combined orbit of Aa,Ab with $P=8.0$ yr and a substantial eccentricity
$e_{\rm Aa,Ab}=0.63$ is presented in Figure 12. The first spectrum has been
taken in 2010.8 using fiber echelle (Tokovinin, 2015), and the 11.9 yr
coverage defines the orbital period quite well. The pair Aa,Ab goes through
periastron in 2023.2, when it will not be visible behind the Sun.
Unfortunately, the period is an integer number of years and in the foreseeable
future all periastrons will occur during poor visibility periods. The pair was
unresolved at SOAR in 2015.74 and in 2022.68 in agreement with the orbit that
predicted small separations on those dates.

The CCF dips are well separated only near the periastron, as illustrated in
the Figure. In other phases they are blended, and the fits of two overlapping
Gaussians are less reliable. The ratio of the dip areas when they are well
separated corresponds to the magnitude difference of 2.21 mag, in agreement
with the differential photometry at SOAR ($\Delta y=2.14$ mag, $\Delta I=1.94$
mag). This relatively large magnitude difference does not match the moderate
spectroscopic mass ratio $q_{\rm Aa,Ab}=0.80$. The mass ratio and the mass sum
of 2.06 $M_{\odot}$ derived from the visual elements and the parallax of star
D lead to the individual masses of 1.14 and 0.92 $M_{\odot}$ for Aa and Ab,
respectively, while the absolute magnitude of Aa corresponds to a mass of 1.5
$M_{\odot}$ on the main sequence. In fact, A is elevated above the main
sequence by $\sim$1 mag, so Aa starts to evolve into a subgiant. This explains
the apparent discrepancy between mass ratio and magnitude difference in the
inner pair. The spectroscopic mass sum is 2.2 $M_{\odot}$ , suggesting that
the RV amplitudes might be slightly over-estimated.

Star D has not been resolved by speckle interferometry at SOAR, it has low
astrometric noise in Gaia and an apparently constant RV that matches the RV of
A. So, it is unlikely that D has close companions.

###  3.13 HIP 109443 (Triple)

Figure 13: RV curve of HIP 109443 Aa,Ab. The dashed line is the Gaia
spectroscopic orbit.

The bright solar-type star HIP 109443 ($V=7.63$ mag, F8V) is an astrometric
binary detected by Hipparcos and confirmed both by Brandt (2021) and by a RUWE
of 10.3 in GDR3. A survey of astrometric binaries with the NICI AO instrument
detected a faint companion B at 1$\farcs$4 separation (Tokovinin et al., 2012,
TOK 216). The estimated period of $\sim$700 yr makes it unlikely that the
acceleration and variable RV (Nordström et al., 2004) are caused by this
companion.

Nine CHIRON spectra show the RV variability, and the GDR3 spectroscopic orbit
matches these RVs quite well (Figure 13). The fit of 6 elements to 9 RVs is
almost perfect, leaving rms residuals of only 0.008 km s-1 .

The minimum mass of Ab is 0.18 $M_{\odot}$ if the mass of Aa is 1.3
$M_{\odot}$ . The large RUWE indicates clear detection of the astrometric
signal, but, for some reason, GDR3 determined only the spectroscopic orbit,
leaving the inclination and the true mass of Ab unconstrained. The mass of B
is about 0.56 $M_{\odot}$ , as inferred from its $K$-band luminosity. It is
detected by Gaia at 1$\farcs$4129 ($\Delta G_{\rm A,B}=4.85$ mag), showing
little motion since 2011. The parallax of B measured by GDR3, 15.58 mas, is
close to the parallax of A in GDR2 (15.33 mas), but GDR3 gives a biased
parallax of 12.74 mas for A. The bias will be removed when the astrometric
orbit of Aa,Ab is determined by Gaia.

###  3.14 HIP 117666 (Quadruple)

Figure 14: CCFs of the first 7 CHIRON spectra of HIP 117666. The curves are
displaced vertically by 0.35 to avoid overlap. The dates are indicated. Thick
red and green lines mark the RVs of Aa and Ba, respectively, according to the
orbits.  Figure 15: RV curves of the subsystems Aa,Ab and Ba,Bb in HIP
117666\. Squares mark the RVs derived from double CCFs, plus signs correspond
to blended CCFs. Motion in the outer orbit is subtracted.  Figure 16: Outer
orbit of HIP 117666 A,B on the sky (top) and the RV curve where motion in the
inner subsystems is subtracted (bottom).

This 9th magnitude star (HD 2236888, G5V) appeared to be a normal tight visual
binary, first resolved by R. Aitken in 1913 (A 2700, ADS 17052, WDS
J23518$-$0637). The visual orbit with a 30 yr period, last updated by Docobo &
Ling (2009), is very well constrained. It is fully covered by accurate speckle
measurements (the first one in 1985) and is rated grade 2 in the orbit
catalog.

The star attracted attention as an X-ray source and for this reason four high-
resolution spectra were taken by Frasca et al. (2018) in 2001\. Double lines
were detected in one spectrum, suggesting presence of a subsystem. Double
lines were also seen in the spectrum taken by Tokovinin (2015) in 2010. This
prompted further monitoring with CHIRON. It was not clear from the outset
whether double lines were produced by motion in the visual orbit or by an
inner subsystem. The first CHIRON spectrum taken in 2017.6 looked single-
lined, but in 2019.6 the lines were double again, so I started regular
monitoring. The first seven CHIRON CCFs are shown in Figure 14, illustrating
blending of two components with independent RV variation. The RVs of both CCF
dips vary faster than prescribed by the visual orbit, so this system is
actually a 2+2 quadruple.

Five RVs of HIP 117666 averaging at $\sim-$1 km s-1 were reported by Tokovinin
& Smekhov (2002). They are not compatible with the orbits presented here. It
turns out that these RVs refer to another 9th magnitude star, HD 223695
(F6IV), which is located at 1′ east of HIP 117666 and has an RV of $-2.3$ km
s-1 according to Simbad. Somehow, the visual binary was misidentified, and the
spectral type of F6V quoted in the above paper (instead of G5V) confirms this
suspicion. One of the RVs reported by Frasca et al. (JD 24 52209.43) also
apparently refers to HD 223695. Proximity of two stars on the sky means that
the X-ray source can be actually associated with HD 223695 (with a fast
rotation of 22.0 km s-1 according to Frasca et al.), rather than with the
slowly rotating components of the HIP 117666 system. The Galactic velocity of
HIP 117666, $U,V,W=(-23.8,-10.1,-21.3)$ km s-1 , does not match any known
kinematic group, and the lithium line in its spectrum is not detectable, so
this star is not young.

Deciphering the two inner orbits from the often-blended CCFs with similar
dips, superposed on the slow RV variation due to the outer orbit, was a
challenging task, addressed iteratively. First, the faster variation of the
smaller dip Ba was matched to a period of $\sim$250 days, then the RVs of Aa
yielded a period of 2 yr with a different systemic velocity. A model was
constructed to represent the blended dips by the outer and two inner orbits
using the dip amplitudes and widths measured in the well-resolved phases.
Comparison of all CCFs to this model inspired confidence in the adopted inner
periods.

The available tool, ORBIT3, does not allow for simultaneous fit of all three
orbits. After several iterations on the orbits of A,B and Aa,Ab, the RVs of Ba
were corrected for the motion in the outer orbit and fitted as a single-lined
binary. Then the motion of Ba,Bb was subtracted from the RVs of Ba, and a
joint fit of the remaining inner orbit Aa,Ab and the outer orbit A,B was done
using ORBIT3, including the speckle measurements. The astrometric elements of
Aa,Ab (wobble) were also determined. The rms residuals of accurate SOAR
speckle positions without wobble, 6 mas, are reduced to 2 mas when the wobble
is fitted. The smaller wobble caused by the Ba,Bb motion is left unmodeled. In
the orbital fit, I used the RVs measured in 2002 by Frasca et al. with a small
weight and a correction of +1 km s-1 .

Speckle interferometry at SOAR establishes the magnitude difference $\Delta
m_{\rm A,B}=0.14$ mag (WDS quotes 0.2 mag), so the individual $V$ magnitudes
of A and B are 9.41 and 9.55 mag, respectively. The Gaia DR2 parallax of
13.4$\pm$1.3 mas is inaccurate and potentially biased, GDR3 gives no parallax,
so I adopt the dynamical parallax of 13.2 mas that follows from the good-
quality outer orbit and the estimated masses. Neglecting the light of the
secondaries Ab and Bb, the masses of Aa and Ba matching their absolute
magnitudes are 0.98 and 0.97 $M_{\odot}$ ; they agree with the combined
spectral type G5V and the $V-K$ color. The mass of Ab deduced from the RV
amplitude and inclination (see below) is 0.45 $M_{\odot}$ , the minimum mass
of Bb is 0.31 $M_{\odot}$ . Small masses of the inner secondaries explain why
their lines are not visible in the spectra. The estimated system mass is
therefore 2.70 $M_{\odot}$ .

The estimated masses, periods, and parallax yield the semimajor axes of the
inner orbits, 25.1 and 11.2 mas. The ratio of the measured photo-center
amplitude of Aa,Ab, 7.9 mas, to the semimajor axis equals the wobble factor
$f_{\rm Aa,Ab}=q_{\rm Aa,Ab}/(1+q_{\rm Aa,Ab})=0.31$, hence the mass ratio is
$q_{\rm Aa,Ab}=0.46$ and the estimated mass of Ab is 0.45 $M_{\odot}$ . The
astrometric orbit of Aa,Ab yields a loosely constrained inclination $i_{\rm
Aa,Ab}=141\arcdeg\pm 13\arcdeg$. The inner inclination of $i_{\rm
Aa,Ab}=143\arcdeg$ matches the Ab mass estimated from the wobble, so I fixed
this value. The minimum mass of Bb leads to an estimated wobble amplitude of 2
mas for Ba. This unmodeled (so far) wobble contributes to the residuals of
accurate speckle positions.

As noted, the outer orbit (Figure 16) is very well constrained. However, the
fitted inclination of $i_{\rm A,B}=149\fdg 6\pm 1\fdg 5$ and the RV amplitudes
of 3.42 and 4.15 km s-1 lead to the outer mass sum of 3.25 $M_{\odot}$ ,
substantially larger than the estimated 2.7 $M_{\odot}$ and in disagreement
with the absolute magnitudes and spectral type. This discrepancy is removed by
fixing the outer inclination to a slightly smaller value of 147$\fdg$5\. So,
the inclinations of both Aa,Ab and A,B are fine-tuned (within limits allowed
by the data) to reach consistency between all orbital parameters and the
estimated masses. The nodal angles $\Omega$ in both orbits are similar, hence
Aa,Ab and A,B have well aligned orbits. If the orbit of Ba,Bb were also
coplanar with A,B, the mass of Bb would be 0.55 $M_{\odot}$ , making B more
massive than A. This contradicts the measured outer mass ratio $q_{\rm
A,B}=0.82$. The inclination $i_{\rm Ba,Bb}$ could be close to 110° in order to
avoid the Lidov-Kozai oscillations (the eccentricity of Ba,Bb is only 0.27).

The architecture of this remarkable quadruple and its internal dynamics
deserve further investigation. The period ratio $P_{\rm A,B}/P_{\rm
Aa,Ab}=14.05$ is small, so the orbits interact dynamically and the motion is
more complex than the simple superposition of Keplerian orbits fitted here;
our orbits represent osculating elements in the current epoch. Furthermore,
the ratio of two inner periods $P_{\rm Aa,Ab}/P_{\rm Ba,Bb}\approx 3$ is close
to an integer number. The two inner orbits could be trapped into a 1:14:42
mean motion resonance with the outer orbit.

##  4 Summary

The original goal of this project has been inspired by the lack of known
orbital elements for inner subsystems revealed previously by variable RV or
astrometric acceleration. Periods and mass ratios inferred from the orbits are
necessary for a statistical study of nearby hierarchies. However, our RV
monitoring has shown that some hierarchies, believed to be triple, are in fact
2+2 quadruples, as both visual components have variable RVs. Orbits of the
short-period subsystems in these quadruples have been quickly determined and
reported in the first papers of this series. Observation of other components
with slow RV variation continued for several years, eventually yielding their
spectroscopic orbits as well. Four such “returning clients” from the previous
papers are presented here: HIP 41171, 49336, 75663, and 78163. In the first
two, the outer pairs are sub-arcsecond, so the spectra of all visible stars
are blended. Recovering RVs of slowly varying subsystems from blended spectra
dominated by fast RV variation of other pairs required careful planning of
observations at phases where the blending is minimized.

HIP 117666 is another tricky quadruple studied here. It is a well-known visual
binary where existence of an inner subsystem has been suggested but remained
unproven. Unexpectedly, our observations discovered that both visual
components contain subsystems. Patient accumulation of blended spectra was
needed to decipher the underlying orbits, including the outer one. A similar
case (HIP 12548) has been presented in paper 8.

The perturbing effects of binaries on the astrometry were anticipated in the
design of the Gaia mission, and GDR3 delivered a large set of orbits which
reduce biases in the astrometric solutions. However, complexity of some triple
and quadruple hierarchies precludes their modeling by the Gaia pipeline. Only
dedicated monitoring with adequate cadence, time coverage, and spectral
resolution can reveal the true nature of systems like HIP 12548 and 117666.
Even relatively easy cases of spectroscopic subsystems in well-resolved visual
pairs (HIP 75663A, 79163B, and 103814A) demonstrate that some Gaia orbits can
be inaccurate or even wrong. Gaia is an outstanding astrometric facility which
has not been designed to deal with complex hierarchies.

Long orbital periods of subsystems studied here favor their direct resolution.
Six combined orbits based on CHIRON RVs and speckle-interferometric
measurements at SOAR were determined. Another two are added from modeling
wobble in the motion of their relatively close outer pairs. Spatial resolution
(or wobble detection) complements spectroscopic orbits, allowing to measure
masses and to deduce orbit orientation. The latter is particularly valuable
when orientation of the outer orbit is also known. Architecture of
hierarchical systems (mutual orbit orientation, periods and masses) contains
information on their still debated origin.

I thank operators of the 1.5-m telescope for executing observations of this
program and the SMARTS team for scheduling and pipeline processing. The
research was funded by the NSF’s NOIRLab. 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. This work has made use of
data from the European Space Agency (ESA) mission Gaia
(https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing and
Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement. This research has made use
of the services of the ESO Science Archive Facility. CTIO:1.5m, SOAR, Gaia

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