# Silicon rich nitride-lithium niobate on insulator platform for photonics
integrated circuits

Yang Liu  1,2,$\dagger$ Xingrui Huang  1,2,$\dagger$ Zezheng Li  1,2 Huan Guan
1 Zhongchao Fan  3,4 Weihua Han  3,4 and Zhiyong Li1  1State Key Laboratory on
Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of
Sciences, Beijing 100083, China
2College of Materials Science and Opto-Electronic Technology, University of
Chinese Academy of Sciences, Beijing 100083, China
3School of Electronic, Electrical and Communication Engineering, University of
Chinese Academy of Sciences, Beijing 101408, China
4Engineering Research Center for Semiconductor Integrated Technology,
Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083,
China<EMAIL_ADDRESS>
###### Abstract

In this paper, a silicon rich nitride-lithium niobate on insulator (SRN-LNOI)
hybrid platform with waveguides and several key components is proposed. The
propagation loss of the silicon rich nitride-lithium niobate rib-loaded
waveguide (1 $\mu m$ $\times$ 300 nm) is 2.6 dB/cm at 1550 nm. Passive
devices, including adiabatic power splitters, multimode interferometer based
splitters, asymmetrical Mach-Zehnder interferometers and Bragg grating filters
are fully designed and characterized. Moreover, we report the first
demonstration of Mach-Zehnder modulators based on LNOI with high-speed
modulation up to 120 GBaud without digital compensation. Hence, the proposed
platform enables high performance passive and active devices with low loss,
high integration density and complementary metal-oxide-semiconductor
technology (CMOS) compatibility, making it a promising candidate for emerging
photonics integrated circuits.

††journal: osajournal††articletype: Research Article

##  1 Introduction

In the last decades, the demands for high speed optical communication have led
to a significant interest in photonic integrated circuits (PIC). The PIC,
which integrates active and passive optical components on a single chip, has
been developed on several platforms, including silicon on insulator (SOI) [1],
silicon nitride (SiN) [2], indium phosphate (InP) [3], and lithium niobate on
insulator (LNOI) [4]. Among those platforms, LNOI is a promising PIC platform
because of its strong electro-optical coefficient ($r_{33}$ = 30.8 pm/V at
$\lambda$ = 630 nm) and high refractive index contrast ($\Delta n\approx 0.7$
at $\lambda$ = 1550 nm) [5]. Up to now, various high-performance optical
devices such as modulators, low-loss waveguides, and micro-ring resonators
fabricated by constructing microstructures on the LNOI platform have been
reported. And such tremendous progress benefits from the rapid development of
manufacturing methods for LNOI microstructures.

Generally, there are two mainstream manufacturing methods for LNOI
microstructures: 1) direct etching of LNOI (monolithic integration) and 2)
combining the lithium niobate (LN) thin film with other materials (hybrid
integration). For the monolithic integration, waveguides with propagation
losses of 5 dB/cm [6], $3\pm 0.2$ dB/cm [7], 0.4 dB/cm [8], 0.15 dB/cm [9]
and, 2.7 dB/m [10] are demonstrated in pioneering works. And high performance
modulators with 3 dB bandwidth of 100 GHz [11], 60 GHz [9] and >100 GHz [12]
have been reported. However, because of the chemical stability of LN, the
direct etching approach has strict requirements for the laboratory equipment
and often results in non-vertical waveguide sidewalls.

Considering challenges in the direct etching approach, hybrid integration is
an attractive choice. On the hybrid LNOI platform, a waveguide is formed by
loading a strip of other material on LN thin films as the core, or bonding LN
thin films onto other materials as the top cladding [5]. Several remarkable
studies have been made by the bonding approach. For instance, Cai et al. have
reported a series of high-performance photonics devices, including a grating
coupler with 3.06 dB coupling efficiency [13], a Michelson interferometer
modulator with 3 dB bandwidth of 17.5 GHz [14], and a Mach-Zehnder modulator
with 3 dB bandwidth of 70 GHz [15], by bonding LN films on the SOI platform.
But the bonding approach will come up with complex fabrication and reliability
problems under high temperature.

Besides, an alternative is loading LN thin film with a of material that has a
similar refractive index, such as SiN [16], tantalum pentoxide ($Ta_{2}O_{5}$)
[17], and chalcogenide glass [18]. And a high-efficiency modulator with 3 dB
bandwidth of 40 GHz has been proposed on the SiN-LNOI platform [19]. However,
the refractive indexes of those materials are lower than LN and the mode field
mainly distributes in the LN film, which leads to a number of disadvantages,
such as large bending radius (> 200 $\mu m$), difficulties in regulating the
optical profile and the lack of efficient input/output components.

To address those issues, we propose an ultra-compact and CMOS-competitive
solution: the silicon rich nitride-lithium niobate (SRN-LNOI) platform. In
this work, we present the SRN-LNOI platform with rib-loaded waveguides and
several basic components for PIC. In Section 2, the design and fabrication of
the silicon rich nitride-lithium niobate (SRN-LN) rib-loaded waveguide are
presented. In Section 3, compact passive devices, including power splitters,
Bragg grating filters, and asymmetric Mach–Zehnder interferometers (AMZI) are
proposed. Then, we demonstrated a Mach-Zehnder modulator with a recorded high
symbol rate of 120 GBaud in Section 4. And Section 5 presents the conclusion
of this research.

##  2 SRN-LN rib-loaded waveguide

Figure 1: (a) Refractive index dispersion curve of the proposed SRN. (b) AFM
micrographs with the RMS roughness of SRN films.

The first step to build up the SRN-LN rib-loaded waveguide is the deposition
of SRN [20]. An X-cut LNOI wafer with 400 nm thin film LN and 4.7 $\mu m$
buried oxide (BOX) layer (from NanoLN) was used as the substrate. Thin film
SRN was deposited by Oxford Plasma Technology 100 plasma enhanced chemical
vapor deposition (PECVD) system, employing the deposition recipe as following:
$SiH_{4}$ (4 sccm)/ $N_{2}$ (800 sccm), chamber pressure of 800 mTorr, RF
power of 30 W, and temperature of 300 °C. The recipe was optimized to obtain
an appropriate refractive index and a small roughness. It is worth noting that
50 nm silica was deposited between the LN layer and SRN layer to improve the
thickness uniformity of SRN films. The ellipsometer measurement presented in
Fig. 1 (a) shows that the refractive index of the SRN layer is 2.53 (at 1550
nm). Moreover, other refractive indexes of SRN can be achieved by changing the
N/Si ratio of SRN. The root mean square (RMS) roughness, which is one of the
main sources of scattering losses, is as low as 0.192 nm measured by the
atomic force microscope (AFM). It is the smallest RMS roughness among the
reported SRN films to the best of our knowledge. The SRN film with a high
refractive index and a small roughness lays down a solid foundation for SRN-LN
rib-loaded waveguides.

Figure 2: (a) The refractive index ellipsoid of LN. (b) Schematic of the
proposed SRN-LN rib-loaded waveguide. Effective index with different waveguide
widths along crystallographic Y (c) and Z (d) directions.

Based on the smooth SRN film with a refractive index of 2.53, a SRN-LN rib-
loaded waveguide was designed and fabricated. The waveguide direction plays an
important role in the waveguide design because of the inherent birefringence
of LN. From the Fig. 2 (a) we can see that the LN exhibits a strong
birefringence with an extraordinary refractive index ($n_{e}$) of 2.14 and
ordinary refractive index ($n_{o}$) of 2.21 at 1550 nm. For example, the
refractive index of the LN layer is $n_{e}$ ($n_{o}$) with the waveguide
direction along the crystallographic Y (Z) direction for the transverse
electric (TE) mode. As a result, the waveguides along both of the
crystallographic Y and Z directions were considered. The schematic of the SRN-
LN rib-loaded waveguide is shown in Fig. 2 (b). The SRN-LN rib-loaded
waveguide is composed of a silicon substrate layer, a BOX layer, a LN layer, a
silica buffer layer, and a SRN layer from bottom to top. The main parameters
of the waveguide are the waveguide width ($W_{SRN}$) and waveguide height
($H_{SRN}$). The $H_{SRN}$ of 300 nm was selected considering the moderate
optical confinement. A finite difference eigenmode solver (Lumerical MODE
Solutions) was utilized to analyze the single-mode condition of SRN-LN rib-
loaded waveguides. Figure 2 (c) and (d) show effective indexes with different
$W_{SRN}$ along crystallographic Y and Z directions of LN layer. The effective
index rises with the increasing of $W_{SRN}$. And the single-mode condition
can be maintained with $W_{SRN}$ < 1.1 $\mu m$ along both crystallographic Y
and Z directions.

Figure 3: Mode field distributions of waveguides with width of 1 $\mu m$ along
crystallographic Z (a) and Y (b) direction. (c) Mode field distributions of
waveguides with width of 0.4 $\mu m$ along crystallographic Z direction. (d)
Simulated bend loss versus the radius.

Despite the single-mode condition, the $W_{SRN}$ and the waveguide direction
impact greatly on the optical confinement and the minimum bend radius of
waveguides as well. In order to identify the influences of $W_{SRN}$ clearly,
a comparison of waveguides with different $W_{SRN}$ were performed. Firstly,
the birefringence was taken into account. Figure 3 (a) and (b) depicte the
simulated mode fileds of waveguides with $W_{SRN}$ = 1 $\mu m$ along the
crystallographic Z and Y direction. The mode fileds are mostly confined in the
SRN strip. The confinement fraction in the LN layer ($\Gamma_{LN}$) and the
SRN layer ($\Gamma_{SRN}$) are 36.7% (29.9%) and 50.9% (57.3%) along the
crystallographic Z (Y) direction. Patently, the waveguides (Y direction) have
better optical confinement than the waveguides (Z direction). The influences
of $W_{SRN}$ were then analyzed. The Fig. 3 (c) presents the $\Gamma_{LN}$ and
$\Gamma_{SRN}$ of waveguides with different $W_{SRN}$ along the
crystallographic Z and Y directions. As the $W_{SRN}$ increasing, the
$\Gamma_{LN}$ will decrease and the $\Gamma_{SRN}$ will rise. This result
indicates that the optical confinement decreases with the decline of
$W_{SRN}$. And the weaker optical confinement is, the larger the bend radius
of the waveguide will be. Figure 3 (d) shows the bend loss of waveguides with
different widths and directions. For the crystallographic Z direction, the
bend losses of waveguides with $W_{SRN}$ = 1 and 0.9 $\mu m$ sharply drop with
the increase of bend radius. And a wider $W_{SRN}$ results in a smaller bend
radius. Meanwhile, the bend loss of waveguides (Y direction) is smaller than
waveguides (Z direction) under the same structures. Overall, waveguides with
radius of 50 $\mu m$ and $W_{SRN}$ of 1 $\mu m$ can achieve a negligible bend
loss in both crystallographic Y and Z directions. Consequently, $W_{SRN}$ of 1
$\mu m$ was chosen to maintain low waveguide loss and single-mode condition.

Figure 4 (a)-(d) shows the fabrication process of the SRN-LN rib-loaded
waveguide. To define the waveguides, electron beam photoresist hydrogen
silsesquioxane (HSQ, XR1541) was spin-coated on the SRN layer and soft baked
on an 80 °C hot plate for 4 min. Afterward, HSQ was patterned by electron beam
lithography (EBL, Raith e-Line plus). The patterns were then transferred to
the SRN film using fluorine-based reactive ion etching (RIE). Finally, the
fabrication of the SRN-LN rib-loaded waveguides were completed after removing
the resist, and the scanning electron microscope (SEM) image of the fabricated
waveguide is shown in Figs. 4 (e).

Figure 4: (a)-(d) Fabrication process of SRN-LN rib-loaded waveguides. (e) SEM
image of the fabricated SRN-LN rib-loaded waveguides. Figure 5: Measured
propagation loss and linear fitting line. Insertion image: layout of the
meandered waveguides.

The propagation loss of the SRN-LN rib-loaded waveguide was measured by the
cut-back method. Waveguides with different lengths (1-15 mm) were fabricated
and measured. A tunable laser working at 1550 nm was used as the source. The
light was coupled from fiber to waveguides by utilizing the grating couplers
based on our previous work [21], and the optical output was measured by an
optical spectrum analyzer. For 1-$\mu m$ wide waveguides, the propagation loss
of the fundamental TE mode is 2.6 dB/cm, as presented in Fig. 5. As far as we
know, the propagation loss of SRN waveguides is comparable to the lowest loss
of PECVD SiN waveguides proposed in Ref. [22, 23]. Consequently, SRN-LN rib-
loaded waveguides can provide low-loss optical interconnection as well as high
integration density for various functional devices.

##  3 Passive devices

In this section, several functional passive components for PIC, including
optical power splitters, and filters are designed, fabricated, and tested. The
finite difference time domain method (FDTD, Lumerical) is used to simulate the
passive devices. Besides, the fabrication process and measurement approach are
the same as those of the SRN-LN rib-loaded waveguides mentioned above. The
light is coupled in and out from the passive devices using the grating
couplers based on our previous work [21].

###  3.1 Power splitters

Figure 6: (a) SEM image of the fabricated adiabatic power splitter. (b)
Measured excess loss of adiabatic power splitters. (c) Measured spectrum of
the adiabatic power splitter.

Optical power splitters (OPS) are essential components for optical power
distributions in PIC. Various power splitters of different structures have
been realized, including Y-branches [24], directional couplers (DC) [25], bent
directional couplers (bent DC) [26], multimode interferometers (MMI) [27], and
adiabatic taper [28]. The Y-branches power splitters are the simplest
structures but introduce large mode mismatch loss or large device length. The
DC and bent DC structures require for long device length (50 $\mu m$).
Comparing with those structures, the adiabatic power splitter with adiabatic
taper is an attractive option for its low excess loss (EL), small footprint,
and broad bandwidth.

We experimentally demonstrate the adiabatic power splitter (APS) on the SRN-
LNOI platform. Figure 6 (a) shows the structure of the APS, which consists of
one input taper and two symmetrical output tapers. The parameters of the APS
are the input waveguide width of 900 nm, the tip width of 150 nm, the taper
length of 20 $\mu m$, and the gap of 200 nm between two adjacent tapers. After
fabrication, an adiabatic power splitter with the input waveguide width of 870
nm, the tip width of 115 nm, the gap of 175 nm, and the taper length of 20
$\mu m$ was obtained. To determine the EL of APS, three cascaded splitters
were measured, and the results are presented in Figure 6 (b). By linear
fitting, the EL of The APS is about 0.136 dB. The optical spectrum of the
single APS indicate that uniform outputs are achieved from 1500 nm to 1600 nm,
as shown in Fig. 6 (c).

Figure 7: (a) SEM image of the MMI based power splitter. (b) Measured excess
loss of MMI based power splitters. (c) Measured spectrum of the MMI based
power splitter.

Moreover, a multimode interferometer (MMI) based optical power splitter is
demonstrated. The SEM image of MMI splitter with a multimode waveguide length
of 16.8 $\mu m$ and width of 4.8 $\mu m$ is shown in Fig. 7 (a). To reduce the
EL, the input and output waveguides are linearly tapered from 1 $\mu m$ to 1.5
$\mu m$ before connecting to the multimode waveguide. The measurement method
is the same as the APS. As shown in Fig. 7 (b), the EL of 0.096 dB is
obtained. Figure 7 (c) presents the optical spectrum of an MMI splitter.
Uniform outputs are achieved from 1500 nm to 1580 nm.

###  3.2 filters

Apart from optical splitters, filters play an important role in PIC. Based on
the proposed optical power splitters, AMZIs were fabricated with arm length
differences of 50 $\mu m$. The microscope image of the proposed AMZIs based on
MMI splitter and APS are shown in Fig. 8 (a) and (b), respectively. Figure 8
(c) shows the transmission spectrum of the AMZI and the extinction ratio (ER)
of both AMZIs are larger than 20 dB from 1500 nm to 1600 nm. The high
extinction ratio also proves that the high power uniformity of the proposed
optical power splitter is achieved.

Figure 8: Microscope images of AMZIs based on the MMI splitter (a) and the APS
(b). (c) Measured spectrum of the AMZIs.

Meanwhile, a Bragg grating filter was also designed and fabricated. The Bragg
grating filter has a width of 1 $\mu m$, a grating period of 395 nm, a period
number of 100, a grating length of 39.5 $\mu m$, a side corrugation depth of
250 nm, and a teeth width of 185 nm. Figure 9 (a) shows the SEM image of the
Bragg grating filter. Because of the fabrication error, a Bragg grating filter
with a side corrugation depth of 280 nm, and a teeth width of 160 nm was
obtained. The deviation of 25-30 nm from the designed value leads to a blue
shift of the center wavelength compared with the simulation. Figure 9 (b)
shows the measured transmission of the Bragg grating filter. And a Bragg
grating filter with center wavelength of 1538 nm, ER of 19 dB, and 3 dB
bandwidth of 14 nm was achieved with a period number of 100. By contrast, a
Bragg grating filter based on monolithic LNOI platform exhibits a ER of 14 dB
with a period number of 1000 [29]. This result suggests that the SRN-LNOI
platform is more suitable for high perfoemance Bragg grating filters with high
ER and compact footprints.

Figure 9: (a) SEM image of the fabricated Bragg grating filter. (b) Measured
spectrum of the Bragg grating filter.

##  4 Mach–Zehnder modulators

LN is a promising material for electro-optical modulation because of its
strong electro-optical coefficient ($r_{33}$ = 30.8 pm/V at $\lambda$ = 630
nm). In this section, a high performance Mach–Zehnder modulator (MZM) is
demonstrated on the SRN-LNOI hybrid platform. As mentioned above, an x-cut
LNOI wafer with 400 nm thin-film LN and 4.7 $\mu m$ BOX layer wafer was used
as the substrate, and 300 nm SRN was deposited as the waveguide layer. The
optical part of MZM comprises two regions: the passive region and the active
region. The passive region consists of waveguides (1 $\mu m$ $\times$ 300 nm),
bend waveguides with 50 $\mu m$ radius and optical splitters proposed in
section 3.1. At the passive region, the optical power is mostly confined in
the upper SRN waveguide. As shown in Fig 10. (a), the confinement fraction in
the LN layer ($\Gamma_{LN}$) and the SRN layer ($\Gamma_{SRN}$) are 29.9% and
57.3%, respectively. At the active region, a 5 mm long waveguides with width
of 500 nm and height of 300 nm are applied. As Fig. 10 (b) shows, light is
almost guided in the LN slab layer, with $\Gamma_{LN}=67.4\%$,
$\Gamma_{SRN}=14.1\%$, and group index ($n_{g}$) of 2.373. As a result, the
large $\Gamma_{LN}$ enables efficient modulation at the active region. A 100
$\mu m$ long adiabatic waveguide taper is utilized to connect the passive and
active regions.

Figure 10: Mode field distributions of waveguides with width of 1 $\mu m$ (a)
and 500 nm (b). (c) Microscope images of the proposed Mach–Zehnder modulators.

In the active region of the modulator, a ground-signal-ground (GSG) traveling
wave electrode is utilized to perform the single-drive push-pull operation, as
shown in Fig. 10 (c). After sputtering a 30 nm chromium adhesion layer, 1 $\mu
m$ aluminum was sputtered and patterned by photolithography. The signal
electrode width is 16 $\mu m$, and the ground electrodes widths are 200 $\mu
m$ with the electrode gap of 6 $\mu m$. The gap of 6 $\mu m$ is optimized to
balance the optical loss caused by aluminum electrodes and modulation
efficiency. The electrode transmission line characteristic impedance ($Z_{0}$)
and microwave index ($n_{m}$) are 50 $\Omega$ and 2.04, respectively. As we
know, the maximal 3-dB electrical roll-off frequency ($f_{3dB,el}$) can be
obtained by matching the velocity between the optical wave and microwave,
matching the characteristic impedance to the load and source impedance, and
minimizing the RF loss. Assuming impedance matching and no RF loss [30], the
theoretical bandwidth limitation is given as: $f_{3dB}$ (GHz) =
$0.13/(L|n_{m}-n_{g}|)$, where L is the length of phase-shifter arm.
Consequently, the bandwidth limitation of the proposed MZM is 79 GHz with L =
5 mm and $(|n_{m}-n_{g}|)$ = 0.33. Moreover, it is worthy to note that the
bandwidth limitation caused by velocity mismatch can be optimized by changing
the LNOI wafer with a thinner BOX layer.

Figure 11: (a) Testing image of the Mach–Zehnder modulators. (b) Experimental
setup for small signal measurements. (c) Experimental setup for large signal
measurements.

After fabricating the MZM, RF measurements including small signal and larger
signal characterization were performed, as shown in Figs. 11 (a). Firstly, the
DC characterization was measured. As shown in Fig. 12 (a), a ER of 25.8 dB and
a modulation efficiency figure-of-merit ($V_{\pi}L$) of 3.7 V.cm were obtained
for a 5 mm long device.

Figure 12: (a) Normalized optical transmission as a function of applied
voltage on travelling-wave electrodes at 1550 nm. (b) Measured EO S21
parameters under bias voltage of 7 V.

Afterward, the characterizations of small signal were performed using a 40 GHz
vector network analyzer (VNA, Anritsu MS4640). The light was coupled in and
out from the MZM by two grating couplers. Then the optical signal was received
by a 50 GHz electro-optical (EO) bandwidth photodetector (PD, Finisar
XPDV2150), which was connected with the VNA. A pair of 67 GHz GSG high-
frequency RF probes were used to apply RF signal and connect with a 50
$\Omega$ terminator, respectively. By de-embedding the known EO S21 parameters
of the PD, the EO bandwidth of the proposed MZM was obtained. The measured EO
S21 parameters at the DC bias voltage of 7 V are shown in Fig. 12 (b). The EO
response decays about 1.1 dB from DC to 40 GHz and the EO 3 dB-bandwidth is
predicted to be 67 GHz.

Figure 13: Electrical (a) and optical (b) eye diagrams at the rates of 72
GBaud OOK. Electrical (c) and optical (d) eye diagrams at the rates of 120
GBaud OOK.

Then the large signal experiments were conducted as shown in Fig. 11 (c).
Firstly, a 72 GBaud RF signal from a bit pattern generator (BPG, SHF 12103A)
is applied on the MZM through a 67 GHz GSG microwave probe after
amplification. The MZM was set at the quadrature point through the phase
shifter. Meanwhile, the modulated optical signal was amplified by an erbium-
doped fiber amplifier (EDFA) and filtered using a band-pass filter (BPF). A
Tektronix DSA 8300 Digital Serial Analyzer (DSA) with 80 GHz Sampling Module
was used to detect the optical signal. Figure 13 (a) and (b) compare the input
electrical eye diagram and output optical eye diagram at 72 GBaud on-off
keying (OOK) modulation format. Moreover, The BPG and an SHF 2:1 multiplexer
(MUX) were used to generate the electrical signals up to 120 GBaud. The input
electrical eye diagram and output optical eye diagram at 120 GBaud OOK
modulation format are demonstrated in Fig. 13 (c) and (d). The measured ER are
7.6 dB and 5.6 dB for 72 GBaud and 120 GBaud with a 7 V peak-to-peak input
voltage, respectively. As far as we know, it is the highest symbol rate
achieved in the LNOI MZM, experimentally.

##  5 Conclusion

To draw a conclusion, we present a SRN-LNOI hybrid platform with waveguides
and several key components for PIC. Several fundamental components, such as
waveguides, optical splitters, and filters were designed, fabricated and
tested. A high performance MZM with A EO 3 dB bandwidth of 67 GHz and a
recorded high symbol rate of 120 GBaud was experimentally demonstrated. With
those proposed fundamental components, the SRN-LNOI hybrid platform provides a
solution with high integration density and CMOS compatibility for PIC.

Funding National Key Research and Development Program of China (Grant
No.2018YFE0201900).

Disclosures The authors declare no conflicts of interest.

† These authors contributed equally to this work.

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# Spectroscopic orbits of subsystems in multiple stars. VIII.

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

Periods, eccentricities, and masses in hierarchical stellar systems inform us
on the formation and early evolution of these fascinating objects. To
complement the multiplicity statistics of nearby solar-type stars, 19 new
spectroscopic orbits of inner subsystems in 15 hierarchies (10 triples and 5
quadruples) are determined based on high-resolution echelle spectra collected
during several years. While previous papers of this series contained mostly
short-period orbits, here most periods are on the order of a year. The main
components of these hierarchies are HIP 7852, 9148, 12548, 21079, 24320,
27970, 34212, 56282, 57860, 76400, 76816, 81394, 96284, 100420, and HD
108938\. Noteworthy systems are HIP 12548 and 24230 (hierarchies of 2+2
architecture with low-mass spectroscopic secondaries), HIP 56282 (a planetary-
type 3+1 hierarchy), and HIP 27970 (a compact triple with periods of 15 and
1049 days).

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), lack
orbits and therefore confuse the statistics. This paper presents results of
the long-term program conducted at the 1.5 m telescope at Cerro Tololo with
the CHIRON high-resolution optical echelle spectrograph. Previous publications
of this series (Tokovinin, 2016a, b; Tokovinin et al., 2018; Tokovinin, 2018a,
b, 2019a, 2020a, 2019b, 2020b) focused primarily on the short-period
subsystems. Continued accumulation of the spectra allows calculation of orbits
with periods on the order of a year presented here. Knowledge of these orbits
adds missing parameters of the nearby hierarchies and contributes to the
collection of such data in the Multiple Star Catalog (MSC, Tokovinin, 2018c).

Figure 1: Architecture of five quadruple systems. Green circles denote subsystems, small pink circles – individual stars with masses indicated below.  Table 1: Basic parameters of observed multiple systems  WDS | Comp. | HIP | HD | Spectral | $V$ | $V-K_{s}$ | $\mu^{*}_{\alpha}$ | $\mu_{\delta}$ | RV |  $\varpi$aaProper motions and parallaxes are from Gaia EDR3 (Gaia Collaboration et al., 2021). Colons mark parallaxes biased by subsystems, in which case the PMs are from Brandt (2018).
---|---|---|---|---|---|---|---|---|---|---
(J2000) |  |  |  | type | (mag) | (mag) | (mas yr-1) | (km s-1) | (mas)
01410$-$0524 | A | 7852 | 10353 | G5V | 8.48 | 1.69 |  $-$69 |  $-$27 | 0.7 | 19.44:
| B | … | … | K5 | 11.84 | 3.46 |  $-$69 |  $-$26 |  $-$0.4 | 22.03
01579$-$2851 | A | 9148 | 12068 | G3V | 8.27 | 1.67 | 212 | 57 | 23.2 | 12.45:
| B | … | … | M: | 13.07 | 3.18 | 212 | 57 | 23.5 | 11.24
02415$-$7128 | AB | 12548 | 17215 | G6V | 7.82 | 1.76 | 158 |  $-$61 | 45.1 | 18.6:bb Hipparcos parallax (van Leeuwen, 2007).
04311$-$4522 | AB | 21079 | 28904 | G3V | 8.29 | 1.71 |  $-$50 | 17 |  $-$3.5 | 21.87:
05131$-$5959 | A | 24320 | 34377 | G5V | 8.87 | 1.73 | 30 | 126 | 16.1 | 15.87:
| B | … | … | … | 10.13 | 2.55 | 19 | 125 | 16.5 | 16.43:
05550$-$1256 | A | 27970 | 39899 | F7V | 7.73 | 1.28 |  $-$23 |  $-$42 |  $-$12.0 | 15.78:
07056$-$7116 | A | 34212 | 55197 | F8V | 7.66 | 1.30 |  $-$5 | 267 | 52.1 | 14.39:
| B | … | … | … | 16.91 | 5.24 |  $-$5 | 270 | … | 16.55
11323$-$0025 | A | 56282 | 100269 | F8V | 8.09 | 1.35 | 43 |  $-$161 | 8.3 | 15.13:
| B | … | … | … | 16.23 | 5.15 | 41 |  $-$162 | … | 16.28
11520$-$4357 | A | 57860 | 103076 | G5V | 9.02 | 1.64 |  $-$20 |  $-$21 | 38.5 | 12.09
| B | … | … | … | 9.27 | … |  $-$24 |  $-$25 | 36.4 | 12.31
12314$-$5659 | AB | … | 108938 | G8V | 8.98 | 2.17 | 45 | 7 | 39.0 | 6.35
15362$-$0623 | A | 76400 | 139059 | G6V | 7.90 | 1.62 |  $-$103 |  $-$179 |  $-$7.3 | 15.28:
| B | … | … | … | 17.82 | 5.81 |  $-$99 |  $-$174 | … | 15.29
15410$-$1449 | A | 76816 | 139864 | F8V | 9.47 | 1.62 |  $-$26 |  $-$1 |  $-$39.2 | 3.25
| B | … | … | … | 9.74 | 2.50 |  $-$25 |  $-$2 |  $-$40.3 | 3.32
16374$-$6133 | A | 81394 | 149261 | F5 | 8.54 | 1.28 | 11 |  $-$17 |  $-$15.3 | 5.02
| B | 81395 | 149262 | F2 | 9.22 | 1.17 | 11 |  $-$17 |  $-$14.1 | 4.96
19583$-$5154 | A | 98294 | 188557 | A9IV | 7.40 | 0.54 | 46 |  $-$44 |  $-$5.0 | 10.41
| B | 98278 | 188534 | F6V | 8.17 | 1.18 | 46 |  $-$43 |  $-$6.3 | 10.49
20218$-$3654 | A | 100420 | … | F6V | 8.31 | 0.94 | 2 |  $-$16 | 49.1 | 5.61:
| B | … | 193465 | … | 9.60 | 1.29 | 2 |  $-$18 | 49.1 | 5.65

The hierarchical systems studied here are listed in Table 1. The data are
collected from Simbad and Gaia (Gaia Collaboration et al., 2021, hereafter
EDR3), 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.

This paper is organized similarly to the previous ones. The data and methods
are briefly outlined in section 2, where the orbital elements are also given.
Then each multiple system is discussed in section 3. Figure 1 illustrates the
architecture of quadruple systems (triples are obvious and do not need
illustration). The paper closes with discussion of the results in section 4.

##  2 Observations and Data Analysis

###  2.1 Spectroscopic Observations

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. Fifteen
hours of observing time were allocated to this program per semester.
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 based on the solar spectrum, as
detailed in Tokovinin (2016a). The RVs derived by this method rely on the
instrument wavelength calibration and should be on the absolute scale, so no
instrumental corrections are applied (an offset of $+0.15$ km s-1 relative to
established RV standards was found in Tokovinin, 2018a). The RV errors depend
on several factors such as the width and contrast of the CCF dip, presence of
other dips, and signal-to-noise ratio. The rms residuals from the orbits can
be as low as 0.01 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 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/HD | Comp. | $N$ | $a$ | $\sigma$ | $a\sigma$ | $V\sin i$ | Li
---|---|---|---|---|---|---|---
|  |  |  | (km s-1) | (km s-1) | (km s-1) | 6708Å
7852 | Aa | 7 | 0.359 | 4.228 | 1.52 | 4.5 | Y
9148 | Aa | 7 | 0.370 | 3.634 | 1.35 | 2.3 | Y
9148 | Ab | 7 | 0.090 | 3.764 | 0.34 | 2.9 | N?
12548 | Aa | 15 | 0.330 | 3.773 | 1.25 | 2.9 | N
12548 | Ba | 15 | 0.130 | 3.677 | 0.48 | 2.5 | N
21079 | Aa | 8 | 0.319 | 4.549 | 1.45 | 5.4 | Y
24320 | Aa | 14 | 0.401 | 4.198 | 1.68 | 4.4 | Y?
24320 | Ba | 13 | 0.414 | 4.354 | 1.80 | 4.9 | N
27970 | Aa1 | 6 | 0.299 | 3.751 | 1.12 | 2.8 | Y!
34212 | Aa | 12 | 0.287 | 4.490 | 1.29 | 5.3 | N
56282 | Aa1 | 15 | 0.297 | 3.933 | 1.17 | 3.6 | Y!
57860 | Aa | 7 | 0.187 | 3.551 | 0.66 | 1.8 | N
57860 | Ab | 7 | 0.141 | 3.539 | 0.50 | 1.8 | N
57860 | B | 7 | 0.134 | 3.596 | 0.48 | 2.1 | N
108938 | Aa | 2 | 0.324 | 3.490 | 1.13 | 1.4 | N
108938 | Ab | 2 | 0.048 | 3.130 | 0.15 | 0 | N
108938 | B | 2 | 0.061 | 3.845 | 0.23 | 3.2 | N
76400 | Aa | 9 | 0.234 | 3.735 | 0.88 | 2.8 | N
76400 | Ab | 9 | 0.233 | 3.726 | 0.87 | 2.7 | N
76816 | Ba | 13 | 0.507 | 3.806 | 1.93 | 3.1 | Y?
81394 | Ba | 13 | 0.086 | 7.471 | 0.65 | 12.0 | N
81394 | Bb | 13 | 0.098 | 6.064 | 0.59 | 9.0 | N
98278 | Ba | 8 | 0.070 | 10.68 | 0.75 | 18.2 | Y
98278 | Bb | 8 | 0.029 | 12.75 | 0.37 | 22.1: | …
100420 | Aa | 12 | 0.215 | 4.628 | 1.00 | 5.7 | N
100420 | Ab | 12 | 0.070 | 4.218 | 0.30 | 4.5 | N
100420 | B | 3 | 0.241 | 5.435 | 1.31 | 7.6 | …

###  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
ORBIT111Codebase: http://www.ctio.noirlab.edu/ãtokovin/orbit/ and
https://doi.org/10.5281/zenodo.61119 was used (Tokovinin, 2016c). 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: Spectroscopic orbits  HIP/HD | System | $P$ | $T$ | $e$ | $\omega_{\rm A}$ | $K_{1}$ | $K_{2}$ | $\gamma$ | rms1,2 | $M_{1,2}\sin^{3}i$
---|---|---|---|---|---|---|---|---|---|---
|  | (d) | (JD +24,00,000) |  | (deg) | (km s-1) | (km s-1) | (km s-1) | (km s-1) | (${\cal M}_{\odot}$)
7852 | Aa,Ab | 1177.9 | 58615.0 | 0.349 | 260.5 | 7.320 | … | 0.677 | 0.014 | 0.98:
|  |  $\pm$3.4 |  $\pm$16.0 |  $\pm$0.015 |  $\pm$3.6 |  $\pm$0.116 | … |  $\pm$0.105 | … | 0.43
9148 | Aa,Ab | 1272.3 | 58531.6 | 0.0 | 0.0 | 7.711 | 9.550 | 23.163 | 0.16 | 0.37
|  |  $\pm$6.0 |  $\pm$2.2 | fixed | fixed |  $\pm$0.099 |  $\pm$0.099 |  $\pm$0.057 | 0.16 | 0.30
12548 | Aa,Ab | 1851.9 | 59023.7 | 0.544 | 151.7 | 5.02 | … | 45.1 | 0.11 | 1.07:
|  |  $\pm$18.4 |  $\pm$29.6 |  $\pm$0.040 |  $\pm$5.4 |  $\pm$0.66 | … | fixed | … | 0.32
12548 | Ba,Bb | 108.18 | 59241.648 | 0.823 | 201.3 | 21.36 | … | 47.60 | 0.26 | 0.89:
|  |  $\pm$0.10 |  $\pm$0.087 |  $\pm$0.005 |  $\pm$0.7 |  $\pm$0.28 | … |  $\pm$0.12 | … | 0.31
21079 | Aa,Ab | 217.04 | 58044.39 | 0.491 | 336.6 | 5.949 | … |  $-$3.525 | 0.024 | 0.98:
|  |  $\pm$0.23 |  $\pm$1.66 |  $\pm$0.008 |  $\pm$1.1 |  $\pm$0.103 | … |  $\pm$0.041 | … | 0.16
24320 | Aa,Ab | 1430.3 | 58800.2 | 0.393 | 136.6 | 3.46 | … | 16.14 | 0.034 | 1.00:
|  |  $\pm$10.6 |  $\pm$10.2 |  $\pm$0.018 |  $\pm$1.5 |  $\pm$0.03 | … |  $\pm$0.05 | … | 0.19
24320 | Ba,Bb | 7.94292 | 58190.82 | 0.0240 | 287.5 | 36.76 | … | 16.46 | 0.038 | 0.82:
|  |  $\pm$0.00002 |  $\pm$0.10 |  $\pm$0.0005 |  $\pm$4.5 |  $\pm$0.11 | … |  $\pm$0.02 | … | 0.39
27970 | Aa1,Aa2 | 15.3230 | 56600.996 | 0.504 | 197.8 | 25.48 | … | … | 0.22 | 1.25:
|  |  $\pm$0.0001 |  $\pm$0.041 |  $\pm$0.007 |  $\pm$1.3 |  $\pm$0.36 | … | … | … | 0.35
27970 | Aa,Ab | 1049.4 | 57207.6 | 0.359 | 231.4 | 6.13 | … |  $-$11.95 | 0.22 | 1.60:
|  |  $\pm$4.3 |  $\pm$11.6 |  $\pm$0.028 |  $\pm$5.5 |  $\pm$0.20 | … |  $\pm$0.11 | … | 0.44
34212 | Aa,Ab | 1246.7 | 57902.5 | 0.163 | 192.3 | 7.265 | … | 52.051 | 0.015 | 1.24:
|  |  $\pm$2.9 |  $\pm$12.7 |  $\pm$0.005 |  $\pm$3.6 |  $\pm$0.058 | … |  $\pm$0.031 | … | 0.53
56282 | Aa1,Aa2 | 122.177 | 58945.35 | 0.046 | 264.9 | 8.284 | … | … | 0.066 | 1.14:
|  |  $\pm$0.058 |  $\pm$2.23 |  $\pm$0.006 |  $\pm$6.6 |  $\pm$0.063 | … | … | … | 0.24
56282 | Aa,Ab | 3650 | 57233 | 0.056 | 228.5 | 2.527 | … | 8.254 | 0.066 | 1.38:
|  | fixed |  $\pm$1271 |  $\pm$0.066 |  $\pm$123.4 |  $\pm$0.520 | … |  $\pm$0.455 | … | 0.25
57860 | Aa,Ab | 891.9 | 58137.7 | 0.101 | 6.0 | 11.75 | 12.42 | 38.47 | 0.11 | 0.66
|  |  $\pm$2.7 |  $\pm$ 9.3 |  $\pm$0.005 |  $\pm$4.0 |  $\pm$0.06 |  $\pm$0.09 |  $\pm$0.04 | 0.06 | 0.62
108938 | Aa,Ab | 342.48 | 59321.34 | 0.517 | 208.6 | 17.72 | 21.66 | 39.01 | 0.22 | 0.75
|  |  $\pm$1.20 |  $\pm$0.82 |  $\pm$0.018 |  $\pm$1.3 |  $\pm$0.32 |  $\pm$0.32 |  $\pm$0.30 | 0.41 | 0.61
76400 | Aa,Ab | 368.51 | 58235.66 | 0.137 | 192.0 | 18.64 | 18.70 |  $-$7.28 | 0.05 | 0.96
|  |  $\pm$0.74 |  $\pm$3.66 |  $\pm$0.039 |  $\pm$3.7 |  $\pm$0.47 |  $\pm$0.47 |  $\pm$0.71 | 0.04 | 0.96
76816 | Ba,Bb | 208.918 | 59185.16 | 0.420 | 43.2 | 15.265 | … |  $-$40.323 | 0.016 | 1.67:
|  |  $\pm$0.011 |  $\pm$0.34 |  $\pm$0.005 |  $\pm$0.9 |  $\pm$0.082 | … |  $\pm$0.062 | … | 0.68
81395 | Ba,Bb | 224.804 | 58319.14 | 0.418 | 147.6 | 11.14 | 12.04 |  $-$14.13 | 0.34 | 0.11
|  |  $\pm$0.028 |  $\pm$0.46 |  $\pm$0.006 |  $\pm$1.2 |  $\pm$0.21 |  $\pm$0.08 |  $\pm$0.06 | 0.12 | 0.10
98278 | Ba,Bb | 236.15 | 58754.64 | 0.574 | 245.2 | 27.22 | 27.95 |  $-$6.32 | 1.20 | 1.14
|  |  $\pm$0.33 |  $\pm$0.92 |  $\pm$0.008 |  $\pm$1.0 |  $\pm$0.42 |  $\pm$0.32 |  $\pm$0.24 | 0.57 | 1.11
100420 | Aa,Ab | 790.6 | 58395.68 | 0.372 | 73.0 | 14.78 | 17.52 | 49.08 | 0.11 | 1.20
|  |  $\pm$0.46 |  $\pm$0.88 |  $\pm$0.003 |  $\pm$0.5 |  $\pm$0.06 |  $\pm$0.06 |  $\pm$0.03 | 0.13 | 1.00
Table 4: Radial velocities and residuals (fragment)

HIP | System | Date | RV | $\sigma$ | (O$-$C) | Comp.
---|---|---|---|---|---|---
HD |  | (JD +24,00,000) | (km s-1) | Instr.
7852 | Aa,Ab | 53695.0000 | -6.46 | 0.20 | -0.02 | aC
7852 | Aa,Ab | 54046.6120 | 7.18 | 0.10 | -0.01 | aH
7852 | Aa,Ab | 57319.6410 | -6.93 | 0.20 | 0.01 | a
7852 | Aa,Ab | 57983.8210 | 2.30 | 0.20 | 0.00 | a
7852 | Aa,Ab | 58745.7420 | 6.96 | 0.20 | 0.03 | a

††footnotetext: (This table is available in its entirety in machine-readable
form). Instrument codes: C – Chubak et al. (2012); D – Desidera et al. (2006);
H – HARPS; L – Las Campanas (Tokovinin et al., 2015b); R – Radial Velocity
Meter (Gorynya & Tokovinin, 2018).

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. The
Hipparcos or HD 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) and gives references to the published RVs. The RVs of other
visual components are provided, for completeness, in Table 5. 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.

Table 5: Radial velocities of other components  HIP/HD | Comp. | Date | RV
---|---|---|---
|  | (JD +24,00,000) | (km s-1)
57860 | B | 58193.7198 | 36.034
57860 | B | 58194.6254 | 36.005
57860 | B | 58195.6408 | 35.973
57860 | B | 58510.8194 | 35.994:
57860 | B | 58539.7575 | 35.961:
57860 | B | 58559.6517 | 35.942:
57860 | B | 58648.6288 | 36.129:
57860 | B | 59403.4624 | 36.000
108938 | B | 54576.6567 | 38.212
108938 | B | 59316.6752 | 37.679
108938 | B | 59323.6711 | 37.707
108938 | B | 59404.5562 | 38.227:
100420 | B | 57985.5413 | 49.437
100420 | B | 57986.5850 | 49.489
100420 | B | 58549.9038 | 49.408

###  2.3 Other Data

I use here astrometry and photometry from the Gaia third early data release,
EDR3 (Gaia Collaboration et al., 2021). For multiple systems, it can be
compromised by acceleration and/or unresolved companions because the current
astrometric reductions assume single stars. The RUWE parameter (Reduced Unit
Weight Error) captures the excessive astrometric noise, helping to identify
suspicious astrometry in EDR3. Most (but not all) stars with subsystems
studied here have RUWE $>2$. Uncertain Gaia parallaxes are marked by colons in
Table 1. Detection of astrometric subsystems by the difference $\Delta\mu$
(so-called PMA) 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 by Brandt (2018) continued the work by Makarov & Kaplan (2005) at a
new level of accuracy. For stars with 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. (2021). Apart from the position measurements,
speckle interferometry provides differential photometry of close visual pairs.
For binaries wider than $\sim$1″, it is complemented by the Gaia photometry.
Effective temperatures estimated by Gaia give the spectral types of the visual
components, checked by their $V-K$ colors. Spectral types and absolute
magnitudes are used to estimate masses of the stars using standard main-
sequence relations from Pecaut & Mamajek (2013).

##  3 Individual Objects

For double and triple-lined systems, Figures in this section show a typical
CCF (the Julian date and individual components are marked on the plot)
together with the RV curve representing the orbit. For single-lined binaries,
only the RV curves are plotted. In the RV curves, 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. Masses of stars are estimated from absolute magnitudes, orbital
periods of wide pairs — from their projected separations (see Tokovinin,
2018c). Semimajor axes of the 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 7852 (Triple)

Figure 2: RV curve of HIP 7852 Aa,Ab.

This is a chromospherically active star EY Cet (Boro Saikia et al., 2018)
located at 45 pc distance. Luck (2018) used the archive of high-resolution
spectra taken with the HAPRS spectrometer to determine the effective
temperature of 5641 K (spectral type G5V), a mild metal deficiency
[Fe/H]=$-$0.13, and the projected rotation of $V\sin i=5.8$ km s-1 , in good
agreement with 4.5 km s-1 listed in Table 2. The HARPS and CHIRON spectra show
a presence of lithium despite the slow rotation and the age of 5.8 Gyr
estimated by Luck. The common proper motion (CPM) companion B ($V=11.84$ mag,
K5, UCAC2 29946080) at 125″ separation is listed in the WDS as TOK 228. Stars
A and B are located on the main sequence.

The astrometric acceleration of star A was detected by Hipparcos (Makarov &
Kaplan, 2005) and by Brandt (2018); it explains the huge RUWE=15.6 in Gaia
EDR3. The star has been placed on the CHIRON program in 2015 to determine the
period of Aa,Ab. Eight single-lined spectra accumulated to date indicate
$P=3.2$ yr. This orbit (Figure 2) is strengthened by including the RV deduced
from the HARPS spectrum taken in 2006 (JD 2454046.612) and recovered from the
ESO archive and the RV measured in 2005 (JD 2453695.0) by Chubak et al.
(2012). The rms residuals are only 0.014 km s-1 . The RV from Gaia is not used
here because its mean epoch is not known and the error is large (1.9 km s-1 )
owing to variability.

Star Aa has an estimated mass of 0.98 $M_{\odot}$ , the minimum mass of Ab is
0.43 $M_{\odot}$ , and the semimajor axis of the inner orbit is 47.5 mas. The
minimum Ab mass corresponds to the photocenter axis of 14.5 mas. An
astrometric orbit will determined by Gaia, leading to an accurate mass of Ab.

###  3.2 HIP 9148 (Triple)

Figure 3: CCF (top) and RV curve (bottom) of HIP 9148 Aa,Ab.

The outer pair A,B, at 41$\farcs$5 separation, has been identified as CPM by
Luyten (1941) and is listed in the WDS as LDS 61. Gaia confirms that this
high-PM pair is bound. Star B ($V=13.07$ mag) has an estimated mass of 0.55
$M_{\odot}$ . Its EDR3 parallax of 11.24 mas (distance 89 pc) is not biased by
the subsystem. In contrast, star A is a double-lined binary (Nordström et al.,
2004). It has a large $\Delta\mu$, the EDR3 RUWE is also large, 17.6, and the
EDR3 parallax of 12.45 mas is biased. Like the previous object, the star is
chromospherically active (Boro Saikia et al., 2018) and has a detectable
lithium line, although the projected axial rotation is slow.

Ten CHIRON spectra acquired since 2017 show double CCFs with unequal dips
(Figure 3). The magnitude difference between Aa and Ab deduced from the dip
areas is 1.5 mag, hence the $V$ magnitudes of Aa and Ab are 8.51 and 10.01
mag, respectively, and correspond to main-sequence stars with masses of 1.23
and 0.95 $M_{\odot}$ (ratio 0.77). Aa is brighter than inferred from its
spectral type G3V, it is located slightly above the main sequence (evolved),
while star B is just below.

The orbit of Aa,Ab with a period of 3.5 yr is circular. A free fit gives
$e=0.017\pm 0.020$ and does not reduce the residuals, so the circular orbit is
enforced. The spectroscopic mass ratio $q=0.81$ is similar to the ratio of
photometricaly estimated masses, which are much larger than the spectroscopic
masses $M\sin^{3}i$. This means that the Aa,Ab orbit has a large inclination
of 42°. The semimajor axis of Aa,Ab is 33 mas, and the estimated photocenter
amplitude is about 8 mas.

###  3.3 HIP 12548 (Quadruple)

The star HIP 12548 (HD 17215, G6V, $V=7.82$ mag) belongs to the immediate
solar neighborhood: the revised Hipparcos parallax of 18.6$\pm$0.8 mas puts it
at the 54 pc distance. The Gaia DR2 parallax of 15.8$\pm$0.8 mas is
inaccurate, and EDR3 gives no parallax. This is a visual binary B 1923 (WDS
J02415$-$7128) known since 1931; its orbit with a period of $\sim$100 yr and a
semimajor axis of 0$\farcs$6 is now almost fully covered and well constrained
(see below).

Nordström et al. (2004) found that the spectrum is double-lined and,
therefore, there is a spectroscopic subsystem. They even determined a mass
ratio of 0.26 by assuming that the lines belong to the same spectroscopic
system. However, their paper does not contain individual RV measurements,
making it impossible to use or check these findings. Only single lines were
seen in 2008 at Las Campanas (Tokovinin et al., 2015b) and in 2017 with
CHIRON. Occasionally, a double-lined spectrum is observed in a visual binary
near periastron of its eccentric orbit; the existence of a spectroscopic
subsystem remained thus questionable.

The visual binary was monitored by speckle interferometry at SOAR in
2008-2021, allowing us to improve its orbit. To check for potential
spectroscopic subsystems, the object was placed on the CHIRON program in 2017.
The observed CCF profiles varied from narrow single to asymmetric or double,
confirming the existence of a spectroscopic subsystem. Furthermore, it became
clear that the RVs of both components seen in the spectra are variable. Both
visual components A and B are close binaries with periods of 5 yr and 108
days, respectively, and this is a quadruple system of 2+2 hierarchy. Discovery
of the true nature of this seemingly common visual pair was possible only with
high-resolution spectroscopy.

Figure 4: RV curves of the components B (top) and A (bottom) of HIP 12548\.
The RV measurements derived from strongly blended dips (crosses) are assigned
large errors.

Figure 4 illustrates the single-lined orbits of the subsystems Ba,Bb and
Aa,Ab. The orbit of Ba,Bb has a large eccentricity of 0.82. The minimum of its
RV curve was covered by regular observations in 2021 January-February. The
inserts show the CCFs at the RV minimum on JD 2459241.5, where the weaker dip
of Ba was located to the left of the stronger dip of Aa. Twelve days later, on
JD 2459253.5, the lines of Ba were already seen on the right side, partially
blending with the lines of Aa. The RV of Aa on both dates was around 40 km s-1
.

The RV curve of Aa,Ab is shown in the lower panel of Figure 4. Its descending
branch was covered in the fall of 2019\. CHIRON was closed for COVID-19
pandemic in the first half of 2020\. After its re-opening in 2020 October, the
increasing RV was measured. The RVs alone do not fully constrain the orbit,
partly because blended dips of Aa and Ba result in poor accuracy. Reliable dip
splitting is achieved only near the periastron of the Ba,Bb orbit.

Figure 5: The outer orbit of HIP 12548 A,B. Top: positional measurements (crosses denote visual micrometer measurements, squares are accurate speckle measurements, the wavy line is the orbit with wobble), bottom: the RV curve.  Table 6: Visual and astrometric orbits  HIP | System | $P$ | $T$ | $e$ | $a$ | $\Omega_{\rm A}$ | $\omega_{\rm A}$ | $i$ | $K_{1}$ | $K_{2}$ | $\gamma$
---|---|---|---|---|---|---|---|---|---|---|---
|  | (yr) | (yr) |  | (arcsec) | (deg) | (deg) | (deg) | (km s-1) | (km s-1) | (km s-1)
12548 | A,B | 106.3 | 2010.02 | 0.384 | 0.568 | 42.4 | 63.4 | 114.7 | 4.12 | 4.69 | 45.10
|  |  $\pm$4.6 |  $\pm$0.19 |  $\pm$0.020 |  $\pm$0.012 |  $\pm$0.4 |  $\pm$1.6 |  $\pm$0.4 |  $\pm$0.44 |  $\pm$0.88 | fixed
12548 | Aa,Ab | 5.07 | 2020.477 | 0.544 | 0.0117 | 70.5 | 151.7 | 79.7 | 5.02 | … | …
|  |  $\pm$0.05 |  $\pm$0.080 |  $\pm$0.040 |  $\pm$0.0009 |  $\pm$3.2 |  $\pm$5.4 |  $\pm$3.2 |  $\pm$0.66 | … | …
76400 | A,B | 70.0 | 2016.26 | 0.420 | 0.374 | 320.3 | 275.5 | 144.7 | 1.41 | … |  $-$7.28
|  | fixed |  $\pm$0.84 |  $\pm$0.010 |  $\pm$0.008 |  $\pm$11.5 |  $\pm$21.1 |  $\pm$2.9 |  $\pm$0.67 | … |  $\pm$0.71

The semimajor axis of Aa,Ab is 61 mas, and the expected photocenter amplitude
is 14 mas. Wobble in the motion of A,B caused by the 5-yr subsystem is
detectable in accurate speckle-interferometric measurements. The orbits of A,B
and Aa,Ab were fitted jointly using both the positions and the RVs. Star B was
treated as single (its photocenter amplitude is $\sim$2 mas), and its center-
of-mass RV is included as a single measurement. The spectroscopic elements of
Aa,Ab are listed in Table 3, and the updated visual elements of A,B and their
errors are provided in Table 6 together with the astrometric orbit of Aa,Ab.
The outer orbit with wobble is illustrated in Figure 5.

The first three micrometric measurements of A,B made by Bos in 1931–1939 are
modified here by increasing the separations by a factor of 1.2 to match the
orbit (it is well known that micrometric measurements of separations are often
burdened by large errors, while the position angles are more accurate).
Unfortunately, the pair has not been observed for half a century, until 1983.
The Hipparcos and speckle observations in the early 1990s and the SOAR data
from 2008–2021, covering the periastron, fully constrain the outer orbit. The
outer RV curve plots the systemic RV of B, a single blended measurement in
2008 attributed to Aa, and the CHIRON RVs of Aa with subtracted inner orbit.
The weighted rms residuals of SOAR speckle measurements are 0.8 mas in both
coordinates, and the fitted wobble amplitude is 11.7$\pm$0.9 mas, in agreement
with its estimate. Without the wobble, the position residuals increase to 5
mas. Secure detection of the wobble helps to constrain the Aa,Ab orbit in the
joint fit and defines its orientation on the sky. The RV amplitudes of A and B
are 4.1 and 4.7 km s-1 , respectively. However, these amplitudes are poorly
constrained, and I had to select and fix the systemic velocity of A,B to
obtain RV amplitudes that match the estimated masses (see below). The angle
between the angular momentum vectors of A,B and Aa,Ab (mutual inclination) is
45°$\pm$4°.

The $V$ magnitudes of A and B are 8.15 and 9.26 mag, respectively (the
difference of $\sim$1 mag is confirmed at SOAR), and their absolute magnitudes
(using the Hipparcos parallax) correspond to the masses of 1.07 and 0.89
$M_{\odot}$ for Aa and Ba. The minimum masses of the spectroscopic secondaries
Ab and Bb are 0.32 and 0.31 $M_{\odot}$ . The actual mass of Ab equals its
minimum mass because the orbital inclination is large, 80°. Contribution of
the spectroscopic secondaries to the optical fluxes is negligible and their
lines are not seen in the spectra. The total estimated mass of the system is
thus 2.6 $M_{\odot}$ . The outer orbit and mass sum correspond to the
dynamical parallax of 18.5 mas, in good agreement with the Hipparcos parallax
of 18.6 mas. The estimated masses result in the outer mass ratio $q_{\rm
AB}=0.87$.

This quadruple system presents a tough challenge for Gaia. The satellite did
not resolve the A,B pair, which moves fast on the outer orbit. Without prior
knowledge of the orbits, modeling the non-linear photocenter motion that
includes strong wobble signals with periods of 5 yr and 108 days will hardly
be possible even in the final Gaia data release. Blended spectra preclude the
Gaia RV measurements.

###  3.4 HIP 21079 (Triple)

Figure 6: The RV curve of HIP 21079 Aa,Ab.

This object is a nearby (45 pc) solar-type star. Its astrometric acceleration
in Hipparcos (Makarov & Kaplan, 2005) prompted high-resolution observations at
Gemini, detecting a faint companion B at 1$\farcs$62 separation with $\Delta
K=1.91$ and $\Delta H=2.14$ mag (Tokovinin et al., 2012). This pair, TOK 208,
was observed at SOAR at similar position and with $\Delta I=3.52$ mag. Its
components have separate entries in Gaia, adding $\Delta G=3.63$ mag to the
relative photometry.

The absolute magnitude of the primary star A matches its spectral type G3V and
corresponds to the mass of 0.98 $M_{\odot}$ . According to Bensby & Lind
(2018), the effective temperature of A is 5792$\pm$48K, while
[Fe/H]=$-$0.11$\pm$0.05. They detected the lithium line in the spectrum and
determined the Li abundance of 2.50. The multi-color differential photometry
of A,B is consistent with B being an 0.55 $M_{\odot}$ star. The projected
separation of A,B implies a period on the order of 500 yr, in agreement with
the slow observed motion (increasing separation at constant angle). The small
astrometric acceleration revealed by the $\Delta\mu$ could be produced by this
pair.

Nordström et al. (2004) found that the RV of HIP 21079 varies with an
amplitude of 3.8 km s-1 . The star was placed on the CHIRON program in 2015
with the aim of determining its spectroscopic orbit. The spectra show a weak
lithium line and indicate a moderate rotation of $V\sin i=5.4$ km s-1 . A
single-lined orbit of Aa,Ab with $P=217$ days is shown in Figure 6. The
residuals are 0.024 km s-1 owing to the narrow and high-contrast CCF dip. The
minimum mass of Ab is 0.16 $M_{\odot}$ , and no traces of its lines are seen
in the spectra. The semimajor axis of Aa,Ab is 16.2 mas, and the photocenter
amplitude should be 2.3 mas. This system is a planetary-type hierarchy with
two low-mass companions orbiting the central solar-type star.

###  3.5 HIP 24320 (Quadruple)

Figure 7: The RV curves of single-lined spectroscopic subsystems Aa,Ab (top)
and Ba,Bb (bottom) of the HIP 24320 quadruple.

This is a quadruple system of 2+2 hierarchy. The outer visual pair A,B has a
separation of 4$\farcs$63 and a magnitude difference $\Delta V=1.26$, $\Delta
G=1.15$ mag. It is cataloged under the name of HJ 3743, having been discovered
by J. Herschel in 1835. Stars A and B have individual astrometry in Gaia,
proving their physical relation. The estimated period of A,B is 3 kyr.

Nordström et al. (2004) indicate that the RV is variable, but do not specify
which component of the visual pair was observed. Both components were observed
with CHIRON, and both have variable RVs. Their single-lined orbits with
periods of 1430 and 7.9 days are illustrated in Figure 7. Despite the short
period, the Ba,Bb pair has a measurable eccentricity of 0.024. Adopting the
masses of 1.0 and 0.82 $M_{\odot}$ for Aa and Ba, appropriate for their
absolute magnitudes and spectral types G3V and K2V, the minimum masses of the
secondaries are 0.19 and 0.39 $M_{\odot}$ , respectively.

The astrometry of A in Gaia EDR3 is likely distorted by the 3.9 yr subsystem:
the estimated astrometric wobble amplitude is at least 7 mas. The acceleration
of A is evidenced by $\Delta\mu$ (Brandt, 2018) and by RUWE=15.0. Future Gaia
data releases are expected to contain the astrometric orbit of Aa,Ab.

###  3.6 HIP 27970 (Triple)

Figure 8: The RV curves of the inner (top) and outer (bottom) orbits in HIP
27970. Crosses correspond to the RVs from Gorynya & Tokovinin (2018), squares
— to the CHIRON RVs.

HIP 27970 (HD 39899, F7V, $V=7.73$ mag) is a spectroscopic triple in the solar
neighborhood (distance 60 pc). No visual companions are listed in the WDS and
none are found in Gaia within 2′. The Gaia EDR3 parallax of 15.78 mas is
biased by the astrometric acceleration, but nevertheless agrees, within
errors, with the Hipparcos parallax of 16.0$\pm$1.3 mas. The astrometric
acceleration was detected by Hipparcos and confirmed by Brandt (2018).

The RV variability was reported by Nordström et al. (2004). The star was
observed in 2012–2016 with the correlation radial-velocity meter by Gorynya &
Tokovinin (2018), who determined a single-lined spectroscopic orbit with
$P=15.3$ days. Residuals from this orbit suggested presence of another
companion with a longer period that would also explain the acceleration.
Additional observations with CHIRON made in 2020 and 2021 are used here to
determine the orbit of this tertiary companion with $P=1049$ days (2.9 yr).
Both orbits were fitted simultaneously using ORBIT3 (Tokovinin & Latham,
2017). The errors of the published RVs were adjusted by adding quadratically
the instrumental error of 0.3 km s-1 ; the two most deviant RVs were given
larger errors. Another strongly deviant RV from that paper corresponds to the
periastron of the outer orbit, explaining the apparent disagreement with the
initial orbit. The errors of the CHIRON RVs of 0.2 km s-1 were adopted. The
weighted rms residuals are 0.22 km s-1 . Figure 8 shows both RV curves. The
inner and outer eccentricities are 0.504 and 0.359, respectively, and the
center of mass velocity is $-11.95$ km s-1 .

I adopt the mass of 1.25 $M_{\odot}$ for the primary component Aa1, estimated
from its absolute magnitude and matching the spectral type F7V and the $V-K$
color. The orbits give minimum masses of 0.35 and 0.44 $M_{\odot}$ for Aa2 and
Ab, respectively. The semimajor axis of Aa,Ab is 40 mas.

Both orbits have substantial inclinations, otherwise the secondary stars
should be more massive and then would become detectable in the spectra and add
the flux, moving the object above the main sequence in the color-magnitude
diagram (in fact it is right on the main sequence). If the actual masses are
close to their minimum values, the astrometric semimajor axis of the outer
orbit is a 0.22 fraction of the full axis, i.e. 8.6 mas. The PM anomaly
$\Delta\mu$ measured by Brandt (2018) is $(-10.7,-6.0)$ mas yr-1, its modulus
is 12.3 mas yr-1. The outer orbit with an inclination of 90° predicts a photo-
center motion of 18.4 mas yr-1 over the Gaia DR2 time span, in qualitative
agreement with this crude estimate. The position angle of the outer node
should be around 60∘ to match the $\Delta\mu$ direction.

The RV of the center of mass and the long-term PM determined by Brandt (2018)
correspond to the Galactic velocity $(U,V,W)=(17.3,2.4,-7.4)$ km s-1 . The
object thus belongs to the disk population, typical of the solar neighborhood.
A very strong lithium line is present in the CHIRON spectra, despite the slow
rotation of $V\sin i=2.8$ km s-1 .

###  3.7 HIP 34212 (Triple)

Figure 9: RV curve of HIP 34212 Aa,Ab.

This is yet another typical solar-type triple. The outer 11″ pair A,B (TOK
114) has been identified in (Tokovinin, 2011) and confirmed as CPM by Gaia.
The EDR3 parallax of B ($V=16.9$ mag) is 16.55 mas (distance 60.4 pc), its
estimated mass is only 0.2 $M_{\odot}$ . The EDR3 parallax of A, 14.39 mas, is
biased by the subsystem Aa,Ab, which has been revealed by variable RV
(Nordström et al., 2004) and by astrometric acceleration (Makarov & Kaplan,
2005); the large RUWE of 20.7 is caused by the subsystem.

Star A was observed with CHIRON since 2015. The spectrum has single lines
slightly broadened by rotation ($V\sin i=5.3$ km s-1 ). The orbit of Aa,Ab
with $P=3.4$ yr is illustrated in Figure 9; the residuals are only 0.015 km
s-1 . Star Aa (F8V) has an estimated mass of 1.24 $M_{\odot}$ , and the
minimum mass of Ab is 0.53 $M_{\odot}$ . Lines of Ab are not detectable in the
spectra. The semimajor axis of Aa,Ab is 45 mas, the photocenter axis is 13.6
mas.

###  3.8 HIP 56282 (Quadruple)

Figure 10: RV curves of HIP 56282: top – inner orbit, bottom – intermediate
orbit. Crosses denote the less accurate RVs from Gorynya & Tokovinin (2018).
The intermediate orbit is still tentative.

This is a solar-type F8V star located at 61 pc distance. The outer 15$\farcs$9
pair A,B was identified in (Tokovinin, 2011) and confirmed as physical by the
Gaia astrometry. Star B ($V=16.23$ mag) has an estimated mass of 0.30
$M_{\odot}$ , and its EDR3 parallax of 16.28 mas defines the distance. Star A
contains a subsystem, as follows from the variable RV (Nordström et al., 2004)
and the acceleration (Makarov & Kaplan, 2005). Gaia EDR3 gives a biased
parallax of 15.13 mas with a large RUWE of 6.4. The long-term PM of A is in
excellent agreement with the PM of B, but its short-term PM measured by Gaia
is different owing to the subsystem (Brandt, 2018).

The RV of A has been monitored by Gorynya & Tokovinin (2018) since 2016 using
a correlation radial-velocity meter to determine the period of the subsystem.
The data were not sufficient for the orbit calculation, and it was suspected
that star A is triple. This hypothesis is confirmed by the additional CHIRON
data presented here. The inner period of 122 days is clearly identified,
superposed on a slow RV variation. I designate the innermost subsystem as
Aa1,Aa2 and the intermediate one as Aa,Ab. The combined RV data set does not
yet fully cover the Aa,Ab orbit, and I adopt a preliminary period of 10 yr
while fitting both orbits simultaneously using ORBIT3 (Figure 10). With a
coverage of 1841 days, substantially shorter outer periods are excluded.
Longer periods, e.g. 15–20 yr, are possible, but they require a larger RV
amplitude and a larger mass of Ab (no trace of Ab is seen in the CCF). So, the
orbit of Aa,Ab proposed here is hypothetical, but plausible.

The minimum masses of Aa2 and Ab are 0.24 and 0.25 $M_{\odot}$ , respectively,
if the mass of 1.14 $M_{\odot}$ is adopted for Aa1. The semimajor axis of
Aa,Ab is 89 mas, and the photocenter axis is 13.6 mas. The Aa,Ab orbit
predicts a $\Delta\mu$ of the same order as observed, about 5 mas yr-1 (the
orbit orientation is unknown, precluding a more detailed comparison).

The innermost orbit is almost circular, and the middle orbit also seems to
have a small or zero eccentricity. Thus, the 3+1 quadruple HIP 56282 resembles
a planetary system by its quasi-circular orbits and the low masses of all
three companions relative to the main star, making it similar to HD 91962
(Tokovinin et al., 2015a).

Star A has a strong lithium line in its spectrum, although the projected
rotation is slow, $V\sin i=3.6$ km s-1 . Armstrong et al. (2015) found a flux
modulation with an amplitude of 3.17 per cent and no apparent period in the
Kepler K2 data. Chaplin et al. (2015) also used the K2 photometry to detect
astroseismic signals from solar-type stars; none was found in HIP 56282. They
determined stellar parameters from a high-resolution spectrum: $T_{e}=6009$ K,
$V\sin i=4.7$ km s-1 , and [Fe/H] = $-$0.26.

###  3.9 HIP 57860 (Triple)

Figure 11: CCF (top) and RV curve (bottom) of HIP 57860 Aa,Ab.

The spectra of this G5V star are triple-lined. The outer pair A,B has been
known since 1897 and is designated as SEE 137. The separation is 1$\farcs$63\.
Differential speckle photometry at SOAR yields $\Delta I_{\rm AB}=0.40$,
$\Delta y_{\rm AB}=0.25$ mag, Gaia gives $\Delta G_{\rm AB}=0.25$ mag. The
period of A,B is estimated as $\sim$900 yr. Gaia measured matching parallaxes
and PMs of both components.

Observations with CHIRON lead to a double-lined orbit of Aa,Ab with $P=892$
days and a small eccentricity (Figure 11). The spectroscopic masses
$M\sin^{3}i$ of Aa and Ab are 0.66 ans 0.62 $M_{\odot}$ , the masses estimated
from the absolute magnitudes are 0.97 and 0.92 $M_{\odot}$ , suggesting an
inclination of 62°. The inner mass ratio is 0.95, the ratio of the dip areas
implies $\Delta V_{\rm Aa,Ab}=0.30$ mag.

Similar luminosities of Aa and Ab and the estimated semimajor axis of the
inner orbit, 28.7 mas, make this pair potentially resolvable by speckle.
However, seven observations at SOAR made so far only hint at marginal
resolution of the inner subsystem, while the A,B pair is measured.

The RV of the visual secondary B measured from the triple-lined spectra is
36.01 km s-1 with the rms scatter of 0.07 km s-1 . The estimated mass of B is
1.04 $M_{\odot}$ , so all three stars in this system are similar. Their lines
are narrow, indicating slow axial rotation.

###  3.10 HD 108938 (Triple)

Figure 12: CCF (top) and RV curve (bottom) of HD 108938.

This system is an analogue of the previous one, i.e. a classical visual binary
with a triple-lined spectrum. The outer 1$\farcs$23 pair A,B has been known
since 1934 and is designated as RST 2802. The magnitude differences are
$\Delta I_{\rm AB}=1.92$ mag (SOAR) and $\Delta G_{\rm AB}=1.58$ mag (Gaia),
and the estimated period of A,B is 1.4 kyr. Gaia EDR3 gives a biased parallax
of 5.82 mas for A (RUWE=7.1), so the parallax of B, 6.35 mas, is adopted.

The orbit of the subsystem Aa,Ab with $P=343$ days is illustrated in Figure
12. The mass ratio is 0.82 and the magnitude difference estimated from the
ratio of the dip areas is $\Delta V_{\rm Aa,Ab}=2.2$ mag. The estimated
semimajor axis of Aa,Ab is only 8.4 mas, making resolution of the subsystem by
speckle an unlikely prospect. However, its astrometric orbit is expected in
the future Gaia releases. Comparison of $M\sin^{3}i$ with the estimated masses
of Aa and Ab (1.43 and 1.16 $M_{\odot}$ ) leads to an inclination of 53°.
Stars Aa, Ab, and B are less similar between themselves in comparison to HIP
57860, but also rotate slowly and do not have detectable lithium lines in
their spectra. The estimated masses are larger than expected for the spectral
type, so the primary might be leaving the main sequence.

###  3.11 HIP 76400 (Quadruple)

Figure 13: CCF (top) and RV curve (middle) of HIP 76400 Aa1,Aa2 with the trend
subtracted. The lower plot shows the RV curve in the 70-yr visual orbit of
Aa,Ab.

This is a quadruple system of 3+1 hierarchy. A faint ($V=17.82$ mag) CPM
companion B at 80$\farcs$4 separation was discovered from the ground-based
data and confirmed by Gaia. The estimated period of this pair is $\sim$230
kyr. Astrometric acceleration of the main star (Makarov & Kaplan, 2005)
prompted its high-resolution observations at SOAR in 2014, revealing another
companion Ab at 0$\farcs$19 separation with $\Delta I_{\rm Aa,Ab}=3.84$ mag.
This companion has been independently found in 2011 by Horch et al. (2017). A
preliminary visual orbit of this pair with $P=70$ yr and a 0$\farcs$34 axis
based on the 140° arc observed in 2011–2021 was determined by the author.
Motion of the photocenter predicted by this orbit in 1991.25 and 2015.5
matches the actual $\Delta\mu$, strengthening the orbit and suggesting a mass
ratio of 0.25. The masses of B and Ab estimated from their absolute magnitudes
are 0.17 and 0.61 $M_{\odot}$ respectively.

Nordström et al. (2004) noted that this star had double lines. Monitoring with
CHIRON leads to the orbit of the inner pair Aa1,Aa2 with a period of one year
shown in Figure 13. The mass ratio of Aa1,Aa2 equals one within error, the CCF
dips have the same width and contrast, so this is a perfect twin. No
astrometric wobble is expected, therefore the Gaia EDR3 parallax can be
trusted (indeed, it equals the parallax of B within errors). Masses of Aa1 and
Aa2 estimated from the absolute magnitudes are 1.03 $M_{\odot}$ , the
spectroscopic masses are 0.96 $M_{\odot}$ , hence the inner orbital
inclination is $\sim$77° or $\sim$103°. To account for the small RV trend
caused by motion in the visual orbit, I fitted it jointly with the inner orbit
using ORBIT3. As the observed arc does not yet constrain the period, I fixed
it to 70 yr to match the EDR3 parallax and the estimated mass sum, 2.67
$M_{\odot}$ . The outer RV amplitude of 1.4 km s-1 reproduces the observed
trend of the systemic velocity of Aa1,Aa2, as shown in the lower panel of
Figure 13. The elements of this tentative Aa,Ab orbit are given in table 6;
the inclination of 144° indicates that the two orbits are not coplanar.

###  3.12 HIP 76816 (Quadruple)

Figure 14: RV curve of HIP 76816 Ba,Bb.

This quadruple system has been presented in Paper 4 of this series (Tokovinin,
2018b), where the double-lined orbit of Aa,Ab with $P=6.95$ days has been
determined. The outer pair A,B (ADS 9743) has a separation of 5$\farcs$5\.
Gaia EDR3 gives concordant parallaxes and PMs of A and B, placing the system
at a distance of 308 pc; the estimated period of A,B is 32 kyr. Both A and B
are evolved, well above the main sequence.

Early CHIRON observations gave a strong evidence that the RV of star B is
variable. Continued monitoring of this component leads to its orbit with
$P=208.9$ days presented in Figure 14. One RV from Desidera et al. (2006) is
used to increase the period accuracy. The residuals are very small, 0.016 km
s-1 . The estimated mass of Ba is 1.67 $M_{\odot}$ , and the minimum mass of
Bb is then 0.68 $M_{\odot}$ . For reference, the masses of Aa and Ab are 1.72
and 1.27 $M_{\odot}$ , respectively. The semimajor axes of the inner
subsystems are 0.3 and 2.6 mas, none has been resolved by speckle
interferometry at SOAR, and only B gives a marginal evidence of increased
astrometric noise in Gaia (RUWE of A and B are 1.1 and 1.6, respectively).

###  3.13 HIP 81394+81395 (Triple)

Figure 15: CCF (top) and RV curve (bottom) of HIP 81395 Ba,Bb, the visual
companion of HIP 81394.

The outer 10$\farcs$9 pair of this triple system, HJ 4862, has been first
measured by J. Herschel in 1835. Its components have matching parallaxes and
PMs in Gaia EDR3, without astrometric acceleration or increased astrometric
noise (RUWE of 1.3 and 1.6). The small $\Delta\mu$ of these stars computed by
Brandt (2018) are marginally significant, but one has to bear in mind that the
Hipparcos astrometry of such visual binaries has systematic errors caused by
the satellite’s measuring system design.

Double lines in star B were noted by Desidera et al. (2006), prompting its
monitoring with CHIRON since 2017. The orbit of Ba,Bb with $P=225$ days is
presented in Figure 15. The CCF dips are broad and of low contrast, while the
RV amplitudes are small. Reliable fitting of the double dips is possible only
near the periastron; in other orbital phases, the RVs derived from the blended
dips are uncertain, and they were given low weights in the orbit fit, which
also uses the RVs from Desidera et al.

The small RV amplitudes of Ba and Bb are explained by the low inclination of
$\sim$25°, estimated by comparing the expected mass of Ba, 1.35 $M_{\odot}$ ,
with $M_{1}\sin^{3}i=0.11$ $M_{\odot}$ . The semimajor axis of Ba,Bb is 5 mas.
This star was observed by speckle interferometry at SOAR and found unresolved.
Stars A and B are evolved (above the main sequence), and A is slightly redder
than B.

###  3.14 HIP 98294 + 98278 (Triple)

Figure 16: CCF (top) and RV curve (bottom) of HIP 98278 Ba,Bb, the visual
companion of HIP 98294. Crosses denote inaccurate RVs deduced from blended
dips.

The A9IV star HIP 98294 and the F6V star HIP 98278, at 80$\farcs$6 from each
other, have common PMs and parallaxes and form a physical pair DUN 229 with an
estimated period of $\sim$400 kyr.

Nordström et al. (2004) noted that star B has double lines. The CCFs of CHIRON
spectra (Figure 16) have shallow, broad, and partially blended dips that are
more or less separated only around periastron. The RVs of blended dips were
determined by fixing the amplitude of the wide dip belonging to Ba and are
given a lower weight in the orbit fit. The residuals are unusually large, as
can be appreciated in the RV curve.

The ratio of the dip areas gives a crude estimate of the magnitude difference
$\Delta V_{\rm Ba,Bb}\approx 0.8$ mag, hence the individual magnitudes are 8.6
and 9.4, and the masses are 1.25 and 1.08 $M_{\odot}$ (ratio 0.86). The
spectroscopic masses $M\sin^{3}i$ are only slightly less, so the inclination
is high, $i_{\rm Ba,Bb}\approx 76^{\circ}$; the spectroscopically measured
mass ratio is 0.97. The semimajor axis of Ba,Bb is 10.5 mas. A small
$\Delta\mu$ of star B, 0.67 mas yr-1 (Brandt, 2018), is presumably caused by
the wobble of the photocenter.

The double-lined pair B is located above the main sequence, as expected, while
A is not elevated (unevolved), despite its spectral type A9IV. Lithium lines
are detectable in the spectrum of B, confirming relative youth of this system.
Assuming that A and B are single stars, Bochanski et al. (2018) estimated an
age of $\sim$1 Gyr and masses of 1.49 and 1.27 $M_{\odot}$ for both components
by fitting models to the multi-color photometry. Typically, researchers
interested in wide binaries tend to ignore the fact that many of them contain
inner subsystems.

###  3.15 HIP 100420 (Triple)

Figure 17: CCF (top) and RV curve (bottom) of HIP 100420.

This is a typical triple system, where double lines were found by Nordström et
al. (2004) in a visual binary HJ 5189. Its components A and B are separated by
7$\farcs$518 and have a magnitude difference of $\Delta G_{\rm A,B}=0.93$ mag.
The period of A,B is $\sim$25 kyr. The Gaia astrometry yields common PMs and
parallaxes of the components.

Observations of component A with CHIRON confirm is double-lined nature and
lead to the orbit with $P=790.6$ days presented in Figure 17. The mass ratio
of the inner pair Aa,Ab is 0.84, and the magnitude difference between Aa and
Ab deduced from the dip areas is 1.3 mag. The mass of Aa estimated from the
absolute magnitude is 1.53 $M_{\odot}$ , larger than expected for an F6V star,
and this component is slightly evolved (above the main sequence). The
spectroscopic masses of Aa and Ab, $M\sin^{3}i$, are 1.20 and 1.00 $M_{\odot}$
, and the estimated inclination is $i_{\rm Aa,Ab}=67\arcdeg$.

The astrometric acceleration of A detected by Brandt (2018) is likely caused
by the 2-yr spectroscopic subsystem. Its semimajor axis is about 13 mas. The
center of mass RV of A, 49.1 km s-1 , matches the RV of B, measured from three
CHIRON spectra and also by Gaia. It is thus unlikely that star B hosts a
subsystem.

##  4 Discussion

Figure 18: Periods and eccentricities of inner subsystems with solar-type
components in the MSC (crosses). The orbits determined here are plotted by
large red triangles.

Figure 18 contains a period-eccentricity plot for inner subsystems in
hierarchies, updating a similar plot from paper 6. One can appreciate how the
accumulation of CHIRON data during several years results in orbits with
periods longer than 100 days. The time span needed to compute such orbits must
exceed their periods, sometimes substantially. Annual visibility cycles can
restrict coverage of certain orbital phases. This is particularly important
for the eccentric orbits: a missed periastron must be re-observed in the next
cycle(s). The closure of CHIRON in 2020 due to the COVD-19 pandemic also had a
negative impact on this program (note the missing coverage of the periastron
of a 5-yr orbit in the lower panel of Figure 4). Several preliminary orbits
with long periods determined with CHIRON still await additional coverage
before becoming publishable (e.g. HIP 41171B, 967 days; HIP 75663A, 623 days;
HIP 78163B, 2082 days). The next (and last) paper of this series will present
the long-period orbits and the RVs of stars where orbit determination was not
possible.

The goal of this program is to obtain a complete orbital statistics for
subsystems with periods below 1000 days in nearby solar-type hierarchies. The
difficulty of computing such orbits means that many still remain unknown,
especially those with large eccentricities. Two orbits presented here occupy
the upper envelope of the $P-e$ relation in Figure 18, namely HIP 27970
Aa1,Aa2 ($P=15$ days, $e=0.51$) and HIP 12548 Ba,Bb ($P=108$ days, $e=0.82$).
Both subsystems have small mass ratios and outer companions on relatively
compact orbits. The origin of binary eccentricities is still debated, there
are no models of their distribution. Hopefully, the unbiased statistics
delivered by this program will help to develop such models. The diverse
architecture of stellar hierarchies and its relation to their formation are
discussed further in Tokovinin (2021).

The Gaia mission provides a wealth of information on stars, including
multiples. This work highlights the caveats of the Gaia astrometry related to
multiplicity, namely the missing or biased data. In many cases the future Gaia
data releases will rectify this by including orbital motion in the astrometric
model. However, the presence of additional nearby companions and motion on
several orbits will still present problems. Meanwhile, an elevated RUWE
remains a useful diagnostic of potentially problematic Gaia astrometry, as
demonstrated here.

I thank operators of the 1.5-m telescope for executing observations of this
program and the SMARTS team for scheduling and pipeline processing and the
referee, K. Fuhrmann, for careful check of the manuscript. 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 paper includes data collected by
the TESS mission funded by the NASA Explorer Program. 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,
TESS

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