Spectroscopic Orbits for Three SB2s and One Hierarchical Triple Using SALT Data

Abstract

We confirmed four spectroscopic binary candidates using new observations obtained with SALT. Three SB2 systems (HD 20784, HD 43519A, HD 62153A) exhibit circular orbits with periods shorter than 10 days, whereas one hierarchical triple system (HD 56024) contains a close binary with an inner eccentric orbit with a period of approximately 14 days, composed of nearly identical stellar components, and a rapidly rotating star on an outer eccentric orbit with a period of approximately 400 days. For two additional SB2 candidates (HD 198174 and HD 208433), our new observations do not allow us to derive reliable orbital solutions.

1. Introduction

Binary and higher-order multiple stellar systems are important astrophysical objects, as approximately half of all stars in the Milky Way are not single [1]. The investigation of their orbital properties (e.g., period, eccentricity) and fundamental stellar parameters (e.g., masses, radii, effective temperatures) is essential for the development and calibration of binary population synthesis models, which in turn are required for a robust understanding of star formation processes and the subsequent evolution of binary systems [2]. If orbital orientation allow us to see periodic changes in the radial velocities derived from spectroscopic observations of the stellar system, they are called spectroscopic binaries (SBs). SBs are divided between single-lined (SB1), double-lined (SB2), triple-lined (SB3), and n-lined SBn depending on number n of the visible spectroscopic components. SB2 systems are of particular significance because they permit model-independent determinations of stellar masses, provided that the orbital inclination is constrained through complementary photometric or astrometric observations [3]. SB3 systems predominantly form hierarchical configurations, in which a single star orbits an inner close binary [4,5]. Their dynamical stability, as well as the formation mechanisms, constitute key subjects of current investigation [6,7].

Recently, ref. [8] observed 166 B-type stars with the FEROS spectrograph [9], selected by variability in TESS [10] photometry, and identified 26 SB2 candidates. For one of them, HD 20784, circular orbit was found in [11]; however, it was based only on three spectra with poor phase coverage, so it needs to be verified by additional observations. In this paper we report results for analysis of follow-up observations for 6 of these SB2 candidates, see

Table 1. Observed sample information extracted from Gaia DR3 [12] (right ascension, declination, Gaiaapparent magnitude, parallax, rectilinear unit weighted error) and SIMBAD (spectral type). N is a number of SALT observations.

Star	$\mathit{\alpha }°$ (ICRS)	$\mathit{\delta }°$ (ICRS)	G, mag	$\mathit{\pi }$, mas	RUWE	ST	N
HD 20784	49.60306	−55.82256	8.2720 ± 0.0028	1.407 ± 0.023	0.924	B9.5V	9
HD 43519A	93.13418	−61.47399	7.1102 ± 0.0031	4.015 ± 0.066	1.505	B9.5V	8
HD 56024	107.95909	−58.85062	8.7035 ± 0.0028	2.044 ± 0.056	2.594	B9V	11
HD 62153A	113.84019	−74.27486	7.0581 ± 0.0028	3.943 ± 0.029	1.049	B9IV	5
HD 198174	312.32344	−25.78134	5.8341 ± 0.0028	6.666 ± 0.187	2.721	B8II	6
HD 208433	329.23152	−35.35984	7.5530 ± 0.0028	3.581 ± 0.074	1.328	B9.5V	13

with brief information. None of the systems exhibit eclipses in their light curves, with only HD 20784 displaying ellipsoidal variability [11]. We confirmed that HD 20784 follows a circular orbit, derived detailed orbital solutions for two additional SB2s, HD 49519A and HD 62153A (also known as CD-73 375A), and identified a new hierarchical system, HD 56024. For the remaining two systems, HD 198174 and HD 208433, our new observations are insufficient to derive robust orbital solutions; therefore, they must still be classified as SB2 candidates.

2. Materials and Methods

2.1. Observations

We conducted spectroscopic observations with the Southern African Large Telescope [SALT] [13,14] High Resolution échelle Spectrograph [HRS] [15,16,17,18]. Several spectra (from 5 to 13) were taken for each target using the low resolution mode ($R=\lambda /\Delta \lambda \sim$14,000) in 2023, 2024. The SALT HRS has two arms: blue 3700–5500 Å and red 5500–8900 Å. Since our targets are hot stars, with most of the spectral lines having $\lambda <5500$ Å, we used only the blue arm. The primary reduction of HRS data was produced automatically using the standard pipeline processing described in Crawford et al. [19]. The reduction of spectroscopic data for HRS was performed using the standard data processing system, detailed in Kniazev et al. [20,21]. Since HRS is a thermally stabilized instrument, all standard calibrations are performed weekly, which is sufficient to achieve a radial-velocity precision of 0.2–0.5 $\mathrm{km}{\mathrm{s}}^{-1}$ depending on the observational mode.

2.2. Methods

We use the same code, which was developed and tested to fit the FEROS spectra of HD 20784 [11] to analyze the new SALT spectra. It assumes SB2 configuration and extracts radial velocities $\mathrm{RV}$, effective temperatures $T_{\mathrm{eff}}$, metallicities [Fe/H], microturbulences $V_{\mathrm{mic}}$, and projected rotational velocities $(Vsini)$ for two spectral components, performing full spectrum fitting using a neural network based spectral model. The metallicity was fixed to the same value for two components. This spectral model was trained on a synthetic model grid, generated with the GSSP code [22]. Normalization is done simultaneously with fitting; see [8] for details.

All RV measurements are collected in

Table A1. Radial velocity measurements. Statistical uncertainties are nominal, see text for details.

MJD, Day	${\mathbf{RV}}_2,\mathbf{km}{\mathbf{s}}^{-1}$	${\mathbf{RV}}_1,\mathbf{km}{\mathbf{s}}^{-1}$	${\mathbf{RV}}_3,\mathbf{km}{\mathbf{s}}^{-1}$
HD 20784
60,257.047	−54.16 ± 0.11	5.87 ± 0.06
60,257.073	−51.39 ± 0.13	2.92 ± 0.07
60,258.081	49.49 ± 0.13	−84.92 ± 0.07
60,260.812	−29.87 ± 0.12	−13.64 ± 0.08
60,261.806	51.35 ± 0.15	−85.87 ± 0.08
60,263.031	−63.25 ± 0.08	16.23 ± 0.05
60,264.793	18.86 ± 0.11	−55.85 ± 0.07
60,264.834	22.82 ± 0.09	−59.93 ± 0.06
60,266.018	10.81 ± 0.10	−46.94 ± 0.06
HD 43519 A
60,249.951	31.23 ± 0.05	26.22 ± 0.08
60,256.973	97.35 ± 0.06	−30.34 ± 0.06
60,261.949	0.50 ± 0.08	52.62 ± 0.07
60,262.966	72.89 ± 0.06	−24.22 ± 0.08
60,265.975	55.39 ± 0.03	13.24 ± 0.05
60,267.928	−60.35 ± 0.54	85.84 ± 0.42
60,427.736	114.36 ± 0.24	−39.39 ± 0.20
60,428.714	108.55 ± 0.04	−13.14 ± 0.07
HD 56024
60,250.001	63.65 ± 0.10	−61.28 ± 0.10	16.81 ± 0.42
60,258.011	−25.46 ± 0.11	33.41 ± 0.11	14.77 ± 0.42
60,259.005	−12.12 ± 0.08	18.66 ± 0.09	15.93 ± 0.31
60,271.941	−33.22 ± 0.09	33.96 ± 0.09	15.64 ± 0.35
60,272.989	−20.47 ± 0.14	20.73 ± 0.14	14.54 ± 0.55
60,427.773	−45.75 ± 0.16	48.76 ± 0.17	16.35 ± 0.60
60,429.762	−32.91 ± 0.13	37.03 ± 0.13	16.25 ± 0.54
60,446.692	10.06 ± 0.11	17.77 ± 0.11	5.73 ± 0.32
60,449.695	75.69 ± 0.12	−48.03 ± 0.12	7.79 ± 0.44
60,566.130	88.42 ± 0.10	−43.82 ± 0.10	2.42 ± 0.33
60,571.125	−21.88 ± 0.10	73.11 ± 0.10	−0.14 ± 0.38
HD 62153 A
60,348.882	32.13 ± 0.08	6.95 ± 0.02
60,350.813	−17.24 ± 0.07	36.79 ± 0.02
60,351.819	37.58 ± 0.04	2.61 ± 0.02
60,352.814	57.87 ± 0.05	−10.94 ± 0.06
60,353.881	2.68 ± 0.06	23.97 ± 0.06

and

Table A2. Radial velocity measurements for HD 198174 and HD 208433. Statistical uncertainties are nominal, see text for details.

MJD, Day	${\mathbf{RV}}_{\mathbf{single}},\mathbf{km}{\mathbf{s}}^{-1}$	${\mathbf{RV}}_2,\mathbf{km}{\mathbf{s}}^{-1}$	${\mathbf{RV}}_1,\mathbf{km}{\mathbf{s}}^{-1}$
HD 198174
60,257.807	−7.45 ± 0.10	−4.24 ± 0.10	−14.52 ± 0.08
60,258.795	−7.36 ± 0.08	0.17 ± 0.08	−16.98 ± 0.07
60,259.787	−9.12 ± 0.08	−1.95 ± 0.07	−16.86 ± 0.06
60,261.783	−8.44 ± 0.08	−6.22 ± 0.07	−14.23 ± 0.10
60,262.783	−7.09 ± 0.10	3.57 ± 0.10	−16.99 ± 0.07
60,419.108	−17.25 ± 0.16	−41.04 ± 0.16	−1.08 ± 0.13
HD 208433
60,424.152		−9.62 ± 0.13	−6.79 ± 0.06
60,425.130		−9.69 ± 0.13	0.38 ± 0.06
60,429.121		−9.89 ± 0.09	−0.80 ± 0.05
60,430.113		−9.70 ± 0.12	−4.58 ± 0.06
60,447.085		−10.00 ± 0.06	−0.38 ± 0.03
60,448.068		−10.14 ± 0.07	−2.32 ± 0.04
60,449.070		−10.12 ± 0.08	−0.49 ± 0.04
60,452.050		−9.77 ± 0.09	−3.84 ± 0.05
60,458.039		−9.83 ± 0.10	−4.49 ± 0.05
60,476.996		−10.03 ± 0.09	−0.87 ± 0.05
60,563.754		−10.00 ± 0.11	−2.12 ± 0.05
60,564.773		−10.00 ± 0.12	−0.71 ± 0.07
60,565.768		−9.90 ± 0.09	−5.44 ± 0.05

. Usually RV of brighter component in SB2 are measured with higher precision; however, in our case there are three systems where it rotates significantly faster than the dim component, thus its spectral lines are significantly broadened. For such a system, narrow lines of the secondary will allow for more precise RV measurements. Since statistical uncertainties for our RVs are around $\le 0.2\mathrm{km}{\mathrm{s}}^{-1}$, we artificially increased them by $0.5\mathrm{km}{\mathrm{s}}^{-1}$ for stars with $(Vsini)<100\mathrm{km}{\mathrm{s}}^{-1}$ and by $2.5\mathrm{km}{\mathrm{s}}^{-1}$ otherwise; see Section 3.6. We use radial velocities of the component with better precision with the Generalized Lomb Scargle (GLS) code [23] to fit the circular and Keplerian orbits. We find that for all SB2 systems, except HD 56024, eccentricity of the Keplerian orbit is zero; so the circular orbit is a valid approximation. Therefore, we used output of GLS to fit both RV time series simultaneously using the scipy.optimise.curve_fit function. Orbital parameters include systemic velocity $\gamma$, period P, conjunction time $t_0$, and radial velocity semi-amplitudes for both components $K_{1,2}$. For two systems: HD 198174 and HD 208433 we didn’t find any reasonable orbital solution.

SB3 Analysis

For HD 56024 we were unable to get a good SB2 orbit, therefore we explored its spectra in detail. We found that it is actually a SB3 system consisting of a bright (>90% of total light) fast rotating star and two dim slow rotators. Since narrow lined components look nearly identical, we set their parameters to be same, with the exception of $\mathrm{RV}$. It allows us to simplify the problem and save computational time. With these assumptions in mind, we fit all spectra and derived radial velocities and parameters for spectral components.

Based on radial velocities we conclude that HD 56024 is a hierarchical triple (1 + 2): a bright star orbiting an inner, close binary. Preliminary outer orbit can be derived based only on ${\mathrm{RV}}_3$ assuming it is SB1 with GLS. Since we assumed components in the inner binary to be identical, we need to sort them out before fitting the orbit. We made it using a fit of the circular orbit for the absolute difference $|{\mathrm{RV}}_1-{\mathrm{RV}}_2|$ with GLS, see [24] for details. Once sorting is finished, we fitted all available $\mathrm{RV}$ together, in a hierarchical triple configuration model, constructed using the Keplerian orbit provided in PyAstronomy1 package [25], using the scipy.optimise.curve_fit function.

3. Results

We collect all spectroscopic parameters in

Table 2. Spectroscopic parameters. Here we provide mean and standard deviation among all spectra for each system.

System	HD 20784	HD 43519A	HD 56024 *	HD 62153A
$T_{\mathrm{eff}}$, K	9479 ± 135	10,756 ± 563	11,867 ± 75	11,376 ± 261
	10,364 ± 80	10,067 ± 155	7308 ± 166	10,771 ± 551
$log\left(\mathrm{g}\right)$, cgs	3.51 ± 0.14	3.88 ± 0.16	3.77 ± 0.02	3.84 ± 0.27
	3.77 ± 0.10	4.35 ± 0.14	3.62 ± 0.31	4.27 ± 0.68
$[\mathrm{Fe}/\mathrm{H}]$ **, dex	0.01 ± 0.01	−0.10 ± 0.05	−0.21 ± 0.24	0.24 ± 0.07
$V_{\mathrm{mic}},\mathrm{km}{\mathrm{s}}^{-1}$	1.3 ± 0.2	1.6 ± 0.7	2.2 ± 1.9	0.3 ± 0.2
	0.9 ± 0.2	0.06 ± 0.09	2.8 ± 0.6	1.4 ± 1.9
$(Vsini),\mathrm{km}{\mathrm{s}}^{-1}$	30 ± 4	120 ± 6	248 ± 7	17 ± 6 ***
	17 ± 2	14 ± 7	11 ± 2	13 ± 7

(*) First row represents parameters of third component -brightest one in the triple system, second row represents identical parameters for dim components of triple system. (**) fixed to same value for all components. (***) we excluded one measurement $(Vsini)=96\mathrm{km}{\mathrm{s}}^{-1}$ taken near conjunction from the mean computation.

and

Table 3. Spectroscopic parameters for HD 198174 and HD 208433. Here we provide mean and standard deviation among all spectra for each system.

System	HD 198174	HD 208433
$T_{\mathrm{eff}}$, K	13,453 ± 746	10,967 ± 37
	9686 ± 1213	8013 ± 38
$log\left(\mathrm{g}\right)$, cgs	3.00 ± 0.01	4.19 ± 0.01
	3.27 ± 0.38	4.25 ± 0.08
$[\mathrm{Fe}/\mathrm{H}]$ *, dex	−0.32 ± 0.03	−0.01 ± 0.01
$V_{\mathrm{mic}},\mathrm{km}{\mathrm{s}}^{-1}$	0.15 ± 0.31	1.00 ± 0.01
	0.0 ± 0.1	1.31 ± 0.27
$(Vsini),\mathrm{km}{\mathrm{s}}^{-1}$	50 ± 8	168 ± 1
	44 ± 3	27 ± 1

(*) fixed to same value for all components.

and orbital solutions listed in

Table 4. Circular orbits.

System	HD 20784	HD 43519A	HD 62153A
P, days	3.58221 (fixed)	8.188 ± 0.001	4.545 ± 0.011
$t_0$, days 1	60,259.094 ± 0.001	60,258.198 ± 0.004	60,353.693 ± 0.007
$\gamma ,\mathrm{km}{\mathrm{s}}^{-1}$	−21.55 ± 0.10	26.11 ± 0.26	15.80 ± 0.18
$K_2,\mathrm{km}{\mathrm{s}}^{-1}$	74.09 ± 0.24	91.85 ± 0.45	44.84 ± 0.43
$q=K_1/K_2=M_2/M_1$	0.856 ± 0.004	0.696 ± 0.016	0.605 ± 0.011

¹ MJD.

and

Table 5. Orbital parameters for HD 56024.

Parameter	HD 56024 Inner Orbit	HD 56024 Outer Orbit
P, days	14.3834 ± 0.0002	403.73 ± 3.84
$t_p$, days 1	60,264.375 ± 0.008	58,854.273 ± 16.480
e	0.194 ± 0.001	0.338 ± 0.004
${\displaystyle \omega °}$	31.38 ± 0.19	305.4 ± 1.6
$\gamma ,\mathrm{km}{\mathrm{s}}^{-1}$	–	9.93 ± 0.06
$K_i,\mathrm{km}{\mathrm{s}}^{-1}$	57.65 ± 0.06, 58.60 ± 0.12	18.47 ± 0.12 2, 20.76 ± 0.41

¹ MJD, ² for barycenter of inner binary.

. Below we present a short summary for each individual system.

3.1. HD 20784

This is a SB2 system with relatively narrow spectral lines. We show a circular orbit fit for it in Figure 1. Fundamental parameters for HD 20784 were estimated for the first time in [11] using TESS [26,27] photometry and RV from FEROS spectra, however all these spectra were taken near the conjunction, so these RVs were not used during the detailed modelling with PHOEBE [28]. In this work we are confirming the circular orbit for this SB2 and improve estimation of projected semi-major axis $asini=9.735\pm 0.038R_{\odot }$ (previous estimate $asini={9.7}_{-3.2}^{+3.6}{R}_{\odot }$), thanks to our orbital solution. We note that we used only new SALT based RV data to get this solution, which has a significantly smaller timebase than TESS photometry, thus we fixed period to the value $P=3.58221$ days from [11]. For verification, we also plotted previous RV measurements from FEROS, and they agree very well with the new orbit. The new value of mass ratio is slightly smaller than previous estimate.

HD 20784 has radial velocity measurement in RAVE DR6 [29]: $\mathrm{RV}=86.92\pm 33.76\mathrm{km}{\mathrm{s}}^{-1}$, which is not compatible with our orbital solution. Possibly, this is because the Ca triplet is poorly visible in the spectrum of the hot stars. This system is also absent in RAVE based SB1 and SB2 catalogs [30,31].

3.2. HD 43519A

We show the circular orbit for this system in Figure 2. More precise RV of the secondary were fitted very well, while the primary RV shows some deviation because ${(Vsini)}_1\sim 120\mathrm{km}{\mathrm{s}}^{-1}$ of the primary is quite large. Primary is also hotter and heavier than secondary.

APOGEE DR17 [32] is observed nearby to (∼1″) the star HD 43519B2 at MJD = 58,912.078 days and provided these parameters: $\mathrm{RV}=27.70\pm 0.47\mathrm{km}{\mathrm{s}}^{-1}$, $T_{\mathrm{eff}}=9678$ K, $log\left(\mathrm{g}\right)=4.33$ cgs, $[\mathrm{Fe}/\mathrm{H}]=-1.68$ dex. Its radial velocity is very similar to the systemic velocity of the SB2 solution $\gamma =26.22\pm 0.47\mathrm{km}{\mathrm{s}}^{-1}$, so this nearby star can be bound to our SB2, forming a wide hierarchical triple. Gaia DR3 astrometry also supports this idea, see [33] where authors provide chance-alignment probability of only ∼${10}^{-4}$ and estimated projected separation as $a\sim 271$ a.u. with an eccentricity $e={0.90}_{0.66}^{1.00}$3 for this wide system.

3.3. HD 56024

This is a hierarchical triple system, which is clearly resolved in SALT spectra, see Figure 3 panel (a). The brightest component is a hot, fast rotating star, while the two others are significantly cooler and rotate much slower. We found that the inner binary have an eccentric orbit with period $P_{\mathrm{in}}\sim 14.3$ days, while outer orbital period $P_{\mathrm{out}}\sim 403.7$ days, which is ∼$28$ times larger, see panel (b). Currently SALT observations have relatively small phase coverage for the outer orbit. To check our orbital solutions for HD 56024, we fed its spectra with orbital solution to spectral disentangling code FD3 [34], which can handle hierarchical triple configuration. We provided identical light factors $LF=1$ for all components, therefore disentangled spectra will the have same baseline 0.33 [35]. All three spectral components were separated and they are consistent with previous results from spectral fitting. FD3 works in Fourier space, so derived spectral components are shifted relative to their baselines with sine-like modulations [34], which we tried to remove by fitting the high-order Chebyshev polynomial, to make comparison with panel (a) easier, see panel (c) in Figure 3. Also, no further optimisation of orbital parameters was required4, which proves that our solution is reliable. Based on radial velocity semi-amplitudes for the outer orbit, the close twin binary is slightly more massive than the hot, fast rotating primary $q_{\mathrm{out}}=M_{1-2}/M_3\equiv K_3/K_{1-2}=1.12\pm 0.02$, while the mass ratio in the inner close system is near unity $q_{\mathrm{in}}=M_2/M_1\equiv K_1/K_2=0.98\pm 0.02$. Kepler’s third law allow us to estimate minimal masses: $(M_1+M_2)sin{i_{1-2}}^3\sim 2.2M_{\odot }$ and $(M_1+M_2+M_3)sin{i_3}^3\sim 2.1M_{\odot }$ using the inner and outer orbit’s parameters respectively. Obviously, the outer orbit has significantly smaller inclination ($i_3<i_{1-2}$) to the sky-plane, than the inner one.

APOGEE DR17 [32] observed this star twice: on MJD = 58,503.293, 58,831.359 days and provided the following parameters assuming a single star: $\mathrm{RV}=17.91\pm 0.17, -10.64\pm 0.44\mathrm{km}{\mathrm{s}}^{-1}$, $T_{\mathrm{eff}}=7663,10856$ K, $log\left(\mathrm{g}\right)=4.25,4.11$ cgs, $[\mathrm{Fe}/\mathrm{H}]=-2.21,-1.07$ dex. It is highly likely their pipeline completely removed bright, fast rotator features during the normalisation of the first spectrum (see [36], where a similar problem was described), so they get parameters for one of the cool components. Note that the first spectrum indicates an extremely metal-poor star, since relative contribution of the cool components is small; while in the second spectrum derived parameters corresponds to a bright, hot primary.

3.4. HD 62153A

The orbital solution for this system is presented in Figure 4. Both components exhibit relatively narrow spectral lines. The primary star is hotter and more massive than the secondary.

The derived orbital period, $P=4.545\pm 0.011$ d, is in good agreement with the rotational period, $P_{\mathrm{rot}}={\nu }_{\mathrm{rot}}^{-1}=1/0.216367=4.622$ d, measured by [37], who inferred the presence of photospheric spots on one or both stars in this system. The system was first identified as SB2 by [38], who determined a mass ratio of $q=0.58\pm 0.02$, in good agreement with our estimate of $q=0.605\pm 0.011$.

3.5. HD 198174

HD 198174 is the sole bright giant (its SIMBAD spectral type is B9 II) in our sample, and it is the only object that appears in the Gaia Non-Single Star catalogue [3] with a SB1 orbital solution5. Unfortunately, our $\mathrm{RV}$ measurements are inconsistent with this orbital solution for both components (see Figure 5); however we should mention that HD 198174 is the only system where none of the spectra were showing clear composite structure. Therefore, we also included single-star model $\mathrm{RV}$ measurements in the Figure 5. We have only one good match with SB1 orbit, although it looks like accidental agreement. The Renormalised Unit Weight Error (RUWE) for this system is relatively high, with a value of 2.72. This suggests that the source is unlikely to be a single star. Consequently, forthcoming Gaia data releases may yield an improved orbital solution for this object.

3.6. HD 208433

Although we obtained 13 radial-velocity measurements for this system, we did not detect any statistically significant temporal variability that would support its classification as SB2; see Figure 6. The narrow-lined ($(Vsini)=28\mathrm{km}{\mathrm{s}}^{-1}$) spectral component exhibits an approximately constant radial velocity of ${\mathrm{RV}}_2=-9.90\pm 0.16\mathrm{km}{\mathrm{s}}^{-1}$, whereas the bright, rapidly rotating component ($(Vsini)=168\mathrm{km}{\mathrm{s}}^{-1}$) shows only marginal variations in radial velocity, with ${\mathrm{RV}}_1=-2.5\pm 2.5\mathrm{km}{\mathrm{s}}^{-1}$. A GLS periodogram analysis did not reveal any statistically significant periodic signal in ${\mathrm{RV}}_1$, and we therefore interpret the observed variations as arising from random measurement errors. Consequently, we propose that HD 208433 is a chance alignment of two unrelated stars, a scenario further supported by the relatively low RUWE value of 1.328 reported in Gaia DR3. Under this assumption of constant $\mathrm{RV}$ for both spectral components, we use these measurements to characterize the performance of our radial-velocity determination method for rapidly rotating stars ($\sigma \mathrm{RV}=2.5\mathrm{km}{\mathrm{s}}^{-1}$) and slowly rotating stars ($\sigma \mathrm{RV}=0.16\mathrm{km}{\mathrm{s}}^{-1}$).

4. Discussion

The discovery of the hierarchical nature of SB3 in the HD 56024 system opens a great opportunity to study the formation scenario and dynamical evolution of this multiple system. This system has many high quality TESS observations (currently 44 sectors are available) which show low amplitude (≤$0.1\%$) sine like variability with a period of ∼$1.2$ days. [8] classified it as a slowly pulsating B-type variable, which can be a hot, fast rotating primary component; however, this can also be explained by spots on one or both cool components of the inner binary. We think that thanks to the relatively large outer orbit we can identify which of the SB3 components is the source of this variability through the light time travel effect (LTTE) [36]. The expected semi-amplitude for the “light” orbit is $A=a_{\mathrm{out}}sin{i}_{\mathrm{out}}/c\sim 0.004$ days, with c-speed of light, which should be detectable in TESS data. Also, “light” orbit will help us to constrain the value of the outer period and test if it is in resonance 1:28 with the inner period. Additional SALT observations are being planned for HD 56024 (Kovalev et al, in prep).

In this study we used only data from SALT spectra; however, in principle it is possible to combine our analysis with previous observations from [8,29,32,38].

5. Conclusions

We confirmed four spectroscopic binary candidates using new observations by SALT. Three SB2 systems have circular orbits with periods less than 10 days, while one hierarchical triple has a close binary with an inner elliptical orbit with period ∼$14$ days, consisting of nearly identical components, and a fast rotator on an outer elliptical orbit with period ∼$400$ days. For two other SB2 candidates, our observations did not allow orbit determination.