Double- and Triple-line Spectroscopic Candidates in the LAMOST Medium-Resolution Spectroscopic Survey

Chun-qian Li; Jian-rong Shi; Hong-liang Yan; Jian-Ning Fu; Jia-dong Li; Yong-Hui Hou

doi:10.3847/1538-4365/ac22a8

1. Introduction

Since approximately half of the stars in our Galaxy are in double, triple, or high-order systems (Raghavan et al. 2010), multiple-star systems play an essential role in astrophysics, especially binary systems. The characterization of multiple-star systems, e.g., orbital parameters can be investigated by combining spectroscopic and photometric information.

Spectroscopic multiple-star systems can be classified according to the number of stellar components in the spectra because their spectral lines split due to the different radial velocities (RVs). A target can be considered as a spectroscopic binary (SB) or spectroscopic triple (ST) candidate if it has a double- or triple-line spectrum. The single-line SBs can also be identified as their RVs are variable.

Catalogs of spectroscopic multiple-star systems that have been published include ${{\rm{S}}}_{{{\rm{B}}}^{9}}$ , the recent version of the ninth catalog of SB orbits that includes more than 4004 SBs, around one third of them double-line systems (Pourbaix et al. 2004), and the Geneva–Copenhagen Survey Catalogue that presents 3223 SBs from 16,682 nearby F and G dwarf stars (Nordström et al. 2004; Holmberg et al. 2009). Recent spectroscopic surveys providing many spectra that have substantially expanded the number of spectroscopic multiple-star systems include the Radial Velocity Experiment (RAVE) survey (Matijevič et al. 2010) that has found 123 SBs, the Gaia-ESO survey (Merle et al. 2017) that has detected 342 SBs, 11 STs, and even 1 quadruple-line candidate, the Apache Point Observatory Galaxy Evolution Experiment (APOGEE) survey that has discovered more than 3000 binaries (Fernandez et al. 2017; El-Badry et al. 2018), and the Galactic Archaeology with HERMES (GALAH) survey that has derived 12,760 FGK SBs with stellar properties (Traven et al. 2020).

The Large Sky Area Multi-Object fiber Spectroscopic Telescope (LAMOST) is a 4 m Schmidt telescope with a 5° field of view, and is equipped with 4000 fibers (Zhao et al. 2006, 2012; Cui et al. 2012; Luo et al. 2015). The medium-resolution spectroscopic (MRS) survey includes both blue and red arms, and the wavelength coverage of them are 4950–5350 Å and 6300–6800 Å, respectively. The resolution power of MRS is 7500. There are more absorption lines in the blue arm than in the red one, which enables us to measure the RVs with a precision of 1 km s⁻¹ for most of the stars (Liu et al. 2019). The efficiency of observations and the achieved precision makes LAMOST-MRS an exceptional database for measuring RVs and detecting multiple-star systems.

The purpose of this work is to detect the multiple-line candidates (SBs and STs) from the LAMOST-MRS database following the method of Merle et al. (2017). This paper is organized as follows. In Section 2, we describe the LAMOST-MRS spectral data set. The methods used to normalize spectra, calculate cross correlation functions (CCFs), and detect peak positions in CCFs are introduced in Section 3, and a catalog that contains SB and ST candidates detected from LAMOST-MRS is presented in Section 4. In Section 5, we discuss the detection efficiency, the stellar parameters of the SB and ST candidates, RV differences, and caveats, and the conclusions are given in Section 6.

2. Data Selection

The LAMOST-MRS test observation started in 2017 September, and the LAMOST-MRS survey began in 2018 October. The first- and second-year MRS data has been released as LAMOST Data Release 7⁵ (DR7). The wavelength ranges of the LAMOST-MRS blue and red arms are 4950–5350 Å and 6300–6800 Å. Up to 2019 April 11, the LAMOST-MRS survey obtained 5,369,891 spectra of 759,886 objects. Only the spectra of blue arms have been chosen to detect multiple-line candidates and measure their RVs, as there are more absorption lines in the blue arms. The distributions of the signal-to-noise ratio (S/N) of the blue-arm spectra versus the Sloan Digital Sky Survey (SDSS) g magnitude of the first-year survey and the Gaia DR2 G magnitude of the second-year survey are displayed in Figure 1. It can be seen that most of the objects have g or G magnitudes between 10 and 15. It is found that a spectrum with low S/N will lead to challenges for detecting reliable SBs and STs (Fernandez et al. 2017). Therefore, the blue-arm spectra with an S/N higher than 10 have been selected. In addition to S/N, the header keywords objtype and fibermas have also been taken into consideration. Only these spectra with an objtype of star and fibermas of 0 have been chosen, because a header keyword fibermas that is not 0 indicates that this fiber may have problems. Finally, 1,383,831 spectra of 281,437 stars were selected.

**Figure 1.** The distributions of S/N vs. SDSS g magnitude of the first-year survey (upper panel) and the Gaia DR2 G magnitude of the second-year survey (lower panel).
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Figure 2 shows the number of exposures for these stars; most of them have been observed three times because the LAMOST-MRS no-time-domain observation takes three consecutive exposures (Liu et al. 2020). The number and cumulative distribution function versus S/N of all the selected spectra are presented in Figure 3.

**Figure 3.** Number and cumulative distribution function diagram of S/N of all the selected spectra.
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3. Method

Based on the Gaia-ESO survey, Merle et al. (2017) have developed a method to search for multiline spectroscopic candidates. Their method utilizes the Gaussian kernel to smooth the successive derivatives of the CCF. Following their method, we detect SB and ST candidates and derive their RVs from the LAMOST-MRS spectra. A Monte Carlo (MC) simulation is adopted to estimate the RV uncertainties for each spectrum.

3.1. Calculating the CCF

The CCF is usually used to measure RVs and to find multiple-line spectra. We use Equation (1) to calculate the values of the normalized CCF according to the normalized correlation coefficient (Gubner 2006). The range of the normalized CCFs is between −1 and +1, with +1 indicating a perfect correlation and −1 a perfect anticorrelation.

$\begin{eqnarray}&&\mathrm{CCF}(v)=\sum _{i=1}^{n}\displaystyle \frac{({O}_{i}-\overline{O})}{{\sigma }_{O}}\cdot \displaystyle \frac{({T}_{i,v}-\overline{T})}{{\sigma }_{T}},\end{eqnarray} \tag{ 1 }$

Here, O_i and T_i,v are the normalized flux of the observed and template spectra at a same wavelength-sampling point i, and the RV value of the template is located at v. $\overline{O}$ and σ_O are the mean and scatter of the flux values of the observed spectrum, while $\overline{T}$ and σ_T are the mean and scatter of the flux values for the template. In this work, we generate a set of template spectra with a series of RVs based on the normalized solar spectrum (Kurucz et al. 1984). The RV variations are from −500 to +500 km s⁻¹ with a step of 1 km s⁻¹. To decrease the sampling points, we reduce the resolution of the templates to 100,000.

It is noted that the peaks in some CCFs are too low to be detected, therefore, these spectra with a maximum CCF value less than 0.2 and/or a difference between the maximum and minimum values of CCF less than 0.1 have been not considered. About 80,000 spectra have been excluded by these criteria.

The spectra need to be normalized, and we apply a general normalization procedure to all the selected spectra. The normalization procedure is as follows:

1.
splitting each spectrum evenly into 10 bins by wavelength;
2.
quadratic spline interpolation with the median flux values of the 10 bins;
3.
masking the cosmic rays, absorption, and emission lines.

As the cosmic rays and emission lines will lead to negative values of the CCF, they need to be masked during normalization. Thus, we calculate the standard deviation (σ) of the residual between the observed spectrum and the continuum, and mask these points where the residuals are higher than +5σ.

The whole process is iterated three times to improve the continuum. The left panel of Figure 4 shows an example: the normalized spectrum of HD 47775.

3.2. Detecting the Number of RV Components and Determining their RVs

To obtain the number of RV components and their values, Merle et al. (2017) have designed a detection of extrema code to identify the peaks in CCFs. In their Figure 1, Merle et al. (2017) presented simulated CCFs and their derivatives, and there is a peak in the CCF diagram, where 72 km s⁻¹is the value of RV. By detecting where the first derivative passes zero in the declining phase or the third derivative passes zero in the ascending phase, it is possible to identify the RV components of the spectrum and calculate their RV values.

We note that small bulges (CCF values are around zero) can also be identified as peaks for the first or third derivatives, for instance, in the right panel of Figure 5. The reason is that there is more noise in the higher-order derivatives for a discrete CCF. To avoid the impact of these spurious peaks, it is necessary to select the RV range and smooth the derivatives. Therefore, the Gaussian filter function Gaussian_filter1d of the scipy.ndimage package (Virtanen et al. 2020) in Python is adopted to smooth the derivatives.

Two thresholds are used to select the RV range: the first one is the percentile of the CCF, and the other one is the percentile of the smoothed second derivative. Only the ranges where the CCF values are higher than the 75th percentile and the smoothed second derivative values are lower than the sixth percentile have been selected, as shown in Figure 5. If the selected ranges are separate, some triple-line spectra would be identified as double-line spectra (see the right panel of Figure 5). Thus, the middle part between the separate ranges is also selected.

As shown in the middle panel of Figure 5, the two peaks are strongly blended in the CCF diagram, and only one peak can be detected by the first derivative. Meanwhile, there are still two peaks that can be detected from the third derivative, therefore, we derive the RVs from the third derivatives. A linear fit using the two near zero-points of the ascending third derivative is adopted to calculate the RV value.

An appropriate standard deviation (σ) of the Gaussian kernel is important for smoothing, and we choose an initial σ = 13 km s⁻¹ for the LAMOST-MRS spectra. However, this value is too small for some cases, and it may lead to an extra spurious RV component as shown in the left panel of Figure 6. In this case, we increase the σ by 1 km s⁻¹ until the number of RV components detected with the third derivative is equal to the number of valleys in the second derivative, and the σ has been increased from 13 to 20 km s⁻¹ (see the right panel of Figure 6).

**Figure 6.** The example of finding an appropriate σ of Gaussian smoothing.
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3.3. Uncertainties

An MC simulation is applied to estimate the uncertainties of our RV measurements. The main idea is to generate a set of simulated spectra based on each observed spectrum, and derive their RV values from the CCFs. For each RV component, we take the standard deviation of these RVs as its RV uncertainty.

For each observed spectrum, we generate 100 simulated spectra. For a simulated spectrum, the flux at each wavelength point is a random value generated from a Gaussian distribution, and the mean and variance of the Gaussian distribution are the flux and flux error of the corresponding observed spectrum. The CCFs of an observed spectrum and the 100 simulated spectra are presented in Figure 7. We notice that the amplitudes of the simulated CCFs are lower than that of the observed one because the process of generating simulated spectra introduces additional error, therefore, the S/Ns of the simulated spectra are lower than that of the observed spectrum.

**Figure 7.** Original CCF of a double-line spectrum and MC simulation ones.
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It should be noted that if the number of RV components detected from the simulated spectrum is different from the observed one, this spectrum is discarded.

Figure 8 shows the distribution of S/N and RV uncertainties of all the detected SB candidates. The scatter of the RV errors (∼1 km s⁻¹) is in line with the value of Liu et al. (2019) for LAMOST-MRS spectra.

4. Results

After examining the LAMOST-MRS spectra, we detect 3133 SB and 132 ST candidates, which account for 1.2% of the LAMOST-MRS stars.

4.1. SB and ST Candidates and RVs

There are 14,647 double- and 1065 triple-line spectra that have been detected with this method, and 11,648 double- and 388 triple-line spectra are confirmed after checking the CCF diagrams by eye. The proportions are 80% and 36% for the double- and triple-line spectra, respectively.

We present all the SB and ST candidates and their RV values and uncertainties in Table 1, including the celestial coordinates, source id from Gaia Early Data Release 3 (Gaia Collaboration et al. 2021), Gaia G magnitude, and the number of exposures. Four items of spectral information from the LAMOST data release (the LAMOST-MRS plan name (planID), spectrograph ID (spID), fiber ID, and local modified Julian minute (LMJM)) are also presented. It needs to be pointed out that the RV values rv1, rv2, and rv3 are arranged in order of values as it is difficult to identify which RV component corresponds to each star when they have a similar spectral type.

Table 1. The Information of SB, ST Candidates and their RVs

R.A.(2000)	Decl.(2000)	Gaia Source id	G (mag)	SB/ST	${N}_{\mathrm{Exp}}$	planID	spID	fiberID	LMJM	S/N	rv1 (km s⁻¹)	rv2 (km s⁻¹)	rv3 (km s⁻¹)
0.01948	57.48923	422589945455866496	12.1	SB	1	HIP11784201	9	62	83604881	17	−36.7 ± 0.7	20.7 ± 0.7	⋯
0.13490	63.87285	431630508024107392	12.7	SB	1	NGC778801	12	27	83650762	15	−57.0 ± 3.3	39.5 ± 15.1	⋯
0.23830	40.43928	2881984048448075264	12.4	SB	1	HIP11776901	6	17	83609143	14	−58.5 ± 0.8	−6.9 ± 0.5	⋯
0.29125	58.69553	422768646150973696	12.2	SB	3	NGC778901	12	240	83647859	15	−9.3 ± 5.5	62.6 ± 1.6	⋯
0.29125	58.69553	422768646150973696	12.2	SB	3	NGC778901	12	240	83647873	14	−11.0 ± 5.6	63.7 ± 7.8	⋯
0.29125	58.69553	422768646150973696	12.2	SB	3	NGC778901	12	240	83647886	16	−19.2 ± 7.5	59.8 ± 8.5	⋯
0.34767	41.11409	2882225867991453056	12.2	SB	9	HIP11776901	6	39	83604805	21	−95.4 ± 0.4	32.4 ± 0.7	⋯
0.34767	41.11409	2882225867991453056	12.2	SB	9	HIP11776901	6	39	83604818	20	−96.0 ± 0.3	31.0 ± 0.8	⋯
0.34767	41.11409	2882225867991453056	12.2	SB	9	HIP11776901	6	39	83604832	22	−94.6 ± 0.3	30.9 ± 0.7	⋯
0.34767	41.11409	2882225867991453056	12.2	SB	9	HIP11776901	6	39	83607704	27	−85.3 ± 0.6	9.2 ± 0.4	⋯

5.34918	58.28837	422132853553794816	12.9	ST	3	NT002740N583314C02	3	187	84196452	49	−72.7 ± 1.5	−0.4 ± 1.5	61.1 ± 2.2
5.34918	58.28837	422132853553794816	12.9	ST	3	NT002740N583314C02	3	187	84196476	47	−69.6 ± 1.9	−2.2 ± 1.0	58.6 ± 2.0
5.34918	58.28837	422132853553794816	12.9	ST	3	NT002740N583314C02	3	187	84196499	49	−74.7 ± 1.4	−1.4 ± 1.1	63.1 ± 2.4
17.51845	2.00869	2538630790708445312	10.7	ST	4	TD010605N031628K01	7	113	84118991	58	−20.9 ± 0.5	63.4 ± 0.4	⋯
17.51845	2.00869	2538630790708445312	10.7	ST	4	TD010605N031628K01	7	113	84119014	50	−20.3 ± 0.6	64.6 ± 0.5	⋯
17.51845	2.00869	2538630790708445312	10.7	ST	4	TD010605N031628K01	7	113	84119038	39	−18.5 ± 0.6	65.7 ± 0.7	⋯
17.51845	2.00869	2538630790708445312	10.7	ST	4	TD010605N031628K01	7	113	84166383	46	−65.7 ± 0.5	−15.6 ± 0.4	79.5 ± 0.5
18.16407	45.78222	400867753213471744	11.9	ST	4	TD012220N453143T01	14	68	84156353	15	−97.8 ± 2.1	0.2 ± 3.1	⋯
18.16407	45.78222	400867753213471744	11.9	ST	4	TD012220N453143T01	14	68	84156377	14	−97.3 ± 2.3	−0.5 ± 3.6	⋯
18.16407	45.78222	400867753213471744	11.9	ST	4	TD012220N453143T01	14	68	84156400	12	−95.3 ± 1.6	3.2 ± 1.5	⋯
18.16407	45.78222	400867753213471744	11.9	ST	4	TD012220N453143T01	14	68	84156423	11	−96.3 ± 2.2	−46.4 ± 3.5	0.3 ± 2.2

Note. The RV values rv1, rv2, and rv3 are arranged in order of values. Forty-one ST candidates show both double- and triple-line spectra.

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We consider a star to be an ST candidate as long as one of its spectra has been detected with three RV components. Accordingly, we classified 41 stars with both double- and triple-line spectra as ST candidates. The RV variations indicate that they are probably physical binaries or triples. Further checking of the RV variations of these candidates will help us to identify more physical multiple-star systems.

Figure 9 shows the distribution of the number of exposures of the detected candidates. There are 525 SB and 31 ST candidates with more than six observations, these need to be investigated as their orbital parameters may be derived by RV curves.

The detected RV difference limit is around 50 km s⁻¹ for all of the SB and ST candidates (Figure 10), which meets the resolution of the LAMOST-MRS spectra. The largest RV differences are around 250 km s⁻¹ and 300 km s⁻¹ for SB and ST candidates, respectively.

In order to improve the detection efficiency, an artificial method is needed. Among machine-learning and deep-learning (DL) techniques, a recurrent neural network (RNN) is proven to perform well for this classification (Jamal & Bloom 2020). To test its feasibility, we designed an RNN to derive the peak numbers from the CCF diagrams. Our RNN is trained by the CCF diagrams of the confirmed SB and ST candidates, and the details of the RNN can be found in Appendix A. The total classification accuracy of our RNN is 0.96, which is a significant improvement compared to the traditional method. Therefore, we will use the RNN to detect SB and ST candidates in a future study.

4.2. New Binary Candidates

We crossmatch our LAMOST-MRS SB and ST candidates with these of the other binary catalogs, including ${{\rm{S}}}_{{{\rm{B}}}^{9}}$ (Pourbaix et al. 2004), the Geneva–Copenhagen Survey of the Solar Neighborhood III (Holmberg et al. 2009), the RAVE SB2 (Matijevič et al. 2010), the Gaia-ESO multiline SB (Merle et al. 2017), the Washington Visual Double Star (WDS; Mason et al. 2001), the binaries of APOGEE (Fernandez et al. 2017; El-Badry et al. 2018), the FGK binary stars of the GALAH survey (Traven et al. 2020), and the third revision of the Kepler Eclipsing Binary Catalog (KEBIII; Kirk et al. 2016), and there are 107 stars in common. The information about these stars is listed in Table B1.

Table B1. List of the Common SB and ST Candidates with other Binary Catalogs

R.A.(2000)	Decl.(2000)	Gaia Source id	G	SB/ST	${N}_{\mathrm{Exp}}$	Catalog
4.31148	0.55870	2545576336943059072	12.7	SB	3	GALAH
6.35503	59.11604	428267308105062528	11.1	SB	4	WDS
9.78481	59.81764	425556805786609408	10.9	SB	14	WDS
10.17108	57.76887	424898679355325312	11.3	SB	2	WDS
13.49841	10.08698	2582339740871439360	12.2	SB	1	GALAH
15.04087	12.21674	2584289591599704064	11.5	SB	1	GALAH
15.23534	11.58956	2584040273042478208	12.8	SB	2	GALAH
19.44386	0.62884	2535048989846592768	13.1	SB	2	GALAH
29.76969	58.39781	505491850882835584	11.0	ST	3	WDS
31.96472	13.79138	77202449462513024	12.1	SB	3	APOGEE
46.84714	40.80111	239854583246385408	10.3	SB	1	WDS
46.91366	66.17673	492339320985355648	10.6	SB	3	WDS
50.59945	51.66556	442912798683449088	12.1	ST	9	WDS
51.47665	18.13560	55926869402261760	12.5	SB	4	GALAH
51.85738	19.01199	57544044849005440	13.0	SB	2	GALAH
52.37579	19.41492	57640320835799808	12.3	SB	4	GALAH
55.16722	45.77760	244833962172857728	11.2	ST	3	WDS
62.05420	19.94418	51832421242688128	12.4	SB	3	WDS
63.01352	48.26905	246251095218220160	11.0	SB	1	WDS
63.01540	21.94700	52684199156684032	8.9	SB	3	SB9, WDS
63.29504	61.55950	475258132965412224	13.1	SB	3	WDS
66.44780	18.31499	3314466360138302592	13.0	SB	2	GALAH
68.20363	16.02178	3312652582565893632	13.0	SB	9	GALAH
71.04484	26.76769	154533339923810688	13.7	SB	11	GALAH
71.43970	23.53370	146573528573114240	12.9	SB	4	GALAH
71.99216	22.95037	3413141584496385792	12.0	SB	11	GALAH
72.16204	15.36070	3405024886580964736	12.9	SB	3	GALAH
72.21994	14.71636	3308722103373770496	13.4	SB	3	GALAH
72.40034	56.28887	274601899464974592	10.6	SB	3	WDS
73.58480	20.85980	3411716548707061376	11.7	ST	8	GALAH
73.72125	24.23559	3419659356282987008	12.5	SB	9	GALAH
74.90812	21.79690	3412251701632573312	11.7	ST	5	GALAH
75.05998	24.13008	3419410763576132352	10.9	ST	12	WDS
76.05618	24.30754	3418774008905352704	10.3	SB	3	WDS
77.57841	24.48785	3419012499849582464	11.5	SB	3	GALAH
83.88432	35.85607	183166645640035584	11.9	SB	3	WDS
92.23265	22.14776	3423547328182688640	10.9	SB	1	WDS
98.13701	8.59674	3326258557925415936	11.2	SB	3	WDS
98.72293	9.43785	3326828345466157952	10.8	SB	5	WDS
100.44896	9.86729	3326737665818107008	13.1	SB	2	Gaia-ESO
101.89452	8.47141	3134190163070718464	10.4	ST	7	WDS
101.93376	23.12819	3379557723381624832	11.2	SB	3	WDS
102.21957	17.33513	3358396660030939776	12.0	SB	6	WDS
103.79022	22.80749	3380050961721719680	10.5	SB	7	WDS
106.83926	45.75925	977374646347674624	12.5	SB	3	WDS
115.99661	24.74451	867894834757702400	13.5	SB	1	WDS
123.65855	14.73966	655293644368357120	11.7	SB	3	GALAH
123.72821	16.71239	655829140890694016	13.0	SB	5	GALAH
123.85360	16.22931	655726439632891648	12.7	SB	3	GALAH
124.00038	17.45520	657004106505230336	12.6	SB	4	GALAH
124.14557	19.41296	663514555370788224	12.4	SB	7	GALAH
124.24190	17.65389	657014483146180352	11.8	SB	4	GALAH
124.47248	14.38159	652210957361785728	11.7	SB	1	GALAH
124.72561	18.90909	663247374044278912	11.8	SB	5	GALAH
124.96669	17.39997	656285232057964800	13.7	SB	11	GALAH
126.15704	16.84889	656018841006561792	11.7	SB	3	GALAH
126.95277	13.03253	650982218756793984	12.8	SB	5	GALAH
126.95640	11.58378	601155100565167872	12.9	SB	3	GALAH
127.19336	19.00738	662878900210497408	11.5	SB	11	GALAH
127.23194	18.76372	662309731144349184	10.9	SB	5	GALAH
130.17758	17.23037	658488928236761600	13.8	SB	2	GALAH
130.86018	12.41902	602244372990566400	11.1	SB	3	WDS
131.03050	20.07688	661380815618317312	10.0	SB	3	SB9
132.52700	23.75079	689509857812011392	12.4	SB	11	WDS
132.70634	12.28767	605014833054650880	11.5	SB	3	APOGEE
132.82328	11.66001	604897803786032768	13.4	SB	11	GALAH
132.85539	12.04901	604972089540120832	13.4	SB	2	APOGEE, GALAH
133.01907	19.60290	660730076531974016	11.2	SB	14	GALAH
133.27465	10.34295	597812482136772608	12.8	SB	24	GALAH
133.34198	19.34574	660661013457939200	11.6	SB	2	GALAH
133.41641	23.21572	689235946273862016	13.1	SB	21	GALAH
133.57891	12.65805	605136088570783104	11.2	SB	13	APOGEE, WDS
133.68605	11.50144	604716006409635456	10.3	SB	11	APOGEE, GALAH
133.89588	16.75347	611576370555983872	12.3	SB	10	GALAH
133.99515	22.92465	686164387525931648	13.0	SB	29	GALAH
143.96777	37.43883	799090386388958720	13.3	SB	6	APOGEE
144.06575	37.52891	799092516692729344	10.3	SB	5	SB9
168.54278	4.98812	3816819414549676544	11.1	SB	3	GALAH
170.48610	3.71580	3812680406106190848	12.7	SB	3	WDS
173.17225	1.59537	3799929369758876032	13.4	SB	6	GALAH
173.69728	2.06516	3800061409937591552	12.7	SB	1	GALAH
174.26187	2.27368	3799346834754684544	13.3	SB	3	GALAH
179.39510	3.22525	3893093635680954496	10.7	SB	3	GALAH
184.90873	25.29859	4008485212056046208	11.3	SB	8	APOGEE
185.32486	50.97667	1547679958899540224	10.4	SB	3	WDS
207.00384	−0.78145	3662029274238005120	11.5	SB	3	WDS
207.24577	−8.31973	3619010057167751808	10.9	SB	10	GALAH
207.60620	−6.40342	3620621460177550592	11.2	SB	5	GALAH
226.29512	26.56544	1268407888092649344	10.5	SB	1	APOGEE
263.88506	23.17511	4557402515188596224	10.9	SB	1	SB9, WDS
266.19860	6.03134	4474130344924152192	12.1	SB	2	GALAH
276.72032	25.83382	4584847493651016064	12.1	SB	2	WDS
284.75986	41.04340	2104025523931432704	10.5	SB	2	KEBIII
289.86104	41.40818	2101467956809222912	10.5	SB	1	KEBIII
289.88398	45.30403	2127090146848465152	11.6	SB	3	KEBIII
290.48320	43.62231	2126083307735831936	12.3	SB	1	KEBIII
290.51746	40.69681	2101192082470870912	11.3	SB	3	KEBIII
290.80668	42.34393	2101942327356009216	12.0	SB	3	APOGEE, WDS, KEBIII
290.95133	40.54793	2101510803402761344	14.1	SB	22	KEBIII
291.31991	43.59553	2126044240713250304	10.7	SB	26	KEBIII
292.05871	43.92521	2125971226269667584	12.7	SB	6	KEBIII
292.29674	44.28051	2126356983051726720	13.2	SB	25	KEBIII
292.71791	41.92241	2077667962475652864	10.1	ST	1	KEBIII
293.20532	42.19786	2077683321279046016	12.1	SB	2	APOGEE
294.47828	46.86376	2128532603025164288	12.5	SB	3	KEBIII
305.54277	40.21833	2067518679871015168	11.7	SB	4	WDS
332.42002	58.31327	2199510343510448768	10.3	SB	3	WDS

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Except for these common stars, there are 3034 SB and 124 ST candidates (over 95% of the total candidates) that are newly discovered. These RVs can be used to derive the orbital parameters of these systems (Pan et al. 2021; Wang et al. 2021).

5. Discussion

5.1. Detection Efficiency

To test the detection efficiency of the method, we use the radiative transfer code SPECTRUM (Gray & Corbally 1994) and the Kurucz (Kurucz 1979) stellar atmosphere models to generate six synthetic spectra of the given stellar parameters. They include cool and hot (T_eff = 5000, 8000 K), giant and dwarf ( $\mathrm{log}g=2.0$ , 4.0 dex), and metal-rich and metal-poor ([Fe/H] = 0.0, −2.0 dex) models. All of the synthetic spectra have been reduced to the same wavelength range and resolution (R ∼ 7500) as the LAMOST-MRS blue-arm ones. We generate a set of double-line synthetic spectra by shifting a synthetic spectrum with different RVs and combining it with the original ones, and the synthetic double-line SBs have equal masses.

A similar MC simulation (see Section 3.3) is adopted to test the detection efficiency. We add the random Gaussian distribution noises to each point of the synthetic spectrum and generate 100 spectra for a specific S/N to detect RV components. We count the number of spectra detected as SBs, and the success rate represents the detection efficiency.

Our simulation results are presented in Figure 11, and it can be seen that the detection limit of RV differences is between 40 and 50 km s⁻¹, and this limit is consistent with the LAMOST-MRS resolution power. The detection efficiency of the method is similar except for hot metal-poor dwarfs.

5.2. Stellar Parameters

It is useful to investigate the distribution of stellar atmospheric parameters of SB and ST candidates, although the general method for determining the stellar atmospheric parameters may not be appropriate for multiline spectra. We adopt the stellar atmospheric parameters of 1470 SB and 65 ST candidates from the LAMOST DR7 low-resolution spectroscopic survey (LAMOST-LRS; Luo et al. 2015), and present their distribution in T_eff versus $\mathrm{log}g$ , T_eff versus [Fe/H], and $\mathrm{log}g$ versus [Fe/H] plots in Figure 12.

**Figure 12.** The distribution of stellar atmospheric parameters of common stars between the LAMOST DR7 LRS and the selected LAMOST-MRS data. The black crosses are the SB candidates, and white pentagons are ST candidates. The left panel is T_eff vs. $\mathrm{log}g$ , the middle panel is T_eff vs. [Fe/H], and the right panel is $\mathrm{log}g$ vs. [Fe/H]. All atmospheric parameters are provided by the LAMOST DR7 LRS.
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**Figure 12.** The distribution of stellar atmospheric parameters of common stars between the LAMOST DR7 LRS and the selected LAMOST-MRS data. The black crosses are the SB candidates, and white pentagons are ST candidates. The left panel is T_eff vs. $\mathrm{log}g$ , the middle panel is T_eff vs. [Fe/H], and the right panel is $\mathrm{log}g$ vs. [Fe/H]. All atmospheric parameters are provided by the LAMOST DR7 LRS.
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We note that about 90% of the SB and all the ST candidates are on the main sequence, only 155 SBs may have one or two components on the red giant branch ( $\mathrm{log}g\lt 3.5$ dex). The reason is that when the massive component climbs the red giant branch, its radius increases, and mass transfer occurs after it reaches the Roche lobe. The interaction between the components can modify the evolution and lead to fewer giant binary systems. The lack of metal-poor candidates is due to fewer low-metallicity stars in our sample.

5.3. Caveats

There are some caveats that we need to point out before utilizing the SB or ST catalog for further studies. Since the completeness of the multiline spectroscopic candidate catalog is not the primary goal of this work, the selection effects of the LAMOST-MRS data and the detection process of the method must be considered in further statistical studies.

Another caveat is that the SB and ST candidates are not necessarily physical binaries or triples. The CCFs of double- and triple-line spectra may be mimicked by emission lines or stellar pulsations, etc. (Merle et al. 2017). Considering the LAMOST fibers have a diameter of 3 farcs 3 (Cui et al. 2012), one spectrum may contain light from multiple stars when they are very close to each other in the sky. Investigating the RV variations of the SB and ST candidates is essential to identifying the physical binaries and triples.

6. Conclusions

Based on the CCF and Gaussian smoothing for the derivatives of CCFs, we detected 14,647 double-line and 1065 triple-line spectra from the blue-arm spectra with S/N ≥ 10 in the LAMOST DR7 MRS. After checking the CCF diagrams by eye, 11,648 double-line and 388 triple-line spectra are confirmed, 80% and 36% of the total, respectively. They belong to 3133 SB and 132 ST candidates, and these confirmed candidates account for 1.2% of the LAMOST-MRS stars. Among the ST candidates, 41 of them show double- and triple-line cases, which indicates that they are physical binaries because of the variations of RVs. Comparing with the other binary-star catalogs, we find that about 95% of them are newly discovered. For the 1470 SB and 65 ST candidates that have stellar atmospheric parameters from the LAMOST-LRS survey, 90% of the SB and all the ST candidates are on the main sequence.

An MC simulation is used to estimate the RV uncertainties, and the RV error is of the order of 1 km s⁻¹. Our results indicate that the detection limit of RV differences is between 40 and 50 km s⁻¹.

The LAMOST-MRS survey is ongoing, and will continue to provide a great opportunity to study binary- and multiple-star systems.

We thank the referee for the useful comments, which have helped us to improve the manuscript. Our research is supported by the National Key R&D Program of China No. 2019YFA0405502 and the National Natural Science Foundation of China under grant Nos. 12090040, 12090042, 12090044, 11833002, 11833006, 12022304, 11973052, 11973042, and U1931102. This work is supported by the Astronomical Big Data Joint Research Center, cofounded by the National Astronomical Observatories, Chinese Academy of Sciences and Alibaba Cloud. H.-L.Y. acknowledges the support from the Youth Innovation Promotion Association, Chinese Academy of Sciences (id. 2019060) and NAOC Nebula Talents Program. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences.

Appendix A: Detecting Peaks

We design a simple RNN to inspect the peak numbers of CCF diagrams automatically. Because of the incremental data of the LAMOST-MRS survey, an artificial classification method is urgently needed to analyze these spectra. Among the most-common machine-learning and DL techniques, an RNN proves to be highly performant for the classification of one-dimensional data (Jamal & Bloom 2020) compared to a convolutional neural network.

RNNs refer to a class of artificial neural networks where the network architecture is composed of interconnected nodes through a directed graph along a temporal sequence. A long short-term memory network (LSTM; Hochreiter & Schmidhuber 1997) is one of the RNN variants with a gated state or memory. LSTMs have been found to be extremely successful in many applications, such as speech recognition (Graves et al. 2013), handwriting generation (Graves 2013), and machine translation (Sutskever et al. 2014). At the same time, RNNs have been applied on astronomical data (Jamal & Bloom 2020) including variable stars (Naul et al. 2018), periodic variable stars (Tsang & Schultz 2019) and supernovae classifications, (Charnock & Moss 2017) and online transient event detection (Muthukrishna et al. 2019; Möller & de Boissière 2020).

We set up our RNN with a three-layer LSTM, with a hidden size of 256 units, and three output features. This RNN is trained by 12,136 CCF diagrams with labels as the number of peaks (0, 2, 3) together with 4046 groups of test data. We split the training data into batches to speed up the training process. After 100 training epochs, we stop the training process to avoid overfitting (with a training loss of 0.003 and test loss of 0.100). The final classification accuracy and precision are shown in Table A1 and the confusion matrix obtained on the test-set predictions for the RNN classifier is shown in Figure A1.

**Figure A1.** Confusion matrix obtained on the test-set predictions for the RNN classifier. The values in each box refer to the number of predictions vs. the true labels.
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Table A1. The Precision, Recall, and F₁ Score of the Prediction of Classification

Peak Number	Precision	Recall	F₁ Score
0	0.91	0.92	0.92
2	0.97	0.97	0.97
3	0.84	0.72	0.78

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The F₁ score is the harmonic mean of precision and recall:

$\begin{eqnarray}&&{F}_{1}=\displaystyle \frac{2}{{\mathrm{precision}}^{-1}+{\mathrm{recall}}^{-1}}.\end{eqnarray} \tag{ A1 }$

Two peaks are recognized well (precision ∼0.97) since there are the most training data for two-peak CCFs. On the contrary, the three-peak group is the most difficult one to recognize due to there being less data. In total, the final classification accuracy is 0.96, which means that for a given CCF diagram, we can detect the correct peak number successfully with a probability of 0.96. This method can improve the productiveness and robustness. We use the DL method along with manual checks to confirm our results.

Appendix B: Common SB and ST Candidates with Other Binary Catalogs

The information about the common stars of between our LAMOST-MRS candidates and the other binary catalogs are listed in Table B1.

Double- and Triple-line Spectroscopic Candidates in the LAMOST Medium-Resolution Spectroscopic Survey

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Abstract

1. Introduction

2. Data Selection