New SB1s with Spectroscopic Orbits from LAMOST-LRS

The LAMOST Low-Resolution Spectroscopic (LAMOST-LRS) Survey provides radial velocities of 10 million stars. These observations can be used to identify new single-lined spectroscopic binaries (SB1s) with their preliminary spectroscopic orbits. First, we perform a statistical χ 2 test on a subsample of LAMOST-LRS stars with velocity observations sufficient for the present work to obtain a set of 6852 radial velocity variables. Subsequently, we discard 399 astrophysical variables through crossmatching with variable catalogs, resulting in 1297 SB1 candidates. Finally, in order to reliably identify SB1s among these SB1 candidates, we employ a combination of The joker, rvfit, and Levenberg–Marquardt algorithms to give the best-fit solutions. An SB1 is identified if its orbital solution satisfies the criteria of the goodness-of-fit statistic (F2) < 3.1, the signal significance > 10, and the maximum gap in phase (phase_gap_max) < 0.3. Our final catalog of SB1s contains 255 systems, 168 of which are newly discovered ones. Cross validation results indicate that the determined orbital periods are consistent with periods of external catalogs within 1σ uncertainties. The period–eccentricity diagram illustrates that a majority of short-period binaries have small eccentricities. Furthermore, in comparison to the general sample, the SB1 catalog exhibits a relatively higher ratio of dwarfs than giants and a slightly lower metallicity.


Introduction
Binaries are prevalent in our Galaxy, with about 50% of stars existing in binaries (Raghavan et al. 2010;Chini et al. 2012;Sana et al. 2012;Moe & Di Stefano 2017).These systems play a crucial role in many fields of astrophysics.For instance, binaries are implicated in the production of all Type Ia supernovae (Marietta et al. 2000), short-duration gamma-ray bursts (Narayan et al. 1992), kilonovae (Metzger 2017), X-ray binaries, and the majority of gravitational-wave sources (Abbott et al. 2017).Additionally, statistical properties associated with stellar multiplicities (such as the period distribution, mass ratio distribution, eccentricity distribution, etc.) provide fundamental information for both stellar formation and evolution theories (Duquennoy & Mayor 1991;Raghavan et al. 2010;Moe & Di Stefano 2017).It should be pointed out that orbital fitting of binaries is one of the few reliable methods for determining stellar masses, with an accuracy that can reach 1% (Torres et al. 2010).Therefore, it has important implications in stellar physics, including the validation and constraint of stellar evolution models.
Binaries can be classified into four types (i.e., visual binaries, astrometric binaries, eclipsing binaries, and spectroscopic binaries, SBs) depending on the way by which they are observed.Compared with astrometric or visual binaries, SBs have relatively short orbital periods.With this property, it is easier to construct their full orbital solutions by observing the two stars orbiting each other multiple times.According to whether the secondary is visible in spectra, SBs can be categorized into two types: single-lined SBs (SB1s) and double-lined SBs (SB2s).SB1s are identified by the observation of periodic variations in the radial velocity (RV) of specific sources over time.In comparison with SB2s, SB1s generally exhibit significant differences in the physical properties of their respective two components forming at almost the same time.Consequently, their orbital solutions can provide further constraints on stellar evolution models.
Recently, significant progress has been made in large spectroscopic surveys, e.g., the Radial Velocity Experiment (RAVE; Steinmetz et al. 2006), GALactic Archaeology with HERMES (GALAH; De Silva et al. 2015), the Apache Point Observatory Galactic Evolution Experiment (APOGEE; Majewski et al. 2017), the Gaia-ESO Survey (GES; Gilmore et al. 2012;Randich et al. 2013), Gaia (Gaia Collaboration et al. 2016), and the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST; Luo et al. 2015).These surveys have greatly enlarged the number of SBs by providing millions of spectra.For instance, Birko et al. (2019) identified 3,838 SB1 candidates using RAVE and Gaia DR2 data, and estimated the most probable orbital parameters of mainsequence dwarf candidates.Price-Whelan et al. (2020) discovered 19,635 APOGEE-SB1s and gave multiple possible orbital solutions for each system.Traven et al. (2020) presented 12,760 binaries detected as SB2s in GALAH.Merle et al. (2020) found 641 FGK SB1 candidates at the 5σ level in GES.Furthermore, Gaia DR3 (GDR3; Gaia Collaboration et al. 2022) released 181,327 SBs with their corresponding orbital parameters.
In these surveys, only LAMOST is capable of obtaining spectra for up to 4000 stars simultaneously.Additionally, LAMOST DR8 Low-Resolution Spectroscopic (LRS) has accumulated data for nearly nine years, thus there are multiple Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
observations for a significant number of sources.Previous studies have identified some RV variable candidates and SB candidates based on LAMOST spectral data.For example, Qian et al. (2019) and Tian et al. (2020) discovered 256,000 and 80,702 RV variable candidates, respectively.Li et al. (2021) obtained 3133 SB2s based on the cross correlation function and successive derivatives.Wang et al. (2021) analyzed light curves, fitted RV data, calculated the binarity parameter from medium-resolution spectra, and crossmatched a spatially resolved binary catalog from Gaia EDR3 to construct a catalog of about 2700 candidate binaries, of which 878 initial spectroscopic orbits were provided.In Kovalev et al. (2022), a total of 2460 SB2 candidates were detected in LAMOST Medium-Resolution Spectroscopic (MRS), with 1410 of them being newly discovered.Zhang et al. (2022) presented a sample containing 8,003 spectra for 2198 SB2 candidates in LAMOST-MRS.However, none of these studies provided spectroscopic orbital solutions precise enough to be claimed as reliable.Therefore, in this work, we focus on the objects with multiepoch spectroscopic data observed by the LAMOST-LRS surveys to identify SB1s by RV fitting and provide reliable spectroscopic orbital solutions for them.
The paper is organized as follows.In Section 2, we describe the used sample.In Section 3 we use a χ 2 test to search for RV variables and remove known variable stars.The methods used in orbital fitting and acceptable criteria of SB1 systems are introduced in Section 4. In Section 5, we compare our SB1s with other catalogs to validate our orbital solutions and analyze the dependence of eccentricity on the orbital period.Finally, in Section 6 we offer conclusions.

Sample Selection
LAMOST is located at the Xinglong Station of the National Astronomical Observatory, China (40°N, 105°E).It is a reflecting Schmidt telescope that has both a large aperture (effective aperture of 3.6-4.9m) and a wide field of view (FOV ∼5°).Forty thousand fibers are installed on its focal plane with a diameter of 1.75 m.With a parallel and controllable fiber positioning technology, up to 4000 spectra can be obtained simultaneously for spectroscopic surveys of stars and other objects for the Northern Hemisphere (Cui et al. 2012;Deng et al. 2012;Zhao et al. 2012).From 2011 October 24 to the present, a large amount of LRS data have been obtained.The LRS data have a resolution of R ∼ 1800 (at 550 nm) with spectral wavelength coverage from 369 to 910 nm.
In the present paper, we use the LAMOST DR8 v2 LRS data,4 which were obtained from October 2011 to 2020 June.There are about 10.3 million stellar spectra, of which 9.3 million have a signal-to-noise ratio (S/N) greater than 10 in the g or i bands.
In particular, we find that about 1.9 million (26%) stars are observed at multiple epochs.This provides an opportunity to identify a large sample of binaries and determine their orbits.
Information on structures of the DR8 LRS data products can be found in the online LAMOST document. 5The products include FITS files and 11 spectroscopic parameter catalogs.The FITS files contain not only relative flux (relatively)-and wavelength-calibrated sky-subtracted spectra, but also some useful information such as exposure parameters with sufficient decimal places and measured redshifts (z) with errors (ò z ).
These zʼs and ò z ʼs are mainly derived from the LAMOST onedimensional and stellar parameter pipeline (LASP; Luo et al. 2015).And RV measurements (v) and errors (ò v ) can be calculated by dividing them by the speed of light.The ò v distribution peaks around 5 km s −1 (Tsantaki et al. 2022).The spectroscopic parameter catalogs include more calibration information.For example, for each spectrum, the LRS General Catalog includes S/N, spectrum type, and source ID in Gaia DR3.This information is helpful for the stellar sample selection in our SB1 identification.In this paper, the identification of SB1s is based on orbital fitting with multiple high-quality RV measurements.Therefore, we applied the following selection criteria for stellar samples: 1.The spectral parameters, z ≠ −9999 and z err 0; 2. LAMOST-LRS spectral S/N g > 10; 3. The RV measurements are at least 12 (N 12).
The first criterion leaves us with reliable RV measurements and their uncertainties.The second criterion aims to safeguard against systematic problems with measurements of noisy spectra.As a result, these two criteria reduce the initial number of stars to 5.2 million, comprising approximately 70% of all stars.In the third criterion, the lower limit of 12 is selected as twice the number of SB1 orbital parameters to ensure a robust SB1 orbital fitting process in Section 4. Ultimately, 123,514 spectral data of 6852 (∼0.09%) stars (defined here as the sample) are retained (the white histogram on Figure 1).

Searching for SB1 Candidates
In this section, we perform a preliminary selection based on the aforementioned sample to obtain RV variables.To assess whether there are significant changes in RV, we use χ 2 and F2 tests.It is worth noting that some variable stars can produce intrinsic RV jitter, which may be easily mistaken for orbital variations.Therefore, reasonable exclusion of false positives is necessary.

Statistical χ 2 and F2 Test
The statistic χ 2 is the sum of the squared normalized residuals computed by where N is the number of RV measurements, v i and ò i are the ith RV measurement and the corresponding uncertainties, and v represents the weighted RV mean.If the null hypothesis, which assumes that the star has a constant velocity, could be accepted, then χ 2 follows the chi-square c n 2 distribution with ν = N − 1 degrees of freedom (d.o.f.).
The c n 2 distribution depends on d.o.f., ν, which is generally not the same for different stars.To eliminate this inconvenience, it can be transformed into a d.o.f.-independent distribution, called F2 (Wilson & Hilferty 1931).F2 is expected to obey approximately normal distribution with zero mean and unit standard deviation, and is given by the following formula: The F2 distribution of the sample is shown in Figure 2. Note that its distribution is peaking at negative values, which suggests that the uncertainties used to derive the χ 2 are most probably overestimated.This is consistent with the previous conclusion (Tsantaki et al. 2022) that LAMOST RV has overestimated errors.
We adopt a confidence level of 99.9%, and the corresponding value of F2 is 3.1 (∼3σ).This means that the null hypothesis is rejected when F2 is larger than 3.1.After applying the selection criteria to the sample of 6852 objects, 1696 objects were left (defined here as sample I).The shaded area of Figure 2 shows the F2 distribution of sample I.

False Positives
Stellar pulsations, rotation of an ellipsoidal-shaped, episodic dust ejection, and starspot cycles all can produce photometric and RV variations (Wood et al. 2004).Therefore, a fraction of sample I are not binary, but variable stars.Additionally, some variables may produce pseudo-orbits.If the time span of the RV measurements is not long enough, the Keplerian solution may be problematic, resulting in the erroneous identification of SB1s (Famaey et al. 2009).Therefore, it is essential to eliminate these variable stars as much as possible.
One way to eliminate variables from sample I is to crossmatch with the variable catalogs, including GDR3 variable catalogs (Eyer et al. 2023), the General Catalogue of Variable Stars (GCVS; Samus' et al. 2017), the All-Sky Automated Survey for Supernovae (ASAS-SN) catalog of variable stars (Jayasinghe et al. 2018), and the International Variable Star Index (VSX; Watson et al. 2006).We perform a crossmatch search within a radius of 3″ for these variable catalogs.If several sources are crossmatched within 3″ of a target, we always keep the closest one.
For sample I, a crossmatch of 195 variables is found in GDR3 variable catalogs.Simultaneously, we crossmatch sample I with GCVS, ASAS-SN variable catalogs, and VSX.There are 11, 61, and 263 common sources flagged as variables, respectively.Of the 530 sources, 131 sources exist repeatedly in multiple catalogs.We remove these 399 variable stars out of sample I and finally obtain 1297 SB1 candidates (defined here as sample II; see the shaded area of Figure 1).These SB1 candidates are listed in Table 1 in machine-readable format and are also available in the China-VO at doi:10.12149/101309.Note that the LAMOST designation for the same star can slightly vary between observation times, therefore the Gaia DR3 source_id will be used.

SB1 Catalogs
To identify SB1s from sample II and determine the corresponding orbital parameters, we need to fit the spectroscopic orbits.With the LAMOST DR8 v2 LRS data, the maximum likelihood estimate of orbital parameters are usually obtained by minimizing the following objective function where N is the number of RV measurements of each source, and v i and ò i are the measured velocities and their associated uncertainties.In addition, V calc;i in this equation corresponds to the expected RV calculated by the RV Keplerian orbit equation: where M 0 is the mean anomaly at reference time t 0 , which is always set to the minimum observation time for a given set of RV observations.In this model, the orbital parameters to determine are P, M 0 , e, ω, γ, K-the period, the mean anomaly at reference time t 0 , the eccentricity, the longitude of periastron, the center-of-mass velocity, and the semiamplitude.

Fitting Results of the Spectroscopic Orbital Solutions
The common approach of spectroscopic orbit fitting involves two steps: first, a global optimization method is used to determine the region where the possible best orbital solution is located, and then a local optimization method is used to improve the solution.Nevertheless, some global optimization methods are devoted to finding appropriate parameters within a limited time and specific initial parameter regions, which may cause them to be stuck in local minima.Therefore, it is necessary to provide multiple sets of appropriate initial estimates.In this paper, we first use the Monte Carlo sampler to return a sequence of likely orbits for each system.Then global and local optimizations are performed for each system with multiple initial estimates.The specific implementation is described below.
First, we use The Joker (Price-Whelan et al. 2017; Price-Whelan & Goodman 2018; Price-Whelan et al. 2020) to perform custom-built Monte Carlo rejection sampling over a large range of possible orbital parameters to determine a series of likely orbits.For each system of sample II, we initialize The Joker with five million prior samplings and then derive the appropriate range of orbital solutions.The number of possible orbital solutions returned by The Joker for each system is denoted by m.
In the second step, we further derive the possible orbital solutions of each system in sample II with the IDL code rvfit (Iglesias- Marzoa et al. 2015).This code uses the adaptive simulated annealing (ASA) global minimization method to fit RV curves of binaries.However, before running the rvfit code, it is necessary to define the boundary of parameters and provide initial parameter estimates.Multiple initial estimates for each system in sample II have been obtained from The Joker.The parameter range is subject to the following constraints: 1.The ranges of M 0 and ω in radians are [0,2π), and e is [0,1); 2. According to Equation (4), we can obtain: where V min and V max are the expected maximum and minimum RV provided by the model.We replace V min and V max with the minimum (v min ) and maximum (v max ) of the RV observations, and the ranges of K and γ are set 3. The number of changes in the sign of the RV derivative (n) is related to the period P. Following Birko et al.
(2019), we roughly infer the upper bound of P by the size of n, when n = 0 (the RV derivative is either positive or negative), or 1, assuming that P is not greater than 8 times the time span between the first and the last observation.
For n = 2, it is assumed that P is not longer than 3 times the time span.Moreover, when n > 2, P is in the time span.The lower bound of P is set as 0.25 days.
Finally, during the local fitting, we directly use the lmfit Python package, which provides a simple, flexible interface to nonlinear optimization problems (Newville et al. 2021).It provides several optimization methods available from scipy.optimize.Here we choose the Levenberg-Marquardt algorithm (LM; Levenberg 1944;Marquardt 1963) to fit each system with a series of preliminary parameter values provided by the rvfit.Once the current best-fit orbital solution with the LM method has been completed, uncertainties of the fitted parameters and correlations between pairs of fitted parameters are automatically calculated from the covariance matrix.
The combination of The Joker, rvfit, and lmfit yields m fitting orbital solutions for each system, from which we select the one with the minimum c orb 2 as the best and final solution.

Criteria for the Acceptance of Orbital Solutions
We define hereafter three quality indices, i.e., the goodness of fit, the signal significance, and the maximum gap in a phase.These indices will be used in distinguishing acceptable orbital solutions from those that are irrelevant or at least potentially wrong.
As described in Section 3.1, the goodness-of-fit statistic, F2 (Equation ( 2)) gives a quantitative measurement of whether an orbital solution is compatible with the real observations.Here the null hypothesis is the orbital solution derived through an adequate model, and χ 2 is given by Equation (3) with d.o.f., N − 6.Therefore, a large F2 means that the model is inadequate, or that the uncertainties used to derive the χ 2 are underestimated.We adopt a 99.9% confidence level, implying that the null hypothesis is accepted when F is less than 3.1.However, as mentioned in the Gaia DR3 validation (Babusiaux et al. 2023), F2 is not always sufficient enough to decide whether an orbital solution is worth keeping or not.6 So, we also consider two other criteria, the significance and maximum gap in phase.The significance is equivalent to an S/N and addresses some of these limitations.For SB1s, the signal significance is defined as the RV semiamplitude, K, divided by its uncertainty: The above definition of significance is adopted since a spectroscopic orbit generally possesses a large K. Indeed, an orbit with K close to or smaller than its uncertainty may be obtained for a single star.Solutions with s 10 will be considered as acceptable.The final index is the maximum gap in phase (phase_gap_max).Phase is calculated according to the period (P) and the reference time t 0 for each system.We sort the phases of all identified systems and then calculate the maximum gap in phase (phase_gap_max).It is obvious that the larger phase_gap_max equates to the poorer orbit coverage, which indicates that the orbit has not been well constrained during this region.The phase_gap_max of an acceptable orbit is taken to be less than 0.3, for which the observation is expected to be around 70%.
Combining the above three criteria, the orbital solutions with F2 < 3.1, s > 10, and phase_gap_max < 0.3 are reliable enough to be retained.A total of 255 sources in sample II are retained and identified as SB1s.The orbital information of these systems is listed in Table 2, and is also available in the China-VO at doi:10.12149/101309.

Comparison with Other Catalogs
We perform crossmatching of our LAMOST SB1s with the other binary catalogs.Among those works based on LAMOST data (Zhang et al. 2019;Wang et al. 2021;Kovalev et al. 2022;Zhang et al. 2022) we find 84 systems in common.Among the SBs of the GALAH (Traven et al. 2020) and APOGEE surveys (El-Badry et al. 2018;Price-Whelan et al. 2020;Kounkel et al. 2021), there is one system in common.We crossmatch with GDR3's non-single star catalogs (NSS; Gaia Collaboration et al. 2023).There are 10 systems in common, of which 9 systems have GDR3 orbital solutions.We also find two systems labeled as SB * in the SIMBAD database (Wenger et al. 2000).One of the SB * systems provides a complete spectroscopic orbit (Leiner et al. 2015), while the other SB * system only provides the period and eccentricity (Meibom & Mathieu 2005).Except for these common stars, there are 168 SB1s that are newly discovered and listed in our catalog.In Table 2, we assign flag_new = 1 for new SB1s.Otherwise, the flag_new is set to zero.The orbits of best fit and the corresponding residuals for three typical examples of new SB1s are shown in Figure 3.
The best way of validating our SB1 orbits is to compare them with existing orbits.Table 3 presents a comprehensive list of systems with known reliable orbits, including our orbital solutions as well as those derived from previous studies.The corresponding RV curves and the residuals (O -C) of the fitting for each system are shown in Figure 4.When comparing the orbital parameters between our work and the previous studies, we find that the orbital periods of all 11 systems are consistent with those of previous works within the 1σ uncertainties (see Figure 5).However, there are also discrepancies in certain orbital parameters for some systems.As shown in Figure 4, we can also see that certain systems exhibit significant differences in ω between LAMOST and Gaia orbits, which are due to the phase differences presented in the phase-RV diagrams.As suggested by the e − Δ ω diagram (Figure 6), a plausible cause is that the data available to us is not sufficient for a precise ω in the case of small e.So in this case, it becomes important to conduct further fitting studies using multitype observation data.

Orbital Properties
The period-eccentricity (p − e) diagram provides valuable diagnostic information about the physical processes occurring in binary systems.For example, the dynamical evolution of these systems leads to a gradual transition toward more circular orbits.The timescale of this circularization process depends on  the length of the orbital period; short-period systems circularize quickly, while long-period systems can maintain substantial eccentricity for much of their stellar lifetimes (Kounkel et al. 2021).Figure 7 illustrates the distribution of eccentricity of LAMOST SB1s as a function of their orbital period and colored by surface gravity, log g.The dotted line represents the upper envelope, which was derived by Mazeh (2008) through the statistics of 2751 systems in the 9th Catalog of Spectroscopic Binaries (Pourbaix et al. 2004).Out of all SB1s, the eccentricity of 225 (88%) systems is significantly lower than the upper-envelope line.Notably, sources with P < 10 days tend to exhibit circularized orbits.In systems with giant-star members (darker points), circularization occurs at longer periods.These findings align consistently with previously established distributions (Price-Whelan et al. 2020; Kounkel et al. 2021).
However, there are still some SB1s with large e outside the upper-envelope line.We perform statistical analyses of the stellar parameters (i.e., LAMOST effective temperature, T eff , and Gaia FLAME age) for systems situated on either side of the envelope (Table 4), with the objective of exploring the factors contributing to their higher eccentricities.We find that stars located outside the envelope line tend to be younger and exhibit higher surface temperatures, implying that they have not yet been circularized.However, this statistical result is insufficient to fully explain the existence of all exceptionally high eccentric orbits, as Gaia Age parameters were available for only six systems.Moreover, Figure 7 shows that there are also some eccentric orbits (e > 0.1) with orbital periods around 1 day falling within the envelope line.Upon analyzing their spectral types, there is no apparent tendency for them to be early-type stars.Consequently, the exact cause of their higher  Leiner et al. (2015), and Meibom & Mathieu (2005).The orange and light purple solid lines depict spectroscopic orbits provided by LAMOST and other works, respectively.The light orange and light purple shading indicates the corresponding 1σ uncertainties.Note that the dots in each graph represent LAMOST observation data, with the same color denoting observations conducted in the same year.In the left panel of the last row, the data from Leiner et al. (2015) are also illustrated using star-shaped symbols.
eccentricities remains unclear at present.For certain systems within this category, the orbit is driven toward a larger e solution due to the presence of only a few RV data points or large RV measurement errors.However, for systems with wellsampled RV curves, the high e may be attributed to specific astrophysical scenarios, such as a high primordial eccentricity or the presence of an unseen tertiary companion, which affects their orbital evolution (Mazeh & Shaham 1979).
In Figure 8, we present the histograms of P and K for our SB1s.It is evident that the number of SB1s decreases as the P increases and over 80% of the systems have P shorter than 100 days.Additionally, we observe that the number of SB1s decreases with the increase in K, with only two systems having K greater than 90 km s −1 .

Stellar Parameter Properties
It is useful to investigate the distribution of stellar parameters of SB1s, although the general method for determining the stellar parameters may not be appropriate for binaries.We adopt the stellar parameters derived from the LAMOST DR8 LRS (i.e., T eff , surface gravity ( g log ), and metallicity ([Fe/H]))      9.It is apparent from these diagrams that SB1 dwarfs outnumber giants.Additionally, we calculated the ratios of dwarfs within the sample, sample II, and SB1s, resulting in percentages of 78%, 65%, and 82%, respectively.The reason for the highest proportion of dwarfs in SB1s could be attributed to the increase in radius when the massive component climbs the red giant branch.Due to Roche lobe radius limits, the smallest binary orbits that can host giant stars must be larger than the orbits of main-sequence stars.Consequently, the periods of host giant SB1s will be longer and RV changes will be smaller, making their detection more challenging (Matijevič et al. 2011).Interestingly, we have discovered that compared to the sample and SB1s, the proportion of giants is the highest among the SB1 candidates (sample II).These candidates exhibit brighter and higher effective temperatures.This outcome implies that a significant portion of sources within the SB1 candidates may be variables.
The left panel of Figure 10 presents the cumulative distributions of the distances for sample, sample II, and LAMOST SB1s.We find that the number of SB1s decreases with the increase of distance, which is consistent with the change in the number of the sample with distance.This confirms the detection efficiency of SB1s is not affected by the target distance.Additionally, our investigation reveals that SB1 candidates are observed with larger distances than LAMOST SB1s.As mentioned above, this is because SB1 candidates are brighter.We examine the metallicity distribution function of our SB1s.In the middle and right panels of Figure 10, we display the distribution of metallicities produced by LAMOST LASP ([Fe/H]) and Gaia GSP-Phot ([M/H]) for different samples.As expected, the SB1s are systematically more metalpoor than the general population, although the effect is more pronounced when adopting metallicities from Gaia GSP-Phot than from LAMOST LASP.This is consistent with previous conclusions (Moe et al. 2019).

Caveats
There are several caveats about utilizing our SB1 catalog.The employed algorithm is designed to obtain SB1 orbits of best fit.However, owing to the insufficient orbital phase coverage and precision, the observed data can be compatible with several alternative orbits, and the best-fitting solution might not necessarily represent the true orbital parameters Additionally, it is important to emphasize that all criteria for the acceptance of orbital solutions are determined statistically.This implies that the resulting outcomes are statistically correct, but some incorrect individual fits can survive near the borders where the decisions are taken.Lastly, as the primary objective of this work does not focus on the completeness of the SB1 catalog, it is essential to take into account the selection effects of the LAMOST-LRS data and the detection process of the method in subsequent statistical studies.

Summary
Based on LAMOST DR8 LRS data, we applied the χ 2 test on a sample of 6852 stars that have at least 12 measurements with S/ N g > 10.The χ 2 test identifies 1696 RV variables at the ∼3σ confidence level.Note that some variable stars can produce the intrinsic RV jitter, which is easily confused with orbital variations.Therefore, we performed a crossmatch with GDR3 variable catalogs, GCVS, ASAS-SN of variable stars, and VSX and discarded 399 variables, resulting in 1297 SB1 candidates.Next, we employed a combination of The joker, rvfit, and LM algorithms to fit the spectroscopic orbital solutions of SB1 candidates.We defined these SB1s as sources that pass the following criteria: F2 < 3.1, s > 10, and phase_gap_max < 0.3.
In total, the catalog of SB1s contains 255 systems with spectroscopic orbital solutions.When comparing with other binary catalogs, we found that approximately 66% of the systems in our catalog are newly discovered.Among the known SB1 systems, a total of 10 systems have provided complete spectroscopic orbits, while one system has provided P and e.We present a comparison between our SB1 orbital parameters and those from external catalogs to validate our orbital solutions.Notably, the orbital P of all 11 systems exhibit compatibility with our results.
The p-e diagram shows consistency with previously derived distributions, particularly in the circularization tendency of sources with a period <10 days.The presence of selection effects led to approximately 80% of the SB1s having an orbital P of less than 100 days, and the distribution peak of γ is a positive value.
Based on stellar parameters from LAMOST-LRS and GDR3, we find that, in comparison to the general sample, the SB1 catalog contains a higher proportion of dwarfs as opposed to giants.Furthermore, the number of SB1s decreases with increasing distance.Additionally, the outcomes suggest that SB1s tend to be more metal-poor compared to the overall stellar population.
As a follow-up to this work, we will focus on conducting a comprehensive analysis by jointly fitting astrometric, photometric, and spectroscopic data from various surveys for our SB1s, aiming to obtain complete orbital solutions.Additionally, it is noteworthy that the ongoing LAMOST survey will continue to offer excellent opportunities for studying binaries.

Figure 1 .
Figure 1.Histogram of the number of LAMOST observations per object of sample (empty histogram), sample II (filled orange).

Figure 3 .
Figure 3.The RV curves (the solid orange lines) and residuals (bottom row) for three examples of new SB1s.The dots in each graph represent LAMOST observation data, and their identical colors indicate observations taken in the same year.

Figure 4 .
Figure4.The RV curves and residuals for 11 common sources with Gaia DR3,Leiner et al. (2015), andMeibom & Mathieu (2005).The orange and light purple solid lines depict spectroscopic orbits provided by LAMOST and other works, respectively.The light orange and light purple shading indicates the corresponding 1σ uncertainties.Note that the dots in each graph represent LAMOST observation data, with the same color denoting observations conducted in the same year.In the left panel of the last row, the data fromLeiner et al. (2015) are also illustrated using star-shaped symbols.

Figure 5 .
Figure 5.Comparison of the orbital periods of 11 common systems between our work and the previous studies.

Figure 6 .
Figure 6.The absolute difference in ω between LAMOST and other works plotted against e.

Figure 7 .
Figure 7. Period-eccentricity relationship of the fitted orbit for our SB1s.Markers are colored by surface gravity, g log .The dotted line represents the upper envelope, which was derived by Mazeh (2008).

Figure 8 .
Figure 8. Histograms of P and K.

Figure 9 .
Figure 9. Left: Gaia DR3 absolute magnitude (M G ) vs. color (G RP − G BP ) diagram (CMD) and the corresponding density distributions for sample, sample II, and LAMOST SB1s.The dashed line denotes a dwarf-giant distinction given by Merle et al. (2020).Right: Kiel diagram and density distributions of effective temperature (T eff ) and surface gravity ( g log ) obtained by LAMOST LASP for different samples of stars as indicated in the legend.

Figure 10 .
Figure 10.Left: cumulative distribution of Gaia DR3 distances toward sources for different samples of stars.Middle and right: cumulative distribution function of metallicity derived by LAMOST LASP ([Fe/H]) and Gaia GSP-Phot ([M/H]).

Table 1
Description of the Data Table Containing Summary Information for Sample II (This table is available in its entirety in machine-readable form.)wheref is the true anomaly deduced from the eccentric anomaly E by

Table 2
Description of the Data Table Containing Summary Information for 255 SB1s (This table is available in its entirety in machine-readable form.)

Table 3
The Orbital Parameters of LAMOST Sources, Compared with Elements of Previous Studies

Table 4
Statistics of Age and T eff for Systems on Both Sides of the Upper- Note.Outside and Inside represent systems located outside and inside the upper-envelope line, respectively.N is the number of LAMOST T eff and Gaia ages (Age_flame) that are available.and Gaia DR3 (i.e., absolute magnitude (M G ), color (G RP − G BP ), distance (distance_gspphot), and