A Sample of Compact Object Candidates in Single-lined Spectroscopic Binaries from LAMOST Medium Resolution Survey

Compact objects (black holes, neutron stars and white dwarfs) represent the final products of stellar evolution. The search for compact objects provides significant implications for understanding stellar physics and interstellar medium. Notably, astrometric observations from Gaia were used to identify compact objects. For instance, El-Badry et al. (2023a) and El-Badry et al. (2023b) reported two binaries containing stellar black holes (Gaia BH1 and Gaia BH2) from Gaia data release 3, whose companions are respectively a G-type star and a red giant. Recently, Panuzzo et al. (2024) discovered a black hole of $32.70\pm 0.82$ $M_{\odot}$  existed in a wide binary system Gaia BH3.

The Doppler spectroscopy have yielded interesting discoveries. Casares et al. (2014) claimed a black hole of $3.8M_{\odot}$  to $6.9M_{\odot}$  in MWC 656, which was challenged by Janssens et al. (2023) who derived a much lower mass of $0.94\pm 0.34~{}M_{\odot}$  for the unseen companion. Liu et al. (2019) reported that the binary LB-1 consists of a B-type star and a black hole of $68^{+11}_{-13}~{}M_{\odot}$  albeit this system is also likely to host two luminous stars (Shenar et al., 2020). Saracino et al. (2022) reported the detection of a black hole of $11.1^{+2.1}_{-2.4}$ $M_{\odot}$  in NGC 1850, which was later shown to be a stripped-star binary (El-Badry & Burdge, 2022). In addition, several black hole candidates are also reported in quiescent binary systems (Thompson et al., 2019; Lam et al., 2022; Shenar et al., 2022).

Long-term spectroscopic monitoring has also yielded valuable research in dynamically identifying compact binary, containing a neutron star or a white dwarf (Rebassa-Mansergas et al., 2016; Cojocaru et al., 2017; Rebassa-Mansergas et al., 2017; Ren et al., 2018; Hernandez et al., 2021; Mazeh et al., 2022). Increasingly, attention has been given to the search of compact objects through time-domain surveys, particularly via the spectroscopic surveys that frequently generate potential candidates. Through comprehensive advantages in terms of data potential, such time-domain spectroscopic surveys have great predominance and prospects to identify compact object candidates.

The Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST), a large spectroscopic survey covering the north sky, offers tens of millions of spectra (Cui et al., 2012). The Data Release 10 (DR10) represents a significant milestone in the project, indicating the accumulation of a large volume of observational data and the completion of data processing and analysis up to that release. The DR10 provides multiple spectral observations for individual targets in the Low Resolution Survey (LRS) and the Medium Resolution Survey (MRS). The MRS observation is conducted in about 50% nights of the LAMOST second stage (since 2018) and have a resolution of 7500 respectively at 5163 Å (blue band) and 6593 Å (red band), which allows for accurate measurement of radial velocities and improved identification of spectral components. Based on the DR10-MRS data, single-lined spectroscopic binary stars can be easily classified and compact objects can be potentially identified in them.

Previous researches on LAMOST data have made significant progresses, with several compact binary candidates discovered, where the unseen companions are neutron stars and high-mass white dwarfs (Gu et al., 2019; Zheng et al., 2019; Mu et al., 2022; Zhang et al., 2022; Yuan et al., 2022; Li et al., 2022; Qi et al., 2023; Yuan et al., 2023; Zhang et al., 2024). With the accumulation of data from LAMOST and ongoing observations, there are more compact object candidates yet to be identified. Especially in DR10-MRS, which includes a decade of LAMOST spectral data, it provides an excellent opportunity for searching for compact object binary candidates. Moreover, the DR10-MRS data has relatively high spectral resolution and single-exposure data from the same day, which not only meets the precision requirements for radial velocity measurements but also provides supplementary data for the short-period binary star dynamical analysis. We collect the DR10-MRS data as much as possible, and try to search for the compact object candidates in it. The benefit of this search strategy represents on the larger sample coverage and observation data space to obtain more compact objects candidates.

The crux, however, is to overcome the abundance of false data and spurious samples. Previous work relies on designed selecting methods or complex parameter spaces to circumvent most of the false data. In this work, we are shifting focus to radial velocity curves, making everything less cumbersome. We introduce how we generate input-sample relying on raw data from public DR10-MRS catalog and how our pipeline works in Section 2. We try to fit the radial velocity curve for every target in input-sample, and then exclude those double-lined spectroscopic binaries and eclipsing binaries. As a result, we obtain a sample with a size of 95 for compact object binary candidate. Our results are displayed in Section 3. We summarize and discuss our results in Section 4. Details and techniques are provided in the Appendix.

We download a complete LAMOST MRS General Catalog, named dr10_v1.0_MRS_catalogue, from LAMOST DR10’s data access, and remove invalid data in it. In total, we obtain a catalog containing 1134865 sources, including 984719 with repeated observations. In this catalog, 130332 sources have more than 3 medium-resolution observational nights and 85062 sources have more than 5 nights. In each observational night, LAMOST conducts commonly 3 medium-resolution exposures for each source. This provides abundant time-domain spectral observation data for a large number of targets, offering a substantial data foundation for dynamic analysis. In this work, we are dedicated to comprehensively searching for compact object candidates in binaries among sources in DR10. We aim to select candidates from those sources with repeated observations, and the targets should satisfy the following conditions:

• •

  Requirement: Radial velocity data should be well-folded.

• •

  Exclusion: Consisting of two main-sequence stars.

We aim to filter spectroscopic binary through the variation in radial velocity and exclude those consisting of two main-sequence stars, including eclipsing binaries and double-lined spectroscopic binaries. As for the first condition, starting from the spectra, we tend to select targets with well-folded radial velocity data, which exhibit relatively high acceptability in terms of their orbital parameters. As for the second condition, we adopted the approach as described in Fu et al. (2022) to exclude: visually inspecting eclipsing binaries by folding photometric data and exclude double-lined spectroscopic binaries referred to the Cross-Correlation Function (CCF) peaks and profiles.

Here, we qualitatively describe our processing workflow as follows. For each target, We collect photometric data and search for its photometric period $P_{\rm pho}$. We consider $P_{\rm pho}$  as a potential orbital period, no matter which specific pattern exhibited in the light curve. Then we search the period of the radial velocity data based on $P_{\rm pho}$  or without a reference period, and fold radial velocities to fit radial velocity curve. We select possible candidates among those targets have smaller fitting residuals. After we have selected targets whose radial velocities can be well-folded, we then rule-out those targets with inconsistencies existing in spectroscopy and photometry.

For this investigation, we do not expect to narrow down the input-sample size by individually inspecting. Instead, we attempt to directly fold radial velocities, fit velocity curves, and utilize fitting residuals to select targets. We select targets with well-folded radial velocities before verifying them for single-lined spectroscopic binaries, which has alleviated several manual inspections of photometric types and spectroscopic data. we reduce artificial involvement with imperative visual inspections positioned as the ultimate step. This strategic approach is devised to contend with the large volume of sources within the DR10 catalog.

The above procedure produces possible radial velocity curves for every target in our input-sample. After period search and folding, over 1500 targets did not show well-converged radial velocity curve profiles, meaning them lack periodic variations in their radial velocity observations, possibly due to insufficient exposures or incorrect adopted period. We conducted a manual review of approximately 300 targets with complete radial velocity curves, excluding those exhibiting variability attributed to various types of eclipses (As shown in Figure 7 in the Appendix E) and those with double-lined spectroscopic spectra. We do the spectroscopic exclusion by proofreading shifted spectra and double-peaked structure in the CCF. We have provided an explanation of the types of CCF structure in the Appendix E.

We select the candidates from the input-sample, and through manual examination of both photometric and spectroscopic data, we eliminate potential spectroscopic binaries, leaving us with 89 candidates. These targets all possess a complete folded velocity curve with a sufficient number of radial velocity points. 64 targets also have light curves that synchronize with the orbit phase, indicating orbital modulation in the photometric variation. For other targets, either no light curve is available or the light curve does not show clearly converge at some period. For these targets, the orbital period is primarily determined through period searching in the radial velocity data.

Fitting the radial velocity curves yielded orbital parameters for the targets, including the radial velocity semi-amplitude $K$ and orbital period $P_{\rm orb}$. Then, the mass of the invisible object can be constrained by the mass function, expressed as (Remillard & McClintock, 2006):

where $M_{1}$ is the mass of the optically visible star; $M_{2}$ is the mass of the unseen companion; $K_{1}$ is the semi-amplitude of the radial velocity; $P_{\rm orb}$ is the orbital period; $i$ is the inclination, and $G$ is the gravitational constant. We calculate the mass function for our sample using parameters obtained from the radial velocity curve fitting. The distribution of all targets in the mass function space is shown in Figure 1, and listed in Appendix G.

In the Figure 1, we present the distributions of radial velocity semi-amplitudes and orbital periods for all 89 candidates in our sample. The orbital periods of our candidates range from 0.1 days to approximately 10 days, and the radial velocity semi-amplitudes span from about 30 $\rm km\,s^{-1}$to approximately 200 $\rm km\,s^{-1}$. Nearly all of the sources fall above the green reference curve, indicating their mass functions are greater than 0.01 $M_{\odot}$. There are 69 targets reside in the region above the orange reference curve which corresponds to a mass function greater than 0.05 $M_{\odot}$. Among these targets, targets No.1-26 in the sample have mass functions exceeding 0.1 $M_{\odot}$.

In our result, there are three published identifications of inclusive targets (J0419, J2354 and J1729), which are marked with colored asterisks in figures. Target No.1 (J0419) contains an extremely low mass pre-white dwarf and a compact object, with $M_{1}=0.176\pm 0.014\,M_{\odot}$ and $M_{2}=1.09\pm 0.05\,M_{\odot}$ (Zhang et al., 2022). Target No.2 (J2354) contains an K-type star and a neutron star candidate, with $M_{1}=0.70\pm 0.05\,M_{\odot}$ and $M_{2}=1.26\pm 0.03\,M_{\odot}$ (Zheng et al., 2023). Target No.18 (J1729) contains an K-type star and a white dwarf, with $M_{1}=0.81\pm 0.07\,M_{\odot}$ and $M_{2}\geq 0.63\,M_{\odot}$ (Zheng et al., 2022). The remaining targets currently await individual analysis.

In addition, compared to the three identified candidates, the other candidates in our sample can exhibit relatively longer orbital periods. Leveraging tens of observations provided by LAMOST and employing period analysis, we also obtained targets with relatively minor radial velocity variations. As shown in Table 3, except for Target No.18 (J1729), which only has one day of effective observational data, the rest of the targets have multiple days of LAMOST observations. Half of the targets have more than ten days of spectroscopic observations, with dozens of radial velocities. We examined the spectra of the candidates to ensure accurate radial velocity measurements. Well-folded radial velocity data provided reliable orbital parameters. We have ruled out double-lined spectroscopic binaries among the candidates in our sample, and it is worth to further identify our candidates, especially for candidates resembling the green asterisk marker (J1729) in the Figure 1.

We collect the parallax and the stellar parameters including effective temperature $T_{\rm{eff}}$, surface gravity log$g$, metallicity [Fe/H], and radius from Gaia DR3 (Gaia Collaboration et al., 2023). We use the stellar evolution models to evaluate the mass of visible stars by utilizing the python package isochrones⁵⁵5https://isochrones.readthedocs.io/en/latest/. We use the Gaia DR3 parameters and photometry as inputs to derive isochrone interpolated mass with MESA Isochrones & Stellar Tracks isochrones (MIST; Dotter, 2016). The isochrone mass of visible star is shown in Table 2. Combined with the mass function equation, the lower limit of the invisible object’s mass $M^{\rm{min}}_{2}$ is calculated under the assumption that $i=90^{\circ}$. We find that the lower limit of the invisible object’s mass $M^{\rm{min}}_{2}$ is above or close to half of the visible stellar mass $M_{1}$ for the first thirty or so targets in our sample. A normal main-sequence star at a such mass would contribute non-negligible optical flux and manifest double-lined spectroscopic features, thus these single-lined spectroscopic binaries could conceal a compact object. The binary mass for target No.1-26 is presented in Figure 2 and listed in Table 2. Parameters for all candidates is presented in in Appendix F and Appendix G.

In this paper, we have constructed a catalog of 89 compact object candidates in single-lined spectroscopic binaries using the LAMOST DR10-MRS observations. All candidates have well-folded radial velocity data. Overall, the results are very encouraging: a large number of candidate compact objects are discovered in a single pipeline execution, among which our existing identifications are also included (i.e., target No.1 J0419, target No.2 J2354 and target No.18 J1729). For 64 out of 89 objects, their phase folded light curves are consistent with the radial velocity variations; hence, their orbital parameters (e.g., orbital period and semi-amplitude) are more reliable. Our main results are as follows:

1. 1.

   Initial target selection: We utilize data from the DR10-MRS catalog to establish selection criteria to pre-select targets, particularly introducing variability rates $\mathrm{d}v/\mathrm{d}t$  to selective focus on the shorter-period targets. By imposing constraints on the variance of $\mathrm{d}v/\mathrm{d}t$  we additionally obtain a larger number of targets with reliable radial velocity measurements, expanding sample pool for subsequent verification. Combining criteria on radial velocity variation, we create an initial sample of 1822 targets, all of which have the potential to possess large mass function because of large or rapid radial velocity variations.

2. 2.

   Compact object candidates: We ultimately select 89 single-lined spectroscopic binaries with well-folded radial velocity data, which probably contain compact object candidates. The mass function of 26 candidates are larger than 0.1 $M_{\odot}$. Among them, 18 targets also exhibit ellipsoidal type light curves. These candidates fulfill the criteria wherein the minimum limit of the unseen object’s mass $M^{\rm{min}}_{2}$ is above or approximately half of the half of the visible stellar mass $M_{1}$. This estimation strongly supports the presence of compact objects within these candidates.

3. 3.

   Optimization of selection procedures： We directly fit radial velocity curves for 1822 targets, selecting those with well-converged curves. We deferred manual inspection (for both photometry and spectroscopy) until after the source selection stage, which saved us from manually inspecting over a thousand targets and greatly reduced the time resource waste caused by erroneous measurements both in photometric and spectroscopic. In order to achieve this goal, we use the workflow described in Section 2 for handling photometric and spectral data, generating reliable radial velocity curves for potential targets.

To further constrain the mass determination of the unseen object, precise inclination measurement is imperative. Ellipsoidal modulation has been detected in part of our candidates, allowing for inclination analysis through fitting light curves. However, a majority of reported candidates lack observable ellipsoidal light curves because the insufficiently close proximity of the binary stars results in tidal deformation not obvious. Besides, there are challenges in accurately constraining the rotational velocity of the visible stars, limiting our ability to determine inclination by measuring $v\sin i$. While this paper focused on compiling the compact object binary catalog, it is important to highlight these potential researches for the sampled candidates, which will be pursued in the future work.

We thank the anonymous referee for their constructive suggestions to improve the paper. This work was supported by the National Key R&D Program of China under grants 2023YFA1607901 and 2021YFA1600401, the National Natural Science Foundation of China under grants 11925301, 12033006, 12221003, 12263003 and 12322303, the Natural Science Foundation of Fujian Province of China under grants 2022J06002, and the fellowship of China National Postdoctoral Program for Innovation Talents under grant BX20230020. J.Z.L was supported by the Tianshan Talent Training Program through the grant 2023TSYCCX0101. This paper uses the data from the LAMOST survey. 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. This paper includes data collected by the TESS mission obtained from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope Science Institute. The specific observations can be accessed via STScI (2018). ZTF is a public-private partnership, with equal support from the ZTF Partnership and from the U.S. National Science Foundation through the Mid-Scale Innovations Program (MSIP).