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Searching for Double-line Spectroscopic Binaries in the LAMOST Medium-resolution Spectroscopic Survey with Deep Learning

Searching for Double-line Spectroscopic Binaries in the LAMOST Medium-resolution Spectroscopic... Double-line spectroscopic binaries (SB2s) are a vital class of spectroscopic binaries for studying star formation and evolution. Searching for SB2s has been a hot topic in astronomy. Although considerable efforts have been made with fruitful outcomes, limitations in automation and accuracy still persist. In this study, we developed a convolutional neural network model to search for SB2 candidates in LAMOST medium-resolution survey (MRS) data release (DR) 9 v1.0 by detecting double peaks in the cross-correlation function (CCF).We first generated a large number of spectra of single stars and binaries using the iSpec spectral synthesis software. The CCFs of these synthesized spectra were then calculated to form our training set. To efficiently detect the peaks of the CCFs, we applied a Softmax function-based noise reduction method. After testing and validation, the model achieved an accuracy of 97.76% in the testing set and was validated for more than 90% of the sample in several published SB2 catalogs. Finally, by applying the model to examine approximately 1.59 million LAMOST-MRS DR9 spectra, we identified 728 candidate SB2s, including 281 newly discovered ones. Unified Astronomy Thesaurus concepts: Convolutional neural networks (1938); Spectroscopic binary stars (1557) Supporting material: machine-readable tables 1. Introduction Bate et al. (2002) studied the formation of SBs and provided evidence that high-frequency close binaries can be formed by Binary systems play an essential role in modern astrophysics dynamical interactions in unstable multiple systems and orbital (Raghavan et al. 2010; Duchêne & Kraus 2013). Investigating decay of initially broader binaries. the distributions of the period, mass, and eccentricity of binary The search for and identificationofSBs,drivenbyscientific systems can provide valuable insights into the origin and research, remains a popular direction for current binary star evolution of stars (Moe & Di Stefano 2017). studies. Spectroscopic surveys have produced large numbers of The common types of binary systems are visual binaries and spectra, which have facilitated the search for SBs. Merle et al. spectroscopic binaries (SBs). SBs can be further classified into (2017) detected 354 SB candidates in Gaia–ESO Survey internal single-line SBs (SB1s) and double-line SBs (SB2s), depending data release (DR) 4 by calculating the successive derivatives of on the number of stellar components of the spectra. SB1s have CCFs to detect multiple peaks. Matijevič et al. (2010) found 123 single-line spectra that are dominated by the flux of the primary SB2 candidates in RAVE DR2 by analyzing the shapes and star. They can be identified by the periodic changes in radial properties of the CCFs. Kounkel et al. (2019) identified 399 velocity (RV) observed over multiple epochs (Merle et al. binaries in the APOGEE-2 spectra using Gaussian fitting to find 2020). In contrast, SB2s have double-line spectra that are peaks from the CCFs. Building on this work, Kounkel et al. jointly dominated by the fluxes of the primary and secondary (2021) found 7273 SB2s, 813 SB3s, and 19 SB4s in the stars. They can be identified by the presence of double peaks in APOGEE DR16 and DR17 data. Skinner et al. (2018) detected 44 the cross-correlation function (CCF; Matijevič et al. 2010; SB2 candidates by measuring the degree of asymmetry of CCFs Merle et al. 2017; Kounkel et al. 2021; Li et al. 2021). of Sloan Digital Sky Survey III DR13. El-Badry et al. (2018) The study of SBs holds significant scientificvalue, as identified over 3000 SBs in APOGEE DR13 using a data-driven exemplified by numerous studies in recent years. Mahy et al. spectral model. Traven et al. (2020) obtained 12,760 SB2s in (2022) utilized the physical properties of SBs to successfully detect GALAH using t-distributed stochastic neighbor embedding stellar-mass black holes. Moe & Di Stefano (2017) demonstrated classification and CCF analysis. Kovalev et al. (2022) obtained that early-type SBs exhibit distinct eccentricity and mass 2460 SB2 candidates in the LAMOST medium-resolution survey distributions. Tokovinin et al. (2006) surveyed solar-type SBs (MRS) by analyzing the V sin i values in the spectral FITS files. and established that the periods of SB systems with triples were LAMOST-MRS (Liu et al. 2020), which began in 2017, further shortened by angular momentum exchange with compa- contains blue and red arms, covering 4950 Å to 5350 Å and nions. Maxted et al. (2001) showed that binary evolution was the 6300 Å to 6800 Å, respectively. The resolution of LAMOST- basis for the formation of the most extreme horizontal branch stars. MRS is 7500, and its limiting magnitude is around G ∼ 15. LAMOST-MRS DR9 V1.0 published more than 15 million Original content from this work may be used under the terms spectra from over 2.18 million targets (signal-to-noise ratio or of the Creative Commons Attribution 4.0 licence. Any further S/N … 10). LAMOST-MRS is capable of measuring RVs with distribution of this work must maintain attribution to the author(s) and the title −1 of the work, journal citation and DOI. a precision of 1 km s , making it effective for searching for 1 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. SB2s (Liu et al. 2019; Li et al. 2021). Using the method of Table 1 Parameter Space for the Synthetic Spectra multiple derivative determination of CCF peaks described in Merle et al. (2017), Li et al. (2021) identified 3133 SB2 and Parameter Distribution Unit 132 spectroscopic triple candidates in LAMOST-MRS DR7. T  (2500, 8000) K eff1,2 As several spectral surveys are launched, massive amounts log g  (−0.5, 5.5) dex 1,2 of spectra will be released, making the search for SB2s M/H  (−4.5, 1.0) dex 1,2 increasingly challenging. The development of deep learning −1 Vi sin  (0.0, 10.0) km s 1,2 techniques has demonstrated remarkable results and efficien- 2 −1 V  (0,25 ) km s cies in data mining and pattern recognition, leading scientists to −1 V V +  (−200, 200) km s 2 1 utilize this excellent tool in the search for SB2s. Li et al. (2021) S/N  (50, 300) dB constructed a recurrent neural network model for identifying SB2s using CCF images with labeled training samples. Zhang Note.  (a,b) represents a uniform distribution from a to b.  (a, b) represents a et al. (2022) built a convolution neural network (CNN) model 2 normal distribution with mean μ and variance σ . The numerical subscripts of based on synthetic spectra and obtained 2198 SB2 candidates Column 1 represent the parameters of the two single stars combined into a in LAMOST-MRS DR8. binary system. Overall, the deep-learning-based search and recognition of SB2s can significantly reduce the difficulty of manual Based on these parameters, we obtained the normalized recognition and obtain credible results. However, the number spectra of single stars using iSpec. We combined the synthetic of SB2 candidates from the published SB catalogs is relatively spectra of two single stars without adding noise to create binary small to meet the requirements for training deep learning spectra. The resulting spectra were then normalized, and models. To solve this problem, we synthesized the spectra of Gaussian noise was added to achieve a given S/N, resulting in single and binary stars and calculated the CCFs of these the SB2 spectra (Zhang et al. 2022). In addition to generating synthetic spectra, which were then used to construct the SB2 spectra as positive samples in this study, two single-star training set and testing set for the CNN model. spectra corresponding to each SB2 spectrum were also utilized The remaining sections of this paper are organized as follows. In as negative samples. Table 1 summarizes the parameter space Section 2,wedescribethe processofsynthesizing the spectra of of the synthesized spectra. The process of synthesizing the single and binary stars and acquiring the training and testing sets spectra and examples of the synthesized spectra can be seen in through CCFs. The model’s training process and its performance Figures 1 and 2, respectively. on the testing set, along with the validation results on some published SB2 catalogs, are presented in Section 3.In Section 4, 2.2. Calculation of CCF some newlydiscoveredSB2 candidates forLAMOST-MRSDR9 V1.0 are described. There is a brief discussion in Section 5 and we We utilized the iSpec application interface to calculate the summarize our work in Section 6. spectral CCFs using Equation (2)(Pepe et al. 2002): 2. Data and Preprocessing CCF()VS = (ll ) ·M( )dl. (2) SB2s can be identified by the double peaks of the CCFs in their spectra (Matijevič et al. 2010; Merle et al. 2017; Kounkel In this equation, S represents the spectrum that is subject to et al. 2021; Li et al. 2021). To this end, we employed a CNN CCF calculation, while M denotes the template spectrum. As model to detect SB2 candidates by recognizing the double the template spectrum, we used the NARVAL solar spectrum peaks of CCFs. covering 370−1048 nm, which was provided by iSpec (Blanco-Cuaresma et al. 2014b). The RV variations ranged 2.1. Spectra Synthesis −1 −1 from −500 to 500 km s , with a step of 1 km s . The results We utilized the iSpec spectral synthesis software (Blanco- of the CCFs calculated from the synthetic spectra in Figure 2 Cuaresma et al. 2014a; Blanco-Cuaresma 2019) to generate by iSpec are shown in Figure 3. spectra, along with the radiative transfer code SPECTRUM (Gray & Corbally 1994) and the stellar atmospheric models 2.3. Processing of CCF MARCS (Gustafsson et al. 2008) in iSpec. The blue arm of After calculating the CCFs of the spectra using iSpec in LAMOST-MRS, which covers 4950 to 5350 Å with more Section 2.2, we inverted and normalized the CCFs, which made absorption lines and distinctive features, was selected for the the peaks more prominent in value. Figure 4 shows the results synthetic spectra (Li et al. 2021). of the inversions and normalizations of the CCFs from We specified a set of parameters for the synthesized spectra, Figure 3. To better highlight the peaks of the CCFs and reduce as shown in Equation (1): the interference of the wings, the Softmax function is used to {} Tg ,log  ,M// H,V sini,V,S N . (1) suppress the wings of the CCFs, which is defined as eff Equation (3): Here, T , log g, and M/H represent the atmospheric eff parameters of the star, i.e., the effective temperature, surface s()zz = foriK =¼ 1, , and = (z ,¼,z )Î  , i 1 K K z gravity, and metal abundance, respectively. V sin i and V are S e j=1 the rotation velocity and the RV of the star, respectively. S/N () 3 indicates the given signal-to-noise ratio achieved by adding Gaussian noise to the whole of the synthetic spectrum, which is where z is a K-dimensional vector and the Softmax function derived from Zhang et al. (2022). polarizes its distribution and transforms it into a probability 2 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 1. Synthesis process of single- and binary star spectra. Figure 2. Examples of synthetic spectra. The top and middle panels are synthetic single-star spectra; the bottom panel is the normalized double-star spectrum after summing two single-star spectra. distribution. When the CCFs are processed using the Softmax In this work, we applied five Softmax calculations to the function, wings with smaller values are suppressed, while CCFs, and the results for the CCFs in Figure 4 are shown in Figure 5. As seen from Figure 5, the Softmax function peaks with significant features are enhanced. Therefore, this effectively suppresses the disturbance of the CCF wings, method can be considered as a noise reduction method. 3 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 3. The results of the CCFs calculated from the synthetic spectra in Figure 2. The red points are the peaks of the CCF, representing the RV of the spectra. Figure 4. The results of the inversion and normalization of the CCFs from Figure 3. Figure 5. The results of the original CCFs (dashed lines) and the CCFs after five Softmax calculations (solid lines). Table 2 The Architecture of Our CNN Model Layer Type Input Channels Output Channels Kernel Size Stride Input Shape Output Shape Activation C1 Conv 1 64 3 1 1, 1001 64, 999 ReLU B1 BN 64 64 LL 64, 999 64, 999 L C2 Conv 64 64 3 1 64, 999 64, 997 ReLU B2 BN 64 64 LL 64, 997 64, 997 L C3 Conv 64 128 3 2 64, 997 128, 498 ReLU B3 BN 128 128 LL 128, 498 128, 498 L C4 Conv 128 128 3 1 128, 498 128, 496 ReLU B4 BN 128 128 LL 128, 496 128, 496 L C5 Conv 128 256 3 2 128, 496 256, 247 ReLU B5 BN 256 256 LL 256, 247 256, 247 L C6 Conv 256 256 3 1 256, 247 256, 245 ReLU B6 BN 256 256 LL 256, 245 256, 245 L C7 Conv 256 512 3 2 256, 245 512, 122 ReLU B7 BN 512 512 LL 512, 122 512, 122 L C8 Conv 512 512 3 1 512, 122 512, 120 ReLU B8 BN 512 512 LL 512, 120 512, 120 L F9 Flatten LL L L 512, 120 61440 L D10 Dense 61440 1000 LL 61440 1000 L D11 Dense 1000 2 LL 1000 2 Softmax Note. Convolution layers. Batch normalization layers. making the processed CCFs more obvious in their features. The synthesized a total of 605,500 single-star spectra, which were processed CCFs are used as data for training the CNN model. combined to generate the corresponding 302,750 SB2 spectra. After completing the processes described above, we obtained Following the calculation and processing of the CCFs of all the the training and testing sets for the CNN model. We synthetic spectra, we selected 100,000 single-star CCFs and 4 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Table 3 Validation of SB2 Catalogs Survey Catalog All Identify Percentage LAMOST Li et al. (2021) 3244 3014 92.9% Kovalev et al. (2022) 2431 2378 97.8% Zhang et al. (2022) 3135 2819 89.9% Wang et al. (2021) 2357 2309 98.0% APOGEE El-Badry et al. (2018) 2637 2611 99.0% Kounkel et al. (2021) 8019 7824 94.6% Mazzola et al. (2020) 3566 3437 96.4% GALAH Traven et al. (2020) 11,351 11,345 99.9% Note. Column (1): catalog name. Column (2): spectroscopic survey. Column (3): the number of sources acquired to the spectrum. Column (4): the number of sources identified by the model. Column (5): the percentage of identified sources to all sources. Figure 6. Confusion matrix of the model on the testing set. accuracy of 97.76%, with a recall of 95.13%, a precision of 50,000 SB2 CCFs to constitute the testing set, while the 98.09%, and an F1 score of 96.59%. In this classification task, remaining 505,500 single-star CCFs and 252,750 SB2 CCFs the most important metrics are accuracy and recall, as the formed the training set. former represents the model’s overall predictive capability, while the latter measures the model’s ability to identify the full 3. CCF Classification Model Based on CNN SB2 sample. 3.1. Design and Performance of Model In this section, a CNN model for classifying single stars and 3.2. Validation of Model SB2s is proposed. The detailed structure of the CNN model To validate our model, we selected several published and used in this study is presented in Table 2, based on the work of representative SB2 spectroscopic observational catalogs, LeCun et al. (1989). including LAMOST, APOGEE, and GALAH. The corresp- We used the cross-entropy function as the loss function and onding spectral files were downloaded from the sources of applied the stochastic gradient descent optimizer for the these SB2 catalogs, and their corresponding CCFs were optimization of the model parameters. The batch size was set calculated to serve as validation data for the model. The model to 2048, and the learning rate was set to 0.0001. In each epoch is considered to have successfully detected an SB2 source as of training, the model was validated with the testing set, and the long as it can identify any of the source’s spectra with a learning rate was reduced by a factor of 5 for every 10 epochs threshold of 0.5, which is consistent with the detection criterion of training. Based on several experiments and comparisons, we in Li et al. (2021). noticed that the model generally achieved convergence after We searched for the FITS files in LAMOST-MRS DR9 approximately 25 epochs of training. To prevent overfitting, we using the coordinates provided in Li et al. (2021), Kovalev restricted the training to only 30 epochs to obtain the final et al. (2022), Zhang et al. (2022), and Wang et al. (2021). For model. each FITS file, we extracted the normalized spectra of the blue The performance of a CNN model is typically evaluated arm from the “NORMALIZATION” field and calculated the using metrics such as accuracy, precision, recall, and the F1 corresponding CCFs with iSpec to validate our model. The score, which are defined as follows: procedure for calculating and processing the CCFs was TP + TN consistent with the data set described in Section 2. Accuracy = ,4 () Based on the APOGEE IDs provided in El-Badry et al. TP++ FP FN+ TN (2018), Kounkel et al. (2021), and Mazzola et al. (2020),we TP Precision = ,5 () searched for spectra in APOGEE DR17 (Abdurro’uf et al. TP + FP 2022) and used all the spectra found for model validation. We TP cropped the precalculated CCFs (Nidever et al. 2015) of all −1 Recall = ,6 () spectra to the RV interval of −500–500 km s and TP + FN interpolated them using numpy.interp to fit the size of the 2** Precision Recall data identified by the model. F1 = .7 () Precision + Recall In addition, a large SB2 catalog from GALAH (Traven et al. 2020), in GALAH DR3 (Buder et al. 2021), based on the These metrics can be calculated from the confusion matrix, spectrum IDs (i.e., the sobject_id in the GALAH data release) which provides the values of TP, FP, TN, and FN. In this paper, provided by Traven et al. (2020), were searched. TP and FN represent positive samples (i.e., SB2s) that are Table 3 shows the number of sources acquired and the correctly and incorrectly predicted, while TN and FP represent percentage of sources that our model successfully identified. the cases of negative samples (i.e., single stars). Based on the information presented in the table, our model can The performance of the CNN model on the testing set is evaluated using the confusion matrix with a classification https://numpy.org/doc/stable/reference/generated/numpy.interp.html? threshold of 0.5, as shown in Figure 6. The results indicate an highlight=interp#numpy.interp 5 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Table 4 Information of the 2139 SB2 Candidate Spectra R.A. Decl. Gaia Source ID G LAMOST Name S/N Index 0.459621 61.623334 429522400634115840 10.87 med-58091-NGC778802_sp06-245 113.13 1 0.598203 34.112471 2875159070536814464 10.98 med-59186-TD000246N354855T01_sp01-152 89.22 1 0.598203 34.112471 2875159070536814464 10.98 med-58826-TD000246N354855T01_sp01-152 77.50 3 0.598203 34.112471 2875159070536814464 10.98 med-58826-TD000246N354855T01_sp01-152 52.35 4 1.100686 60.765479 429366132543539456 11.38 med-58091-NGC778801_sp07-138 77.81 1 1.180746 9.616956 2753156160807080192 11.74 med-58450-NT000608N094253M01_sp04-155 110.13 3 1.180746 9.616956 2753156160807080192 11.74 med-58450-NT000608N094253M01_sp04-155 108.47 4 1.180746 9.616956 2753156160807080192 11.74 med-58450-NT000608N094253M01_sp04-155 105.49 5 1.280438 34.606983 2876695599381581312 12.46 med-59186-TD000246N354855T01_sp08-190 59.97 1 1.418796 34.633028 2876700856421550336 11.08 med-58832-TD000246N354855T01_sp08-178 81.60 3 1.418796 34.633028 2876700856421550336 11.08 med-58832-TD000246N354855T01_sp08-178 188.68 1 1.418796 34.633028 2876700856421550336 11.08 med-58832-TD000246N354855T01_sp08-178 72.18 5 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 179.42 1 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 77.14 5 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 61.07 3 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 83.51 6 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 85.32 4 1.673898 56.120912 420952669561729920 11.02 med-58059-HIP11784201_sp06-093 51.63 5 1.673898 56.120912 420952669561729920 11.02 med-58089-NGC778901_sp06-093 120.99 1 1.673898 56.120912 420952669561729920 11.02 med-58059-HIP11784201_sp06-093 97.82 1 Note. Columns (1) and (2): the coordinates of the sources. Column (3): the ID of the source in Gaia DR3. Column (4): the sources of magnitude in Gaia DR3. Column (5): the FITS file name of the spectrum. Column (6): the S/N of the spectrum. Column (7): the index of the spectrum in the FITS file. (This table is available in its entirety in machine-readable form.) effectively detect the sources in these SB2 catalogs, indicating less than 0.3. Ultimately, a total of 1,589,215 CCFs were its reliability in identifying SB2s. chosen, and we searched for SB2 candidates among them with the model after applying the five Softmax calculations. To ensure a high confidence level, we considered only those samples with an SB2 prediction probability of greater than 99% 4. Result as SB2 candidates. After the model predicted the CCFs of all 4.1. SB2 Candidates the selected spectra, we obtained a total of 39,218 SB2 candidate spectra. We visually inspected each of these We employed the method described in this study to compute candidate CCFs to remove samples with insufficiently clear the CCFs of the normalized spectra from the blue arm of double-peak features, and after rigorous manual inspection, we LAMOST-MRS DR9 V1.0. These CCFs will be utilized to identified 2139 of these spectra as the final SB2 candidate identify potential SB2 candidates. However, as described in spectra. These 2139 spectra came from 728 sources, and their Merle et al. (2017), stars belonging to associations and clusters information is shown in Table 4. containing hot and cold gas, hot and pulsating stars, or young hot stars with disks may produce bumps in the CCFs of the 4.2. Comparison with Other SB2 Catalogs spectra, which may be recognized as peaks by the model and thus interfere with the identification of SB2s. We collated 15 other SB2 catalogs from multiple spectro- Therefore, before applying the model to search for SB2 scopic surveys, including LAMOST, Gaia-ESO, RAVE, candidates, we referred to the selection method for CCFs in GALAH, and APOGEE. These catalogs are Zhang et al. Merle et al. (2017) and visually examined a representative (2022), Li et al. (2021), Matijevič et al. (2010), Traven et al. (2020), Merle et al. (2017), Wang et al. (2021), Pourbaix et al. sample of CCFs from LAMOST-MRS DR9 to develop a (2004), Fernandez et al. (2017), Chojnowski (2015), Skinner selection criterion based on experience after several et al. (2018), Kovalev et al. (2022), El-Badry et al. (2018), experiments. First, to ensure the high quality of the spectra, we selected Kovalev & Straumit (2022), Mazzola et al. (2020), and those with an S/N greater than or equal to 50, and calculated Kounkel et al. (2021). We crossmatch the coordinates of all their CCFs using the application interface provided by iSpec. sources listed in these catalogs with Strasbourg astronomical We then identified the CCFs whose mean value on both the left Data Center. After eliminating the duplicates from the and the right continua of the CCF peak was less than 0.5, and matched coordinates, a total of 36,470 coordinates of SB2 inverted and scaled them to fit within the [0, 1] interval. Next, candidate sources were obtained as the complete catalog. We we applied one of the following three criteria to further select crossmatched these sources in Gaia DR3 and the details are the continua: (1) a standard deviation less than 0.1; (2) if the shown in Table 5. standard deviation was not satisfied, both the range (i.e., the difference between the maximum and minimum values) and the maximum values must be less than 0.5; or (3) if the maximum value was greater than 0.5 but less than 0.6, the range must be http://cdsxmatch.u-strasbg.fr/ 6 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Table 5 Information on the Complete Table of the Total 36,470 SB2 Candidates R.A. Decl. Gaia Source ID GT Fe/H eff log g 0.017042 34.188556 LL L L L 0.019482 57.489233 422589945455866496 12.13 5565.87 4.06 −0.45 0.045208 −81.089667 4634208693785476224 13.62 5087.31 4.20 −0.44 0.104125 34.114306 2875121652781859200 12.99 5937.45 4.08 −0.52 0.119730 84.442932 LL L L L 0.130167 −61.744639 4905551636485886976 13.22 5593.15 4.33 −0.01 0.133689 34.662862 2875424224637648128 14.71 5061.88 4.20 −0.38 0.134899 63.872851 431630508024107392 12.73 LL L 0.165333 57.375806 422586750000407168 13.40 4330.24 4.45 0.31 0.222657 0.683168 2738248909142217600 12.15 5831.42 4.15 −0.44 0.238298 40.439281 2881984048448075264 12.43 5526.89 4.25 −0.24 0.240088 2.611469 2739886979605384192 12.88 6013.02 4.19 −0.45 0.291246 58.695528 422768646150973696 12.24 5839.52 3.74 −0.42 0.347601 41.114090 2882225867991453056 12.22 5864.61 3.88 −0.40 0.363208 1.472028 2738434765263109888 14.76 4606.11 4.46 −0.08 0.383208 −79.087861 4635419599685161984 13.36 5553.89 3.60 −1.07 0.387139 63.517770 431593395196335488 12.83 LL L 0.392958 −57.493056 4919416031435609984 12.25 4930.74 4.35 −0.42 0.393120 −45.929500 4991193799764176640 11.61 6201.85 4.06 −0.35 0.414417 73.611833 537612876192148096 6.48 7894.46 4.14 −0.56 Note. Columns (1) and (2): coordinates. Column (3): Gaia DR3 source ID of the source. Columns (4) to (7): magnitude and stellar atmosphere parameters of the source from Gaia DR3. (This table is available in its entirety in machine-readable form.) Table 6 Details of the Total 728 SB2 Candidates Eventually Obtained R.A. Decl. Gaia Source ID G T log g Fe/H New eff 0.459621 61.623334 429522400634115840 10.87 9265.71 3.85 −0.32 0.598203 34.112471 2875159070536814464 10.98 5761.36 3.73 −0.41 1.100686 60.765479 429366132543539456 11.38 LL L 1.180746 9.616956 2753156160807080192 11.74 5816.68 3.70 −0.28 1.280438 34.606983 2876695599381581312 12.46 LL L 1.418796 34.633028 2876700856421550336 11.08 6127.75 3.10 −0.76 1.654627 56.741165 420997337221993472 10.47 7769.98 3.93 −0.50 1.673967 56.120924 420952669561729920 11.02 LL L 2.021230 8.099695 2752002292073197952 10.06 7323.74 3.98 −0.24 2.796898 57.199411 422425740266770048 11.26 7906.81 4.02 −0.36 3.254797 53.513156 420004375142233344 11.86 7043.39 4.23 0.04 3.424739 58.638924 422941067620538880 13.20 LL L 3.931877 58.901100 422964977698391168 10.08 7610.40 3.98 −0.34 5.198236 60.060925 428383890699390464 9.76 6611.53 4.06 −1.20 5.575783 57.982586 422101968450119424 12.64 LL L 5.921559 60.902786 428852179572814208 11.96 LL L 6.297442 56.241245 421353883926439552 11.93 LL L 6.355069 59.116074 428267308105062528 11.10 LL L 6.476312 28.369284 2857128381215141120 12.01 6066.17 3.93 −0.24 6.892713 59.441307 428116503215078912 11.19 6836.84 3.61 −0.17 Note. Columns (1) and (2): coordinates. Column (3): Gaia DR3 source ID of the source. Columns (4) to (7): magnitude and stellar atmosphere parameters of the source from Gaia DR3. Column (8): “ ” represents a newly discovered SB2 candidate. (This table is available in its entirety in machine-readable form.) We performed a crossmatch of the 728 sources obtained from catalog. This implies that our catalog includes 447 SB2 candidates LAMOST-MRS DR9withthe complete catalog, resultinginthe that are already known, while 281 new SB2 candidates were identification of 447 SB2 candidates that match with the complete discovered. The details of these sources are shown in Table 6. 7 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 7. CCFs (after inversion and normalization) of a binary star with different T , calculated using various templates. The top, middle, and bottom panels display eff the CCFs of the binary star with T values of approximately 2500 K, 5500 K, and 8000 K, respectively. The red, blue, and green dashed lines represent the CCFs eff calculated using templates with T values of 2500 K, 5000 K, and 8000 K, respectively. The black solid line corresponds to the CCF calculated from the template eff used in this study, i.e., the solar spectrum. 5. Discussions samples account for 4.87% of all SB2 samples. Further analysis revealed that, despite the application of five Softmax calcula- 5.1. Limitations in Data Set Preparation tions, misclassified single-star samples still showed fluctuations In creating the data set, we used some simplified methods, on both sides of the peaks of the CCFs, which could easily be which may pose some problems. In Section 2.1, binary spectra mistaken as double peaks by the model, leading to the are obtained by combining the spectra of single stars with misclassification of both single stars and SB2s. Some SB2 random T , which might produce binary spectra that do not spectra with a lower contribution from the secondary star may eff exist in reality. In order to evaluate the method’s reliability, we have much smaller secondary peaks in the CCFs. After the validate the model using eight published binary catalogs (as Softmax calculations, these peaks may be suppressed, leading discussed in Section 3.2). Based on the high recognition rates to the misclassification of some SB2s as single stars. (>90%) achieved by these catalogs, we tentatively conclude Additionally, some SB2s with primary and secondary stars that although the data set may contain potentially misleading having RVs that are too close together will show only one peak features, they did not significantly impact the model’s in the CCFs, making them appear as single stars to the model. performance. Figure 8 illustrates these issues. Another potential problem is that we used a solar spectrum template to create the CCF, rather than a set of templates 5.3. Model Tendency and Performance covering the T range. This could potentially affect the CCF, eff particularly for stars with T parameters near 2500 or 8000 K. eff The composition of misclassified samples indicates a higher Nonetheless, our model’s classification principle is based on proportion of misclassified SB2 samples compared to single- the number of peaks in the CCF. Our experiments demonstrate star samples. This suggests that our model tends to classify that the number of peaks in the CCF remains consistent CCFs as single stars when their features are not obvious. regardless of the template used (see Figure 7). Nevertheless, this behavior is beneficial in terms of effectively detecting SB2 candidates without misclassifying a significant number of single-star samples as SB2 candidates. Thus, our 5.2. Analysis of Misclassified Samples model achieves the effective detection of SB2 candidates, From the confusion matrix shown in Figure 6 on the testing which is supported by our model confidence validation in set, it can be seen that misclassified single stars account for Section 3.2, where the model achieves high accuracy in only 0.925% of all single-star samples, while misclassified SB2 identifying true SB2 candidates. 8 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 8. Examples of misclassified CCFs. Left: CCFs of misclassified single stars. Right: CCFs of misclassified SB2s. The top panel on the right shows a CCF with a secondary peak too small to be ignored by the model, while the bottom panel shows a CCF with primary and secondary star RVs that are too close to be distinguished by the model. The red dashed line represents the RV component of the CCF. 6. Conclusions Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (11961141001), In this study, we have developed a CNN model for detecting the National Science Foundation of China (12173028), the SB2 candidates in LAMOST-MRS DR9 V1.0. To address the Basic and Applied Basic Research Funds of Guangdong limitations of the existing SB2 catalog, we generated a spectral Province (2022A1515011558), Guangzhou Science and Tech- data set and calculated their CCFs for training our model. In the nology Funds (202102010433, 202102020677), and Innova- preprocessing of the data, we applied a novel technique of tion Research for the Postgraduates of Guangzhou University performing five Softmax calculations on the CCFs of the under grant 2021GDJC-M15. spectra to suppress the interference, and this method proved to We thank the anonymous referee for valuable and helpful be effective in the experiments. Our model achieved a high comments and suggestions. accuracy of 97.76% and a recall of 95.13% on the testing set. Moreover, the model identified up to 99.9% of the SB2 samples ORCID iDs in several large-scale SB2 catalogs. Zhong Cao https://orcid.org/0000-0002-2301-8030 Based on the preprocessed blue-arm spectra in LAMOST- Hui Deng https://orcid.org/0000-0002-8765-3906 MRS DR9 V1.0 with an S/N of at least 50, we applied our Ying Mei https://orcid.org/0000-0002-7960-9251 CNN model and conducted a rigorous visual inspection to Feng Wang https://orcid.org/0000-0002-9847-7805 identify 728 SB2 candidates. After crossmatching with a general catalog consisting of 15 other existing SB2 catalogs, we finally found 281 newly discovered SB2 candidates. References In addition to the discovery of new SB2 candidates, our Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35 approach is beneficial for utilizing deep learning techniques to Bate, M. R., Bonnell, I. A., & Bromm, V. 2002, MNRAS, 336, 705 search for unique targets from vast amounts of spectral data. In Blanco-Cuaresma, S. 2019, MNRAS, 486, 2075 particular, the spectral generation method we employed Blanco-Cuaresma, S., Soubiran, C., Heiter, U., & Jofré, P. 2014a, A&A, 569, A111 provides a solution to the issue of insufficient sample sizes, Blanco-Cuaresma, S., Soubiran, C., Jofré, P., & Heiter, U. 2014b, A&A, and effectively guarantees the reliability of deep learning 566, A98 models. Considering the enormous amounts of data generated Buder, S., Sharma, S., Kos, J., et al. 2021, MNRAS, 506, 150 by spectroscopic surveys, the use of deep learning to search for Chojnowski, S. D. 2015, APOGEE SB2s, NMSU Astronomy, http:// astronomy.nmsu.edu/drewski/apogee-sb2/apSB2.html other special stars is deemed an effective approach. Duchêne, G., & Kraus, A. 2013, ARA&A, 51, 269 El-Badry, K., Ting, Y.-S., Rix, H.-W., et al. 2018, MNRAS, 476, 528 This work is supported by the National SKA Program of Fernandez, M. A., Covey, K. 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Searching for Double-line Spectroscopic Binaries in the LAMOST Medium-resolution Spectroscopic Survey with Deep Learning

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© 2023. The Author(s). Published by the American Astronomical Society.
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Abstract

Double-line spectroscopic binaries (SB2s) are a vital class of spectroscopic binaries for studying star formation and evolution. Searching for SB2s has been a hot topic in astronomy. Although considerable efforts have been made with fruitful outcomes, limitations in automation and accuracy still persist. In this study, we developed a convolutional neural network model to search for SB2 candidates in LAMOST medium-resolution survey (MRS) data release (DR) 9 v1.0 by detecting double peaks in the cross-correlation function (CCF).We first generated a large number of spectra of single stars and binaries using the iSpec spectral synthesis software. The CCFs of these synthesized spectra were then calculated to form our training set. To efficiently detect the peaks of the CCFs, we applied a Softmax function-based noise reduction method. After testing and validation, the model achieved an accuracy of 97.76% in the testing set and was validated for more than 90% of the sample in several published SB2 catalogs. Finally, by applying the model to examine approximately 1.59 million LAMOST-MRS DR9 spectra, we identified 728 candidate SB2s, including 281 newly discovered ones. Unified Astronomy Thesaurus concepts: Convolutional neural networks (1938); Spectroscopic binary stars (1557) Supporting material: machine-readable tables 1. Introduction Bate et al. (2002) studied the formation of SBs and provided evidence that high-frequency close binaries can be formed by Binary systems play an essential role in modern astrophysics dynamical interactions in unstable multiple systems and orbital (Raghavan et al. 2010; Duchêne & Kraus 2013). Investigating decay of initially broader binaries. the distributions of the period, mass, and eccentricity of binary The search for and identificationofSBs,drivenbyscientific systems can provide valuable insights into the origin and research, remains a popular direction for current binary star evolution of stars (Moe & Di Stefano 2017). studies. Spectroscopic surveys have produced large numbers of The common types of binary systems are visual binaries and spectra, which have facilitated the search for SBs. Merle et al. spectroscopic binaries (SBs). SBs can be further classified into (2017) detected 354 SB candidates in Gaia–ESO Survey internal single-line SBs (SB1s) and double-line SBs (SB2s), depending data release (DR) 4 by calculating the successive derivatives of on the number of stellar components of the spectra. SB1s have CCFs to detect multiple peaks. Matijevič et al. (2010) found 123 single-line spectra that are dominated by the flux of the primary SB2 candidates in RAVE DR2 by analyzing the shapes and star. They can be identified by the periodic changes in radial properties of the CCFs. Kounkel et al. (2019) identified 399 velocity (RV) observed over multiple epochs (Merle et al. binaries in the APOGEE-2 spectra using Gaussian fitting to find 2020). In contrast, SB2s have double-line spectra that are peaks from the CCFs. Building on this work, Kounkel et al. jointly dominated by the fluxes of the primary and secondary (2021) found 7273 SB2s, 813 SB3s, and 19 SB4s in the stars. They can be identified by the presence of double peaks in APOGEE DR16 and DR17 data. Skinner et al. (2018) detected 44 the cross-correlation function (CCF; Matijevič et al. 2010; SB2 candidates by measuring the degree of asymmetry of CCFs Merle et al. 2017; Kounkel et al. 2021; Li et al. 2021). of Sloan Digital Sky Survey III DR13. El-Badry et al. (2018) The study of SBs holds significant scientificvalue, as identified over 3000 SBs in APOGEE DR13 using a data-driven exemplified by numerous studies in recent years. Mahy et al. spectral model. Traven et al. (2020) obtained 12,760 SB2s in (2022) utilized the physical properties of SBs to successfully detect GALAH using t-distributed stochastic neighbor embedding stellar-mass black holes. Moe & Di Stefano (2017) demonstrated classification and CCF analysis. Kovalev et al. (2022) obtained that early-type SBs exhibit distinct eccentricity and mass 2460 SB2 candidates in the LAMOST medium-resolution survey distributions. Tokovinin et al. (2006) surveyed solar-type SBs (MRS) by analyzing the V sin i values in the spectral FITS files. and established that the periods of SB systems with triples were LAMOST-MRS (Liu et al. 2020), which began in 2017, further shortened by angular momentum exchange with compa- contains blue and red arms, covering 4950 Å to 5350 Å and nions. Maxted et al. (2001) showed that binary evolution was the 6300 Å to 6800 Å, respectively. The resolution of LAMOST- basis for the formation of the most extreme horizontal branch stars. MRS is 7500, and its limiting magnitude is around G ∼ 15. LAMOST-MRS DR9 V1.0 published more than 15 million Original content from this work may be used under the terms spectra from over 2.18 million targets (signal-to-noise ratio or of the Creative Commons Attribution 4.0 licence. Any further S/N … 10). LAMOST-MRS is capable of measuring RVs with distribution of this work must maintain attribution to the author(s) and the title −1 of the work, journal citation and DOI. a precision of 1 km s , making it effective for searching for 1 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. SB2s (Liu et al. 2019; Li et al. 2021). Using the method of Table 1 Parameter Space for the Synthetic Spectra multiple derivative determination of CCF peaks described in Merle et al. (2017), Li et al. (2021) identified 3133 SB2 and Parameter Distribution Unit 132 spectroscopic triple candidates in LAMOST-MRS DR7. T  (2500, 8000) K eff1,2 As several spectral surveys are launched, massive amounts log g  (−0.5, 5.5) dex 1,2 of spectra will be released, making the search for SB2s M/H  (−4.5, 1.0) dex 1,2 increasingly challenging. The development of deep learning −1 Vi sin  (0.0, 10.0) km s 1,2 techniques has demonstrated remarkable results and efficien- 2 −1 V  (0,25 ) km s cies in data mining and pattern recognition, leading scientists to −1 V V +  (−200, 200) km s 2 1 utilize this excellent tool in the search for SB2s. Li et al. (2021) S/N  (50, 300) dB constructed a recurrent neural network model for identifying SB2s using CCF images with labeled training samples. Zhang Note.  (a,b) represents a uniform distribution from a to b.  (a, b) represents a et al. (2022) built a convolution neural network (CNN) model 2 normal distribution with mean μ and variance σ . The numerical subscripts of based on synthetic spectra and obtained 2198 SB2 candidates Column 1 represent the parameters of the two single stars combined into a in LAMOST-MRS DR8. binary system. Overall, the deep-learning-based search and recognition of SB2s can significantly reduce the difficulty of manual Based on these parameters, we obtained the normalized recognition and obtain credible results. However, the number spectra of single stars using iSpec. We combined the synthetic of SB2 candidates from the published SB catalogs is relatively spectra of two single stars without adding noise to create binary small to meet the requirements for training deep learning spectra. The resulting spectra were then normalized, and models. To solve this problem, we synthesized the spectra of Gaussian noise was added to achieve a given S/N, resulting in single and binary stars and calculated the CCFs of these the SB2 spectra (Zhang et al. 2022). In addition to generating synthetic spectra, which were then used to construct the SB2 spectra as positive samples in this study, two single-star training set and testing set for the CNN model. spectra corresponding to each SB2 spectrum were also utilized The remaining sections of this paper are organized as follows. In as negative samples. Table 1 summarizes the parameter space Section 2,wedescribethe processofsynthesizing the spectra of of the synthesized spectra. The process of synthesizing the single and binary stars and acquiring the training and testing sets spectra and examples of the synthesized spectra can be seen in through CCFs. The model’s training process and its performance Figures 1 and 2, respectively. on the testing set, along with the validation results on some published SB2 catalogs, are presented in Section 3.In Section 4, 2.2. Calculation of CCF some newlydiscoveredSB2 candidates forLAMOST-MRSDR9 V1.0 are described. There is a brief discussion in Section 5 and we We utilized the iSpec application interface to calculate the summarize our work in Section 6. spectral CCFs using Equation (2)(Pepe et al. 2002): 2. Data and Preprocessing CCF()VS = (ll ) ·M( )dl. (2) SB2s can be identified by the double peaks of the CCFs in their spectra (Matijevič et al. 2010; Merle et al. 2017; Kounkel In this equation, S represents the spectrum that is subject to et al. 2021; Li et al. 2021). To this end, we employed a CNN CCF calculation, while M denotes the template spectrum. As model to detect SB2 candidates by recognizing the double the template spectrum, we used the NARVAL solar spectrum peaks of CCFs. covering 370−1048 nm, which was provided by iSpec (Blanco-Cuaresma et al. 2014b). The RV variations ranged 2.1. Spectra Synthesis −1 −1 from −500 to 500 km s , with a step of 1 km s . The results We utilized the iSpec spectral synthesis software (Blanco- of the CCFs calculated from the synthetic spectra in Figure 2 Cuaresma et al. 2014a; Blanco-Cuaresma 2019) to generate by iSpec are shown in Figure 3. spectra, along with the radiative transfer code SPECTRUM (Gray & Corbally 1994) and the stellar atmospheric models 2.3. Processing of CCF MARCS (Gustafsson et al. 2008) in iSpec. The blue arm of After calculating the CCFs of the spectra using iSpec in LAMOST-MRS, which covers 4950 to 5350 Å with more Section 2.2, we inverted and normalized the CCFs, which made absorption lines and distinctive features, was selected for the the peaks more prominent in value. Figure 4 shows the results synthetic spectra (Li et al. 2021). of the inversions and normalizations of the CCFs from We specified a set of parameters for the synthesized spectra, Figure 3. To better highlight the peaks of the CCFs and reduce as shown in Equation (1): the interference of the wings, the Softmax function is used to {} Tg ,log  ,M// H,V sini,V,S N . (1) suppress the wings of the CCFs, which is defined as eff Equation (3): Here, T , log g, and M/H represent the atmospheric eff parameters of the star, i.e., the effective temperature, surface s()zz = foriK =¼ 1, , and = (z ,¼,z )Î  , i 1 K K z gravity, and metal abundance, respectively. V sin i and V are S e j=1 the rotation velocity and the RV of the star, respectively. S/N () 3 indicates the given signal-to-noise ratio achieved by adding Gaussian noise to the whole of the synthetic spectrum, which is where z is a K-dimensional vector and the Softmax function derived from Zhang et al. (2022). polarizes its distribution and transforms it into a probability 2 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 1. Synthesis process of single- and binary star spectra. Figure 2. Examples of synthetic spectra. The top and middle panels are synthetic single-star spectra; the bottom panel is the normalized double-star spectrum after summing two single-star spectra. distribution. When the CCFs are processed using the Softmax In this work, we applied five Softmax calculations to the function, wings with smaller values are suppressed, while CCFs, and the results for the CCFs in Figure 4 are shown in Figure 5. As seen from Figure 5, the Softmax function peaks with significant features are enhanced. Therefore, this effectively suppresses the disturbance of the CCF wings, method can be considered as a noise reduction method. 3 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 3. The results of the CCFs calculated from the synthetic spectra in Figure 2. The red points are the peaks of the CCF, representing the RV of the spectra. Figure 4. The results of the inversion and normalization of the CCFs from Figure 3. Figure 5. The results of the original CCFs (dashed lines) and the CCFs after five Softmax calculations (solid lines). Table 2 The Architecture of Our CNN Model Layer Type Input Channels Output Channels Kernel Size Stride Input Shape Output Shape Activation C1 Conv 1 64 3 1 1, 1001 64, 999 ReLU B1 BN 64 64 LL 64, 999 64, 999 L C2 Conv 64 64 3 1 64, 999 64, 997 ReLU B2 BN 64 64 LL 64, 997 64, 997 L C3 Conv 64 128 3 2 64, 997 128, 498 ReLU B3 BN 128 128 LL 128, 498 128, 498 L C4 Conv 128 128 3 1 128, 498 128, 496 ReLU B4 BN 128 128 LL 128, 496 128, 496 L C5 Conv 128 256 3 2 128, 496 256, 247 ReLU B5 BN 256 256 LL 256, 247 256, 247 L C6 Conv 256 256 3 1 256, 247 256, 245 ReLU B6 BN 256 256 LL 256, 245 256, 245 L C7 Conv 256 512 3 2 256, 245 512, 122 ReLU B7 BN 512 512 LL 512, 122 512, 122 L C8 Conv 512 512 3 1 512, 122 512, 120 ReLU B8 BN 512 512 LL 512, 120 512, 120 L F9 Flatten LL L L 512, 120 61440 L D10 Dense 61440 1000 LL 61440 1000 L D11 Dense 1000 2 LL 1000 2 Softmax Note. Convolution layers. Batch normalization layers. making the processed CCFs more obvious in their features. The synthesized a total of 605,500 single-star spectra, which were processed CCFs are used as data for training the CNN model. combined to generate the corresponding 302,750 SB2 spectra. After completing the processes described above, we obtained Following the calculation and processing of the CCFs of all the the training and testing sets for the CNN model. We synthetic spectra, we selected 100,000 single-star CCFs and 4 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Table 3 Validation of SB2 Catalogs Survey Catalog All Identify Percentage LAMOST Li et al. (2021) 3244 3014 92.9% Kovalev et al. (2022) 2431 2378 97.8% Zhang et al. (2022) 3135 2819 89.9% Wang et al. (2021) 2357 2309 98.0% APOGEE El-Badry et al. (2018) 2637 2611 99.0% Kounkel et al. (2021) 8019 7824 94.6% Mazzola et al. (2020) 3566 3437 96.4% GALAH Traven et al. (2020) 11,351 11,345 99.9% Note. Column (1): catalog name. Column (2): spectroscopic survey. Column (3): the number of sources acquired to the spectrum. Column (4): the number of sources identified by the model. Column (5): the percentage of identified sources to all sources. Figure 6. Confusion matrix of the model on the testing set. accuracy of 97.76%, with a recall of 95.13%, a precision of 50,000 SB2 CCFs to constitute the testing set, while the 98.09%, and an F1 score of 96.59%. In this classification task, remaining 505,500 single-star CCFs and 252,750 SB2 CCFs the most important metrics are accuracy and recall, as the formed the training set. former represents the model’s overall predictive capability, while the latter measures the model’s ability to identify the full 3. CCF Classification Model Based on CNN SB2 sample. 3.1. Design and Performance of Model In this section, a CNN model for classifying single stars and 3.2. Validation of Model SB2s is proposed. The detailed structure of the CNN model To validate our model, we selected several published and used in this study is presented in Table 2, based on the work of representative SB2 spectroscopic observational catalogs, LeCun et al. (1989). including LAMOST, APOGEE, and GALAH. The corresp- We used the cross-entropy function as the loss function and onding spectral files were downloaded from the sources of applied the stochastic gradient descent optimizer for the these SB2 catalogs, and their corresponding CCFs were optimization of the model parameters. The batch size was set calculated to serve as validation data for the model. The model to 2048, and the learning rate was set to 0.0001. In each epoch is considered to have successfully detected an SB2 source as of training, the model was validated with the testing set, and the long as it can identify any of the source’s spectra with a learning rate was reduced by a factor of 5 for every 10 epochs threshold of 0.5, which is consistent with the detection criterion of training. Based on several experiments and comparisons, we in Li et al. (2021). noticed that the model generally achieved convergence after We searched for the FITS files in LAMOST-MRS DR9 approximately 25 epochs of training. To prevent overfitting, we using the coordinates provided in Li et al. (2021), Kovalev restricted the training to only 30 epochs to obtain the final et al. (2022), Zhang et al. (2022), and Wang et al. (2021). For model. each FITS file, we extracted the normalized spectra of the blue The performance of a CNN model is typically evaluated arm from the “NORMALIZATION” field and calculated the using metrics such as accuracy, precision, recall, and the F1 corresponding CCFs with iSpec to validate our model. The score, which are defined as follows: procedure for calculating and processing the CCFs was TP + TN consistent with the data set described in Section 2. Accuracy = ,4 () Based on the APOGEE IDs provided in El-Badry et al. TP++ FP FN+ TN (2018), Kounkel et al. (2021), and Mazzola et al. (2020),we TP Precision = ,5 () searched for spectra in APOGEE DR17 (Abdurro’uf et al. TP + FP 2022) and used all the spectra found for model validation. We TP cropped the precalculated CCFs (Nidever et al. 2015) of all −1 Recall = ,6 () spectra to the RV interval of −500–500 km s and TP + FN interpolated them using numpy.interp to fit the size of the 2** Precision Recall data identified by the model. F1 = .7 () Precision + Recall In addition, a large SB2 catalog from GALAH (Traven et al. 2020), in GALAH DR3 (Buder et al. 2021), based on the These metrics can be calculated from the confusion matrix, spectrum IDs (i.e., the sobject_id in the GALAH data release) which provides the values of TP, FP, TN, and FN. In this paper, provided by Traven et al. (2020), were searched. TP and FN represent positive samples (i.e., SB2s) that are Table 3 shows the number of sources acquired and the correctly and incorrectly predicted, while TN and FP represent percentage of sources that our model successfully identified. the cases of negative samples (i.e., single stars). Based on the information presented in the table, our model can The performance of the CNN model on the testing set is evaluated using the confusion matrix with a classification https://numpy.org/doc/stable/reference/generated/numpy.interp.html? threshold of 0.5, as shown in Figure 6. The results indicate an highlight=interp#numpy.interp 5 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Table 4 Information of the 2139 SB2 Candidate Spectra R.A. Decl. Gaia Source ID G LAMOST Name S/N Index 0.459621 61.623334 429522400634115840 10.87 med-58091-NGC778802_sp06-245 113.13 1 0.598203 34.112471 2875159070536814464 10.98 med-59186-TD000246N354855T01_sp01-152 89.22 1 0.598203 34.112471 2875159070536814464 10.98 med-58826-TD000246N354855T01_sp01-152 77.50 3 0.598203 34.112471 2875159070536814464 10.98 med-58826-TD000246N354855T01_sp01-152 52.35 4 1.100686 60.765479 429366132543539456 11.38 med-58091-NGC778801_sp07-138 77.81 1 1.180746 9.616956 2753156160807080192 11.74 med-58450-NT000608N094253M01_sp04-155 110.13 3 1.180746 9.616956 2753156160807080192 11.74 med-58450-NT000608N094253M01_sp04-155 108.47 4 1.180746 9.616956 2753156160807080192 11.74 med-58450-NT000608N094253M01_sp04-155 105.49 5 1.280438 34.606983 2876695599381581312 12.46 med-59186-TD000246N354855T01_sp08-190 59.97 1 1.418796 34.633028 2876700856421550336 11.08 med-58832-TD000246N354855T01_sp08-178 81.60 3 1.418796 34.633028 2876700856421550336 11.08 med-58832-TD000246N354855T01_sp08-178 188.68 1 1.418796 34.633028 2876700856421550336 11.08 med-58832-TD000246N354855T01_sp08-178 72.18 5 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 179.42 1 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 77.14 5 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 61.07 3 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 83.51 6 1.654627 56.741165 420997337221993472 10.47 med-59184-HIP472H382601_sp15-139 85.32 4 1.673898 56.120912 420952669561729920 11.02 med-58059-HIP11784201_sp06-093 51.63 5 1.673898 56.120912 420952669561729920 11.02 med-58089-NGC778901_sp06-093 120.99 1 1.673898 56.120912 420952669561729920 11.02 med-58059-HIP11784201_sp06-093 97.82 1 Note. Columns (1) and (2): the coordinates of the sources. Column (3): the ID of the source in Gaia DR3. Column (4): the sources of magnitude in Gaia DR3. Column (5): the FITS file name of the spectrum. Column (6): the S/N of the spectrum. Column (7): the index of the spectrum in the FITS file. (This table is available in its entirety in machine-readable form.) effectively detect the sources in these SB2 catalogs, indicating less than 0.3. Ultimately, a total of 1,589,215 CCFs were its reliability in identifying SB2s. chosen, and we searched for SB2 candidates among them with the model after applying the five Softmax calculations. To ensure a high confidence level, we considered only those samples with an SB2 prediction probability of greater than 99% 4. Result as SB2 candidates. After the model predicted the CCFs of all 4.1. SB2 Candidates the selected spectra, we obtained a total of 39,218 SB2 candidate spectra. We visually inspected each of these We employed the method described in this study to compute candidate CCFs to remove samples with insufficiently clear the CCFs of the normalized spectra from the blue arm of double-peak features, and after rigorous manual inspection, we LAMOST-MRS DR9 V1.0. These CCFs will be utilized to identified 2139 of these spectra as the final SB2 candidate identify potential SB2 candidates. However, as described in spectra. These 2139 spectra came from 728 sources, and their Merle et al. (2017), stars belonging to associations and clusters information is shown in Table 4. containing hot and cold gas, hot and pulsating stars, or young hot stars with disks may produce bumps in the CCFs of the 4.2. Comparison with Other SB2 Catalogs spectra, which may be recognized as peaks by the model and thus interfere with the identification of SB2s. We collated 15 other SB2 catalogs from multiple spectro- Therefore, before applying the model to search for SB2 scopic surveys, including LAMOST, Gaia-ESO, RAVE, candidates, we referred to the selection method for CCFs in GALAH, and APOGEE. These catalogs are Zhang et al. Merle et al. (2017) and visually examined a representative (2022), Li et al. (2021), Matijevič et al. (2010), Traven et al. (2020), Merle et al. (2017), Wang et al. (2021), Pourbaix et al. sample of CCFs from LAMOST-MRS DR9 to develop a (2004), Fernandez et al. (2017), Chojnowski (2015), Skinner selection criterion based on experience after several et al. (2018), Kovalev et al. (2022), El-Badry et al. (2018), experiments. First, to ensure the high quality of the spectra, we selected Kovalev & Straumit (2022), Mazzola et al. (2020), and those with an S/N greater than or equal to 50, and calculated Kounkel et al. (2021). We crossmatch the coordinates of all their CCFs using the application interface provided by iSpec. sources listed in these catalogs with Strasbourg astronomical We then identified the CCFs whose mean value on both the left Data Center. After eliminating the duplicates from the and the right continua of the CCF peak was less than 0.5, and matched coordinates, a total of 36,470 coordinates of SB2 inverted and scaled them to fit within the [0, 1] interval. Next, candidate sources were obtained as the complete catalog. We we applied one of the following three criteria to further select crossmatched these sources in Gaia DR3 and the details are the continua: (1) a standard deviation less than 0.1; (2) if the shown in Table 5. standard deviation was not satisfied, both the range (i.e., the difference between the maximum and minimum values) and the maximum values must be less than 0.5; or (3) if the maximum value was greater than 0.5 but less than 0.6, the range must be http://cdsxmatch.u-strasbg.fr/ 6 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Table 5 Information on the Complete Table of the Total 36,470 SB2 Candidates R.A. Decl. Gaia Source ID GT Fe/H eff log g 0.017042 34.188556 LL L L L 0.019482 57.489233 422589945455866496 12.13 5565.87 4.06 −0.45 0.045208 −81.089667 4634208693785476224 13.62 5087.31 4.20 −0.44 0.104125 34.114306 2875121652781859200 12.99 5937.45 4.08 −0.52 0.119730 84.442932 LL L L L 0.130167 −61.744639 4905551636485886976 13.22 5593.15 4.33 −0.01 0.133689 34.662862 2875424224637648128 14.71 5061.88 4.20 −0.38 0.134899 63.872851 431630508024107392 12.73 LL L 0.165333 57.375806 422586750000407168 13.40 4330.24 4.45 0.31 0.222657 0.683168 2738248909142217600 12.15 5831.42 4.15 −0.44 0.238298 40.439281 2881984048448075264 12.43 5526.89 4.25 −0.24 0.240088 2.611469 2739886979605384192 12.88 6013.02 4.19 −0.45 0.291246 58.695528 422768646150973696 12.24 5839.52 3.74 −0.42 0.347601 41.114090 2882225867991453056 12.22 5864.61 3.88 −0.40 0.363208 1.472028 2738434765263109888 14.76 4606.11 4.46 −0.08 0.383208 −79.087861 4635419599685161984 13.36 5553.89 3.60 −1.07 0.387139 63.517770 431593395196335488 12.83 LL L 0.392958 −57.493056 4919416031435609984 12.25 4930.74 4.35 −0.42 0.393120 −45.929500 4991193799764176640 11.61 6201.85 4.06 −0.35 0.414417 73.611833 537612876192148096 6.48 7894.46 4.14 −0.56 Note. Columns (1) and (2): coordinates. Column (3): Gaia DR3 source ID of the source. Columns (4) to (7): magnitude and stellar atmosphere parameters of the source from Gaia DR3. (This table is available in its entirety in machine-readable form.) Table 6 Details of the Total 728 SB2 Candidates Eventually Obtained R.A. Decl. Gaia Source ID G T log g Fe/H New eff 0.459621 61.623334 429522400634115840 10.87 9265.71 3.85 −0.32 0.598203 34.112471 2875159070536814464 10.98 5761.36 3.73 −0.41 1.100686 60.765479 429366132543539456 11.38 LL L 1.180746 9.616956 2753156160807080192 11.74 5816.68 3.70 −0.28 1.280438 34.606983 2876695599381581312 12.46 LL L 1.418796 34.633028 2876700856421550336 11.08 6127.75 3.10 −0.76 1.654627 56.741165 420997337221993472 10.47 7769.98 3.93 −0.50 1.673967 56.120924 420952669561729920 11.02 LL L 2.021230 8.099695 2752002292073197952 10.06 7323.74 3.98 −0.24 2.796898 57.199411 422425740266770048 11.26 7906.81 4.02 −0.36 3.254797 53.513156 420004375142233344 11.86 7043.39 4.23 0.04 3.424739 58.638924 422941067620538880 13.20 LL L 3.931877 58.901100 422964977698391168 10.08 7610.40 3.98 −0.34 5.198236 60.060925 428383890699390464 9.76 6611.53 4.06 −1.20 5.575783 57.982586 422101968450119424 12.64 LL L 5.921559 60.902786 428852179572814208 11.96 LL L 6.297442 56.241245 421353883926439552 11.93 LL L 6.355069 59.116074 428267308105062528 11.10 LL L 6.476312 28.369284 2857128381215141120 12.01 6066.17 3.93 −0.24 6.892713 59.441307 428116503215078912 11.19 6836.84 3.61 −0.17 Note. Columns (1) and (2): coordinates. Column (3): Gaia DR3 source ID of the source. Columns (4) to (7): magnitude and stellar atmosphere parameters of the source from Gaia DR3. Column (8): “ ” represents a newly discovered SB2 candidate. (This table is available in its entirety in machine-readable form.) We performed a crossmatch of the 728 sources obtained from catalog. This implies that our catalog includes 447 SB2 candidates LAMOST-MRS DR9withthe complete catalog, resultinginthe that are already known, while 281 new SB2 candidates were identification of 447 SB2 candidates that match with the complete discovered. The details of these sources are shown in Table 6. 7 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 7. CCFs (after inversion and normalization) of a binary star with different T , calculated using various templates. The top, middle, and bottom panels display eff the CCFs of the binary star with T values of approximately 2500 K, 5500 K, and 8000 K, respectively. The red, blue, and green dashed lines represent the CCFs eff calculated using templates with T values of 2500 K, 5000 K, and 8000 K, respectively. The black solid line corresponds to the CCF calculated from the template eff used in this study, i.e., the solar spectrum. 5. Discussions samples account for 4.87% of all SB2 samples. Further analysis revealed that, despite the application of five Softmax calcula- 5.1. Limitations in Data Set Preparation tions, misclassified single-star samples still showed fluctuations In creating the data set, we used some simplified methods, on both sides of the peaks of the CCFs, which could easily be which may pose some problems. In Section 2.1, binary spectra mistaken as double peaks by the model, leading to the are obtained by combining the spectra of single stars with misclassification of both single stars and SB2s. Some SB2 random T , which might produce binary spectra that do not spectra with a lower contribution from the secondary star may eff exist in reality. In order to evaluate the method’s reliability, we have much smaller secondary peaks in the CCFs. After the validate the model using eight published binary catalogs (as Softmax calculations, these peaks may be suppressed, leading discussed in Section 3.2). Based on the high recognition rates to the misclassification of some SB2s as single stars. (>90%) achieved by these catalogs, we tentatively conclude Additionally, some SB2s with primary and secondary stars that although the data set may contain potentially misleading having RVs that are too close together will show only one peak features, they did not significantly impact the model’s in the CCFs, making them appear as single stars to the model. performance. Figure 8 illustrates these issues. Another potential problem is that we used a solar spectrum template to create the CCF, rather than a set of templates 5.3. Model Tendency and Performance covering the T range. This could potentially affect the CCF, eff particularly for stars with T parameters near 2500 or 8000 K. eff The composition of misclassified samples indicates a higher Nonetheless, our model’s classification principle is based on proportion of misclassified SB2 samples compared to single- the number of peaks in the CCF. Our experiments demonstrate star samples. This suggests that our model tends to classify that the number of peaks in the CCF remains consistent CCFs as single stars when their features are not obvious. regardless of the template used (see Figure 7). Nevertheless, this behavior is beneficial in terms of effectively detecting SB2 candidates without misclassifying a significant number of single-star samples as SB2 candidates. Thus, our 5.2. Analysis of Misclassified Samples model achieves the effective detection of SB2 candidates, From the confusion matrix shown in Figure 6 on the testing which is supported by our model confidence validation in set, it can be seen that misclassified single stars account for Section 3.2, where the model achieves high accuracy in only 0.925% of all single-star samples, while misclassified SB2 identifying true SB2 candidates. 8 The Astrophysical Journal Supplement Series, 266:18 (10pp), 2023 June Zheng et al. Figure 8. Examples of misclassified CCFs. Left: CCFs of misclassified single stars. Right: CCFs of misclassified SB2s. The top panel on the right shows a CCF with a secondary peak too small to be ignored by the model, while the bottom panel shows a CCF with primary and secondary star RVs that are too close to be distinguished by the model. The red dashed line represents the RV component of the CCF. 6. Conclusions Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (11961141001), In this study, we have developed a CNN model for detecting the National Science Foundation of China (12173028), the SB2 candidates in LAMOST-MRS DR9 V1.0. To address the Basic and Applied Basic Research Funds of Guangdong limitations of the existing SB2 catalog, we generated a spectral Province (2022A1515011558), Guangzhou Science and Tech- data set and calculated their CCFs for training our model. In the nology Funds (202102010433, 202102020677), and Innova- preprocessing of the data, we applied a novel technique of tion Research for the Postgraduates of Guangzhou University performing five Softmax calculations on the CCFs of the under grant 2021GDJC-M15. spectra to suppress the interference, and this method proved to We thank the anonymous referee for valuable and helpful be effective in the experiments. Our model achieved a high comments and suggestions. accuracy of 97.76% and a recall of 95.13% on the testing set. Moreover, the model identified up to 99.9% of the SB2 samples ORCID iDs in several large-scale SB2 catalogs. Zhong Cao https://orcid.org/0000-0002-2301-8030 Based on the preprocessed blue-arm spectra in LAMOST- Hui Deng https://orcid.org/0000-0002-8765-3906 MRS DR9 V1.0 with an S/N of at least 50, we applied our Ying Mei https://orcid.org/0000-0002-7960-9251 CNN model and conducted a rigorous visual inspection to Feng Wang https://orcid.org/0000-0002-9847-7805 identify 728 SB2 candidates. After crossmatching with a general catalog consisting of 15 other existing SB2 catalogs, we finally found 281 newly discovered SB2 candidates. References In addition to the discovery of new SB2 candidates, our Abdurro’uf, Accetta, K., Aerts, C., et al. 2022, ApJS, 259, 35 approach is beneficial for utilizing deep learning techniques to Bate, M. R., Bonnell, I. A., & Bromm, V. 2002, MNRAS, 336, 705 search for unique targets from vast amounts of spectral data. 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