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Yin-Bi Li

Publications and source records attributed to Yin-Bi Li.

At least 19 recordsLinked to original sources

Spectra as Language: Large Language Models for Scalable Stellar Parameter and Abundance Inference

Stellar spectra encode key information on the physical properties and chemical compositions of stars. Accurate stellar parameter determination is essential for addressing major questions such as galaxy and stellar evolution. Large-scale spectroscopic surveys have accumulated unprecedented spectral data. Traditional feature extraction or model-fitting approaches struggle with high-dimensional, massive datasets, limited generalization, and computational inefficiency. Recent advances in large language models demonstrate strong generalization and feature-learning in tasks like natural language processing, DNA/RNA sequence analysis, and protein/chemical parsing. Stellar spectra are continuous sequential signals, enabling the transfer of language models to stellar spectroscopy. Here, we propose a two-stage large language model framework for stellar parameter inference, achieving accurate estimation of effective temperature, surface gravity, metallicity, and abundances of ~20 chemical elements. Scaling-law analyses show systematic performance improvements with increasing data, providing a scalable framework for forthcoming large-scale surveys.

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PISP: Projected-Space Inference of Stellar Parameters

To improve the accuracy and efficiency of high-dimensional stellar parameter inference in large spectroscopic datasets, we propose a projection-assisted parameter-inference framework -- Projected-Space Inference of Stellar Parameters (PISP). PISP constructs an orthonormal basis and optimizes in the projected space, reducing the impact of parameter correlations on inference. The basis is constructed using either principal component analysis (PCA) or the active-subspace (AS) method and is combined with two inference strategies -- Non-L1, which optimizes the projection coefficients for a user-specified projected dimensionality, and L1, which introduces L1 regularization in the full projected space to adaptively select projection directions -- yielding four strategies: PCA-Non-L1, AS-Non-L1, PCA-L1, and AS-L1. For different computational scenarios, we implement two versions: PISP-CurveFit for fast single-spectrum inference and PISP-Adam for large-scale GPU-parallel inference. Using a fully connected neural network and a residual network as spectral emulators, we evaluate PISP on Kurucz synthetic spectra and on $722{,}896$ APOGEE DR$17$ observed spectra. Compared to the baseline strategy, PISP improves inference accuracy for multiple parameters across all emulator-optimizer combinations. In synthetic data, PCA-L1 performs best, reducing the standard deviation of differences ($\sigma(\Delta)$) by at least $0.01$ dex for $12$ of $20$ elemental abundances, with [N/H], [O/H], [Na/H], [Co/H], [P/H], [V/H], [Cu/H] showing $0.05$--$0.72$ dex reductions. In observed data, PCA-Non-L1 reduces $\sigma(\Delta)$ by $>30$ K for effective temperature and by at least $0.01$ dex for $9$ of $17$ elemental abundances, with [O/H], [Na/H], [V/H] showing $0.05$--$0.20$ dex reductions, while achieving a $\sim$$4\times$ efficiency gain, slightly outperforming PCA-L1.

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Scalable Stellar Parameter Inference Using Python-based LASP: From CPU Optimization to GPU Acceleration

To enhance the efficiency, scalability, and cross-survey applicability of stellar parameter inference in large spectroscopic datasets, we present a modular, parallelized Python framework with automated error estimation, built on the LAMOST Atmospheric Parameter Pipeline (LASP) originally implemented in IDL. Rather than a direct code translation, this framework refactors LASP with two complementary modules: LASP-CurveFit, a new implementation of the LASP fitting procedure that runs on a CPU, preserving legacy logic while improving data I/O and multithreaded execution efficiency; and LASP-Adam-GPU, a GPU-accelerated method that introduces grouped optimization by constructing a joint residual function over multiple observed and model spectra, enabling high-throughput parameter inference across tens of millions of spectra. Applied to 10 million LAMOST spectra, the framework reduces runtime from 84 to 48 hr on the same CPU platform and to 7 hr on an NVIDIA A100 GPU, while producing results consistent with those from the original pipeline. The inferred errors agree well with the parameter variations from repeat observations of the same target (excluding radial velocities), while the official empirical errors used in LASP are more conservative. When applied to DESI DR1, our effective temperatures and surface gravities agree better with APOGEE than those from the DESI pipeline, particularly for cool giants, while the latter performs slightly better in radial velocity and metallicity. These results suggest that the framework delivers reliable accuracy, efficiency, and transferability, offering a practical approach to parameter inference in large spectroscopic surveys. The code and DESI-based catalog are available via \dataset[DOI: 10.12149/101679]{https://doi.org/10.12149/101679} and \dataset[DOI: 10.12149/101675]{https://doi.org/10.12149/101675}, respectively.

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Estimating stellar atmospheric parameters and elemental abundances using fully connected residual network

Stellar atmospheric parameters and elemental abundances are traditionally determined using template matching techniques based on high-resolution spectra. However, these methods are sensitive to noise and unsuitable for ultra-low-resolution data. Given that the Chinese Space Station Telescope (CSST) will acquire large volumes of ultra-low-resolution spectra, developing effective methods for ultra-low-resolution spectral analysis is crucial. In this work, we investigated the Fully Connected Residual Network (FCResNet) for simultaneously estimating atmospheric parameters ($T_\text{eff}$, $\log g$, [Fe/H]) and elemental abundances ([C/Fe], [N/Fe], [Mg/Fe]). We trained and evaluated FCResNet using CSST-like spectra (\textit{R} $\sim$ 200) generated by degrading LAMOST spectra (\textit{R} $\sim$ 1,800), with reference labels from APOGEE. FCResNet significantly outperforms traditional machine learning methods (KNN, XGBoost, SVR) and CNN in prediction precision. For spectra with g-band signal-to-noise ratio greater than 20, FCResNet achieves precisions of 78 K, 0.15 dex, 0.08 dex, 0.05 dex, 0.10 dex, and 0.05 dex for $T_\text{eff}$, $\log g$, [Fe/H], [C/Fe], [N/Fe] and [Mg/Fe], respectively, on the test set. FCResNet processes one million spectra in only 42 seconds while maintaining a simple architecture with just 348 KB model size. These results suggest that FCResNet is a practical and promising tool for processing the large volume of ultra-low-resolution spectra that will be obtained by CSST in the future.

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Refined M-type Star Catalog from LAMOST DR10: Measurements of Radial Velocities, $T_\text{eff}$, log $g$, [M/H] and [$\alpha$/M]

Precise stellar parameters for M-type stars, the Galaxy's most common stellar type, are crucial for numerous studies. In this work, we refined the LAMOST DR10 M-type star catalog through a two-stage process. First, we purified the catalog using techniques including deep learning and color-magnitude diagrams to remove 22,496 non-M spectra, correct 2,078 dwarf/giant classifications, and update 12,900 radial velocities. This resulted in a cleaner catalog containing 870,518 M-type spectra (820,493 dwarfs, 50,025 giants). Second, applying a label transfer strategy using values from APOGEE DR16 for parameter prediction with a ten-fold cross-validated CNN ensemble architecture, we predicted $T_\text{eff}$, $\log g$, [M/H], and [$\alpha$/M] separately for M dwarfs and giants. The average internal errors for M dwarfs/giants are respectively: $T_\text{eff}$ 30/17 K, log $g$ 0.07/0.07 dex, [M/H] 0.07/0.05 dex, and [$\alpha$/M] 0.02/0.02 dex. Comparison with APOGEE demonstrates external precisions of 34/14 K, 0.12/0.07 dex, 0.09/0.04 dex, and 0.03/0.02 dex for M dwarfs/giants, which represents precision improvements of over 20\% for M dwarfs and over 50\% for M giants compared to previous literature results. The catalog is available at https://nadc.china-vo.org/res/r101668/.

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New Symbiotic Stars from LAMOST DR10 Spectra and Multi-band Photometry

Symbiotic star (SySt) is long-period interacting binary system, typically consisting of a white dwarf and a red giant surrounded by a nebula. These systems are natural astrophysical laboratories for investigating binary star evolution. In this paper, we identified nine SySts from the LAMOST DR10 low-resolution spectra survey, seven of which were previously known, while two are newly identified. Initially, we selected LAMOST spectra exhibiting typical SySt emission lines (e.g., $\rm H_{\alpha}, ~H_{\beta}, ~H_{\gamma}, ~and ~He II$). Subsequently, we utilized the distribution of known SySts on the HR diagram to select SySt candidates, and visually inspected their spectra. Ultimately, we classified all nine as S-type SySts using the $J - H$ vs. $H - K$ diagram. Additionally, based on multi-band photometric data from GALEX, Gaia, 2MASS, ALLWISE, and several X-ray catalogs, we found 12 accreting-only SySt (acc-SySt) candidates, characterized by concurrent ultraviolet and infrared excess and accretion process. Furthermore, we estimated the white dwarf temperatures by fitting their observed SEDs using a combination of Kurucz stellar atmosphere model and Koester white dwarf model. We compared the accretion rates of acc-SySt candidates and confirmed SySts, and found they have similar accretion rate distribution, providing evidence that these acc-SySt candidates constitute bona fide SySts.

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Estimating Stellar Atmospheric Parameters and [{\alpha}/Fe] for LAMOST O-M type Stars Using a Spectral Emulator

In this paper, we developed a spectral emulator based on the Mapping Nearby Galaxies at Apache Point Observatory Stellar Library (MaStar) and a grouping optimization strategy to estimate effective temperature (T_eff), surface gravity (log g), metallicity ([Fe/H]) and the abundance of alpha elements with respect to iron ([alpha/Fe]) for O-M-type stars within the Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) low-resolution spectra. The primary aim is to use a rapid spectral-fitting method, specifically the spectral emulator with the grouping optimization strategy, to create a comprehensive catalog for stars of all types within LAMOST, addressing the shortcomings in parameter estimations for both cold and hot stars present in the official LAMOST AFGKM-type catalog. This effort is part of our series of studies dedicated to establishing an empirical spectral library for LAMOST. Experimental results demonstrate that our method is effectively applicable to parameter prediction for LAMOST, with the single-machine processing time within $70$ hr. We observed that the internal error dispersions for T_eff, log g, [Fe/H], and [alpha/Fe] across different spectral types lie within the ranges of $15-594$ K, $0.03-0.27$ dex, $0.02-0.10$ dex, and $0.01-0.04$ dex, respectively, indicating a good consistency. A comparative analysis with external data highlighted deficiencies in the official LAMOST catalog and issues with MaStar parameters, as well as potential limitations of our method in processing spectra with strong emission lines and bad pixels. The derived atmospheric parameters as a part of this work are available at https://nadc.china-vo.org/res/r101402/ .

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Deep learning interpretability analysis for carbon star identification in Gaia DR3

Context. A large fraction of Asymptotic Giant Branch (AGB) stars develop carbon-rich atmospheres during their evolution. Based on their color and luminosity, these carbon stars can be easily distinguished from many other kinds of stars. However, numerous G, K, and M giants also occupy the same region as carbon stars on the HR diagram. Despite this, their spectra exhibit differences, especially in the prominent CN molecular bands. Target. We aim to distinguish carbon stars from other kinds of stars using $Gaia$'s XP spectra, while providing attributional interpretations of key features necessary for identification, and even discovering additional new spectral key features. Method. We propose a classification model named `GaiaNet', an improved one-dimensional convolutional neural network specifically designed for handling $Gaia$'s XP spectra. We utilized the SHAP interpretability model to determine SHAP values for each feature in a spectrum, enabling us to explain the output of the `GaiaNet' model and provide further meaningful analysis. Compared to four traditional machine-learning methods, the `GaiaNet' model exhibits an average classification accuracy improvement of approximately 0.3% on the validation set, with the highest accuracy reaching 100%. Utilizing the SHAP model, we present a clear spectroscopic heatmap highlighting molecular band absorption features primarily distributed around CN773.3 and CN895.0, and summarize five key feature regions for carbon star identification. Upon applying the trained classification model to the CSTAR sample with Gaia `xp_sampled_mean' spectra, we obtained 451 new candidate carbon stars as a by-product.

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S-type stars from LAMOST DR10: classification of intrinsic and extrinsic stars

In this paper, we found 2939 S-type stars from LAMOST Data Release 10 using two machine-learning methods, and 2306 of them were reported for the first time. The main purpose of this work is to study how to divide S-type stars into intrinsic and extrinsic stars with photometric data and LAMOST spectra. Using infrared photometric data, we adopted two methods to distinguish S-type stars, i.e., XGBoost algorithm and color-color diagrams. We trained XGBoost model with 15 input features consisting of colors and absolute magnitudes of Two Micron All Sky Survey (2MASS), AllWISE, AKARI, and IRAS, and found that the model trained by input features with 2MASS, AKARI, and IRAS data has the highest accuracy of 95.52%. Furthermore, using this XGBoost model, we found four color-color diagrams with six infrared color criteria to divide S-type stars, which has an accuracy of about 90%. Applying the two methods to the 2939 S-type stars, 381 (XGBoost)/336 (color-color diagrams) intrinsic and 495 (XGBoost)/82 (color-color diagrams) extrinsic stars were classified, respectively. Using these photometrically classified intrinsic and extrinsic stars, we retrained XGBoost model with their blue and red medium-resolution spectra, and the 2939 stars were divided into 855 intrinsic and 2056 extrinsic stars from spectra with an accuracy of 94.82%. In addition, we also found four spectral regions of Zr I (6451.6A), Ne II (6539.6A), Hα (6564.5A), and Fe I (6609.1A) and C I (6611.4A) are the most important features, which can reach an accuracy of 92.1% when using them to classify S-type stars.

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M Subdwarf Research III. Spectroscopic Diagnostics for Breaking Parameter Degeneracy

To understand the parameter degeneracy of M subdwarf spectra at low resolution, we assemble a large number of spectral features in the wavelength range of 0.6-2.5 μm with band strength quantified by narrowband indices. Based on the index trends of BT-Settl model sequences, we illustrate how the main atmospheric parameters (Teff, log g, [M/H], and [alpha/Fe]) affect each spectral feature differently. Furthermore, we propose a four-step process to determine the four parameters sequentially, which extends the basic idea proposed by Jao et al. Each step contains several spectral features that break the degeneracy effect when determining a specific stellar parameter. Finally, the feasibility of each spectroscopic diagnostic with different spectral qualities is investigated. The result is resolution-independent down to R~200.

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S-type stars discovered in Medium-Resolution Spectra of LAMOST DR9

In this paper, we report on 606 S-type stars identified from Data Release 9 of the LAMOST medium-resolution spectroscopic (MRS) survey, and 539 of them are reported for the first time. The discovery of these stars is a three-step process, i.e., selecting with the ZrO band indices greater than 0.25, excluding non-S-type stars with the iterative Support Vector Machine method, and finally retaining stars with absolute bolometric magnitude larger than -7.1. The 606 stars are consistent with the distribution of known S-type stars in the color-magnitude diagram. We estimated the C/Os using the [C/Fe] and [O/Fe] provided by APOGEE and the MARCS model for S-type stars, respectively, and the results of the two methods show that C/Os of all stars are larger than 0.5. Both the locations on the color-magnitude diagram and C/Os further verify the nature of our S-type sample. Investigating the effect of TiO and atmospheric parameters on ZrO with the sample, we found that log g has a more significant impact on ZrO than Teff and [Fe/H], and both TiO and log g may negatively correlate with ZrO. According to the criterion of Tian et al. (2020), a total of 238 binary candidates were found by the zero-point-calibrated radial velocities from the officially released catalog of LAMOST MRS and the catalog of Zhang et al. (2021). A catalog of these 606 S-type stars is available from the following link https://doi.org/10.12149/101097.

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Ultracool dwarfs identified using spectra in LAMOST DR7

In this work, we identify 734 ultracool dwarfs with a spectral type of M6 or later, including one L0. Of this sample, 625 were studied spectroscopically for the first time. All of these ultracool dwarfs are within 360~pc, with a \textit{Gaia} G magnitude brighter than ~19.2 mag. By studying the spectra and checking their stellar parameters (Teff, logg, and [FeH] derived with the LAMOST pipeline, we found their cool red nature and their metallicity to be consistent with the nature of Galactic thin-disk objects. Furthermore, 77 of them show lithium absorption lines at 6708A, further indicating their young ages and substellar nature. Kinematics obtained through LAMOST radial velocities, along with the proper motion and parallax data from Gaia EDR3, also suggest that the majority of our targets are thin-disk objects. Kinematic ages were estimated through the relationship between the velocity dispersion and the average age for a certain population. Moreover, we identified 35 binaries, with 6 of them reported as binaries for the first time.

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Rotational Velocities of Am and Non-CP Stars based on Kepler and LAMOST DR5

Rotation is a critical physical process operating in the formation of Am stars. There is a strong correlation between low-velocity rotation and chemical peculiarity. However, the existence of many non-CP slow rotators challenges the understanding of Am stars. The purpose of our work is to search for low-velocity rotating non-CP A-type stars and Am stars and to make a comparative analysis. In this paper, we pick out a sample from the LAMOST-Kepler project, including 21 Am stars, 125 non-CP slow rotators, and 53 non-CP fast rotators. We calculate the rotational frequencies through periodic change of light curves caused by inhomogeneous stellar surfaces and then obtain the rotational velocities. For slow rotators, the age of Am stars is statistically younger than that of non-CP stars in the same temperature bin. In the comparison of the period, the average amplitude, and stellar mass of Am and non-CP stars, we discover that there is no difference in the photometric variability between Am and non-CP stars, which implies similar inhomogeneities on the surfaces. The average amplitude of non-CP stars has a downward trend with the increase of effective temperature and stellar mass, which is consistent with the theoretical prediction caused by weak dynamo-generated magnetic fields in A-type stars. In addition, we confirm four non-non-CP stars which have flares by checking FOV images, 24 pixel images, and pixel-level light curves.

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A catalog of early-type Hα emission line stars and 58 newly confirmed Herbig Ae/Bes from LAMOST DR7

We derive a catalog of early-type emission-line stars including 30,048 spectra of 25,886 stars from LAMOST DR7, in which 3,922 have Simbad records. The sample is obtained using K-Nearest Neighbor and Random Forest methods and visually inspected. The spectra are classified into 3 morphological types (10 subtypes) based on H$α$ emission line profiles. Some spectra contaminated by nebula emission lines such as from HII regions are flagged in the catalog. We also provide a specific sub-catalog of 101 stars with the stellar wind by calculating stellar wind or accretion flow velocities based on P Cygni or inverse P Cygni profiles, in which 74\% of them having velocities below 400km/s. More important, with two color-color diagrams (H-K, K- W1) and (H-K, J-H) of a collection of known Herbig Ae/Be stars (HAeBes) and classical Ae/Be stars (CAeBes), we propose an updated criterion to separate HAeBes from CAeBes. By the criterion, we select 201 HAeBes candidates and 5,547 CAeBes candidates from the sample. We confirmed 66 of the 201 HAeBes by using both WISE images and LAMOST spectra and present a specific HAeBe sub-catalog, in which 58 are newly identified. In addition, the WISE colors (W1-W2, W1- W3, and W1-W4) show the distribution consistency between our confirmed HAeBes and that of the known HAeBes. Most of the 66 confirmed HAeBes locate in the lower edge of the main sequence of hot end in the HR diagram, while the distances of about 77\% exceed 1Kpc, which enlarges the number of far distant known HAeBes.

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Self-consistent Stellar Radial Velocities from LAMOST Medium-Resolution Survey (MRS) DR7

Radial velocity (RV) is among the most fundamental physical quantities obtainable from stellar spectra and is rather important in the analysis of time-domain phenomena. The LAMOST Medium-Resolution Survey (MRS) DR7 contains 5 million single-exposure stellar spectra at spectral resolution $R\sim7\,500$. However, the temporal variation of the RV zero-points (RVZPs) of the MRS survey, which makes the RVs from multiple epochs inconsistent, has not been addressed. In this paper, we measure the RVs of the 3.8 million single-exposure spectra (for 0.6 million stars) with signal-to-noise ratio (SNR) higher than 5 based on cross-correlation function (CCF) method, and propose a robust method to self-consistently determine the RVZPs exposure-by-exposure for each spectrograph with the help of \textit{Gaia} DR2 RVs. Such RVZPs are estimated for 3.6 million RVs and can reach a mean precision of $\sim 0.38\,\mathrm{km\,s}^{-1}$. The result of the temporal variation of RVZPs indicates that our algorithm is efficient and necessary before we use the absolute RVs to perform time-domain analysis. Validating the results with APOGEE DR16 shows that our absolute RVs can reach an overall precision of 0.84/0.80 $\mathrm{km\,s}^{-1}$ in the blue/red arm at $50<\mathrm{SNR}<100$, while 1.26/1.99 $\mathrm{km\,s}^{-1}$ at $5<\mathrm{SNR}<10$. The cumulative distribution function (CDF) of the standard deviations of multiple RVs ($N_\mathrm{obs}\geq 8$) for 678 standard stars reach 0.45/0.54, 1.07/1.39, and 1.45/1.86 $\mathrm{km\,s}^{-1}$ in the blue/red arm at 50\%, 90\%, and 95\% levels, respectively. The catalogs of the RVs, RVZPs, and selected candidate RV standard stars are available at \url{https://github.com/hypergravity/paperdata}.

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591 high velocity stars in the Galactic halo selected from LAMOST DR7 and Gaia DR2

In this paper, we report 591 high velocity star candidates (HiVelSCs) selected from over 10 million spectra of the data release seven (DR7) of the Large Sky Area Multi-object Fiber Spectroscopic Telescope and the second Gaia data release, with three-dimensional velocities in the Galactic rest-frame larger than 445 km/s. We show that at least 43 HiVelSCs are unbound to the Galaxy with escape probabilities larger than 50%, and this number decreases to eight if the possible parallax zero-point error is corrected. Most of these HiVelSCs are metal-poor and slightly alpha-enhanced inner halo stars. Only 14% of them have [Fe/H] > -1, which may be the metal-rich "in situ" stars in halo formed in the initial collapse of the Milky Way or metal-rich stars formed in the disk or bulge but kinematically heated. The low ratio of 14% implies that the bulk of stellar halo was formed from the accretion and tidal disruption of satellite galaxies. In addition, HiVelSCs on the retrograde orbits have a slightly lower metallicities on average compared with these on the prograde orbits, meanwhile metal-poor HiVelSCs with [Fe/H] < -1 have an even faster mean retrograde velocity compared with metal-rich HiVelSCs. To investigate the origins of HiVelSCs, we perform orbit integrations and divide them into four types, i.e., hypervelocity stars, hyper-runaway stars, runaway stars and fast halo stars. A catalog for these 591 HiVelSCs, including radial velocities, atmospheric parameters, Gaia astrometric parameters, spatial positions, and velocities, etc., is available at http://paperdata.chinavo.org/LYB/lamostdr7_gaiadr2_hvs_591.csv.

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Spectroscopically Identified Cataclysmic Variables from LAMOST survey. I. The Sample

A sample of Cataclysmic Variables (CVs) is presented including spectroscopically identified 380 spectra of 245 objects, of which 58 CV candidates are new discoveries. The BaggingTopPush and the Random Forest algorithms are applied to the Fifth Data Release (DR5) of LAMOST to retrieve CVs with strong emission lines and with broad absorption lines respectively. Based on spectroscopic classification, 134 dwarf novae, 41 nova-like variables and 19 magnetic CVs are identified from the sample. In addition, 89 high--inclination systems and 33 CVs showing companion stars are recognized and discussed for their distinct spectral characteristics. Comparisons between CVs from LAMOST and from published catalogs are made in spatial and magnitude distribution, and the difference of their locus in Gaia color--absolute magnitude diagram (CaMD) are also investigated. More interestingly, for two dwarf novae observed through LAMOST and SDSS in different epoch, their spectra both in quiescence phase and during outburst are exhibited.

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Bivariate Luminosity Function of Galaxy Pairs

We measure the bivariate luminosity function (BLF) of galaxy pairs and use it to probe and characterize the galaxy-galaxy interaction between pair members. The galaxy pair sample is selected from the main galaxy sample of Sloan Digital Sky Survey and supplied with a significant number of redshifts from the LAMOST spectral and GAMA surveys. We find the BLFs depend on the projected distance $d_{\text{p}}$ between pair members. At large separation $d_{\text{p}} > 150 h^{-1}\ \text{kpc}$, the BLF degenerates into a luminosity function (LF) of single galaxies, indicating few interactions between pair members. At $100 h^{-1}\ \text{kpc} \leq d_{\text{p}} \leq 150 h^{-1}\ \text{kpc}$, the BLF starts to show the correlation between pair members, in the sense that the shape of the conditional luminosity function (CLF) of one member galaxy starts to depend on the luminosity of the other member galaxy. Specifically, the CLF with a brighter companion has a steeper faint-end slope, which becomes even more significant at $50 h^{-1}\ \text{kpc} \leq d_{\text{p}} \leq 100 h^{-1}\ \text{kpc}$. This behavior is consistent with the scenario, \textit{and also is the observational evidence}, that dynamic friction drives massive major merger pairs to merge more quickly. At close distance $d_{\text{p}} \leq 50 h^{-1}\ \text{kpc}$, besides the merging time-scale effect, the BLF also shows an overall brightening of $ΔM_r \geq 0.04$ mag, which reveals the enhanced star formation of the close-pair phase. By combining another statistical conclusion that the star formation rate of late-type galaxies in close pairs is enhanced at a level of about 40\%, we further conclude that the average starburst time-scale of close pairs is as long as 0.4 Gyr.

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