Analysis of Stellar Spectra from LAMOST DR5 with Generative Spectrum Networks
Wang Rui, Luo A-li, Zhang Shuo, Hou Wen, Du Bing, Song Yi-Han, Wu Ke-Fei, Chen Jian-Jun, Zuo Fang, Qin Li, Chen Xiang-Lei, Lu Yan
aa r X i v : . [ a s t r o - ph . I M ] N ov Draft version November 21, 2018
Typeset using L A TEX twocolumn style in AASTeX62
Analysis of Stellar Spectra from LAMOST DR5 with Generative Spectrum Networks
Wang Rui,
1, 2,3
Luo A-li,
Zhang Shuo,
Hou Wen,
1, 3
Du Bing,
1, 3
Song Yihan,
Wu Kefei,
Chen Jianjun,
Zuo Fang,
Qin Li,
Chen Xianglei,
1, 2, 3 and Lu Yan
1, 2,3 National Astronomical Observatories, Chinese Academy of Sciences,Beijing 100012, China University of Chinese Academy of Sciences, Beijing 100049, China Key Laboratory of Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences,Beijing 100012, China
Submitted to PASPABSTRACTIn this study, the fundamental stellar atmospheric parameters ( T eff , log g , [Fe/H] and [ α /Fe])were derived for low-resolution spectroscopy from LAMOST DR5 with Generative Spectrum Networks(GSN). This follows the same scheme as a normal artificial neural network with stellar parameters asthe input and spectra as the output. The GSN model was effective in producing synthetic spectra aftertraining on the PHOENIX theoretical spectra. In combination with Bayes framework, the applicationfor analysis of LAMOST observed spectra exhibited improved efficiency on the distributed computingplatform, Spark. In addition, the results were examined and validated by a comparison with referenceparameters from high-resolution surveys and asteroseismic results. Our results show good consistencywith the results from other survey and catalogs. Our proposed method is reliable with a precision of80 K for T eff , 0.14 dex for log g , 0.07 dex for [Fe/H] and 0.168 dex for [ α /Fe], for spectra with asignal-to-noise in g bands (SNR g ) higher than 50. The parameters estimated as a part of this workare available at http://paperdata.china-vo.org/GSN parameters/GSN parameters.csv Keywords: stars: atmospheres – methods: data analysis – techniques: spectroscopic INTRODUCTIONMost sky surveys result in extensive databases ofstellar spectra for dissecting and understanding theMilky Way. The fundamental information derivedfrom such spectra includes the effective temperature( T eff ), logarithm of surface gravity (log g ), abun-dance of metal elements with respect to hydrogen([Fe/H]), and the abundance of alpha elements withrespect to iron ([ α /Fe]), are valuable for Galactic ar-chaeology and stellar evolution history. Many projectshave been carried out to detect specific objects athigh/low resolution covering a range of wavelengths(e.g., the Large Sky Area Multi-Object Fiber Spectro-scopic Telescope (LAMOST) Experiment for GalacticUnderstanding and Exploration (LEGUE; Luo et al.2015; Cui et al. 2012; Deng et al. 2012; Zhao et al. 2012;Liu et al. 2015), the Sloan Extension for Galactic Un- Corresponding author: Luo [email protected] derstanding and Exploration (SEGUE; Yanny et al.2009), the Apache Point Observatory Galactic Evolu-tion Experiment (APOGEE; Allende Prieto et al. 2008;Majewski et al. 2017), the RAdial Velocity Experi-ment (RAVE; Steinmetz et al. 2006), Gaia-ESO Pub-lic Spectroscopic Survey (GES; Gilmore et al. 2012),the GALAH Survey (De Silva et al. 2015) and Gaia-RVS (Katz et al. 2004)).Automatic and accurate estimation of stellar parame-ters from large spectroscopic survey databases requiresa wide array of different techniques and methods. Al-most each spectroscopy survey results in the establish-ment of its own stellar parameter pipeline, such as: theofficial LAMOST Stellar Parameter Pipeline (LASP;Luo et al. 2015; Wu et al. 2011) based on UlySS pack-age (Koleva et al. 2009), LAMOST Stellar Parame-ter Pipeline at PKU (LSP3; Xiang et al. 2015, 2017;Ren et al. 2016) which combines spectral fitting with anempirical spectral library and the application of Kernel-based Principal Component Analysis (KPCA) on dif-ferent training sets to obtain parameters of interest,
Wang Rui et al.
SEGUE Stellar Parameter Pipeline (SSPP; Lee et al.2008) using multiple techniques (e.g., spectral fittingwith synthesis spectra grids, making use of compar-isons to theoretical ugr colors and line parameters fromsythetic spectra(WBG; Wilhelm et al. 1999) and neu-ral network approaches), the APOGEE Stellar Param-eter and Chemical Abundances Pipeline (ASPCAP;Garc´ıa P´erez et al. 2016) parametrizing near-infraredspectra by minimizing χ between observed and theoret-ical spectra, and the RAVE pipeline (Steinmetz et al.2006) which exploits a best-matched template to mea-sure radial velocities and atmospheric parameters.In these listed pipelines, the methods that most com-monly used include spectral fitting based on gridsof spectral libraries which can classify high/median-resolution observations based on empirical measure-ments, for example, ELODIE (Prugniel et al. 2007),STELIB (Le Borgne et al. 2003) and MILES (Falc´on-Barroso et al.2011), and theoretical synthetic spectra derived from at-mospheric models such as: instance, ATLAS9 (Kurucz1993), Kurucz2003 (Castelli & Kurucz 2004), MARCS(Gustafsson et al. 2008) and PHOENIX (Allard & Hauschildt1995; Husser et al. 2013). However, neither of thesespectral libraries offer a perfect solution to the prob-lem of deriving stellar atmospheric parameters. Theempirical spectral libraries are limited in wavelengthand parameter space coverage, for example, the latestversion v3.2 of the ELODIE library lacks a template ofK giant stars, and most libraries are incomplete or lackchemical abundance data. The synthetic spectra wouldintroduce large systematic uncertainties, mainly becauseof the impertinent stellar atmospheric models, such asthe assumptions of one-dimensional models and the factthat local thermodynamic equilibrium for hot and coolstars is not completely consistent with actual condi-tions. Also, it is computationally expensive to generatesynthetic spectra starting from physical assumptions.However, synthetic libraries have many advantages: therange of stellar parameters, elemental abundances, andboth the wavelength coverage and the spectral resolutioncan be adjusted as needed. In this work, we employedthe least version of Phoenix (Husser et al. 2013), andthe details are provided in Section 2.The effective utilization of synthetic spectra informa-tion is a critical process in the analysis of observed spec-tra. The increase in the number of spectra with time,both synthetic and observed, provides an opportunityto apply various learning methods to derive stellar pa-rameters, independent of a large number of syntheticspectra. Bailer-Jones et al. (1997); Bailer-Jones (2000)performed the incipient study on the application ofArtificial Neural Network(ANN) for spectral classifica- tion and parameter estimation. Subsequently, numer-ous related techniques have been explored such as theNon-linear regression model (Re Fiorentin et al. 2007)and Support Vector Regression+LASSO (Li et al. 2014)for estimation of parameters from SDSS/SEGUE spec-tra, KPCA (Xiang et al. 2017) and Cannon (Ness et al.2015; Ho et al. 2017) adopted an data-driven approachfor the analysis of LAMOST stellar spectra, Star-Net (Fabbro et al. 2018) and AstroNN (Leung & Bovy2018) applied Convolutional Neural Networks techniqueto an APOGEE data-set, and MATISSE (Recio-Blanco et al.2006), ANN (Manteiga et al. 2010) and Aeneas (Liu et al.2012) employed machine learning method for Gaia RVSlow S/N stellar spectra parametrization. All the afore-mentioned algorithms have their own unique strengthsfor constraint mapping from spectral flux to parameters( T eff , log g and metal abundance). However, many ofthem take spectrum fluxes as inputs with the param-eters and stellar labels as outputs of the algorithms.As such, they cannot directly determine the errors ofthe outputs because these methods cannot produce thepost-distribution of the parameters for a given spectrum.The error information they generate is most relevant tothe internal errors of each method or the dispersionof the difference between their results and that of ex-ternal counterparts. Simple linear interpolation couldnot precisely characterize the complex relationship be-tween flux and stellar parameters until Rix et al. (2016);Ting et al. (2016, 2018) put forward a polynomial spec-tral model and the Payne method, that are both basedon the training of a mathematical model using ab initiospectral model grids. These approaches benefit fromartificial neural networks because they are effective atfitting complex non-linear relations.In this report, we designed a new structure of artificialneural networks, Generative Spectrum Networks(GSN),a similar neural network proposed by Dafonte et al.(2016), which follows the same scheme as a typicalANN, except that the inputs and outputs are inverted.This approach was proposed and applied to simulationsof prospective Gaia RVS spectra based on the Kuruczmodel. However, real observed spectra were not tested.It should be noted that there is a sign discrepancy be-tween the synthetic and observed spectra for errors fromextinction, redden, seeing, contamination of stray light,instruments and post data processing. We improve thegenerative artificial neural network training on Phoenixspectra for estimation of the parameters of LAMOSTobservations. In combination with a Bayesian frame-work and Monte Carlo(MC) method, the networks canbe used to derive not only stellar atmospheric param-eters, but also their posterior distribution. The com-puting cost is always an insurmountable obstacle duringthe application of the MC method for a large number ofdata-sets. However, the distributed computing platformSPARK improves the viability of employing MC sam-pling methods based on Bayes theory. To the best ofour knowledge, we are the first group to utilize SPARKestimating stellar parameters in this way. Moreover, ourmethod adds an abundance of alpha elements ([ α /Fe])with respect to the existing catalog provided by LASP.This report is organized as follows. The Phoenixdatasets for training and testing the GSN model, and theLAMOST DR5 observations will be described in Sect.2.The methods for the determination of the stellar atmo-spheric parameters will be presented in Sect. 3. Valida-tion results will be highlighted in Sect. 4. Finally, wewill discuss the challenges associated with this researchin Sect. 5 followed by a summary in Sect. 6. DATAThe spectra employed in this report consist of twoparts: synthetic spectra calculated from PHOENIXmode (Husser et al. 2013) and LAMOST spectra fromthe internal fifth data release(LAMOST DR5; Luo et al.in preparation). The synthetic spectra with referenceparameters( T eff , log g , [Fe/H] and [ α /Fe]) are used fortraining and testing the GSN model. Then, the stel-lar parameters of the LAMOST spectra were estimatedusing the achieved GSN model.2.1. Synthetic Spectra
The synthetic stellar spectral library is a very im-portant tool for analyzing observed spectra and stel-lar population synthesis. The latest extensive libraryof PHOENIX stellar atmospherics and high-resolutionsynthetic spectra are published in Husser et al. (2013).This new spectral library uses version 16 of PHOENIX,which includes a new equation of state, as well as anupdate-to-data atomic and molecular line list. The at-mospheres were calculated based on a spherical modewith 64 layers, and both local thermodynamic equilib-rium (LTE) and non-local thermodynamic equilibrium(N-LTE) have been adopted for an effective tempera-ture T eff ≥ λ = 1 ˚A in the optical wavelengthrange from λ = 3000 ˚A to 10000 ˚A and over-sampled by a factor of ten (the 1 ˚A grid has a sampling rate of 0.1˚A) (Husser et al. 2013). Table 1.
Parameter Space of the Grid.Variable Range Step size T eff g α /Fe] -2.0 - +1.2 0.2 Before spiting the spectral library into training andtesting sets, some adjustments were made to facilitatematching of low-resolution spectra. To fully exploit thespectral information hidden in the LAMOST spectra, weconsider using the largest wavelength range ( λ = 3800 to5700 ˚A for the blue arm, and λ = 5900 to 8800 ˚A for thered arm, and we removed the middle range ( λ = 5700 to5900 ˚A) in which the response efficiency of instrumentsis too low). According to the instrumental full-with-half-maximum of the LAMOST spectrometers (as shown inFigure 1), we respectively convolute the blue and redarms of the Phoenix model spectra to the same reso-lution as the LAMOST observations. Then, we simplynormalized the spectra by dividing them by their medi-ans. For their corresponding parameters, the effectivetemperature was adjusted in a logarithmic scale.2.2. Observed Spectra from LAMOST DR5
The Large Sky Area Multi-Object Fiber SpectroscopicTelescope (LAMOST) general survey is a spectroscopicsurvey (Luo et al. 2015) which has already completedthe first stage of the sky survey plan (from Oct. 24th,2011 to Jun. 16th, 2017). It contains two main parts:the LAMOST ExtraGAlactic Survey (LEGAS) and theLAMOST Experiment for Galactic Understanding andExploration (LEGUE) survey of the Milky Way stel-lar structure. The LAMOST can simultaneously collect4000 fiber spectra in a wild field (5 ◦ ) with a resolvingpower R ≈ Wang Rui et al. N ( x ) blue arm: μ = 3.04, σ = 0.11red arm: μ = 4.57, σ = 0.21 Figure 1.
The distribution of the instrumental full-width-half-maximum(FWHM) of the blue (blue) and red (red)arm for LAMOST. The mean and standard deviation of theFWHM of the blue arm are 3.04 ˚A and 0.11 ˚A respectively.For red the arm, the mean and standard deviation are 4.57˚A and 0.21 ˚A, respectively. calibrated based on standard stars (Luo et al. 2015) orstatistical response curve within an error of 10% for eachpixel (Du et al. 2016). The spectra are re-binned at aconstant interval wavelength for a logarithmic scale.In this work, we exploit artificial neural networks forthe analysis of LAMOST DR5 stellar spectra. The fifthdata release of LAMOST includes a total of 4,154 platescontaining 9,017,844 spectra, of which 8,171,443 areclassified as stars and the rest as galaxies, quasars, or un-known objects via the LAMOST 1D pipeline. The num-ber of stellar spectra with a signal to noise ratio (SNR) ofthe g or i band higher than ten is 7,531,398. LAMOSTDR5 also provide three stellar catalogues: late A andFGK-type stars with high quality spectra (5,344,058)with measured parameters( T eff , log g , [Fe/H], radialvelocities (RV)) derived by LASP (Wu et al. 2011;Luo et al. 2015), early A-type stars (365,101 entries)and M-type stars (436,782 entries) without stellar pa-rameters. METHOD AND APPLICATION3.1.
Generative Spectrum Networks
Similar to Bailer-Jones (2000) and Manteiga et al.(2010), many researcher design traditional artificial neu-ral networks structures with the fluxes of the spectra asthe input and the stellar atmospheric parameters as theoutput, for analysis of spectra. Dafonte et al. (2016)suggested the innovative idea of inverting the inputs andoutputs of the ANNs, with the parameters as inputs andthe flux values as outputs. The
Payne (Ting et al. 2018) also adopted an analogous, fully connected neural net-work to produce reference spectra instead of an interpo-late operator. These kinds of neural networks performa precise fitting of the non-linear relationship betweenfluxes and stellar parameters.In this report, we designed a new structure of artifi-cial neural networks which consists of a fully-connectednetwork with an input layer, three hidden layers, and anoutput layer, to generate spectra by training PHOENIXmodel spectra. The name of the networks was changedfrom generative artificial neural networks (GANN) toGenerative spectrum networks (GSN) for differentiatingwith generative adversarial networks (GAN). The con-nection between all neurons in two layers is constructedby non-linear combinations, at each layer l + 1, and theoutput as a function of the previous layer l is given by: y l +1 j = g ( n P i =0 ( w lij y lij + b lj ),where g is an activation function, w ij is the weightrepresenting the connection of the node i of layer l andnode j of layer l + 1, and b lij is the bias of the node i oflayer l . There are many choices options for the activa-tion function, such as ReLU, Sigmoid, Logistic, Linearetc. All these activation functions can change the linearrelationship between the layers except for the Linear ac-tivation function. We chose ReLU for the middle hiddenlayers and the linear activation function for the outputlayer. The Training model for optimizing the weightsand biases is based on approaches such as stochasticgradient descent (SGD), mining error functions E : E = 1 n n X i =0 ( y li − ˆ y li ) where ˆ y li is the prediction outcome of ANN model and y li is the actual values of the fluxes of the training set.Training the neural network described above is basedon a back propagation (BP) algorithm in which theparameter weights and biases are initialized withrandom values. However, vanishing and explod-ing gradient will occur when the number of hiddenlayers is too large. Here, we introduce an auto-encoder to initialize the weights and biases and thenfine-tune to address the gradient problem describedabove (Hinton & Salakhutdinov 2006). Also, we employearly-stopping to prevent over-fitting from occurringwhen the number of training samples is much less thanthe complexity of the network structure. We randomlysplit the synthetic spectra into the training set, val-idation set and test set in the proportion 5:1:4, andtrain different structures of GSN to obtain the best oneamong them. Finally, a five-layer network, consisting ofthe input layer of 4 stellar parameters, three hidden lay-ers with 40, 400, 1000 nodes, and the final output layerof 3641 spectral fluxes corresponding to the wavelengthpoints of our re-sampled LAMOST spectra, is chosenbecause of its well-documented high performance.3.2. Fully Bayesian
Generative Spectrum Networks can produce modelspectra when a team of parameters is given. Using chi-square distance as a proxy to match the spectrum to bemeasured with model grids is common and most meth-ods use this approach. However, the uncertainty estima-tion would be difficult for template matching. Combinedwith Bayes rule, Monte-Carlo sampling is an effectiveway to obtain the posterior distribution over the param-eters given the observed spectrum, P ( P aram | Spec ), asrepresented by the formula (6) in Dafonte et al. (2016) P ( P aram | Spec ) = P ( Spec | P aram ) P ( P aram ) P ( Spec ) ,where P ( Spec | P aram ) is the probability of the resultparameters
P aram when a spectrum
Spec to be esti-mated is given, P ( P aram ) is the prior distribution ofthe parameters, P ( Spec ) is a normalization factor. Here,we assume that P ( P aram ) is a uniformly distributedand the noise distribution function of the observed spec-trum is a Gaussian-like function although the main noisethat comes from the CCD read noise satisfies a Poisondistribution. Therefore, the P ( Spec | P aram ) can be ex-pressed as: P ( Spec | P aram ) = exp {− N X i =1 ( F obs,i − P oly n,i × F GSN,i σ i ) } ,where F obs,i is the flux of the pixel i of the observedspectrum Spec , P oly n,i is a n order polynomial correc-tion adjustment item for the uncertainty of flux calibra-tion and redden effect, F GSN,i is the flux of the pixel i of the generative spectrum of the GSN model when theinput parameters is P aram and σ i is the error of theobserved flux.3.3. Application to LAMOST DR5
We estimated stellar parameters ( T eff , log g , [Fe/H]and [ α /Fe]) of LAMOST DR5 ∼ g >
30 using GSN and Bayesian methods as de-scribed above. All stellar spectra are initially shiftedto their rest-frame wavelength using the radial velocityprovided by LAMOST 1D pipeline and re-sampled to afixed wavelength range. To obtain the posterirori dis-tribution of the parameters containing the ’real’ values, 5000 groups parameters were sampled from the uniformdistribution U [ µ i − σ i , µ i + 3 σ i ], where i denote param-eter( T eff , log g , [Fe/H] or [ α/F e ]) provided by LASP, µ i and σ i are parameters and their corresponding er-rors. LASP do not supply the parameter [ α/F e ]. In thiscase, [ α/F e ] is set as Lee et al. (2013): α -enhancementratio relative to Fe, is − . × x for x = [Fe/H], and thestandard deviation is set to 0.3. Previous researchershave determined that the log g supplied by LASP isnot accurate for K giants (Liu et al. 2014; Chen et al.2015; Wang et al. 2016). As such, we calibrated the log g supplied by LASP based on the calibration relationgiven by equation (12) of Wang et al. (2016): log g ( adopted ) = 2 . × log g ( lasp ) − . × log g ( lasp ) × T eff ( lasp )1000 + 1 . × T eff ( lasp )1000 − . K ≤ T ef f ≤ K , 1 . ≤ logg ≤ .
2, or 3800 K ≤ T ef f ≤ K , 2 . ≤ logg ≤ . RESULTS AND VALIDATIONTo ensure the reliability and accuracy of the stellarparameters obtained with GSN, we employed the pa-rameter catalogs of some sub-sample catalogs of LAM-OST DR5 common stars, with external precise stellarparameters derived from high-resolution observations,or by other methods used for comparing and validation.To obtain reliable results, we only selected spectra withSNR g >
30 for comparison purposes.4.1.
Comparison with APOGEE Stars
The Apache Point Observatory for Galactic Evo-lution Experiment (APOGEE; Holtzman et al. 2015;Majewski et al. 2017; Holtzman et al. 2018) is a median-high resolution (R ∼
22 500) spectroscopic survey inthe near-infrared spectral range ( λ = 15700 to 17500˚A). From SDSS DR14, APOGEE has already collected ∼ Wang Rui et al. son between the observed and theoretical spectra usingchi-square minimization. The complete SDSS DR14APOGEE sample has 34783 stars in common with theLAMOST DR5 sample which correspond to 146,697spectra. We neglected the dwarf stars(log ≥ .
5) forwhich APOGEE did not provide reliable parameters,in addition to the stars flagged by APOGEE as havingpossible problems in the spectrum or in the ASPCAPprogress. This finally left us with a total of 21,642 spec-tra after the exclusion of repeat observations and theLAMOST spectra with SNR g ≤ T eff , log g ) plane and the bottom panels show the de-tail contradistinction for each parameter. The resultsindicate good agreements between the two parametersets with small offsets and scatter. The offsets of degen-eracies are 20.18 K, 0.00 dex, -0.02 dex, 0.06 dex andthe dispersions are 56.39 K, 0.12 dex, 0.06 dex, 0.08 dexfor T eff , log g , [Fe/H], [ α /Fe], respectively. It shouldbe noted that there is a small degree of systematic off-sets. However, the small dispersions suggest that theestimations are precise. The temperature derived fromthe GSN exhibits an overestimation of the APOGEEresults by 20.18 K. In addition, the estimated [Fe/H]by GSN shows an underestimation of 0.02 dex with re-spect to the [Fe/H] of APOGEE, while [ α /Fe] overesti-mates by 0.06 dex. However, it is worth noting that thestellar atmospheric parameters derived by ASPCAP arecalibrated (Holtzman et al. 2015, 2018). The raw AS-PCAP temperature which is determined to be approx-imately 90K cooler than the photometric temperatureis calibrated by a linear fit relation derived by inferredcolor-temperature. However, our temperature is still un-expectedly higher by approximately 20 K compared tothat of APOGEE. The calibration relation for the sur-face gravity was based on a set of APOKASC catalog(Pinsonneault et al. 2014), therefore the APOGEE log g s were scaled to the asteroseismic results. In this case,no systemic offsets were identified for the surface grav-ity between GSN and ASPCAP, which benefit from therelatively accurate initial value coverage for GSN esti-mation. For [ α /Fe], the APOGEE dataset exhibits asmall offset of 0.06 dex, with a small scatter of 0.08 dex,which would be considered as a precise result for suchlow-resolution spectra. This result is achieved becausethe alpha-to-iron ratio of the APOGEE stars is mea-sured based on the spectra with a resolution that is 11times higher. Moreover, the GSN measures abundanceby computing the posterior probability from the infor-mation in the entire spectral bands (3800-8800˚A), which may lead to a bias of 0.1-0.2 dex (Lee et al. 2015). Wecan shift the [ α /Fe] to the APOGEE’s values to elimi-nate system bias.4.2. Comparison with PASTEL Catalogue
The PASTEL catalogue (Soubiran et al. 2010, 2016)is a bibliographical compilation of stellar parameters( T eff , log g , [Fe/H]) which were obtained from theanalysis of high resolution and high signal-to-noise spec-tra, derived based on various methods. Soubiran et al.(2016) updated the PASTEL catalogue which includes64,082 determinations of either T eff or ( T eff , log g ,[Fe/H]) for 31,401 stars, of which 11,197 stars have avalues for the three parameters ( T eff ,log g , [Fe/H]) witha high-quality spectroscopic metallicity. These stars cantherefore be used as reference to compare with our re-sults. Our LAMOST sample has 1,000 common starswith the PASTEL catalogue, of which there are 579with T eff , 372 with log g and 565 with [Fe/H], afterexcluding the outliers and low signal-to-noise spectrausing the same criteria as Gao et al. (2015): | T eff ( GSN ) − T eff ( P AST EL ) | ≥ | log g ( GSN ) − log g ( P AST EL ) | ≥ . | [ F e/H ]( GSN ) − [ F e/H ]( P AST EL ) | ≥ . g ( LAM OST ) ≤
30A comparison of results between the stellar param-eters derived by GSN and that provided by the PAS-TEL catalog is shown in Fig 3. Most of the LAMOST-PASTEL common stars are dwarfs. The results indicatea good consistency between the parameters of GSN andthat of the PASTEL catalogue: no significant offset wasobserved for log g s or for [Fe/H]s except for T eff withan offset of 62.25 K. The dispersion of their differenceis given as 128.83 K, 0.18 dex and 0.14 dex respectively.Soubiran et al. (2016) noted that the fundamental Teffbased on direct measurements of the angular diametersand the total flux of Earth is cooler than the tempera-ture listed in the 2006 version of the PASTEL catalogby 51 K , with a median absolute deviation of 96 K.Our temperature overestimate of 62.25 K means thatour temperature scale seems to be about 110 K higherthan that of the fundamental temperature.4.3. Comparison with Geneva-Copenhagen SurveyStars
The Geneva-Copenhagen survey (GCS; Nordstr¨om et al.2004; Holmberg et al. 2007) present 16,682 F and Gdwarfs in the solar neighborhood with ages, metallicitiesand kinematic properties. Casagrande et al. (2011) de-rived the effective temperature T eff and gravity log g of l og g APOGEEN=22564 350037504000425045004750500052505500 Teff(K)0.00.51.01.52.02.53.03.54.0 og g GSNN=225644000 4500 5000 5500Teff_APOGEE380040004200440046004800500052005400 T e ff _ G S N μ = 20.18σ = 56.39 0 1 2 3 4 ogg_APOGEE0.00.51.01.52.02.53.03.54.0 ogg_ G S N μ = − 0.00σ = 0.12 −1.0 −0.5 0.0 0.5[Fe/H]_APOGEE−1.0−0.8−0.6−0.4−0.20.00.20.40.6 [ F e / H ] _ G S N μ = − 0.02σ = 0.06 0.0 0.2 0.4[α/Fe]_APOGEE−0.10.00.10.20.30.40.5 [ α / F e ] _ G S N μ = 0.06σ = 0.08 Figure 2.
The density distribution of APOGEE parameters (top left panel) and GSN results (top right panel) for LAMOST23,315 stars with SNR g greater than 30. Also, the comparison between GSN stellar parameters and the APOGEE parametersare showed in the four bottom panels. The red dash lines in the bottom panels are one-to-one lines. T e ff _ G S N l o gg _ G S N −2 −1 0[Fe/H]_PASTEL−2−10 [ F e / H ] _ G S N −250 0 250 500ΔTeff020406080100 N=570μ = 62Δ25σ = 128Δ83 −0Δ50−0Δ25 0Δ00 0Δ25 0Δ50Δlogg01020304050
N=371μ = − 0Δ02σ = 0Δ18 −0Δ4 −0Δ2 0Δ0 0Δ2 0Δ4Δ[Fe/H]020406080
N=556μ = 0Δ03σ = 0Δ14
Figure 3.
The color-coded scatter of GSN stellar parameters compared with the PASTEL catalogue for LAMOST DR5 spectrawith SNR g ≥
30 are showed in the three top panels. The red dash lines in the top panels are one-to-one lines. The distributionsof the discrepancies for T eff , log g and [Fe/H] are shown in the three bottom panels. Wang Rui et al. the GCS sources from photometry based on the infraredflux method (IRFM), and used the derived temperatureto build a consistent metallicity scale. Subsequently, themetallicity was calibrated using high-resolution spec-troscopy. Also, Casagrande derived a proxy for [ α /Fe]abundances from Str¨ o mgren photometry. LAMOSThave 553 stars in common with GCS, of which 366 haveSNR g ≥ T eff , log g , [Fe/H] and [ α /Fe], withsmall dispersions of 109.51 K, 0.20 dex, 0.11 dex and0.13 dex, respectively. The encouraging contiguous re-sults of GSN and GCS show great agreement for all thestellar atmospheric parameters. The offset of 9.65K ofthe surface temperature reminds us that our tempera-ture scale is similar to IRFM’s, which is known to beapproximately 100K hotter than the spectroscopic tem-perature (Casagrande et al. 2011). This is also observedabove.4.4. Comparison with Asteroseismic Results
The highly precise measurement of the asteroseis-mic gravity log g has resulted in their frequent useas a reference for comparison and validation. TheNASA Kepler mission has made available many hoststars oscillations, which is the basis of asteroseismol-ogy. Huber et al. (2014) (hereafter Huber14) reported acatalog, which consisted of a compilation of literaturevalues for stellar parameters derived from photometry,spectroscopy, asteroseismology, or exoplanet transits in-formation of 196,468 stars observed during the Keplermission. Most parameters of Huber14 are more precisethan the results provided by the Kepler Input Catalogue(KIC; Brown et al. 2011), however, the effective tem-perature and metallicities of Huber14 are still inaccu-rate. Mathur et al. (2017) revised the stellar propertiesof this catalog by improving some of the input parame-ters of spectroscopy and asteroseismology and correctingsome of the parameters of misclassified stars. We em-ploy the revised catalogue ( Mathur et al. (2017), here-after Mathur17) for comparison of both giants (with logg ≤ .
5) and dwarfs (with logg ≥ . g ≥
30. The comparison results areshown in Fig 5. The offsets of temperature and [Fe/H]are still evident, which is not useful in the evaluation ofthe accuracy. Although Mathur17 improved many stel- lar properties, the KIC with a systematic overestimationof the temperature of 200 K and an underestimationof [Fe/H] of 0.1 dex, still takes up a large proportionas the input parameters. This may explain the offsetsof the temperature and [Fe/H] shown in Fig 5. How-ever, our surface gravity shows a good agreement withMathur17’s, both for the giants with a tiny offset of -0.03 dex and a scatter of 0.20 dex, and for the dwarfswith a small offset of -0.04 dex and a scatter of 0.26dex. The scatters may arise primarily from the surfacegravity input values of Mathur17 and the gravity uncer-tainty which was reported as associated uncertainties of0.03 dex from seismology and 0.40 dex from the KIC(Mathur et al. 2017).Recently, Yu et al. (2018) (hereafter Yu2018) pro-duced a homogeneous catalogue of asteroseismic stellarproperties for 16,094 red giants. This provides an excel-lent opportunity to test the atmospheric parameters forlarge spectroscopic surveys using asteroseismic results.We also selected the Yu2018 sample as a reference tocompare with our parameters, especially for validatinglog g . There are 10,902 stars in common between Yu2018and LAMOST, out which 8,647 have SNR g ≥ g , the offset of -0.02 dex is almostnegligible and the dispersion of 0.09 dex shows that oursurface gravities results are precisely in line with theasteroseismic surface gravity data.4.5. Comparison between GSN and LASP Parameters
After comparing our results with the external stellarparameters, we finally chose the official parameter cat-alog of LAMOST, produced by the LAMOST StellarParameter Pipeline (LASP; Luo et al. 2015; Wu et al.2011) to compare and analyze the difference betweenthem. LASP determines stellar parameters by employ-ing two methods: the Correlation Function Initial (CFI)method is used to guess the initial values for the pa-rameters, and the ULySS method (Wu et al. 2011) isused to generate the final results. Wu et al. (2011) high-lighted that the precision values of LASP are 167 K, 0.34dex, and 0.16 dex for T eff , log g and [Fe/H], respec-tively, for early LAMOST observations. LASP requiredstars to be processed using the LAMOST 1D pipelineclassified as late A, F, G, or K, the g -band SNR ofSNR g ≥
15 for bright nights and the SNR g ≥ g levels to compare our results and the l og g GCSN=356 450050005500600065007000 Teff(K)2.02.53.03.54.04.55.0 l og g GSNN=3564000 5000 6000 7000Teff_GCS40004500500055006000650070007500 T e ff _ G S N μ = 9.65σ = 109.51 2 3 4 5logg_GCS2.02.53.03.54.04.55.0 l ogg_ G S N μ = 0.05σ = 0.20 −1.0 −0.5 0.0 0.5 1.0[Fe/H]_GCS−1.00−0.75−0.50−0.250.000.250.500.751.00 [ F e / H ] _ G S N μ = 0.02σ = 0.11 −0.4 −0.2 0.0 0.2 0.4[α/Fe]_GCS−0.4−0.20.00.20.4 [ α / F e ] _ G S N μ = 0.04σ = 0.13 Figure 4.
The density distribution of GCS parameters (top left panel) and GSN results (top right panel) for 367 LAMOST-GCScommon stars with SNR g of LAMOST spectra larger than 30. Also, the comparison between GSN stellar parameters and theGCS parameters derived by IRFM are showed in the four bottom panels. The red dash lines in the bottom panels are one-to-oneline. corresponding LASP parameters. As shown in Fig 7,good consistency is observed for the entire three stel-lar parameters at different SNR g levels, with little offsetand small dispersion. Even at SNR g ≥
10, the disper-sion is kept at 100 K for the effective temperature, 0.2dex for gravity and 0.11 dex for [Fe/H]. Also, it can bedetermined that the deviation of the difference of theparameters decrease gradually as the SNR g increases.GSN seems to overestimate temperature while there isan underestimation of [Fe/H] with respect to the LASPparameters.4.6. Comparison with other Spectral Fitting Methods
For comparing the results derived by GSN and inde-pendent spectral fitting methods, we employed a sampleof common stars in 3 surveys: LAMOST DR5, RAVEDR5, and SDSS/APOGEE DR14. There are totallyoverlap 339 stars with stellar parameters determined byrespective pipelines based on spectral fitting with em-pirical or theoretical spectra. The comparison resultsare showed in 8. We found that GSN’s results showgood agreements with both APOGEE’s and RAVE’sresults. Moreover, our parameters are more consistwith APOGEE’s than RAVE. The reason is that theresolution (22,500) of APOGEE is higher than that(7500) of RAVE, while the wavelength range of LAM- OST (3800˚A ∼ ∼ Uncertainties
We generated estimates and error results for the pa-rameters after the posterior distribution of the combina-tion of the stellar atmospheric parameters ( T eff , log g ,[Fe/H] and [ α /Fe]) were obtained. Fig 9 shows the meanand standard deviation of the errors associated with thestellar parameters as a function of SNR g . It is evidentthat the errors have clear dependencies on the SNR g ex-cept for [ α /Fe]. These errors decrease rapidly with anincrease in the SNR g when the value is less than 70,and a flat distribution beyond 70. The scatter of errorsincreases with SNR g for [ α /Fe] which is unusual. Themean uncertainties as shown in Fig 9 are 150 K, 0.25dex, 0,15 dex and 0.17 dex for T eff , log g , [Fe/H] and[ α /Fe] for the corresponding spectrum for SNR g largerthan 30. The uncertainties decrease to 80 K, 0.14 dex,0.07 dex and 0.16 dex when the SNR g of the spectrumis larger than 50. It was noted that the error is abnor-mal for [ α /Fe]. The reason for the irregular trend inthe SNR g may be due to the fact that the initial val-ues for [ α /Fe] cannot effectively constrain the real valuefor local 3- σ coverage, so that an incomplete posteriordistributions for the abundance of metal elements with0 Wang Rui et al. l og g Mathur17N=52109 40005000600070008000 Teff(K)012345 og g GSNN=521094000 5000 6000 7000 8000Teff_Mathur1740005000600070008000 T e ff _ G S N μ = − 101.68σ = 184.89 0 1 2 3 4 5 ogg_Mathur17012345 ogg_ G S N μ g = − 0.03σ g = 0.20μ d = − 0.04σ d = 0.26 −1.5 −1.0 −0.5 0.0 0.5 1.0[Fe/H]_Mathur17−1.5−1.0−0.50.00.51.0 [ F e / H ] _ G S N μ = 0.11σ = 0.23 Figure 5.
The density distribution of Mathur17 parameters (top left panel) and GSN results (top right panel) for 52,109LAMOST stars with SNR g larger than 30. Also, a comparison of GSN stellar parameters with the Mathur17 parameters areshowed in the three bottom panels. The red dash lines in the bottom panels are one-to-one line. respect to hydrogen were obtained. Another reason isthat utilizing all the flux from 3800˚ A to 9000˚ A increasesthe random error when fitting the observed spectrum tothe model template. Most previous studies attempted toestimate [ α /Fe] by fitting a template to feature bandsinstead of the full spectrum (Lee et al. 2011; Li et al.2016). Therefore, the error for [ α /Fe] appears to be anserious overestimation which corresponds to the stan-dard deviation of the external comparison. DISCUSSIONA discussion on the error sources of the results is pre-sented in this section. In general, the following aspectsneed to be carefully considered.1. The pre-treatment. For pre-processing of the spec-tra, we simply normalize the training set andLAMOST spectra by dividing them by the medianof their fluxes instead of dividing by the pseudo-continuum as outlined in SSPP (Lee et al. 2008)and LASP (Luo et al. 2015). We expect to excludethe error brought by pseudo-continuum normaliza- tion. The flux calibration and splicing process ofthe blue and red arms of the LAMOST spectra canincrease the peak of the continuum. This accountsfor the apparent overestimation of the temperaturecompared to the results derived based on the linefeature (pseudo-continuum normalized spectrum).2. The offsets of parameters from different theoret-ical models are inherent, for example, NextGen(Phoenix) T eff estimates are on average 2%higher than ATLAS (Bertone et al. 2004) . TheGSN training was based on the new versionof the Phoenix model spectra, which includedsome changes with respect to the old versionincluding the treatment of the chemical equilib-rium (Husser et al. 2013). Even if ‘perfect’ modelsare assumed, differences would still exist betweendifferent sets of model spectra, which would leadto offsets comparing results based on differentmodels.1 l og g Yu2018N=8647 4000425045004750500052505500 Teff(K)1.01.52.02.53.03.5 l og g GSNN=86473500 4000 4500 5000 5500Teff_Yu2018350037504000425045004750500052505500 T e ff _ G S N μ = − 103.78σ = 140.21 1 2 3logg_Yu20181.01.52.02.53.03.5 l ogg_ G S N μ = − 0.02σ = 0.09 1.5 1.0 0.5 0.0 0.5 1.0[Fe/H]_Yu2018 1.5 1.0 0.50.00.51.0 [ F e / H ] _ G S N μ = 0.01σ = 0.15 Figure 6.
The density distribution of Yu2018 parameters (top left panel) and GSN results (top right panel) for 8647 LAMOSTstars with SNR g larger than 30. Also, a comparison of GSN stellar parameters with the Yu2018 parameters are showed in thethree bottom panels. The red dash lines in the bottom panels are one-to-one line.
3. Sensitivity of [ α /Fe] to spectral features in low res-olution spectra. It is determined that [ α /Fe] arenot as sensitive as effective temperature and sur-face gravity, and is a similar conclusion to thatarrived upon in Yee et al. (2017). This led to ob-vious offsets and dispersion with respect to resultsof APOGEE/ASPCAP and other catalogs. Wewill try to investigate the application of the maxi-mum likelihood probability in the feature space ina future work.4. The micro-turbulence speed and rotation of stars.We did not take the impact of micro-turbulencespeed and the rotation of stars into considera-tion in this work. This is because the resolu-tion of the LAMOST spectra is too low to con-strain the micro-turbulence and rotation of stars, v micro and v rot , which may affect the accuracy ofmatching between the generated synthetic spectraand the observed spectra. SUMMARY We have designed a new structure of networks togenerate labeled simulative LAMOST spectra and es-timated the stellar atmospheric parameters ( T eff , log g , [Fe/H] and [ α /Fe]) of about 5.3 million spectra fromLAMOST DR5 based on GSN combined with Bayesiantheory by exploiting a distributed computing platform–Spark. Then, we utilized some sub-sample catalogsof LAMOST DR5 common stars with external precisestellar parameters derived from high-resolution observa-tions, or by other methods, to ensure the reliability ofour results. Our results show good consistency with theresults from other survey and catalogs, although somesmall system errors were observed in a few instances. Itwas determined that our temperature scale was 100 Khotter than that of the normal spectroscopic tempera-ture scales, similar to the scale of IRFM. Our surfacegravity kept the height values consistent with the as-teroseismic results. The system errors of [ α /Fe] weredetermined by an external comparison, in that thesevalues are not sensitive to Bayesian probability fittingof the entire spectral bands. The precision of the param-2 Wang Rui et al. T e ff _ G S N N=1914833SNRg>50μ = 31.81σ = 43.97 l ogg_ G S N N=1914833SNRg>50μ = − 0.01σ = 0.06 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0[Fe/H]_LASP−2−101 [ F e / H ] _ G S N N=1914833SNRg>50μ = − 0.05σ = 0.03 T e ff _ G S N N=3049980SNRg>30μ = 40.82σ = 60.54 l ogg_ G S N N=3049980SNRg>30μ = 0.00σ = 0.10 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0[Fe/H]_LASP−2−101 [ F e / H ] _ G S N N=3049980SNRg>30μ = − 0.07σ = 0.06 T e ff _ G S N N=4920563SNRg>10μ = 63.83σ = 100.08 l ogg_ G S N N=4920563SNRg>10μ = 0.05σ = 0.20 −2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5 1.0[Fe/H]_LASP−2−101 [ F e / H ] _ G S N N=4920563SNRg>10μ = − 0.09σ = 0.11
Figure 7.
The density distribution for comparison between GSN and LASP parameters ( T eff in left, log g in middle and[Fe/H] in right panels) for LAMOST DR5 spectra with SNR g larger than 50, 30, 10 in the top, middle and bottom panels,respectively. The red dash lines are one-to-one line. eters are listed as 80 K for T eff , 0.14 dex for log g , 0.07dex for [Fe/H] and 0.168 dex for [ α /Fe], for spectra witha SNR g ≥
50. The catalog is available on the internet athttp://paperdata.china-vo.org/GSN parameters/GSN parameters.csvACKNOWLEDGEMENTThis work is supported by the National Key Basic Re-search Program of China (Grant No. 2014CB845700),the National Natural Science Foundation of China(Grant No. 11390371). The Guo Shou Jing Tele-scope (the Large Sky Area Multi-Object Fiber Spec- troscopic Telescope, LAMOST) is a National MajorScientific Project built by the Chinese Academy of Sci-ences. Funding for the project has been provided bythe National Development and Reform Commission.LAMOST is operated and managed by National Astro-nomical Observatories, Chinese Academy of Sciences.
Software:
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30 40 50 60 70 80 90 100SNR_g0.150.160.170.180.19 σ [ α / F e ] Figure 9.
The errors of the stellar parameters estimated byGSN for LAMOST DR5 spectra as a function of SNR g ( σ Teffin the top panel, σ log g in the middle-top panel, σ [Fe/H]in the middle-top panel and [ α /Fe] in the bottom panel).The errorbar denotes the median value and the standarddeviation of the errors in each SNR g bin. The SNR g5