Correction to the photometric magnitudes of the Gaia Early Data Release 3
Lin Yang, Haibo Yuan, Ruoyi Zhang, Zexi Niu, Yang Huang, Fuqing Duan, Yi Fang
DDraft version January 14, 2021
Typeset using L A TEX preprint2 style in AASTeX62
Correction to the photometric magnitudes of the
Gaia
Early Data Release 3
Lin Yang, Haibo Yuan, Ruoyi Zhang, Zexi Niu, Yang Huang, Fuqing Duan, andYi Fang College of Artificial Intelligence, Beijing Normal University No.19, Xinjiekouwai St, Haidian District, Beijing,100875, P.R.China Department of Astronomy, Beijing Normal University No.19, Xinjiekouwai St, Haidian District, Beijing, 100875,P.R.China; [email protected] National Astronomical Observatories, Chinese Academy of Sciences 20A Datun Road, Chaoyang District, Beijing,China South-Western Institute for Astronomy Research, Yunnan University, Kunming 650500, People’s Republic of China
ABSTRACTIn this letter, we have carried out an independent validation of the
Gaia
EDR3 pho-tometry using about 10,000 Landolt standard stars from Clem & Landolt (2013). Usinga machine learning technique, the
U BV RI magnitudes are converted into the
Gaia magnitudes and colors and then compared to those in the EDR3, with the effect ofmetallicity incorporated. Our result confirms the significant improvements in the cali-bration process of the
Gaia
EDR3. Yet modest trends up to 10 mmag with G magnitudeare found for all the magnitudes and colors for the 10 < G <
19 mag range, partic-ularly for the bright and faint ends. With the aid of synthetic magnitudes computedon the CALSPEC spectra with the
Gaia
EDR3 passbands, absolute corrections arefurther obtained, paving the way for optimal usage of the
Gaia
EDR3 photometry inhigh accuracy investigations.
Keywords:
Astronomy data analysis, Fundamental parameters of stars, Stellar photom-etry INTRODUCTIONThe Early Data Release 3 of the ESA’s spacemission
Gaia ( Gaia
Collaboration et al. 2016,2020) has delivered not only the best astromet-ric information but also the best photometricdata for about 1.8 billion stars (Riello et al.2020), in terms of full sky coverage, uniformcalibration at mmag level, and small photo-metric errors for a very wide range of magni-tudes. However, due to the changes of instru-ment configurations, magnitude dependent sys-tematic errors up to 10 mmag or higher havebeen detected in its DR2 (Riello et al. 2018;Casagrande & VandenBerg 2018; Weiler 2018; Ma´ız Apell´aniz & Weiler 2018; Niu et al. 2021,re-submitted). Thanks to significant improve-ments in the calibration process, the magni-tude term found in the
Gaia
DR2 photometry isgreatly reduced in the EDR3. The overall trendis no larger than 1 mmag/mag except for veryblue and bright sources (Riello et al. 2020).Due to the unprecedented photometric qual-ity, it is challenging to identify possible prob-lems of the
Gaia photometry using externalcatalogs. Synthetic magnitudes from well cal-ibrated spectral libraries, such as the CAL-SPEC (Bohlin 2014), have been used to com-pare with the observed ones for the
Gaia
DR2 a r X i v : . [ a s t r o - ph . S R ] J a n Yang et al. (Casagrande & VandenBerg 2018; Weiler 2018;Ma´ız Apell´aniz & Weiler 2018). However, thenumber of available spectra is limited to a fewhundreds, too few to identify any fine structuresin the correction curves. With about 0.5 millionstars selected from the LAMOST DR5 (Luo etal. 2015), Niu et al. (2021, re-submitted) haveapplied the spectroscopy-based stellar color re-gression method (Yuan et al. 2015a) to cali-brate the
Gaia
DR2 G − G RP and G BP − G RP colors. Systematic trends with G magnitude arerevealed for both colors in great detail at a pre-cision of about 1 mmag. However, contributionsfrom each of the three Gaia magnitudes can notbe decoupled.In this letter, we aim to perform an indepen-dent test of the
Gaia
EDR3 photometry by com-paring with the Landolt standard stars. Thehigh-quality CCD-based
U BV RI photometricdata from Clem & Landolt (2013; CL13 here-after) is adopted for three reasons. Firstly, itcontains about 45,000 stars, about two ordersof magnitude larger than the numbers of fluxstandards in spectral libraries. Secondly, it hasa wide magnitude range (10 < G <
20) thatmatches well with the
Gaia photometry. Lastbut not least, it has five filters (
U BV RI ), in-cluding the metallicity sensitive U filter, mak-ing it possible to include the effect of metallic-ity when performing transformations betweendifferent photometric systems, which is essen-tial but ignored in the official validation of the Gaia
EDR3 (Riello et al. 2020; Fabricius et al.2020). Using a machine learning technique, the
U BV RI magnitudes are trained into the
Gaia magnitudes and colors and then compared tothose in the
Gaia
EDR3. Our result confirmsthe significant improvements in the calibrationprocess of the
Gaia
EDR3. Yet modest trendswith G magnitude are found for all magnitudesand colors. By combining the synthetic mag-nitudes computed on the CALSPEC (Bohlin etal. 2014, 2020 April Update) spectra with the Gaia
EDR3 passbands, we further obtain abso-lute corrections to the
Gaia
EDR3 photometry,paving the way for optimal usage of the
Gaia photometry.The paper is organized as follows. In sec-tion 2, we introduce our data and method.The result is presented in Section 3 and dis-cussed in Section 4. We summarize in Sec-tion 5. Note that in this paper, the
Gaia
EDR3 G magnitudes refer to the correctedones (phot g mean mag corrected, Riello et al.2020) DATA AND METHOD2.1.
Data
In this work, we only use main sequence starsthat have high-precision photometry from boththe
Gaia
EDR3 and the CL13. The followingcriteria are adopted to guarantee data quality:1) err( U ) < B ) < V, R, I ) < phot bp rp excess factor < .
26 +0 . ∗ ( G BP − G RP ) to exclude starsof poor Gaia photometry (Evans et al.2018). Note the above criterion is al-most identical to requiring the corrected phot bp rp excess factor (Riello et al.2020) < E ( B – V ) SFD < E ( B – V ) SFD isfrom the Schlegel et al. (1998, hereafterSFD) dust reddening map;4) 0 . < B − V < . G > ∗ ( G BP − RP − . ∗ E ( B − V ) SFD )to exclude giant stars, where G is the in-trinsic G magnitude. Here we adopt anextinction coefficient of 2.5 for the G bandand a reddening coefficient of 1.33 for the G BP − G RP color (Chen et al. 2019). orrection to the photometric magnitudes of the Gaia
EDR3 G BP G RP [mag]0.040.020.000.020.04 G [ m a g ] G [ m a g ] B V ) [mag]0.40.00.40.81.2 ( U B ) [ m a g ] G [ m a g ] G BP G RP [mag]0.040.020.000.020.04 G B P [ m a g ] -0.2±12.7 mmag G B P [ m a g ] B V ) [mag]0.40.00.40.81.2 ( U B ) [ m a g ] G B P [ m a g ] G BP G RP [mag]0.040.020.000.020.04 G R P [ m a g ] G R P [ m a g ] B V ) [mag]0.40.00.40.81.2 ( U B ) [ m a g ] G R P [ m a g ] G BP G RP [mag]0.040.020.000.020.04 ( GG B P ) [ m a g ] ( GG B P ) [ m a g ] B V ) [mag]0.40.00.40.81.2 ( U B ) [ m a g ] ( GG B P ) [ m a g ] G BP G RP [mag]0.040.020.000.020.04 ( GG R P ) [ m a g ] -0.5±7.9 mmag ( GG R P ) [ m a g ] B V ) [mag]0.40.00.40.81.2 ( U B ) [ m a g ] ( GG R P ) [ m a g ] Figure 1.
Residual distributions as functions of G BP − G RP (left panel), reddening (middle panel), andin the ( U − B ) − ( B − V ) diagram (right panel) of the training (black dots) and test (red dots) samplesfor each of the five MLP networks. From top to bottom are the results for G , G BP , G RP , G − G BP , and G − G RP , respectively. The median values and standard deviations of the residuals are also marked in theleft panels. For the reddening correction of the U − B and B − V colors, the SFD reddening map andreddening coefficients of 0.708 and 0.884 are adopted (Schlafly & Finkbeiner 2011). Yang et al.
Finally, 10,294 stars are selected, including1,539 stars of 17 < G < . < G < . U band or 0.005 mag inthe B/V /R/I band. The remaining 1,079 starsare divided into two groups: the training set(90 percent) and the test set (10 percent). Forthe whole sample, the median errors are 4.3,3.3, 2.3, 1.9, and 2.3 mmag for
U, B, V, R, I ,and 2.8, 7.7, and 6.1 mmag for
G, G BP , G RP ,respectively. For the reference sample, the me-dian errors are 3.6, 2.9, 1.9, 1.6, and 1.9 mmagfor U, B, V, R, I , and 2.9, 9.2, and 7.1 mmag for
G, G BP , G RP , respectively.2.2. Method
In this work, multi-layer perceptron neuralnetworks (MLP) with architectures of 4-128-64-8-1 are designed to convert the Landolt
U BV RI photometry of CL13 into the
Gaia
EDR3 mag-nitudes and colors. Each node of the hiddenlayers and the output layer is connected to allnodes of its previous layer, with a nonlinearfunction: f ( X ) = g ( W X + b ) (1)where W and b respectively represent the weightmatric and bias vector, g ( • ) represents theLeakyReLU activation function with negativeslope coefficient α = 0 . Gaia
EDR3magnitudes and two for the
Gaia
EDR3 colors.The four input colors are the same for the fiveMLPs, i.e., U − B, B − V, V − R, R − I . The out-puts are G − A , G BP − A , G RP − A , G − G BP , and G − G RP respectively, where A is an artificialmagnitude defined as the mean of the B, V, R magnitudes. Note that in this work, observed magnitudes/colors are preferred to dereddenedones, to avoid possible systematic errors causedby reddening correction. Systematic errors maycome from at least two aspects: spatially depen-dent systematic errors with the SFD reddeningmap (Sun et al., to be submitted; Niu et al.2021) and overestimates of reddening for brightlocal stars.The training process is carried out with Keras2.2.4 and Tensorflow 1.12. The loss function,Mean Squared Error (MSE) with a L regular-ized term, is optimized using adaptive momentestimation (ADAM, Kingma & Ba 2014) witha mini-batch size of 900 samples. The trade-off coefficient between the MSE and regularizedterm is 0.000001 to avoid overfitting. Otherhyper-parameters set manually in our work aretraining iterations epoch = 100 ,
000 and learn-ing rate η = 0 . σ clipping isperformed to exclude outliers. Then, the train-ing process runs again with the same hyper-parameters. After the networks are well trained,we apply the models to the whole dataset. Thepredicted magnitudes and colors are then ob-tained and compared to those in the EDR3. Themedian differences (predicted − observed) as afunction of G magnitude are regarded as thecalibration curves. RESULTFigure 1 shows the results of the training andtest samples for different MLP neural networks.It can be seen that the residuals show no de-pendence on the G BP − G RP color or the SFDreddening. The residuals also show no system-atic patterns in the ( U − B ) − ( B − V ) diagram.Because dwarf stars of different metallicities arewell separated in the ( U − B ) − ( B − V ) dia-gram (e.g., Sandage & Smith 1963), the resultssuggest that the effect of metallicity has beenfully taken into account in our neural networks.Note that the standard deviations of the resid-uals are 8.5, 12.7, 11.9, 10.1, and 7.9 mmag for orrection to the photometric magnitudes of the Gaia
EDR3 G , G BP , G RP , G − G BP , and G − G RP , respec-tively. The small standard deviations suggestthat the Gaia photometry can be well recov-ered from the Landolt photometry, to a preci-sion of about 1 percent with photometric errorsincluded.Figure 2 shows the residual distributions inthe ( G BP − G RP ) – G diagram for the wholedataset. No obvious dependence on color withinthe two dashed lines is seen for all the pan-els, consistent with the result of Riello et al.(2020). For a few stars of G BP − G RP < . G BP − G RP > .
5, there exist some discrepan-cies, probably caused by the boundary effect inthe training process. Those stars are excludedin the following analysis.The calibration curves as a function of G mag-nitude for the Gaia magnitudes and colors areplotted in Figure 3. The errors are also esti-mated using the Bootstrap method with 500subsamples. The errors at G ∼ Gaia
EDR3. The strong trend in G as afunction of G in DR2 is greatly reduced. Yetmodest trends with G magnitude are found forall magnitudes and colors. A tiny discontinuityof 2–3 mmag at G ∼
13 mag is clearly detectedfor all the magnitude curves, probably relatedto a change in the instrument configuration.The downturn at faint magnitudes visible in the G BP and G RP passbands is possibly caused bysome over-estimation of the background in theBP and RP spectra. Therefore, the trend in G BP − G RP as a function of G is much weakercompared to that in G − G BP and G − G RP .In the above analysis, we have assumed thatthe corrections are zero for stars of 17 < G < . G , G BP , and G RP are computed onthe CALSPEC (Bohlin et al. 2014, 2020 AprilUpdate) spectra with the Gaia
EDR3 pass-bands, with the same approach of Riello et al.(2020). The results are used to obtain the abso-lute corrections.Only 20 stars of G BP − G RP > − . G >
10, and phot bp rp excess factor < . . ∗ ( G BP − G RP ) are used. The meanmagnitude offsets are − − G , G BP , and G RP , respectively. The shiftsof the calibration curves are − − − − G , G BP , G RP , G − G BP ,and G − G RP , respectively.The final calibrationcurves are plotted in Figure 4 and listed in Ta-ble 1. Note that only results directly obtainedfrom the five MLPs (red lines in the top panelsof Figure 4 and blue lines in the two bottompanels on the left) are given in Table 1. Cali-bration curves yielded by different MLPs (blueand red dotted lines in Figure 4) agree with eachother very well, with a typical difference of 0.5mmag, within the training errors. DISCUSSIONFabricius et al. (2020) compare
Gaia
EDR3photometry to a number of external catalogsin their Figure 34, including the one we use inthe current work. They select all stars of | b | > ° and A V < .
05 mag for low latitude stars.Simple color-color relations are then used, X = V + f ( V − I ) where X denotes Gaia magnitude,to transform the Landolt
V, I magnitudes into
Gaia magnitudes.Stellar colors depend mainly on the stellar ef-fective temperature, but also to a fair degree onmetallicity, particularly the blue colors. Yuanet al. (2015) propose to use the metallicity-dependent stellar locus to better describe the
Yang et al. G BP G RP [mag]101214161820 G [ m a g ] G G BP G RP [mag]101214161820 G [ m a g ] G B P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] G R P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] GG B P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] GG R P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] G B P G R P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] GG B P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] GG R P [ m a g ] G BP G RP [mag]101214161820 G [ m a g ] G B P G R P [ m a g ] Figure 2.
Residual distributions in the ( G BP − G RP ) – G diagram for the whole dataset. The top panelsshow the results of the Gaia magnitudes. The middle panels show the results of the
Gaia colors calculatedfrom the top panels. The two left panels in the bottom show the results of the
Gaia colors directly trainedfrom the neural networks, while the right one the result calculated from the two left panels. The two verticaldashed lines indicate G BP − G RP color of 0.6 and 1.5 mag, respectively. transformation relations between different col-ors. Taking the SDSS colors for example, ata given g − i color, they find that typically 1dex decrease in metallicity causes 0.20 and 0.02mag decrease in colors u − g and g − r and 0.02and 0.02 mag increase in colors r − i and i − z ,respectively. The variations are larger for moremetal-rich stars, and for F/G/K stars. The rela-tions are also different between dwarf stars andgiant stars. Therefore, to make optimal trans-formations between different colors, the metal-licity effect shall be taken into account. Huanget al. (2020) have applied a revised stellar colorregression method to re-calibrate the SkyMap-per Southern Survey DR2 (Onken et al. 2019),achieving a uniform calibration with precision better than 1 percent by considering the effectof metallicity on stellar colors. L´opez-Sanjuanet al. (2021) have discussed the impact of metal-licity on photometric calibration of the JPLUSsurvey (Cenarro et al. 2019) with the stellarlocus technique and found significant improve-ments for blue passbands.A large vertical metallicity gradient of theGalaxy at the solar neighborhood is widely re-ported, e.g., 0.15 dex kpc − from Huang etal. (2015). Considering the strong correlationbetween stellar magnitudes and distances fordwarf stars, it implies a strong correlation be-tween stellar magnitudes and metallicities, es-pecially for high Galactic latitude regions. Sucha correlation could cause magnitude dependent orrection to the photometric magnitudes of the Gaia
EDR3
10 12 14 16 18 20G [mag]0.040.020.000.020.04 G [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 G B P [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 G R P [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 ( GG B P ) [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 ( GG R P ) [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 ( G B P G R P ) [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 ( GG B P ) [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 ( GG R P ) [ m a g ]
10 12 14 16 18 20G [mag]0.040.020.000.020.04 ( G B P G R P ) [ m a g ] Figure 3.
Residual distributions as a function of G magnitude for the whole dataset after excluding starsof G BP − G RP < . G BP − G RP > .
5. The panels are arranged in the same way to Figure 2. For eachpanel, stars are divided into different bins of width of 0.4 mag at a step size of 0.1 mag when 12 . < G < . − σ clipping performed and the grey dots dropped.At the bright end, a linear fitting is performed for stars of G < . G < . f rac = 0 .
07. The final results are indicated by red dotted lines. The blue error barsare estimated with 500 subsamples using the Bootstrap method. systematic errors when adopting simple color-color relations and ignoring the effect of metal-licity, at the level of from several mmag to tensof mmag for the
Gaia passbands, depending onwhich colors are used and properties of the sam-ple stars. In our work, by making use of thefull color information of the Landolt photome-try, particularly the U − B color, we can nat-urally incorporate the effect of metallicity andobtain robust results. To validate our result, following the proce-dure in Niu et al. (2021, re-submitted), weselect a high-quality common sample contain-ing 0.7 million stars in LAMOST DR7 and Gaia
EDR3 and plot the residuals from the G − G RP = f ( G BP − G RP , [Fe / H]) relation as afunction of G in Figure 5. The top panel plotsthe result of the published EDR3 data, whichis quite similar to Figure 32 in Fabricius et al.(2020) and shows small but well-detected mag- Yang et al.
10 12 14 16 18 20G [mag]0.040.030.020.010.000.010.02 G [ m a g ]
10 12 14 16 18 20G [mag]0.040.030.020.010.000.010.02 G B P [ m a g ]
10 12 14 16 18 20G [mag]0.030.020.010.000.010.020.03 G R P [ m a g ]
10 12 14 16 18 20G [mag]0.010.000.010.020.03 ( GG B P ) [ m a g ]
10 12 14 16 18 20G [mag]0.030.020.010.000.01 ( GG R P ) [ m a g ]
10 12 14 16 18 20G [mag]0.030.020.010.000.01 ( G B P G R P ) [ m a g ] Figure 4.
Magnitude (top panels) and color (bottom panels) calibration curves. The green dots are resultsfrom synthetic magnitudes/colors of the CALSPEC spectra. The red dotted lines are results from the trainedmagnitudes. The blue dotted lines in the two top panels on the right are results combining the trained G magnitude and trained G − G BP and G − G RP colors. The blue dotted lines in the bottom panels are resultsfrom the trained colors. All the dotted lines are shifted by the median of the differences between the dottedlines and the green dots to match the green dots. nitude dependent deviations from zero. Thebottom panel plots the result after the mag-nitude corrections in this work. Compared tothe published EDR3 data, the deviations aresignificantly reduced to zero along with the G magnitude, especially at the bright and faintends. The result suggests that our correctionsare valid. Note that at G ∼
13 mag where adiscontinuity happens, our corrections are notas good as for fainter magnitudes. This is be-cause we do not have enough stars to samplethe correction curves at a very high resolutionin G magnitude.Note that due to the limited magnitude andcolor ranges (10 < G <
19, 0 . < G BP − G RP < .
5) of our final sample, our correction curvesmay not be valid for stars outside the aboveranges, particularly for the bright and blue(
G <
13 and G BP − G RP < − .
1) ones (Rielloet al. 2020), and thus should be used with cau- tion. Note also that the EDR3 photometry iscalibrated in the absolute flux level using a set ofspectro-photometric standard stars (SPSS; Pan-cino et al. 2012), whose fluxes are tied to the2013 version of CALSPEC (Riello et al. 2020).Adjusting the ab solute flux scale to the currentCALSPEC library will therefore result in an in-consistency with the uncorrected photometry.To avoid discontinuities, the calibration termsat G = 10 are suggested for stars brighter than G = 10. For stars fainter than G = 18 .
7, thecalibration terms at G = 18 . orrection to the photometric magnitudes of the Gaia
EDR3 Table 1.
Magnitude and color calibration curvesin units of mmag. G ∆ G ∆ G BP ∆ G RP ∆( G − G BP ) ∆( G − G RP )10.0 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − G ∆ G ∆ G BP ∆ G RP ∆( G − G BP ) ∆( G − G RP )15.5 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − cause systematic errors in the reddening correc-tion are largely canceled out. SUMMARYIn this work, we have carried out an indepen-dent validation of the
Gaia
EDR3 photometry0
Yang et al. GG R P f ( G B P G R P , F e / H ) [ m a g ] EDR3 N G [mag] GG R P f ( G B P G R P , F e / H ) [ m a g ] This work N Figure 5.
2D histogram of the G − G BP residual af-ter subtracting the metallicity-dependent color lo-cus. Top: published EDR3 data. Bottom: applyingmagnitude corrections from this work. Note thatthe colors here refer to dereddened colors. using about 10,000 well selected Landolt stan-dard stars from Clem & Landolt (2013). Us-ing five MLPs with architectures of 4-128-64-8-1, the U BV RI magnitudes are trained into the
Gaia magnitudes and colors and then comparedto those in the
Gaia
EDR3, with the effect ofmetallicity fully taken into account.Our result confirms the significant improve-ments in the calibration process of the
Gaia
EDR3. The strong trend in G as a function of G in DR2 is greatly reduced. Yet modest trendswith G magnitude are found for all magnitudesand colors for the 10 < G <
19 mag range, par-ticularly at the bright and faint ends. A tiny dis-continuity of 2–3 mmag at G ∼
13 mag is clearly detected for all the magnitude curves, proba-bly related to a change in the instrument con-figuration. The downturn at faint magnitudesvisible in the G BP and G RP passbands is possi-bly caused by some over-estimation of the back-ground in the BP and RP spectra. The trendin G BP − G RP as a function of G is much weakercompared to that in G − G BP and G − G RP . Withsynthetic magnitudes computed on the CAL-SPEC spectra with the Gaia
EDR3 passbands,absolute calibration curves are further provided(Figure 4 and Table 1), paving the way for opti-mal usage of the
Gaia
EDR3 photometry in highaccuracy investigations. In the future
Gaia datareleases, the effect of metallicity should be in-cluded when comparing with external catalogs.Our result demonstrates that mapping fromone set of observables directly to another setof observables with machine learning provides apromising way in the calibration and analysesof large scale surveys.We acknowledge the anonymous referee forhis/her valuable comments that improve thequality of this paper. This work is sup-ported by the National Natural Science Foun-dation of China through the projects NSFC11603002, the National Key Basic R&D Pro-gram of China via 2019YFA0405503, and Bei-jing Normal University grant No.310232102.This work has made use of data from theEuropean Space Agency (ESA) mission
Gaia
Gaia
Gaia
Multilateral Agreement. Gu-oshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope LAM-OST) is a National Major Scientific Projectbuilt by the Chinese Academy of Sciences. orrection to the photometric magnitudes of the
Gaia
EDR311Funding for the project has been provided bythe National Development and Reform Com-mission. LAMOST is operated and managed by the National Astronomical Observatories,Chinese Academy of Sciences. This researchhas made use of the SIMBAD database, oper-ated at CDS, Strasbourg, France.REFERENCES