指導教授：饒兆聰 博士
中 華 民 國 一一二 年 六 月
利用蓋亞DR3星表研究球狀星團的色溫-星等圖，
並利用機器學習作型態上的分類
摘 要
球狀星團是年老與貧金屬恆星，聚集在一個球狀區域。因為球狀星團是最古老的天體之一，研究它們的有助於了解其物性與化性和宇宙的演化史。在我們研究工作的第一部分，使用蓋亞星表為幾個系內球狀星團建構色溫-星等圖。方法為利用Vizier，查詢個別球狀星團的位置、固有運動與光度來建構色溫-星等圖。我們再根據不同準則，篩選成員恆星並排除離異。最終在150個球狀星團中，我們選擇與建構57組色溫-星等圖。在轉換成標準星等方面，是使用距離模數與消光修正。我們的目標是依據色溫-星等圖中主序星、紅巨星與水平分支的屬性，再用機器學習對球狀星團分類並研究之。我們再用TensorFlow與Keras建立與訓練神經網路。之後用ML模型作影像分類，K-mean群集對相似的球狀星團分類。在研究不同組球狀星團的年齡與金屬豐度後，最終找到5個年齡與金屬性非常相似的球狀星團。

關鍵字: 球狀星團、色溫-星等圖、機器學習

Study CMD of Globular Clusters using Gaia DR3
data and classify them according to their morphology
using Machine Learning
by
Bishnu Kumar Sharma
Submitted to the Graduate Institute of Astronomy
in the partial fulfillment of the
requirement for the degree of Master of Astronomy
Abstract
Globular clusters are the agglomeration of the old and metal-poor stars into a
spherical shape. Since they are one of the oldest stellar objects, their study can
help us understand the physical and chemical structure as well as the evolution of the universe. As the first part of our research, we use Gaia DR3 data
to construct color-magnitude diagrams (CMDs) for the Galactic globular clusters (GCs). We use various information like position, proper motion, and photometry of the individual GC and we extract the data using the VizieR Queries
(astroquery.vizier) to construct CMD. We use different selection criteria to select member stars and to remove outliers. Using our selection criteria, among
150 GCs, we are able to get 57 CMDs with proper morphology. Standardization
of magnitudes to absolute magnitude has been done using distance modulus
and extinction correction from Schlegal, Flinkbeiner, and Davis. Our aim is to
classify the GCs based on CMD morphology such as main-sequence, red-giant,
and horizontal branches using a pure machine learning approach and study the
properties of the individual groups. We use TensorFlow, a framework to build
a neural network along with Keras, a high-level API for building and training
neural networks. We make an ML model for image classification and use Kmeans clustering for making groups of similar images. By superimposing the
CMDs of individual groups, and making them one CMD, we studied the properties like age, distance, metallicity, etc of individual clusters of a group. We find
5 groups having nearly similar ages and metallicities and we consider we get 5
GCs groups as twins.
Keywords: Globular clusters, Color-magnitude diagram, Machine learning
Thesis Supervisor: Chow-Choong Ngeow
Title: Associate Professor

Bibliography
Martín Abadi, Ashish Agarwal andPaul Barham andEugene Brevdo,
Zhifeng Chen andCraig Citro andGreg S. Corrado andAndy Davis, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke,
Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-scale machine learning
on heterogeneous systems, 2015. URL https://www.tensorflow.org/.
Software available from tensorflow.org.
René Andrae, Morgan Fouesneau, Orlagh Creevey, Christophe Ordenovic,
Nicolas Mary, Alexandru Burlacu, Laurence Chaoul, Anne Jean-AntoinePiccolo, Georges Kordopatis, Andreas Korn, Yveline Lebreton, Chantal
Panem, Bernard Pichon, Frédéric Thévenin, Gavin Walmsley, and Coryn A. L.
Bailer-Jones. Gaia Data Release 2. First stellar parameters from Apsis. , 616:
A8, August 2018. doi: 10.1051/0004-6361/201732516.
Keith M. Ashman and Stephen E. Zepf. Globular Cluster Systems. Cambridge Astrophysics. Cambridge University Press, 1998. doi: 10.1017/
CBO9780511564604.
Astropy Collaboration, Thomas P. Robitaille, Erik J. Tollerud, Perry Greenfield,
Andrew Droettboom, Andy Ptak, Brian Refsdal, Mathieu Servillat, and Ole
Streicher. Astropy: A community Python package for astronomy. , 558:A33,
October 2013. doi: 10.1051/0004-6361/201322068.
Carine Babusiaux, Floor van Leeuwen, MA Barstow, C Jordi, Antonella Vallenari, D Bossini, Alessandro Bressan, T Cantat-Gaudin, M Van Leeuwen,
AGA Brown, et al. Gaia data release 2-observational hertzsprung-russell diagrams. Astronomy & Astrophysics, 616:A10, 2018.
James Binney and Scott Tremaine. Galactic dynamics. 1987.
James Binney, Michael Merrifield, and Gary A. Wegner. Galactic Astronomy.
American Journal of Physics, 68(1):95–96, January 2000. doi: 10.1119/1.19402.
Christopher M. Bishop. Pattern Recognition and Machine Learning (Information Science and Statistics). Springer-Verlag, Berlin, Heidelberg, 2006. ISBN
0387310738.
C. Bonatto, Fabíola Campos, and S. O. Kepler. Mapping the differential reddening in globular clusters. , 435(1):263–272, October 2013. doi: 10.1093/mnras/
stt1304.
Petra Bosilj, Erchan Aptoula, Tom Duckett, and Grzegorz Cielniak. Transfer
learning between crop types for semantic segmentation of crops versus weeds
in precision agriculture. Journal of Field Robotics, 03 2019. doi: 10.1002/rob.
21869.
61Raymond G. Carlberg. Dynamical simulations of the first globular clusters. The
Astrophysical Journal, 893(2):116, apr 2020. doi: 10.3847/1538-4357/ab80bf.
URL https://dx.doi.org/10.3847/1538-4357/ab80bf.
Bradley W. Carroll and Dale A. Ostlie. An Introduction to Modern Astrophysics.
2nd (international) edition, 2007.
Francois Chollet et al. Keras, 2015. URL https://github.com/fchollet/
keras.
G. S. Da Costa and K. C. Freeman. The structure and mass function of the globular cluster M3. , 206:128–137, May 1976. doi: 10.1086/154363.
Bruno Dias. Gotham survey: Globular cluster homogeneous abundances
measurements, 2019. URL https://www.sc.eso.org/~bdias/files/
dias+16_MWGC.txt.
Sunayana G. Domadia and Tanish Hemalbhai Zaveri. Comparative analysis of
unsupervised and supervised image classification techniques. 2011.
Duncan A Forbes and Terry Bridges. Accreted versus in situ milky way globular
clusters. Monthly Notices of the Royal Astronomical Society, 404(3):1203–1214,
2010.
Gaia Collaboration, T. Prusti, J. H. J. de Bruijne, A. G. A. Brown, A. Vallenari,
and S. Babusiaux. The Gaia mission. , 595:A1, November 2016. doi: 10.1051/
0004-6361/201629272.
A. Ginsburg, B. M. Sip˝ocz, C. E. Brasseur, P. S. Cowperthwaite, M. W. Craig,
C. Deil, J. Guillochon, G. Guzman, J. Liedtke, The Astroquery collaboration,
and a subset of the astropy collaboration. astroquery: An Astronomical Webquerying Package in Python. , 157:98, March 2019. doi: 10.3847/1538-3881/
aafc33.
Ian J. Goodfellow, Yoshua Bengio, and Aaron Courville. Deep Learning. MIT
Press, Cambridge, MA, USA, 2016. http://www.deeplearningbook.
org.
J. A. Hartigan and M. A. Wong. Algorithm AS 136: A K-Means clustering algorithm. Applied Statistics, 28(1):100–108, 1979. ISSN 00359254. doi:
10.2307/2346830. URL http://dx.doi.org/10.2307/2346830.
Holger and Baumgardt. Structural parameters of galactic globular clusters, 2021. URL https://people.smp.uq.edu.au/HolgerBaumgardt/
globular/parameter.html.
David H. Hubel and Torsten N. Wiesel. Receptive fields of single neurons in the
cat’s striate cortex. Journal of Physiology, 148:574–591, 1959.
Petr Kabáth, David Jones, and Marek Skarka. Reviews in Frontiers of Modern Astrophysics; From Space Debris to Cosmology. 2020. doi: 10.1007/
978-3-030-38509-5.
Mina Koleva, Ph Prugniel, Pierre Ocvirk, Damien Le Borgne, and Caroline
Soubiran. Spectroscopic ages and metallicities of stellar populations: validation of full spectrum fitting. Monthly Notices of the Royal Astronomical Society,
385(4):1998–2010, 2008.
62Alex Krizhevsky, Ilya Sutskever, and Geoffrey E. Hinton. Imagenet classification
with deep convolutional neural networks. In F. Pereira, C. J. C. Burges, L. Bottou, and K. Q. Weinberger, editors, Advances in Neural Information Processing
Systems 25, pages 1097–1105. Curran Associates, Inc., 2012.
L. Lindegren, S. A. Klioner, W. Hernández, and A. Vecchiato. Gaia Early Data
Release 3. The astrometric solution. , 649:A2, May 2021. doi: 10.1051/
0004-6361/202039709.
A. Lindholm, N. Wahlström, F. Lindsten, and T.B. Schön. Machine Learning: A
First Course for Engineers and Scientists. Cambridge University Press, 2022.
ISBN 9781108843607. URL https://books.google.com.tw/books?id=
CeSazgEACAAJ.
X. Luri, A. G. A. Brown, L. M. Sarro, F. Arenou, C. A. L. Bailer-Jones, A. CastroGinard, J. de Bruijne, T. Prusti, C. Babusiaux, and H. E. Delgado. Gaia Data Release 2. Using Gaia parallaxes. , 616:A9, August 2018. doi: 10.1051/0004-6361/
201832964.
AD Mackey and Sidney Van Den Bergh. The properties of galactic globular
cluster subsystems. Monthly Notices of the Royal Astronomical Society, 360(2):
631–645, 2005.
Dhendra Marutho, Sunarna Hendra Handaka, Ekaprana Wijaya, and Muljono.
The determination of cluster number at k-mean using elbow method and purity evaluation on headline news. In 2018 International Seminar on Application for Technology of Information and Communication, pages 533–538, 2018. doi:
10.1109/ISEMANTIC.2018.8549751.
Warren Mcculloch and Walter Pitts. A logical calculus of ideas immanent in
nervous activity. Bulletin of Mathematical Biophysics, 5:127–147, 1943.
G. Meylan and D. C. Heggie. Internal dynamics of globular clusters. , 8:1–143,
January 1997. doi: 10.1007/s001590050008.
Elly Muningsih and ABSI Yogyakarta. Optimasi jumlah cluster k-means dengan
metode elbow untuk pemetaan pelanggan. Pros. Semin. Nas. ELINVO, pages
105–114, 2017.
F. Ochsenbein, P. Bauer, and J. Marcout. The VizieR database of astronomical
catalogues. , 143:23–32, April 2000. doi: 10.1051/aas:2000169.
F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel,
M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos,
D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay. Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12:2825–2830,
2011.
Anand Raju, Aravinth Jagatheesan, and S. Veni. An application of image processing techniques for detection of diseases on brinjal leaves using k-means
clustering method. 09 2016.
Ram Sagar and Harish C. Bhatt. Internal kinematics of open star clusters. , 236:
865–874, February 1989. doi: 10.1093/mnras/236.4.865.
Arthur L. Samuel. Some studies in machine learning using the game of checkers.
IBM Journal of Research and Development, 3(3):210–229, July 1959.
63David J. Schlegel, Douglas P. Finkbeiner, and Marc Davis. Maps of Dust Infrared Emission for Use in Estimation of Reddening and Cosmic Microwave
Background Radiation Foregrounds. , 500(2):525–553, June 1998. doi: 10.1086/
305772.
A Vallenari, AGA Brown, and T Prusti. Gaia data release 3. summary of the
content and survey properties. Astronomy & Astrophysics, 2022.
Don A VandenBerg, Karsten Brogaard, Ryan Leaman, and Luca Casagrande.
The ages of 55 globular clusters as determined using an improved method
along with color–magnitude diagram constraints, and their implications for
broader issues. The Astrophysical Journal, 775(2):134, 2013.
Ruoyi Zhang and Haibo Yuan. Empirical Temperature- and Extinctiondependent Extinction Coefficients for the GALEX, Pan-STARRS 1, Gaia, SDSS,
2MASS, and WISE Passbands. , 264(1):14, January 2023. doi: 10.3847/
1538-4365/ac9dfa.
Z.H. Zhou and S. Liu. Machine Learning. Springer Nature Singapore, 2021.
ISBN 9789811519666. URL https://books.google.com.tw/books?id=
Zd5hywEACAAJ.
R. Zinn. The Globular Cluster System of the Galaxy. IV. The Halo and Disk
Subsystems. , 293:424, June 1985. doi: 10.1086/163249.