利用蓋亞 DR3 星表研究球狀星團的 CMD 並利用機器學習作型態上的分類

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謝庫馬(Bishnu Kumar Sharma) 查詢紙本館藏

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天文研究所

論文名稱

利用蓋亞 DR3 星表研究球狀星團的 CMD 並利用機器學習作型態上的分類
(Study CMD of Globular Clusters using Gaia DR3 data and classify them according to their morphology using Machine Learning)

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摘要(中)

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

摘要(英)

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

關鍵字(中)

★ 球狀星團
★ 色溫-星等圖
★ 機器學習

關鍵字(英)

★ Globular Cluster
★ Color-magnitude diagram
★ Machine learning

論文目次

Contents
Coverpage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
1 Introduction 1
1.1 Globular Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Mass and Age . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.4 Metallicity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.5 Importance of Studying GCs . . . . . . . . . . . . . . . . . 4
1.2 Color-Magnitude Diagram . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Motivation of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Gaia and Data Analysis 8
2.1 Gaia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Gaia Data Release 3 (DR3) . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 Extracting Gaia DR3 Data . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Luminosity function of GC . . . . . . . . . . . . . . . . . . . . . . 9
2.5 Data analysis and member selection . . . . . . . . . . . . . . . . . 10
2.5.1 Trigonometric Parallax . . . . . . . . . . . . . . . . . . . . . 10
2.5.2 Astrometric excess noise and RUWE . . . . . . . . . . . . . 12
2.5.3 Proper motions . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.5.4 Some of the CMDs with no proper shape . . . . . . . . . . 14
2.5.5 Extinction and distance correction . . . . . . . . . . . . . . 15
3 Machine Learning 17
3.1 Introduction to Machine Learning . . . . . . . . . . . . . . . . . . 17
3.2 History of Machine Learning . . . . . . . . . . . . . . . . . . . . . 17
3.3 Types of Machine learning . . . . . . . . . . . . . . . . . . . . . . . 18
3.4 Image Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.1 Image clustering methods . . . . . . . . . . . . . . . . . . . 20
3.4.2 Description of model . . . . . . . . . . . . . . . . . . . . . . 21
3.4.3 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.4 Feature extraction/ ML model . . . . . . . . . . . . . . . . 21
3.4.5 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4 Result and discussion 28
4.0.1 Clusters CMDs superimpose perfectly . . . . . . . . . . . 29
4.0.2 Clusters CMDs don’t superimpose perfectly . . . . . . . . 48
ix4.0.3 Singular cluster group . . . . . . . . . . . . . . . . . . . . . 52
5 Conclusion 6

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指導教授

饒兆聰(Chow-Choong Ngeow)

審核日期

2023-6-8

推文