Asis Kumar Chattopadhyay Tanuka Chattopadhyay Statistical Methods for Astronomical Data Analysis Springer Series in Astrostatistics
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Springer Series in Astrostatistics Asis Kumar Chattopadhyay Tanuka Chattopadhyay Statistical Methods for Astronomical Data Analysis Springer Series in Astrostatistics Editor-in-chief: Joseph M. Hilbe, Jet Propulsion Laboratory, and Arizona State University, USA Jogesh Babu, The Pennsylvania State University, USA Bruce Bassett, University of Cape Town, South Africa Steffen Lauritzen, Oxford University, UK Thomas Loredo, Cornell University, USA Oleg Malkov, Moscow State University, Russia Jean-Luc Starck, CEA/Saclay, France David van Dyk, Imperial College, London, UK Springer Series in Astrostatistics, More information about this series at http://www.springer.com/series/1432 Springer Series in Astrostatistics Astrostatistical Challenges for the New Astronomy: ed. Joseph M. Hilbe Astrostatistics and Data Mining: ed. Luis Manuel Sarro, Laurent Eyer, William O’Mullane, Joris De Ridder Asis Kumar Chattopadhyay • Tanuka Chattopadhyay Statistical Methods for Astronomical Data Analysis 123 Asis Kumar Chattopadhyay Tanuka Chattopadhyay Department of Statistics Department of Applied Mathematics University of Calcutta University of Calcutta Calcutta, India Calcutta, India ISSN 2199-1030 ISSN 2199-1049 (electronic) ISBN 978-1-4939-1506-4 ISBN 978-1-4939-1507-1 (eBook) DOI 10.1007/978-1-4939-1507-1 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2014945364 Springer Science+Business Media New York 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publica- tion does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of pub- lication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com) To the Astrostatistics Community Preface Universe is deadly adventurous and man’s eternal quest to unfold its mysteries will never cease. Astronomy, perhaps the oldest observational science, has got its spectacular emergence with the advent of theoretical astrophysics and it has started to spread in India after some important contributions by Indian scientists in 1920s and later. Astronomy in the recent past has developed a lot with the launch of several missions like GALEX (Galaxy Evolution Ex- plorer), Kepler Space Telescope, Hubble Space Telescope (HST), etc. through which terabytes of data are available for preservation. Hence several virtual archives like SDSS (Sloan Digital Sky Survey), MAST (Multimission Archive at STSCI), Vizier, EDD, LEDA, Chandra, etc. have been developed to pre- serve the one-time snapshots of various astronomical events. During the last two decades galaxy formation theory and their related star formation histories have drawn interests among the astrophysicists to a great extent to uncover these mysteries using the reach treasure of virtual archives. While digging the pathway, a new branch ASTROSTATISTICS (or Statistical Astronomy) has emerged since 1980s. It is a blending of statistical analysis of astronomical data along with the development of new statistical techniques useful to analyze astrophysical phenomenon. The target is not only to explore the formation and evolutionary history of galaxies but also to uncover the unknown facts related to star formation, gamma ray bursts, supernova and other intrinsic variable stars. Where much data are not available, model- based approaches may be adopted. In this book we have tried to introduce “Astrostatistics” as a subject just like biostatistics. Through the various chapters we have discussed the basic concepts of both Astrophysics and Statistics along with the possible sources of Astronomical data. Subsequently we have entered into different types of applications of statistical techniques already developed or specifically introduced for astrophysical problems. We have discussed on techniques like regression, clustering and classification, missing data problems, simulation, data mining and time series analysis. Along with the discussion, specific examples are given so that readers can easily digest the method and can apply it to their own problem. Finally we have included a chapter on the use of R package which is an open access software. There we have included several examples which will be helpful for the readers. In the appendix we have included some astronomical data sets which we have used in our examples. We are indeed grateful to many persons and organizations for helping us during the preparation of the manuscript. In particular, we are grate- ful to Professor Ajit Kembhavi, Director, IUCAA, India, for continuous vii viii Preface encouragement and providing new ideas related to “fundamental plane” concept. We are also deeply indebted to Professor Sailajananda Mukherjee, Retired Professor and Former Head, Department of Physics, North Bengal University, India, for carefully reading the Astrophysical part of the book and suggesting significant improvements. We will always remember the cooper- ation and support we have received from Professor Joseph Hilbe, Emeritus Professor, University of Hawaii, USA. We will also remain grateful to Pro- fessors Jogesh Babu and Eric Feigelson, Pensylvania State University, USA, whose contributions inspired us to start work in this area. We offer our heartiest thanks to our collaborators Didier Fraix Burnet, Emmanuel Davoust, Margarita Sharina, Ranjeev Misra and Malay Naskar. We feel proud of our students Saptarshi Mondal, Tuli De, Abisa Sinha, Pradeep Karmakar and Bharat Warule for their sincere efforts and dedication. Being faculty members of Calcutta University, India, we are really grate- ful to our Vice-Chancellor Professor Suranjan Das and Pro-Vice-Chancellor (Academic) Professor D.J. Chattopadhyay for their continuous support. Finally we thank Mr. Aparesh Chatterjee for carefully preparing the typescript of this book. Calcutta, India Asis Kumar Chattopadhyay August 15, 2014 Tanuka Chattopadhyay Contents 1 Introduction to Astrophysics .................. 1 1.1 Light and Radiation ...................... 1 1.2 Sources of Radiation ...................... 7 1.3 Brightness of Stars ....................... 8 1.3.1 Absolute Magnitude and Distance ......... 9 1.3.2 Magnitude–Luminosity Relation .......... 10 1.3.3 Different Photometry Systems ........... 11 1.3.4 Stellar Parallax and Stellar Distances ....... 12 1.3.5 Doppler Shift and Stellar Motions ......... 14 1.4 Spectral Characteristics of Stars ............... 15 1.5 Spectral Features and Saha’s Ionization Theory ...... 17 1.6 Celestial Co-ordinate Systems ................ 23 1.7 Hertzsprung–Russel Diagram ................. 26 1.8 Stellar Atmosphere ...................... 27 1.9 Stellar Evolution and Connection with H–R Diagram ... 41 1.10 Variable Stars ......................... 53 1.11 Stellar Populations ...................... 62 1.11.1 Galactic Clusters ................... 62 1.11.2 Globular Clusters ................... 63 1.11.3 Fragmentation of Molecular Clouds and Initial Mass Function (IMF) ............. 65 1.12 Galaxies ............................ 69 1.13 Quasars ............................. 79 1.14 Pulsars ............................. 81 1.15 Gamma Ray Bursts ...................... 84 Appendix ............................... 85 Exercise ................................ 87 References ............................... 88 2 Introduction to Statistics .................... 91 2.1 Introduction .......................... 91 2.2 Variable ............................. 92 2.2.1 Discrete-Continuous ................. 92 2.2.2 Qualitative–Quantitative ............... 92 2.2.3 Cause and Effects ................... 93 2.3 Frequency Distribution .................... 93 2.3.1 Central Tendency ................... 93 2.3.2 Dispersion ....................... 94 ix x Contents 2.3.3 Skewness ....................... 94 2.3.4 Kurtosis ........................ 95 2.4 Exploratory Data Analysis .................. 95 2.4.1 Histogram ....................... 96 2.4.2 Box Plot ........................ 96 2.5 Correlation ........................... 97 2.5.1 Scatter Plot