Neighbouring Galaxy
Kiran Tikare
Space Engineering, master's level (120 credits) 2020
Luleå University of Technology
A close look at the transient sky in a
neighboring galaxy
Kiran Tikare
Erasmus Mundus SpaceMaster Program
Department of Computer Science, Electrical and Space Engineering Lule˚a University of Technology
Kiruna, Sweden
Supervisors: Examiner:
Prof. Ariel Goobar Prof. Anita Enmark
Mrtyormaa Amrtamgamaya Om Shaantih Shaantih Shaantih
Lead us from the unreal to the real Lead us from darkness to light Lead us from death to immortality Aum peace, peace, peace! – Brihadaranyaka Upanishad (1.3.28)
If I have seen further it is by standing on ye sholders of Giants. – Isaac Newton in a letter to Robert Hooke One thing I have learned in a long life: that all our science, measured against reality, is primitive and childlike — and yet it is the most precious thing we have. – Albert Einstein Bear in mind that the wonderful things you learn in your schools are the work of many generations, produced by enthusiastic effort and infinite labour in every country of the world. All this is put into your hands as your inheritance in order that you may receive it, honour it, add to it, and one day faithfully hand it on to your children. Thus do we mortals achieve immortality in the permanent things which we create in common. If you always keep that in mind you will find a meaning in life and work and acquire the right attitude toward other nations and ages. – Albert Einstein, Ideas and Opinions
Study of the time variable sources and phenomena in Astrophysics provides us with im-portant insights into the stellar evolution, galactic evolution, stellar population studies and cosmological studies such as number density of dark massive objects. Study of these sources and phenomena forms the basis of Time Domain surveys, where the telescopes while scanning the sky regularly for a period of time provides us with positional and tem-poral data of various Astrophysical sources and phenomena happening in the Universe. Our vantage point within the Milky Way galaxy greatly limits studying our galaxy in its entirety. In such a scenario our nearest neighbour The Andromeda galaxy (M31) proves to be an excellent choice as its proximity and inclination allows us to resolve millions of stars using space based telescopes.
Zwicky Transient Facility (ZTF) is a new optical time domain survey at Palomar Observatory, which has collected data in the direction of M31 for over 6 months using multiple filters. This Thesis involves exploitation of this rich data set. Stars in M31 are not resolved in ZTF as it is a ground based facility. This requires us to use the large public catalogue of stars observed with Hubble Space Telescope (HST): The Panchromatic Hubble Andromeda Treasury (PHAT). The PHAT catalogue provides us with stellar co-ordinates and observed brightness for millions of resolved stars in the direction of the M31 in multiple filters.
Processing of the large volumes of data generated by the time domain surveys, requires us to develop new data processing pipelines and utilize statistical techniques for deter-mining various statistical features of the data and using machine learning algorithms to classify the data into different categories. End result of such processing of the data is the astronomical catalogues of various astrophysical sources and phenomena and their light curves.
In this thesis we have developed a data processing and analysis pipeline based on Forced Aperture Photometry Technique. Since the stars are not resolved in ZTF, we per-formed photometry at pixel level. Only small portion of the ZTF dataset has been an-alyzed and photometric light curves have been generated for few interesting sources. In our preliminary investigations we have used a machine learning algorithm to classify the resulting time series data into different categories. We also performed cross comparison with data from other studies in the region of the Andromeda galaxy.
List of Figures 1
List of Tables 3
Chapter 1 – Introduction 5
1.1 Our work . . . 5
1.2 Outline of the Thesis . . . 6
1.3 Scientific Context . . . 7
1.3.1 The Realm of the Nebulae - Island Universe . . . 9
1.3.2 Golden Era of Sky Surveys and Big Data . . . 10
1.3.3 Statistical and Machine Learning Techniques . . . 13
1.3.4 Time Domain Astronomy . . . 13
Stellar Variability . . . 14 Transients . . . 15 Gravitational Lensing . . . 16 Strong Lensing . . . 19 Weak Lensing . . . 19 Microlensing . . . 20
Applications of Gravitational Lensing . . . 22
1.4 Our Testbed - The Andromeda Galaxy . . . 24
Chapter 2 – Studying Stars 29 2.1 Magnitude System . . . 31
2.1.1 Apparent Magnitude - m . . . 31
2.1.2 Absolute Magnitude - M . . . 31
2.1.3 Bolometric Magnitude . . . 32
2.2 Photon Detection using Charge Coupled Devices (CCDs) . . . 33
2.2.1 Key parameters of CCDs . . . 34
2.3 Errors and Noise . . . 35
2.3.1 Dark Current . . . 35 2.3.2 Photon Noise . . . 35 2.3.3 Readout Noise . . . 35 2.3.4 Pixel Saturation . . . 36 2.3.5 Cosmic Rays . . . 36 2.3.6 Sky Background . . . 36
2.3.7 Other sources of Noise . . . 36
2.5 Stellar Photometry . . . 38
2.5.1 Aperture Photometry . . . 39
Extinction correction and Photometric Calibration . . . 41
Uncertainties . . . 41
2.5.2 Light Curves . . . 41
Chapter 3 – Observational Datasets 43 3.1 Panchromatic Hubble Andromeda Treasury(PHAT) . . . 43
3.2 Zwicky Transient Facility (ZTF) . . . 47
Chapter 4 – Data Processing Approach and Pipeline Development 51 4.1 Software Tool Chain . . . 51
4.1.1 Python Programming Language . . . 51
4.1.2 Python Packages . . . 52
4.1.3 Git as Version Control System . . . 52
4.1.4 Imaging and data visualization . . . 52
4.2 HPC Computing Resource - NSC’s Tetralith Supercomputer . . . 52
4.3 Exploratory Data Analysis . . . 53
4.3.1 Data used for processing and Analysis . . . 53
4.3.2 Quality Filtering of ZTF images . . . 56
4.4 Our Approach . . . 57
4.4.1 Pixel Photometry . . . 57
4.4.2 Source Measurement and Estimation . . . 58
4.4.3 Background Measurement and Estimation . . . 58
4.5 Methodology and Workflow . . . 59
4.6 Use of Machine Learning Algorithm for Classification . . . 63
4.6.1 Principal Component Analysis (PCA) . . . 65
4.6.2 Random Forest Algorithm (RFA) . . . 65
4.7 Validating the Pipeline . . . 66
Chapter 5 – Results and Data Analysis 67 5.1 Time Series Data Analysis . . . 67
5.1.1 Visual Assessment . . . 67
5.1.2 Lomb Scargle Periodogram Analysis for Variability . . . 67
5.2 Machine Learning Classification . . . 68
5.2.1 Microlensing Detections . . . 68
5.2.2 Variable Star Detections . . . 69
5.2.3 Cataclysmic Variable Detections . . . 71
5.2.4 Constant Source Detections . . . 72
5.3 Cross Comparisons . . . 73
5.3.1 Comparison with Hubble Catalog of Variables (HCV) . . . 73
5.3.2 Comparison with ZTF Caltech team . . . 73
5.3.3 Comparison with Caldwell Star Catalogue in M31 . . . 74
Appendix – A - Terminology 79 Appendix – B - zwindromeda - python pipeline 83 Python Packages . . . 83
7.1 Zwindromeda - Pipeline . . . 83
References 85
It was in 1999 I first came to know about Gravitational Lensing during one of the thought-provoking classes taught by my physics teacher Shri Arun Pujer. I remember it even after 20 years and that is a testimony to the impression it had created on me and the subsequent curiosity about the phenomena. Coming back to 2019, while looking for a Master Thesis I came across Caltech webpage of Prof. Shrinivas Kulkarni, about whom I had read during my school and college days in various Indian regional and national print media. I was excited to be writing to him to seek his guidance for my Master Thesis. Subsequent to our email exchange, Prof. Shrinivas Kulkarni suggested me to do my Master Thesis under his collaborator Prof. Ariel Goobar at The Oskar Klein Center for Cosmoparticle Physics, Stockholm University in Stockholm, Sweden. I readily accepted the Thesis topic proposed by Prof. Ariel Goobar as I was excited to work on the topic. Coincidentally 2019 also marked the 100th anniversary of observation of deflection of light by gravity, which was predicted by Albert Einstein in his General Theory of Relativity and was observationally confirmed by Sir Arthur Eddington during a Solar Eclipse on 29 May 1919. Apart from this there are four other important historical anniversaries which makes it bit exciting period, namely, the 100th anniversary of Saha Equation (named after Meghnad Saha), 50th anniversary of discovery of CCD, 100th anniversary of Great Debate (April 26, 1920) between Astronomers Harlow Shapley and Heber Curtis. And without those works I would not be doing this thesis work today.
Every thesis work reflects the subject matter understanding (at the time of writing the thesis) of the author or the lack there of. As this work is in the domain of science ideas are put to test rigorously and any lack in understandings or wrong directions or misinterpretations will be found out with subsequent works by the author or the other researcher working on same problems and may require revision in some point in time after the thesis has been published. As one takes a look at History of Science, it is evident that scientific explorations and the insights gained are not linear, it has undergone rigorous tests and revisions and modifications, only those works remain which agree with the experiments.1
As one goes through this thesis, one may notice some mention of historical developments and some quotes from the works which I have read, and which had an impact on me
1It doesn’t matter how beautiful your theory is, it doesn’t matter how smart you are. If it doesn’t
agree with experiment, it’s wrong. - Richard Feynman
me during this time, but I thoroughly enjoyed working on this thesis and reading up invaluable scientific literature. And at the final stages of preparing the thesis report, the COVID-192 virus outbreak begun causing loss of life and impacting economy across the
world, several countries have been forced to lock down. The impact of this pandemic will be tremendous on health of the people and economy across the world. This also had effect on my health, and I had to self-quarantine which has caused some delay with the thesis work.
I am greatly indebted to Prof. Shrinivas Kulkarni for suggesting me to work on my Master Thesis under Prof. Ariel Goobar. And I sincerely thank my thesis advisor Prof. Ariel Goobar for providing me with an opportunity to work on a fascinating topic under his advice, guidance and for his endless encouragement during this Thesis. I am sincerely thank Dr. Rahul Biswas for his valuable support, discussions and providing continuous guidance in particular on High Performance Computing (HPC), Python, data visualization, statistics and Dr. Sem´eli Papadogiannakis for advice and discussions. It was also wonderful to attend various colloquium seminars organized at The Oskar Klein Center, which were insightful and thought provoking for me, I will always cherish these seminars.
I sincerely thank internal examiner Prof. Anita Enmark and have greatly enjoyed her lectures during other courses. I thank Prof. Victoria Barabash, head of Erasmus Mundus SpaceMaster Program at Lule ˙a University of Technology (LTU), Kiruna, Sweden for her constant support throughout the Masters studies. I cannot thank enough Ms Maria Winneb¨ack for all her support with administrative work and making our life easier at Lulea University of Technology, Kiruna, Sweden during my studies. I also would like to thank Anette Sn¨allfot-Br¨andstr¨om for her support with the administrative work.
I am indebted to all those teachers, lecturers, professors, scientists and online resources created by various people across the world from whom I have learnt various things and they have kept me going and have shaped me. Finally, I owe significant thanks to my family and friends who stood by my side and supported me in various ways in pursu-ing this Master Studies. Without their encouragement, moral and financial support this journey would not have been possible. Also I would like to acknowledge NASA ADS Sys-tem3 and Arxiv4 which provided invaluable scientific literature and acknowledge various
Open Source Software’s such as Python, LaTeX, Ubuntu Linux OS, Github which were of enormous use during the course of Master Thesis.
Based on observations obtained with the Samuel Oschin 48-inch Telescope at the Palo-mar Observatory as part of the Zwicky Transient Facility project. ZTF is supported by the National Science Foundation under Grant No. AST-1440341 and a collaboration
Deutsches Elektronen-Synchrotron and Humboldt University, Los Alamos National Lab-oratories, the TANGO Consortium of Taiwan, the University of Wisconsin at Milwaukee, and Lawrence Berkeley National Laboratories. Operations are conducted by COO, IPAC, and UW.
The computations and data handling were enabled by resources provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Centre (NSC), LinkoiU partially funded by the Swedish Research Council through grant agree-ment no. SNIC 2019/3-575”
Based on observations made with the NASA/ESA Hubble Space Telescope, obtained from the MAST Data Archive(https://archive.stsci.edu/prepds/phat/) at the Space Telescope Science Institute, which is operated by the Association of Universities for Re-search in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with the Panchromatic Hubble Andromeda Treasury Multi-cycle Program. This research has made use of the SVO Filter Profile Service (http://svo2.cab.inta-csic.
es/theory/fps/) supported from the Spanish MINECO through grant AYA2017-84089.
1.1 Cosmic Inventory . . . 8
1.2 Comparison of Field of View of various Sky Survey Telescopes. . . 11
1.3 The ray diagram showing the Geometry of Strong lensing. . . 19
1.4 The artistic impression showing the geometry of Microlensing. . . 20
1.5 Magnification of source due to gravitational microlensing . . . 21
1.6 Picture of Andromeda Galaxy (M31) taken from Zwicky Transient Facility (ZTF) . . . 25
1.7 Major Variability Surveys of M31 . . . 27
2.1 Workings of a CCD Camera . . . 33
2.2 Filter transmission for the ZTF g, r, and i-band filters . . . 38
2.3 Aperture Photometry Technique . . . 39
2.4 Aperture Photometry Plots . . . 41
2.5 Light curves of (a) Transient events, (b)Variables . . . 42
3.1 Location and Alignment of PHAT Bricks . . . 44
3.2 HST PHAT Composite color image . . . 45
3.3 RGB image from PHAT Brick 11 ACS-WFC . . . 46
3.4 Comparison of Field of View of various meter class Sky Survey Telescopes. 47 3.5 Specifications of the ZTF Observing System . . . 48
3.6 ZTF CCD readout Channel Layout . . . 49
4.1 PHAT Brick 09 and Brick 11 Overlap Region . . . 53
4.2 Plot showing F814W Vega vs F814W SNR for Brick 11 . . . 54
4.3 Histogram Plot showing number of stars vs F814W Vega Magnitude . . . 54
4.4 ZTF Science images of M31 . . . 55
4.5 Distribution of ZTF Observations under fieldid 695 and r band filter . . . 56
4.6 Plot for Quality Cut . . . 57
4.7 Blending and overlapping ra/dec . . . 58
4.8 Data Processing Workflow . . . 63
5.1 Detections classified as Microlensing from Machine Learning Algorithm LIA 69 5.2 False Positives due to artifacts. North is up and East is left of the image. 69 5.3 Plot of Variable Star detection through Machine Learning classification . 70 5.4 Plot of Cataclysmic Variable Detections through Machine Learning clas-sification . . . 71
5.5 Plot of Constant Source Detections through Machine Learning classification 72
5.7 Cross Match with ZTF Caltech Team data . . . 74
5.8 Cross Match with Caldwell Star Catalogue to identify Star Clusters . . . 74
1.1 Variables and Transients . . . 15
1.2 Sky Surveys towards M31 - Some of these are specific to search for Mi-crolensing Events, while some surveys have different scientific objectives . 28
3.1 Approximate Corners of PHAT Bricks . . . 45
3.2 Downloaded ZTF Science Images listed per field id, filter id, ccdid and qid 49
4.1 Number of Stars in each Band in each Brick of PHAT . . . 55
4.2 Column Names used in the final dataset . . . 60
4.3 List of 47 Statistical features computed using LIA for classification . . . . 64
Introduction
History of astronomy displaces us from cosmic importance. - - Unknown
One of the most remarkable and surprisingly unexpected discovery - based on Type Ia supernovae- in the recent years was that the expansion of the universe is accelerating1 [1, 2, 3] and we don’t yet know much about the source responsible for this cosmic accel-eration. It is generally accepted that this accelerated expansion of the universe begun approximately 4 billion years ago during the dark energy dominated era [4, 5]. But the important thing to know is that without the expansion and cooling of the universe, the atoms, molecules, terrestrial planets, stars, galaxies and all the large scale structures, including life on earth would not come into existence. And how we arrived to this un-derstanding of the universe from the ancient times is an exciting story about human curiosity and ingenuity.
In this chapter we will start with the outline of the Master Thesis work. We provide introductory information about the astrophysical landscape, starting the journey from the beginnings of astronomy to the contemporary times to the sky surveys and statistical techniques used for data processing. After this we will take a look at time domain studies of transients and variability, and to some extent detailed explanation of microlensing. Finally we will take a look at the Andromeda Galaxy and the previous time domain studies of this galaxy.
1.1
Our work
The scope of this thesis work is limited to the following tasks, i). develop a software pipeline for processing the data gathered over 6 months in optical band from the ground based observation using Zwicky Transient Facility (ZTF) towards Andromeda Galaxy ii). process small part of the imaging data using the developed software pipeline and
1The accelerating expansion of the universe is the observation that the expansion of the universe is
such that the velocity at which a distant galaxy is receding from the observer is continuously increasing with time.
generate time series data iii). generate light curves from time series data. We have also made an attempt to show, usage of Machine Learning techniques for classification and cross comparisons with other catalogues.
The scientific motivations behind the thesis work is that with the Zwicky Transient Facil-ity (ZTF) optical survey, the imaging data can be mined to find astrophysical variabilFacil-ity and transients in our neighbouring galaxy the Andromeda galaxy. For this we need stel-lar positional data so we tap into the rich data set of Hubble Space Telescope : Hubble Panchromatic Andromeda Treasury (PHAT) catalogue which provides us with observed brightness and stellar coordinates for millions of resolved stars in the direction of the Andromeda galaxy. It is important to note that stars in the Andromeda galaxy are not resolved in ZTF as it is a ground based facility but are resolved through Hubble Space Telescope. We perform forced aperture photometry on ZTF images, at the stellar coordi-nates provided by HST’s PHAT catalogue. Studying this imaging data will not only help us with a census of transient events and variable sources but also lead to an understand-ing of the distribution of such sources and phenomenology in the Andromeda galaxy and aid in the understanding of stellar and galactic evolution. The technical motivations are that this project involves processing large volume of data and also involves using the data generated by both space based and ground based telescope. Another important aspect is that as with other sciences, Astronomy is also largely becoming data intensive science so the modern astronomer requires knowledge of computer science and statistics. In the coming days Software Engineering and Statistics will be essential tools for Astronomers to do large scale processing of data, this requires development of different automation techniques. The bulk of the thesis work was towards using one approach by means of a semi-automated supervised processing of the data, generation of light curves, preliminary exploratory data analysis, and using a Machine Learning algorithm for classification of the detections.
1.2
Outline of the Thesis
The subsequent chapters will describe the scientific basis and the scientific methods and astrophysical techniques used as well as the data processing pipeline development, data analysis and the results obtained.
variability, various classification schemes, various mechanisms involved and transients. We also introduce the subject of Gravitational Lensing. Since Gravitational Lensing was of particular interest for this thesis work, to some extent a detailed explanations is given. An attempt has been made to give some brief historical developments which I believe helps in getting a broader overview of the topic of interest and gives a glimpse of decisive turning points which shaped this important tool in use today in Astrophysics research. This also in a way serves as a tribute to the few giants - to paraphrase Newton- on whose shoulders we will climb to look further. We then provide details about the Andromeda Galaxy and briefly list down the previous time domain studies carried out in the direction of M31.
Chapter 2, covers the basic theory and practical aspects of astrophysical techniques utilised in this Thesis. The chapter begins with the nature of stars and how we study stars, following this the magnitude system is introduced which helps in quantifying the stellar measurements carried out through observational data. Then a brief introduction to the CCD detectors is provided along with the various errors and noise sources that affect the measurements. In the subsequent sections details of various photometric filter systems are explained and then the stellar photometry technique called aperture photometry will be explained followed by the description of light curves and how photometry helps us with gaining an understanding of the astrophysical aspects of the sources that we measure and quantify.
In Chapter 3, we provide details of the datasets from Hubble Space Telescope and Zwicky Transient Facility which acts as foundation for this entire thesis.
Chapter 4 deals with the data processing techniques, software and computing resources used, pipeline development, verification and validation of the data processing steps and the statistical techniques used. This section discusses the investigations carried out by the author during the course of Master Thesis. This investigation if carried out for few more months this will probably lead to the discovery of interesting objects.
And finally in Chapter 5, will discuss the results of the work carried out for thesis as well as the intended future works.
1.3
Scientific Context
Through such observations our ancestors were trying to understand what was going on in the sky above earth. And our ancestors looked at the sky for various purposes for omens of war and peace, to time keeping, to making predictions of weather, to predicting suitable time for agriculture, for meaning of life and for religious purposes.
Next wave of astronomical observations saw a tremendous progress as astronomers started to take a glimpse at the undiscovered universe through newly invented optical telescopes. This had a tremendous impact not only on physical sciences but also on the society. Physi-cal laws of motion and gravitation provided a way to understand the underlying governing physical principles. Followed by this the invention of camera allowed astronomers to take images of the night sky and store it and process it. With recent development in digital imaging, super fast computers and large data storage systems allowed astronomers to store and share the collected data among other astronomers and perform analysis and study them after carrying out observations. Modern developments in space and ground based telescopes are enabling us to study the cosmos in different spatial and temporal aspects.
Cosmology - being the study of the Universe in its entirety, from its birth to evolution to its fate - is rapidly undergoing change at tremendous scale due to rise in High Performance Computing (HPC) as well as digital storage resources (used for simulations and data processing), and unprecedented growth in precision observational datasets produced by different sky survey programs utilizing the higher sensitivity and higher resolution offered by modern telescopes. This growth in high quality datasets may help observational cosmology to answer some of the fundamental questions.
Figure 1.1: Cosmic Inventory
Contemporary developments have lead us to dis-cover even more astrophysical objects and astro-physical phenomenology. Now we know about dif-ferent structures on a vast range of scale, and each structure is at a different evolutionary stage. Fig.1.1shows the cosmic inventory. Our current sci-entific understanding is limited only to about 5% of the constituents of our Universe, this luminous mat-ter (or baryonic matmat-ter2) comprises of all that we
know and see from stars, planets, moons, comets, asteroids to gas, dust to people. The other 95% of the constituents of the Universe - Dark Matter3 and
Dark Energy - remain hidden from our understand-ing. Our continued observations of the sky reveals that a great deal of mysteries yet to be explained by physical laws.
2Only the baryonic matter produces the light that we observe in stars and galaxies.
3”Dark” as some of the exotic form of non luminous matter (non baryonic matter) that does not
Observations carried out over a millennia have enriched our knowledge and understanding of the universe. We have come a long way and today we live in an era of Multi Messenger Astrophysics. Multi Messenger Astrophysics is an interdisciplinary field that combines data from many different instruments that probe the universe using different cosmic mes-sengers. Cosmic messengers comprise of electromagnetic waves (Gamma Rays, X-Rays, UV, Visual, Infra Red, Microwaves, Radio Waves), neutrinos, cosmic rays and recently in the form of gravitational waves and they play an important role in understanding our Universe. There are many more areas to explore including the origin and fate of the Uni-verse [6]. The ongoing research in many areas will continue to improve our understanding of the cosmos in the years to come.
1.3.1
The Realm of the Nebulae
4- Island Universe
5As we are used to call the appearance of the heavens, where it is surrounded with a bright zone, the Milky Way, it may not be amiss to point out some other very remarkable Nebulae which cannot well be less, but are probably much larger than our own system; and, being also extended, the inhabitants of the planets that attend the stars which compose them must likewise perceive the same phenomena. For which reason they may also be called milky ways by way of distinction. - - William Herschel, [8]
Our understanding of the scale of the universe has undergone tremendous change since the ancient times. Up until 15th century it was believed that based on Aristotelian view, the Earth is at the center of the Universe (Geocentric) and a few astronomical objects (Planets, Moon, Sun and Comets were the only known astronomical objects ) revolve around it in front of a fixed sphere of stars. This view was challenged by Copernicus and others, they proposed Sun centric universe (Heliocentric) which was confirmed by further observations that were carried out. Later Thomas Digges expanded ideas of Copernicus and was probably first one to suggest the infinite universe and stars being located at varying distances rather than fixed to a sphere [9]. Up to the beginning of 18th century the entirety of the universe was largely limited to the solar system, then by the late eighteenth century astronomers found that the solar system was part of a much larger group called a galaxy. Our solar system is located in a spiral arm of a galaxy -containing a vast number of stars (1011 stars) appearing like a great band of scattered light stretching around the sky - 6 which we call the Milky Way galaxy, our own cosmic
4Title of the Book by Edwin Hubble [7]
5Astronomer Heber Doust Curtis’s the Island Universe theory suggesting that the Milky Way was
just one of many galaxies within the universe.
6A gravitationally bound system of distributed vast number of astrophysical sources such as stars,
home. The stars that we see in the night sky through naked eye belong to this Milky Way galaxy, and our Galaxy has been studied extensively. Our home galaxy, belongs to a group called the Local Group[10] - a group of galaxies within 1 Mpc of the Milky way, which are gravitationally bound and hence relatively close to each other. This local group contains 35 other galaxies including the Andromeda Galaxy, the Large and Small Magellanic Clouds, and the Triangulum Galaxy.
The Milky way galaxy together with Andromeda galaxy dominates the Local Group and account for the 90% of the luminosity. Most of the other galaxies in the Local group are clustered around these two galaxies. By modern astronomical convention, concentration of about ∼10 to 40 galaxies with mass range from are called as “groups”, which have mass of the order of ∼ 1013− 1014M
. About ∼40 to 1000 number of galaxies are called
as “clusters”, which have mass more than ∼ 1014M
. Note that these are arbitrarily
defined. Since there are no galaxies between 1.3 Mpc and 2.4 Mpc around our galaxies, our local group can be thought of as an island-like region within the universe and there are several such groups of galaxies have been observed in the universe. And telescopic observations have revealed that the universe contains millions of galaxies clustered around each other and distributed, and some of these clusters themselves grouped around other clusters forming what is known as “superclusters” with sizes ranging from 30 to 60 Mpc.
1.3.2
Golden Era of Sky Surveys and Big Data
It is important to have a census of astronomical objects and their distribution and know how these astronomical objects change over time. Once we gather information about many objects we can study them to understand the underlying governing principles as well as discover basic physical properties of the universe. Some of the astronomical objects and phenomenology associated with them are so rare that to find them we must look at millions of objects. This requires mapping the universe over large areas of the sky at greater depths and over entire wavelength range. Sky surveys provide a best technique in this regard for discovering new objects and phenomenology.
Since the early 20th century, the astronomy community is witnessing the large volumes of scientific data being produced due to various astronomical surveys. Large Field of View (FoV) offered by modern telescopes helps us to scan vast area of the sky in few pointing’s, some of the FoV of various existing and planned Sky Survey Telescopes is shown in fig.1.2. The astronomical surveys in the coming days will even further increase the volume of data. Improvements in computing power, storage and other infrastructure have enriched astronomical image processing and data management capabilities. These large sets of data are processed and maintained in astronomical catalogues.
Figure 1.2: Comparison of Field of View of various Sky Survey Telescopes. The Moon and Andromeda Galaxy are shown to Scale. Credits: Joel Johansson
the way we answer fundamental questions. We are in the golden age of ambitious sky surveys where telescopes - both ground based and space based - have been scanning and will continue to scan large areas of the night sky and penetrating deeper into the universe and generate large volumes of science data - what is known as Big Data 7 science today. Innovative detectors are opening new windows on the universe, creating unprecedented volumes of high-quality data, and coupled with this, the computing technology is driving a shift in the way scientific research is done in astronomy and astrophysics. Some of the frontiers of these survey astronomy include Time Domain studies (of Transients and Variability), Census of the Solar System (NEOs, MBAs, Comets, KBOs, Oort Cloud), Dark energy and Dark matter studies (Gravitational Lensing, Gravitational Waves) etc. The survey data sets have been invaluable resource to the astronomy community in revolutionising astronomy by providing wealth of information, helping the community to observe and analyse changes in large amount of astrophysical sources over the period of time, continuous monitoring of astrophysical phenomena and helping produce catalogue of variety of astrophysical objects and phenomena. Large surveys helps in constructing catalogs and maps of objects in the entire sky. The catalogs will be filled with rich data related to positions, magnitudes, shapes, profiles and temporal behaviors of the objects. This will enable Astronomers with initial classification and discovering objects for further follow up. Based on these studies Astronomers can understand the details of astrophysical processes that govern these objects and further extrapolation leads to understanding of the entire class of such objects.
7Big data in general is characterized by 3 V’s and they are i.) Volume (Data Size varying from
Astronomical Archival data is any kind of organised, systematized information about the sky above us. Historically archives have been very small - contained 10s to 100s of objects, so the Astronomy was data starved science. Some historical catalogues are Hipparcos star catalogue. Then we have catalogues produced by Ptolemy’s Almagest in 138 AD based on Hipparcos Catalogue and Tycho Brahe’s catalogue, each of these catalogues revolutionized Astronomy and Physics. During the early telescopic era, several star catalogues were produced. Johann Bayer produced a star catalogue in 1603, in that he classified stars in various constellations, and named brightest stars in that constellation as α , 2nd brightest as β and so on and he constructed a star chart and a star catalogue. A century later in 1771, Charles Messier produced a catalogue [11] of around 100 extended nebulous objects.8 as he wanted to provide comet hunters of his time with well known
nebulous objects which were frequently being confused with new comets. This was an important catalogue and is still being used today mainly by amateur astronomers. In 1786, William Herschel with the assistance of his sister Caroline Herschel compiled The Catalogue of Nebulae and Clusters of Stars (CN) [12, 13, 14] which was later expanded into the General Catalogue of Nebulae and Clusters of Stars (GC) [15] by his son, John Herschel. This was expanded later in 1888 by John Louis Emil Dreyer where he compiled 7840 deep sky objects under New General Catalogue of Nebulae and Clusters of Stars (NGC) catalogue [16]. Apart from general catalogues, there are specialised catalogues they do not list all the stars in the sky, instead highlight a particular type of star, such as variable stars. The earlier catalogues were small and were in printed form, the modern catalogues are stored on world wide web9, which makes it easy to search and is available for other researchers.
Since the earliest days astronomers have gathered and systematised data in catalogues and made it useful for various purposes from farming to gaining an understanding of the universe. This makes astronomy a data intensive domain due to the availability of large volumes of data from large sky surveys in recent years and it will continue to remain so. Some of the next generation projects such as Wide Field InfraRed Survey Telescope -WFIRST (IR), James Webb Space Telescope - JWST (IR), Vera Rubin Observatory [For-merly, Large Synoptic Survey Telescope - LSST] (Optical), Extremely Large Telescope - ELT (Optical), Atacama Large Millimeter/submillimeter Array - ALMA (Millimeter), Square Kilometer Array -SKA (Radio), Laser Interferometer Gravitational Wave Obser-vatory - LIGO (Gravitational Waves), Laser Interferometer Space Array - LISA (Gravita-tional Waves) with their extraordinary capabilities will lead to unprecedented discovery about our Universe. Each of these astronomical projects will generate terabytes of science data every night. New sky surveys will continue to explore ever-larger survey volumes in the times to come and will discover new transient and variable phenomena thus enriching our knowledge. Technology is a key driver in many of the recent discoveries in Astron-omy. New Technologies enables us to study new phenomena which were inaccessible due
8Today we know that some of them are gaseous nebulae and others as galaxies and star clusters both
open and globular clusters.
9One can refer to CDS site for modern astronomical catalogues
to old technology and helps to develop new approaches for probing the universe.
1.3.3
Statistical and Machine Learning Techniques
The data generated from sky surveys will provide us with important large volume statis-tical data sets. Huge surveys of the sky over many wavelengths of light can be analyzed statistically for hidden correlations and explanations leading to new discoveries. The scale of this dataset requires us to develop innovative, increasingly automated, and increasingly more effective ways to mine scientific knowledge. An emerging branch of Computational Statistics known as Machine Learning (ML) involves a plethora of algorithms and sta-tistical techniques which perform tasks such as regression, classification and clustering analysis using the numerical inferences drawn based on the statistical patterns in the data without explicit instructions. The large volume of data makes it much more complex for any single person or a group of people to analyse. So instead computer algorithms are written in such a way that a computer can process all the data and find correlations on its own. The algorithm then outputs its results that can be put to further analysis. The real power though comes from the fact that it’s very common for these algorithms to feed the results back into themselves learning how it can analyze the data even better for more accurate results.
1.3.4
Time Domain Astronomy
Deceptively, the night sky appears to be unchanging apart from the twinkling of stars due to atmospheric effects but careful observations with naked eye over a period of time and with telescopes (small to wide field of view) in all wavelength of the EM spectrum one can start noticing the changing nature of the sky. There are many astronomical time varying periodic phenomena, aperiodic phenomena and sudden one time events that occur both in the local universe and in the distant universe.
Stellar Variability
Some stars are known to change in brightness over several periods of time from seconds to years and such stars are known as variable stars. Variable stars have periodicity so they are predictable. Variable stars are “Experimental Laboratories” for stellar physics. Earliest record of a variable star was in 1596 when the German astronomer David Fabri-cius accidentally noted a variable star o Ceti (Mira10 type) in the constellation Cetus,
which he could not find in the recorded star catalogue of his time. Later in 1603, Jo-hannes Bayer rediscovered this star and listed it as Omicron in his atlas. And almost a century later in 1782 John Goodricke discovered variability in β Persei (aka Algol) as well as δ Cephei. These discoveries lead to the search for stellar variability. In 1905, Henrietta Levitt was working as a “computer”, studying the stellar variability in Small Magellanic Clouds (SMC) and Large Magellanic Cloud (LMC) [17, 18], discovered the Period Luminosity relation for a group of variable stars known as Cepheids. This impor-tant relation -Leavitt Law- subsequently helped with determination of distances to SMC and LMC and distances of other galaxies. This also contributed to the understanding of the structure and scale of the universe.
In principle during the stellar evolution, each star radiates energy in the form of photons with different intensities due to various mechanisms. The cause of this change in light in-tensity is either intrinsic to the star or extrinsic. If the cause of the variability is intrinsic, this may be due to change in physical properties such as its radius (alternative expansion and contraction either rapidly or slowly) due to internal mechanisms involved with en-ergy production (such as nuclear reactions) as well as enen-ergy transportation mechanisms (radiation, convection, convolution) or due to rapid rotation or due to mass loss of the star. All of these mechanisms affect stellar evolution. If the cause of the variability is extrinsic, then the reason might be due to some orbiting planet or a companion star or due to absorption by interstellar medium. All such mechanisms give us clues about the interstellar medium and immediate vicinity of the star.
Variable stars are divided into different classes, sub classes and types and are listed in the table.1.1. Each of these Pulsating stars, Eclipsing Binaries, Variability induced by rotation, eruptive stars and cataclysmic variables have different time scale and amplitude of variation, from milli-magnitudes to several magnitudes11. The variability may be
periodic or quasi irregular.
Cepheids are young variable stars located in spiral galaxies. They have been used as standard candles for extragalactic distance measurement as they obey period luminosity relation. In cepheid stars, the envelop expands and contracts this causes changes in brightness. Flares are sudden explosions caused by the rearranging of magnetic fields which causes flashes of increased brightness of the stars, they are similar to Solar Flares but some of these flares might be 2 or 3 magnitudes stronger compared to sun. We may
10Mira means the wonderful.
No Category Group Class Sub Class Type
1 Variables Intrinsic Pulsating Stars Cepheids Type I Classical
2 Type II W Virigins
3 RR Lyrae
4 RV Tauri
5 Long Period Variables Mira Type
6 Semi Regular
7 Eruptive (Cataclysmic Stars) Recurrent Novae
8 Dwarf Novae
9 Symbiotic Stars 10 R Coronae Borealis 11 Extrinsic Eclipsing Binaries
12 Rotating Variables 13 Transients Novae
14 Supernovae
15 Gravitational Microlensing 16 Gamma Ray Bursts
Table 1.1: Variables and Transients
also find Cataclysmic Variables (CVs), which are binary stars, where massive primary star transfers matter from its less massive companion star creating accretion discs around itself. As the matter falls into the primary star/ these accretion discs can become unstable and show an increased brightness - 2 or 3 orders of magnitude higher than their original brightness - within few hours and fall back to their original brightness within few days. Historically these CVs were discovered due to their large amplitude variability. The sub-classes of CVs, Classical Novae (White Dwarf interacting with late-type companion star) also have these large amplitude variability where they can show 6 to 19 magnitudes of increase in brightness for several days to years, before fading back to the original brightness level [19, 20].
The basic data in stellar variability studies are the Photometric observational data taken over a period of time - what is known as Time Series Data. The light curves generated from these photometric observational data is an important source for interpretations of stellar variability. This when coupled with spectroscopic follow up observations, helps us in identifying the mechanisms and the causes behind the variability.
Transients
-Gravitational Lensing- which are the result of deflection of light by gravity.
Gravitational Lensing
Nature and Nature’s laws lay hid in night:
God said, Let Newton be! and all was light. - Alexander Pope, Poet
It did not last: the Devil howling ”Ho!
Let Einstein be!” restored the status quo. - Sir J.C. Squire, 1926
Can Gravity12 affect Light? If so in what ways? and how can we make use of such a
phenomena?
These thoughts have captured imaginations of many natural philosophers of medieval times and physicists of modern times, from Laplace, Newton, Soldner, Cavendish to Einstein and Zwicky to modern cosmologists. Einstein’s General Relativity (GR) has given successful framework to study and answer some of these questions.
In our everyday life we perceive reality in terms of Euclidean space, 3 dimensions grid of Space with static time. We are familiar with the idea that the light travels in straight lines and when you look at a star you would think that the light from that star is reaching your eyes in a straight-line from star to your eyes, but across the universe this light follows the curvature of space time as predicted by GR. As light travels it gets stretched(shear), distorted and deflected, shifted and magnified (convergence) due to the nature of spacetime fabric and its curvature around astronomical objects. So many things that we see are not where we perceive them to be. A good analogy is to think of wavy fun house style party mirrors that make you look stretched, twisted and bent, giving you an illusory view of reality.
In 1783 Rev. John Michell an elected member of the Royal Society in London delivered a lecture on the gravity of stars where he reasoned that a massive star’s gravity might be so strong that no light could escape from its surface13. Following this, in 1796, Peter Simon
Laplace wrote an essay14, suggesting the effect of attractive force of heavenly bodies
12According to General Relativity gravity is nothing but the manifestation of curvature of SpaceTime
fabric. In ordinary Eucleadean space without curvature, light travels in a straight line. In curved Riemannian space light travels along the geodesics.
13And he also wrote a letter to Henry Cavendish in 1784 suggesting existence of ”dark stars” [21]. 14A luminous star, of the same density as the earth, and whose diameter should be two hundred and
on light [23]. While he was actively researching on the nature of light and working on Corpuscular Theory of Light, Isaac Newton instead of speculating (Hypotheses non fingo15 - was his attitude) the effect of gravity on light, he listed down this and many
other unsolved queries at the end of his second major treatise Optiks16. Later Johann Georg von Soldner in 1801 proposed deflection of light by gravity and calculated the deflection angle at the solar limb eq.1.1, based on Newtonian Gravitational Theory [26]. But observations were not carried out because of two reasons first one was that this deflection angle is so small that it was beyond the capability of astronomical instruments of his time in early 19th century and the second reason was that the prevalence of wave nature of light at around this time as compared to corpuscular theory.
In the lens like effect, the light ray will travel along a hyperbola near a spherical gravitat-ing mass, this mass will be its focus and the two asymptotes intersect to give a deflection angle α and is given by,
α = 2GM c2R
= 0.”875 (1.1)
where M is the mass of Sun, R is the radius of the Sun, G is Newton’s gravitational
constant, and c is the speed of light. 2GM
c2 is the Schwarzschild Radius.
When one looks at the above equation, one quickly realizes that since c is much larger than G, the deflection angle will be very small. For this reason it was thought that it is almost impossible to observe this.
Almost a century later, In around 1911, Albert Einstein predicted the deflection of light by Sun’s gravity as a consequence of his General Theory of Relativity (GR). Initial calcu-lations by Einstein were similar to the calcucalcu-lations of Soldner but later he revised those calculations in 1915 [27,28] and came up with a value of deflection angle which was dou-ble the value (ref eqn.1.2) calculated by Soldner. This was due to the realization that not only is space bent, but time is distorted as well, thus slowing down near massive objects. This “time dilation” creates an additional deflection of light along with the geometric curvature of space. To observe this deflection angle, Arthur Eddington and others went on an expedition to watch the solar eclipse of 29 May 1919 during which the sun was favourably located in front of the Hyades star cluster, thus allowing for measurements of the positions and deflections of these background stars [29]. The expedition was car-ried out to answer two questions i.) Whether light has any mass? or gravity has any effect on light? ii.) If light has mass, whether the angle of deflection follows Newton’s
Appendix A of Hawking and Ellis ”Large Scale Structure of Space-Time” [24].
15Principia, General Scholium. Third edition, page 943
16When I made the foregoing observations, I designed to repeat most of them with more care and
exactness, .... But I was then interrupted, and cannot now think of taking these things into further consideration. And Since I have not finished this part of my design, I shall conclude with proposing only some queries, in order to a farther search to be made by others.
gravitational laws or Einstein’s General Relativity? The observations revealed that the deflection angle was indeed as predicted by Einstein. The answers to these questions captured public attention and made Einstein famous across nations. And subsequent observations with microwaves improved the accuracy of this deflection angle.
α = 4GM c2R
= 1.”75 (1.2)
where M is the mass of Sun, R is the radius of the Sun, G is Newton’s gravitational
constant, and c is the speed of light.
This bending of light from astronomical objects leads to the lens like effect and is now known as Gravitational Lensing. At around 1924, the Russian physicist Orest Danilovich Khvolson or Orest Chwolson too had arrived at the same value independently but he did not think it as a lens [30]. Although Einstein had thought about lensing like effect due to this deflection of light, he did not pursue it until 1939 when a Czech engineer Rdui W. Mandl paid visit and pursued him to publish17. Reluctantly Einstein published his
calculations concluding that there is no great chance of observing such a phenomena [31]. Soon after this the Swiss-American Astronomer Fritz Zwicky came with ideas about lensing effect due to galaxies and predicted they can be observable18 as the deflection
angle is larger than that of point like sources [33, 32,34, 35].
Astronomers Sydney Liebes and Sjur Refsdal provided all the essential equations to analyse the gravitational lensing, Refsdal was the first one to propose using gravitational lensing for measuring the rate of expansion of the universe i.e., Hubble constant [36,
37]. Later Bohdan Paczynski proposed using gravitational lensing for searching dark matter, brown dwarfs, planets and planetary masses in galactic bulge, halo, and the lo-cal group [38, 39, 40, 41]. It was only in 1979, first gravitationally lensed quasar was discovered [42, 43]. Then in 1988, first partial Einstein ring MG1131+0456 was discov-ered followed by in 1998 first complete Einstein ring B1938+666, was discovdiscov-ered [44]. Since then the gravitational lensing has been used by astrophysicists to discover many gravitational lensing events. Gravitational Lensing can occur in variety of configurations such as individual stars, binary systems, massive compact objects, galaxies, clusters of galaxies, and the filamentary structure of the cosmic web. Depending on the positions of the source, lens, observer, the mass of the lens and shape of the lens, gravitational lensing can occur in three different regimes., namely, Strong lensing, Weak lensing and Microlensing.
In a gravitational lensing system four things are involved Source, Lens, Observer and the image(s)/brightness variation. Source is the one which is being observed, it can be a quasar, a galaxy or cosmic web, cosmic microwave background (CMB), a galaxy cluster
17...It would be, according to my view, in the interest of science to begin with these experiments as
soon as possible...– Rdui W. Mandl in a letter to Albert Einstein, 23 April 1936
18. . . the probability that nebulae which act as gravitational lenses will be found becomes practically
or a star cluster or a star. Lens can be any compact source with mass or energy and this causes deflection of light of the source and the amount is proportional to the mass or energy of the lens. The lens is between the observer and the source either along line of sight or around it. Observer is the one who is observing the source (usually a detector of a telescope). The observer will see either brightness variations or single or multiple images of the source depending on the lens and the configuration of source, lens and observer and the path of the light.
In the next sections we will give brief details about each of the gravitational lensing regimes.
Strong Lensing
Gravitational lensing by elongated sources such as galaxies is known as Strong lensing. The fig.1.3 shows the artistic impression of the geometry of Strong Lensing by extended objects like a galaxy. Here an extended object which distorts the light is marked as Lens and the background extended object is denoted as source. In such configuration we see either multiple images of background sources, or we see luminous rings (called Einstein Rings) and luminous arcs (Einstein arcs), fig.1.5 demonstrates the luminous rings and luminous arcs.
A single lens produces two unresolved images, a binary lens three or five unresolved images depending on the location of the source in comparison to the lens. Stronger lensing effect produces greater distortions and from these we can pinpoint the concentrations of mass responsible for producing such distortions.
Figure 1.3: The artistic impression showing the Geometry of Strong lensing. The figure is not to scale and the distortion shown here is greatly exaggerated relative to real astronomical systems.
Weak Lensing
Microlensing
Gravitational lensing by compact sources where the angular separation between the im-ages is micro arc seconds is known as Microlensing19 and is demonstrated in fig.1.4. The
separation between the two images is of micro-arcsec (hence the name microlensing) or-der for a solar mass located at cosmological distance, is of milli-arcsec oror-der for galactic stars.
The microlensing events are a spacetime geometric effect generated by an object (a lens) passing near the line of sight between the observer (our telescope) and a background source (a star). When this object passes, it generates a deformation in spacetime causing the rays of light that came from the background star to deviate towards itself. Here instead of seeing multiple images of the background source we will see an apparent increase in the brightness of the background sources.
Figure 1.4: The artistic impression showing the geometry of Microlensing. The figure is not to scale (the ”Lens” star here is representational it can be any compact objects) and the distortion shown here is greatly exaggerated relative to real astronomical systems.
The fig.1.4 shows the artistic impression of the geometry of Microlensing. Here you can see that the light from the source gets deflected around a point like source that is another star which we call as lens this deflection causes the source to appear in a different location. The fig.1.5 shows an artistic impression of the apparent increase in the brightness as a compact object passes between the source and observer in the line of sight of the observer. The distance between the images produced by microlensing effect are so small that we can not resolve them through imaging, instead what we see is increase in the brightness
19Bohdan Paczynski suggested the name microlensing to describe gravitational lensing that can be
of the source star as lens moves between observer and the source. In the plot you see the time on the x-axis and in the y-axis the brightness of the microlensing event. So you see that the brightness suddenly increases and then returns to normal. This effect allows us to find dark objects.
Figure 1.5: Artistic impression of the magnification of source due to gravitational microlensing. As the lens (L) and source(S) come in the line of sight of the observer, the observer notices increased brightness if it is a point source. Otherwise rings and arcs in the form of distorted images in case of elongated source like galaxy, quasars etc. The arrow mark indicates the direction of motion of the Lens
Consider a simple configuration as shown in fig.1.4 where a single point like compact ob-ject acting as a lens on a single point like source. The magnification, A, source luminosity as a function at a given time, t , is given by,
A(t) = u(t)
2+ 2
u(t)pu(t)2 + 4 (1.3)
Where u(t) is impact parameter or the distance of the lens star from the line-of-sight to the source star(marked with dashed line), and is expressed in units of the Einstein Radius. The impact parameter u(t) and the magnification of the source changes with time.
If the distance between observer and source is DOS, distance between observer and lens
is DOL, distance between lens and source is DLS, and the lens mass is M, and when the
source is directly behind the lens, then Einstein ring radius, RE is given by,
RE = r 4GM c2 DLSDOL DOS (1.4)
And lensing event Einstein radius crossing time scale tE is given by,
tE =
RE
v⊥
(1.5)
Where V⊥ is the transverse velocity of the lens with respect to the line-of-sight to the
source.
As the lens moves relative to the line of sight, the magnification will change with time. Consider the lens moving at a constant relative transverse velocity V⊥, reaching its
min-imum distance u0 (impact parameter) to the undeflected line of sight at time to, then
u(t) = s u2 o+ t − t0 tE 2 (1.6)
Microlensing events are rare, short lived and are unique events, as a given star may be microlensed at most once in a human lifetime. The magnification is a function of time and depends only on (u0,t0,tE). If we assume no binary stars or planetary systems around
stars, they are achromatic as lensing is independent of wavelength, meaning, source’s color should not change during the microlensing event20. This means, the ratio of flux
change in different filter bands should be constant in time. ∆Fg(t)
∆Fr(t)
= Constant (1.7)
These microlensing events are possible to detect if we have sufficient time baseline and high cadence monitoring. Also the galactic bulge regions are interesting due to the high density of both background stars and ordinary stars in the line of sight, microlensing is guaranteed to occur. As compared to the resolved and bright stars, crowded regions such as bulge of a galaxy pose a serious challenge in the analysis of microlensing events, due to the effect of blending. Also blending occurs due to atmospheric seeing, where several stars are blended together of which typically only one star will be lensed. These limit the determination of different microlensing parameters and detection efficiency. Microlensing events that also exhibit a detectable photometric signature provide lens mass constraints. Most of the surveys used for discovering microlensing events have been photometric monitoring programs.
The other thing to note here is that all stars at a given distance have the same probability of being lensed so the sample of lensed stars should be representative of the monitored population at that distance, particularly with respect to the observed color and mag-nitude distributions. And the probability of a microlensing event is low, so it becomes necessary to monitor a large number of stars for a long period of time.
Applications of Gravitational Lensing
Gravitational lensing was used recently to make a portrait of a black hole located at the center of a galaxy known as M87 and it provided visual evidence for the glowing disk of gas - the radiation ring [61].
With the help of gravitational lensing we will learn more about mass function of stars and brown dwarfs, binary systems and their mass ratios, detect planets and planetary mass objects, stellar evolution, distribution of dark matter and it has also been suggested
20Chromaticity may also arise due to differential amplification for a limb-darkened extended source
for searching intelligent life. This will also allow us to test Einstein’s general theory of relativity ever more rigorously.
Microlensing has become one of the powerful tools in advancing several areas of Astro-physics. Using microlensing we can learn about massive objects surrounding the stars and in the galaxy and cluster of galaxies.
Some probable applications of gravitational lensing at different regimes are listed below. 1. Helps in Understanding the Dark Matter (MACHOs) distribution. Nature of Dark Matter still remains unknown even nearly 8 decades after it was first proposed. Since they do not produce any EM radiation, but show gravitational interaction. Paczynski was the first one to suggest using microlensing to search for them, he also calculated the probability of finding microlensing events along the magellanic cloud to be 10−2.
2. Discovery of Exoplanets [40, 62, 63]
3. Measurement of Hubble Constant [37] - by measuring the path length we can mea-sure the distances - this tells us the rate of expansion of the universe.
4. Search for Extraterrestrial Intelligence [64, 65, 66,67] 5. Microlensing by Cosmic Strings [68]
6. Discovery of Double stars and Eclipsing Binaries [40]
7. Population studies of local isolated neutron stars and black holes
8. Discovery and measurement of masses of nearby Dwarf stars, Brown Dwarfs [69] and Planets
9. Interstellar Communication [70, 71] / Intergalactic Communication Tool [72] 10. Imaging Exoplanets and Extended sources with Solar gravitational lens (SGL) [73] 11. Detection of non-luminous matter in astrophysics in the form of stellar and
plane-tary mass objects [74]
1.4
Our Testbed - The Andromeda Galaxy
“Like a candle seen through a horn” —Simon Marius, 1612[76]
Under dark and clear moonless night sky we could see a fuzzy looking nebulous object in the constellation of Andromeda - which is nothing but a collection of stars and is known as the Andromeda Galaxy. As it is visible to the naked eye, up until 1920s, it was believed that this nebulous object is part of the Milky Way. Several spectroscopic (leading to stellar signatures) [77] and radial velocity studies [78] had indicated it to be extragalactic. These studies lead to great debates [79] and were instrumental in revolu-tionising our understanding of the shape and extent of the cosmos. Edwin Hubble’s [80] observations with the Mount Wilson Observatory Telescopes, proved beyond doubt that the Andromeda Galaxy is - extra-galactic- outside the Milky Way [81,82]. Later Walter Baade carried out observational studies and was able to define different stellar popula-tions in the Andromeda Galaxy. The stellar populapopula-tions categorization continues to be used to this day as it forms an essential feature used in studies of stellar and galactic evolution.
Under Messier Catalogue, Andromeda galaxy is designated as object M31 and under Hubble Galaxy Classification Scheme based on galactic morphology, it is classified as ”Sb” - Intermediate Spiral [81, 83] and ”SA(s)b” according de Vaucouleurs Third Catalogue of Bright Galaxies [84] and modern IR observations have revealed the bar like structure with an estimated length of 4-5kpc in its center [85]. Andromeda galaxy is the nearest major spiral galaxy located at around r = 770 kpc (or ∼ 0.77±0.04 Megapasec or 2.5 million light years, or in terms of red shift z = -0.00121. The apparent size of the Andromeda Galaxy is 3o.1 × 1o.25 and has absolute magnitude of -21.1 mag. Distance
to Andromeda was determined using Period Luminosity relation of Cepheid’s. It has an estimated inclination of 77o relative to Earth and has 13o between plane of galaxy and line-of-sight and is 22oaway from the Galactic plane. Even at 770 kpc distance it is about 2.5o wide on the sky (roughly 5 times the Moon’s diameter). Like other spiral galaxies,
Andromeda has bulge, disc and halo, and has different population of stars distributed in the bulge and disc region. The disc shows two spiral arms marked by dark dust lanes and young star clusters. M31 has high dust content which belongs to 3 different components,a fore-ground component related to Milky Way extinction, mid-plane component related to M31’s internal extinction, and a differential component [86]. Later observations carried out by Hubble Space Telescope (HST) revealed the double central region, indicating galactic merger.
Most galaxies show redshift, meaning they are moving away from the Milky Way, but M31 shows the opposite. So,interestingly, both our own Milky way and Andromeda galaxies are in collision course and approaching each other with a velocity of v=110 km
s−1 (or 402,000kph) and in approximately tc = rv = 6.3 billion years, may merge to form
a giant elliptical galaxy [87].
Figure 1.6: Picture of Andromeda Galaxy (M31), Credit: ZTF/D. Goldstein and R. Hurt (Caltech) [88]
A composite image of the Andromeda galaxy is shown in fig.1.6 made by combining three bands of visible light. The image covers 2.9 square degrees, which is one-sixteenth of ZTF’s full field of view.
Due to its naked eye visibility and proximity, M31’s role as an important test bed was realized very early and several studies of M31 have provided us with important insights in multiple areas of Astrophysics22. Our vantage point within the Milky Way galaxy
22Hubble’s study of Cepheid variable stars in the Andromeda Galaxy helped us determine the
greatly limits studying our galaxy in its entirety as dust clouds hide most of its struc-ture, in such a scenario M31 proves to be an excellent choice and as such it has been responsible for breakthroughs in our understanding with respect to evolution of stars, rotation of galaxies and the scale of distances in the universe. Other than that what makes it important/interesting is its proximity and morphological similarity with Milky Way galaxy. Proximity will allow us to resolve stars as well as we can perform spectro-scopic follow ups. However one limitation with regards to M31 to note is that it is close to being an edge on galaxy.
M31 and the Milky Way both may be similar in size, shape and both have Supermassive Black Holes (SMBH) in their core23. If both share similarity then studying the
An-dromeda Galaxy in entirity allows us to understand our own Milky Way Galaxy. M31 offers many excellent advantages. Barring the high stellar surface density and crowding, its proximity allows us to resolve faint stars, this also helps in avoiding confusion between foreground and background stars, as there is a general understanding of the distances involved due to studies of Cepheids. M31 hosts different stellar populations, in its spiral arms, in its bulge and halo. M31’s halo can be studied globally. The halo region is home to very old stars, while the disk contains mixture of stars of different age groups, this is also home to interstellar matter so it is a region of active star formation. It is an ideal location for the hunt of varied kinds of variable stars and transient events hence it is kind of observational testbed for stellar physics, galaxy formation and evolution, as well as cosmology. This enables us to study about various physical processes which govern the stellar and galactic evolution in their full galactic context as the entire galaxy including its halo is visible for Astrophysical and Cosmological studies. We can probe not only the dark halo of the Milky way along different line of sight (LOS) but also of M31. Its high inclination will provide a strong gradient in the spatial distribution of microlensing events. The microlensing studies of M31 will complement the studies of the Milky Way halo using the the Large and Small Magellanic Clouds. M31 has different metallicity and star forming regions.
M31 has dense stellar field for microlensing studies and is rich with variable stars, and having capability to directly observe their variable phenomena makes it an interesting target for testing various astrophysical stellar theories.
Since both M31 and our galaxy halo can be probed thus we might be able to study galactic dark matter composed of compact objects - such as black holes, faint stars, brown dwarfs, Jupiter like planets - known as MACHOs (”MAssive Compact Halo Objects”)24 and its
distribution. MACHOs are made of non-baryonic matter and they emit little or no radiation, as they are not luminous so they are hard to detect. MACHOs may explain the apparent presence of dark matter in galaxy halos. Various time domain studies have been conducted and being planned to study the Andromeda Galaxy. Some of these time
studies[90] of the rotation curves of the Andromeda Galaxy indicated presence of ”dark matter”.
23The SMBH in our Milky way is known as SgrA* and the one at the center of M31 is known as
M31* [91]
Figure 1.7: Major Variability Surveys of M31 reproduced from[50]. The figure shows different survey under different colors, shape of the symbol points to the type of variables.
