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Analysis of the Spiral Structure in Disk Galaxies Using the Fft Transform

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Analysis of the Spiral Structure in Disk Galaxies Using the Fft Transform ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí ADVERTIMENT. L'accés als continguts d'aquesta tesi doctoral i la seva utilització ha de respectar els drets de la persona autora. Pot ser utilitzada per a consulta o estudi personal, així com en activitats o materials d'investigació i docència en els termes establerts a l'art. 32 del Text Refós de la Llei de Propietat Intel·lectual (RDL 1/1996). Per altres utilitzacions es requereix l'autorització prèvia i expressa de la persona autora. En qualsevol cas, en la utilització dels seus continguts caldrà indicar de forma clara el nom i cognoms de la persona autora i el títol de la tesi doctoral. No s'autoritza la seva reproducció o altres formes d'explotació efectuades amb finalitats de lucre ni la seva comunicació pública des d'un lloc aliè al servei TDX. Tampoc s'autoritza la presentació del seu contingut en una finestra o marc aliè a TDX (framing). Aquesta reserva de drets afecta tant als continguts de la tesi com als seus resums i índexs. ADVERTENCIA. El acceso a los contenidos de esta tesis doctoral y su utilización debe respetar los derechos de la persona autora. Puede ser utilizada para consulta o estudio personal, así como en actividades o materiales de investigación y docencia en los términos establecidos en el art. 32 del Texto Refundido de la Ley de Propiedad Intelectual (RDL 1/1996). Para otros usos se requiere la autorización previa y expresa de la persona autora. En cualquier caso, en la utilización de sus contenidos se deberá indicar de forma clara el nombre y apellidos de la persona autora y el título de la tesis doctoral. No se autoriza su reproducción u otras formas de explotación efectuadas con fines lucrativos ni su comunicación pública desde un sitio ajeno al servicio TDR. Tampoco se autoriza la presentación de su contenido en una ventana o marco ajeno a TDR (framing). Esta reserva de derechos afecta tanto al contenido de la tesis como a sus resúmenes e índices. WARNING. Access to the contents of this doctoral thesis and its use must respect the rights of the author. It can be used for reference or private study, as well as research and learning activities or materials in the terms established by the 32nd article of the Spanish Consolidated Copyright Act (RDL 1/1996). Express and previous authorization of the author is required for any other uses. In any case, when using its content, full name of the author and title of the thesis must be clearly indicated. Reproduction or other forms of for profit use or public communication from outside TDX service is not allowed. Presentation of its content in a window or frame external to TDX (framing) is not authorized either. These rights affect both the content of the thesis and its abstracts and indexes. UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí Analysis of the spiral structure in disk galaxies using the FFT transform CARLOS BARBERÀ ESCOÍ DOCTORAL THESIS 2018 UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí Carlos Barber`aEsco´ı ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM DOCTORAL THESIS Supervised by Dr. Carlos Garc´ıa-G´omez Department of Computer Engineering and Mathematics Tarragona 2018 UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí To my wife Inma and sons Carles and Alex` for unconditional love and support UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí Acknowledgments I would like to express my sincere gratitude to my doctoral thesis and research supervisor, Dr. Carlos Garc´ıa-G´omez,for his constant support, guidance, encouragement and per- spective to my thesis. I have learned and enjoyed working with him during all this time. Over many years, this professional and personal relationship has evolved into a life-long friendship reinforced by the health problems that both of us have successfully overcome. I would also like to thank Dr. Lia Athanassoula for her calm, wise advice and enthusiasm on scientific research. Special thanks to Jean-Charles Lambert for always being available to help on Unix issues and for transforming my stays in the Laboratoire d'Astrophysique de Marseille on dear moments. On a more practical level, I would also like to thank my office mate, office neighbours and the rest of collegues and staff of the Department of Computer Engineering and Mathematics for all the cofees, lunches and good moments we have had together. Finally, my family deserves all my gratitude for their love, support and patience. My wife Inma has been my best friend and helped me get through this long period in the most positive way. My sons Carles and Alex, watching me juggle with family and work. This thesis would not have been possible without your support. UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí Contents 1 Introduction 1 1.1 Motivation . 1 1.2 Galaxy classification . 2 1.3 Spiral structure theories . 3 1.3.1 Density waves . 3 1.3.2 Self-propagation star formation theory . 8 1.4 Comparing theory with observations . 10 1.4.1 Star arms . 10 1.5 Two-dimensional Fourier analysis . 12 1.5.1 Mathematical equations . 13 1.5.2 Equations for HII regions . 13 1.5.3 Equations for galaxy images . 15 1.6 Structure of the Thesis . 18 2 Contributions of the Thesis 19 2.1 Analysis of the distribution of HII regions in external galaxies. IV. The new galaxy sample. Position and inclination angles . 19 2.2 Deprojecting spiral galaxies using Fourier analysis. Application to the Frei sample . 36 2.3 Deprojecting spiral galaxies using Fourier analysis. Application to the Ohio sample . 50 2.4 Measuring bar strength using Fourier analysis of galaxy images . 58 3 Conclusion and Further Work 75 UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí Contents 3.1 Thesis Achievements . 75 3.2 Further Work . 77 UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí Chapter 1 Introduction In this chapter, we introduce and motivate the need for the research conducted in this thesis. To this end, in Section 1.1 we introduce and justify this thesis object of research. Section 1.2 situates the subject of study and introduce the common notation used in our field of research. Section 1.3 gives a complete vision on the different theories which try to explain the spiral structures of galaxies. Section 1.4 focuses on the relevant observations and their interpretations suggested by the theories. Section 1.5 shows the mathematical basis of the methods which are the main subject of this thesis. Finally, the structure of the rest of this thesis report is presented in Section 1.6 1.1 Motivation Our motivation is to give a quantitative classification of disk spiral galaxies according to their morphology, particularly on the presence (or not) of a central bar-shaped structure. A galaxy is a vast collection of stars, gas and dust held together by mutual gravitational attraction. Galaxies are found in a wide range of shapes, sizes and mass, but can usefully be classified into groups according to their morphologies. The first and most famous clas- sification was made by Hubble (1926), hnown as the Hubble sequence. He identified four main types of galaxies: elliptical, lenticular, spiral and irregular. 1 UNIVERSITAT ROVIRA I VIRGILI ANALYSIS OF THE SPIRAL STRUCTURE IN DISK GALAXIES USING THE FFT TRANSFORM Carlos Barberà Escoí 1.2. Galaxy classification 2 1.2 Galaxy classification Elliptical galaxies have smooth, featureless light distributions in three dimensions. Their projected shapes are elliptic. They are denoted by the letter E followed by a number from 0 to 7, which describes their degree of ellipticity on the sky, then E0 corresponds to a round galaxy and E7 would be a strongly elliptical galaxy. The most common shape is close to E3. This classification depends on the intrinsic shape of the galaxy, as well as the angle in which the galaxy is observed. Hence, some galaxies with Hubble type E0 may be actually elongated. Lenticular galaxies consist of a bright central bulge surrounded by an extended flattened disk with no gas, dust, bright young stars, or spiral arms. These galaxies are basically a transition class between elliptical and spiral galaxies and are labeled by the notation S0 in Hubble's classification scheme. Approximately two thirds of all galaxies are spiral galaxies, Eskridge & Frogel (1999). 60% according to Buta (1989). Spiral galaxies consist of a flattened prominent disk of bright young stars, gas, and dust; a near-spherical halo of stars; and a central non-disk-like concentration of stars named bulge which may or may not be present.
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