Dynamics of Galaxies
A.Y. 2024/2025
Learning objectives
The Course offers an introductory overview to many important current themes that play a key role in the so-called "extragalactic astrophysics" and, in particular, to issues that relate the dynamics of galaxies, as studied in the nearby universe, to the problems of galaxy formation and evolution in the cosmological context. The course also addresses some fundamental questions that relate the description of complex self-gravitating systems in astrophysics to other interesting fields, such as plasma physics.
The main goal of the course is to demonstrate the merits of a semi-empirical approach to research. Starting from several substantial and concrete examples offered by extragalactic astrophysics, the student will learn and realize how the most interesting problems, also from the theoretical point of view, are identified from a wide and detailed phenomenological framework (thus, on the basis of modern observations from the ground and from space) and that excellent results in the astrophysics of complex systems such as galaxies derive from a rigorous formulation of relatively simple questions and models.
Course 1 is largely devoted to the study of problems and methods of investigations related to the dynamics of spiral galaxies.
The main goal of the course is to demonstrate the merits of a semi-empirical approach to research. Starting from several substantial and concrete examples offered by extragalactic astrophysics, the student will learn and realize how the most interesting problems, also from the theoretical point of view, are identified from a wide and detailed phenomenological framework (thus, on the basis of modern observations from the ground and from space) and that excellent results in the astrophysics of complex systems such as galaxies derive from a rigorous formulation of relatively simple questions and models.
Course 1 is largely devoted to the study of problems and methods of investigations related to the dynamics of spiral galaxies.
Expected learning outcomes
At the end of the course, the student will master the following skills:
Will know the main structural and kinematical properties, as well as the main scaling laws, that characterize galaxies. With this empirical basis, will be able to undertake research in studies of formation and evolution of galaxies or research in the cosmological context in which galaxies are used as tracers on the grandest scale.
Will be able to calculate and evaluate the collision rate for stellar encounters in various astrophysical contexts, some of which (such as globular clusters or galactic nuclei) are of special interest in modern astrophysics.
Will be able to formulate fluid or kinetic models to study various questions related to the dynamics of stellar systems and some problems in plasma physics.
Will be able to identify and describe several simple orbital properties (precession, resonances) in many contexts, also in the field of celestial mechanics.
Based on the study of density waves as an explanation of the spiral structure in galaxies developed in this course, will be able to calculate various local and global properties of systems subject to dispersive waves, also with application to plasma physics and hydrodynamics.
In particular, will be able to solve problems that require the use of the approximation known as WKB.
Will also acquire a large body of examples that demonstrate the properties of equilibrium and mechanisms of instability in various dynamical contexts.
Will know the main structural and kinematical properties, as well as the main scaling laws, that characterize galaxies. With this empirical basis, will be able to undertake research in studies of formation and evolution of galaxies or research in the cosmological context in which galaxies are used as tracers on the grandest scale.
Will be able to calculate and evaluate the collision rate for stellar encounters in various astrophysical contexts, some of which (such as globular clusters or galactic nuclei) are of special interest in modern astrophysics.
Will be able to formulate fluid or kinetic models to study various questions related to the dynamics of stellar systems and some problems in plasma physics.
Will be able to identify and describe several simple orbital properties (precession, resonances) in many contexts, also in the field of celestial mechanics.
Based on the study of density waves as an explanation of the spiral structure in galaxies developed in this course, will be able to calculate various local and global properties of systems subject to dispersive waves, also with application to plasma physics and hydrodynamics.
In particular, will be able to solve problems that require the use of the approximation known as WKB.
Will also acquire a large body of examples that demonstrate the properties of equilibrium and mechanisms of instability in various dynamical contexts.
Lesson period: Second semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second semester
Course syllabus
Dynamics of Galaxies addresses selected topics in extragalactic astrophysics, especially those that relate dynamics to formation and evolution of galaxies. It touches on several fundamental issues that relate the study of complex self-gravitating systems to other fields, such as plasma physics and fluid dynamics.
Equilibrium and stability. The paradigm "equilibrium and stability/symmetry and symmetry break" at the basis of the study of the evolution of galaxies and other physical systems. Dynamical stability, dissipative stability, normal modes: analysis of two simple examples. (4 hours)
Principles of stellar dynamics. Relaxation times for star-star encounters.; dynamical friction. Galaxies as collisionless stellar systems. Continuum description of stellar systems. The collisionless Boltzmann equation and the problem of self-consistent dynamics. Moments of the collisionless Boltzmann equation, fluid equations, virial equations. Analogies with electromagnetic plasmas. (8 hours)
Spiral galaxies. The problem of spiral structure; four interpretation scenarios in relation to origin and persistence of the large-scale spiral structure. Jeans instability. The Q parameter and self-regulation. Quasi-stationary density waves: interpretation in terms of discrete, self-excited, global modes, in a WKB investigation leading to the study of modes as eigenstates of a Schroedinger-like equation. (10 hours)
Globular clusters. Truncated quasi-isothermal spheres as models of globular clusters (King models). Merits, limitations, generalizations of King models. Explicit inclusion of tides, rotation, pressure anisotropy, mass segregation, energy equipartition. (10 hours)
Elliptical galaxies. Collisionless collapse and incomplete violent relaxation. Dynamical models and physical interpretation of the observed structure of bright elliptical galaxies. (10 hours)
Equilibrium and stability. The paradigm "equilibrium and stability/symmetry and symmetry break" at the basis of the study of the evolution of galaxies and other physical systems. Dynamical stability, dissipative stability, normal modes: analysis of two simple examples. (4 hours)
Principles of stellar dynamics. Relaxation times for star-star encounters.; dynamical friction. Galaxies as collisionless stellar systems. Continuum description of stellar systems. The collisionless Boltzmann equation and the problem of self-consistent dynamics. Moments of the collisionless Boltzmann equation, fluid equations, virial equations. Analogies with electromagnetic plasmas. (8 hours)
Spiral galaxies. The problem of spiral structure; four interpretation scenarios in relation to origin and persistence of the large-scale spiral structure. Jeans instability. The Q parameter and self-regulation. Quasi-stationary density waves: interpretation in terms of discrete, self-excited, global modes, in a WKB investigation leading to the study of modes as eigenstates of a Schroedinger-like equation. (10 hours)
Globular clusters. Truncated quasi-isothermal spheres as models of globular clusters (King models). Merits, limitations, generalizations of King models. Explicit inclusion of tides, rotation, pressure anisotropy, mass segregation, energy equipartition. (10 hours)
Elliptical galaxies. Collisionless collapse and incomplete violent relaxation. Dynamical models and physical interpretation of the observed structure of bright elliptical galaxies. (10 hours)
Prerequisites for admission
Elementary background in astronomy is desirable, but not necessary.
Good knowledge is required of concepts and methods that are reasonably introduced in the Corso di Laurea Triennale, especially in relation to:
1. Classical Mechanics
2. Classical Electrodynamics
3. Calculus and Mathematical Analysis
Good knowledge is required of concepts and methods that are reasonably introduced in the Corso di Laurea Triennale, especially in relation to:
1. Classical Mechanics
2. Classical Electrodynamics
3. Calculus and Mathematical Analysis
Teaching methods
Attending in presence: strongly recommended.
Format of classes: traditional, with the support of blackboard and handouts.
Format of classes: traditional, with the support of blackboard and handouts.
Teaching Resources
G. Bertin "Dynamics of Galaxies", 2nd ed, Cambridge University Press, New York USA (2014)
G. Bertin, C.C. Lin "Spiral Structure in Galaxies: A Density Wave Theory", The MIT Press, Cambridge, MA USA (1996)
G. Bertin "Visible and Dark Matter in the Universe: A Short Primer on Astrophysical Dynamics", Cambridge University Press, Cambridge UK (2022)
G. Bertin, C.C. Lin "Spiral Structure in Galaxies: A Density Wave Theory", The MIT Press, Cambridge, MA USA (1996)
G. Bertin "Visible and Dark Matter in the Universe: A Short Primer on Astrophysical Dynamics", Cambridge University Press, Cambridge UK (2022)
Assessment methods and Criteria
The exam is oral and addresses the topics presented in class. Typically it lasts 45 minutes and is centered on two questions, one related to phenomenology and the other to basic theoretical issues. In the final evaluation, special attention will be given to whether the main concepts dealt in class have been acquired in depth and clarity.
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 6
Lessons: 42 hours
Professor:
Bertin Giuseppe
Professor(s)