Theoretical astrophysics 1

A.Y. 2020/2021
Overall hours
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.
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.
Course syllabus and organization

Single session

Lesson period
Second semester
Teaching methods
Lectures will be largely given in asynchronous form (detailed lecture notes for each lecture will be distributed one week before the planned lecture, accompanied with some questions and problems on the part of the program presented earlier). During the actual time of class (in synchronous form, by using Zoom or Skype) the contents of each lecture will be illustrated and the specific points developed in the course will be discussed with the students. During the week, in the period of time between classes, students will be encouraged to contact the teacher with queries (in relation to the lecture notes, questions, and problems distributed by the teacher), which will form the focus of the synchronous phase of the course.

Program and reading material
Program and reading material are unchanged with respect to the previous academic year.

The exam will be an oral exam with the use of Zoom or, if the regulations and general situation will allow it, may be an oral exam in traditional form (in person).

The exam, of approximately 45 minutes, will test that the student has reached the relevant objectives in terms of knowledge and understanding, following the structure of traditional oral exams (in person).
Course syllabus
The course addresses many topics in extragalactic astrophysics, especially those relating dynamics to the formation and evolution of galaxies in the cosmological context. It also addresses many fundamental issues that connect the study of complex self-gravitating systems to other interesting fields, such as plasma physics.

Theoretical Astrophysics 1 is dedicated to issues pertaining mostly to spiral galaxies, with a phenomenological introduction devoted to the general empirical properties of galaxies.

1. Physical characteristics of galaxies. Morphological classification, structure (photometry) and kinematics (spectroscopy) of galaxies. Empirical scaling laws: Tully-Fisher relation for spirals and the Fundamental Plane for ellipticals. Supermassive black holes in galactic nuclei.
2. Relaxation times for star-star collisions and some interesting phenomena (for example, dynamical friction). Galaxies as collisionless stellar systems. N-body systems and simulations. Continuous description of stellar systems. The collisionless Boltzmann equation and the problem of self-consistent dynamics. Jeans theorem, symmetries, integrals of the motion, anisotropy of the velocity dispersion tensor. Moments of the collisionless Boltzmann equation, fluid equations, virial equations. Analogies with electromagnetic plasmas. The paradigm of "equilibrium and stability/symmetry and symmetry break" at the basis of studies of the evolution of galaxies and other physical systems. The case of the rotating bowl: dynamical and dissipative stability; normal modes.
3. Description of orbits in galaxy disks. Guiding centers and epicyclic oscillations. Introduction of a stationary spiral potential. Lagrangian points. The winding dilemma. Corotation and Lindblad resonances. Lindblad's kinematic spiral waves.
4. The problem of spiral structure as formulated by Oort; four dynamical scenarios of intepretation in relation to origin and persistence of large-scale structure. Jeans' instability. The Q parameter and the mechanism of self-regulation. Quasi-stationary density waves and three points of criticism raised against the proposed interpretation: solution in terms of discrete, self-excited, global modes, in a WKB formulation and then in terms of eigenstates of a suitable Schroedinger-like equation. Feedback and overreflection. Dynamical classification of spiral galaxies. Importance of recent positive observational tests that confirm the theoretical framework, especially by means of studies in the near infrared (K band).
Prerequisites for admission
Knowledge of basic astronomical concepts and facts is desired but not required. The attending student should have good knowledge of concepts and methods that are normally introduced and taught in the Corso di Laurea Triennale, especially in relation to:
1. Classical mechanics
2. Classical electrodynamics
3. Analysis and calculus
Teaching methods
Attendance: strongly recommended.
Format of the classes: traditional, with the help of blackboard and handouts.
During the period of pandemic emergency, detailed lecture notes will be distributed one week before the class planned.
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)
Assessment methods and Criteria
The exam is an oral exam focusing on the topics presented in the course. Typically the exam takes 45 minutes and is based on two questions, the first of a phenomenological character, the second touching on theoretical/fundamental aspects of the course. In the evaluation of the exam performance special attention will be given to the acquired clarity in relation to the main concepts developed in the course.
FIS/05 - ASTRONOMY AND ASTROPHYSICS - University credits: 6
Lessons: 42 hours
Professor: Bertin Giuseppe