Theoretical astrophysics 2

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 2 is largely devoted to the study of problems and methods of investigations related to the dynamics of globular clusters and elliptical galaxies.
Expected learning outcomes
At the end of the course, the student will master the following skills:

Will acquire a thorough knowledge of methods and results relative to the general problem of the amount and distribution of dark matter in galaxies.
Will be able to apply the Jeans theorem to the constructions of self-consistent collisionless models on the basis of the adopted symmetry of the assumed basic state.
The techniques thus learned, which include also the principles of inversion methods, can also be applied to the study of high temperature plasmas.
Will be able to construct and to physically justify self-consistent models of globular clusters, also in view of non-trivial phenomena, such as the presence of tidal interactions or mass segregation and energy equipartition induced by the cumulative action of weak collisions.
Will be able to compare the models constructed to the observations, either to judge the quality of the models or to measure the mass of the stellar systems under investigation.
Based on the skills developed in the study of elliptical galaxies, will be able to analyze the properties of observations or numerical simulations for stellar systems characterized by a non-trivial distribution of stellar orbits. Furthermore, will be able to use these skills as an interface with complementary studies that involve gravitational lensing or x-ray astronomy.
Course syllabus and organization

Single session

Lesson period
First 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 2 is dedicated to issues pertaining mostly to elliptical galaxies and globular clusters, with a phenomenological introduction devoted to the problem of dark matter.

1. Dark matter. History of the problem. Supermassive central black holes as examples of compact non-visible matter. Clusters of galaxies and the vertical structure of the disk in the solar neighborhood as precursors of the discovery of dark matter. The discovery of dark halos in spiral galaxies from the study of rotation curves. The decisive role of 21cm observations.
The maximum disk hypothesis. Conspiracy and degeneracy. Self-consistent disk-halo decomposition of a rotation curve. Dynamical arguments related to disk stability (Ostriker & Peebles 1973; warps). Modern studies of scaling relations, extraplanar gas, dwarf galaxies, compact dwarfs, ultra-diffuse galaxies, hypervelocity stars, disks of satellites.
2. A short description of fluid ellipsoidal figures of equilibrium. The collisionless nature of large stellar systems. Properties of the collisionless Boltzmann equation. Self-consistency and the Vlasov-Poisson system of equations. The collisionless isothermal slab and the isothermal sphere as local models for stellar systems. Collisionless spherical polytropes.
3. Truncated quasi-isothermal spheres as global models of globular clusters (isotropic, spherical King models). Gravothermal catastrophe. Merits, limits, generalizations of King models. Explicit inclusion of tides, rotation, pressure anisotropy, mass segregation, energy equipartition.
4. Collisionless collapse and incomplete violent relaxation. Dynamical models and physical interpretation of the observed structure of ellipticals (in particular, of the R1/4 law). Stability and radial-orbit instability. Dark matter in ellipticals and in clusters of galaxies. The Fundamental Plane. Galaxies as cosmological probes.
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 pandemic emergency, detailed lecture notes will be distributed one week before the planned lecture.
Teaching Resources
G. Bertin "Dynamics of galaxies", 2nd ed, Cambridge University Press, New York USA (2014)
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