HUOM! OPINTOJAKSOJEN TIETOJEN TÄYTTÄMISTÄ KOORDINOIVAT KOULUTUSSUUNNITTELIJAT HANNA-MARI PEURALA JA TIINA HASARI

### 1. Course title

Galaksien dynamiikka

Galaxdynamik

Galactic dynamics

2. Course code

PAP317

Aikaisemmat leikkaavat opintojaksot 53918 Dynamiikan jatkokurssi tähtitieteessä, 5 op

3. Course status: optional

*-Which degree programme is responsible for the course?*Master’s Programme in Particle Physics and Astrophysical Sciences

*-Which module does the course belong to?*

PAP3001 Advanced Studies in Astrophysical Sciences (optional forStudy Track in Astrophysical Sciences)

*-Is the course available to students from other degree programmes?*Yes

4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)

Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle

degree/EQF level 7

Doctoral level = third-cycle (doctoral) degree/EQF level 8

*-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree**on University Degrees)?*Advanced studies

5. Recommended time/stage of studies for completion

This course is lectured every two years, so the student should take it when it is on offer.

6. Term/teaching period when the course will be offered

This course will be offered in the Spring semester, periods 3-4, every two years. The course will be

lectured odd years, next time in the Autumn of 2023.

### 7. Scope of the course in credits

5 cr

### 8. Teacher coordinating the course

Peter Johansson

### 9. Course learning outcomes

The student will be able to calculate the relaxation and dynamical timescales for galaxies. The student will be able to calculate the gravitational potential for spherical and flattened systems. The student will understand the basic principles of direct summation codes, tree codes and particle-mesh codes used to perform numerical galaxy formation simulations. The student will be able to describe the orbits of stars in spherical, axisymmetric and simple non-axisymmetric potentials. The student will understand the how the Boltzmann and Jeans equations can be used in galaxy dynamics. The student will be able to calculate the distribution functions for isotropic spherical systems. The student will be able to derive the tensor virial theorem. The student will

understand the principles of relaxation processes in galaxies. The student will understand the principles underlying linear response theory and the disk dynamics of spiral galaxies. The student will understand kinetic theory and the thermodynamics of self-gravitating systems.

The student will be able to derive the formula for dynamical friction and understand its application. The student will understand the importance of galaxy mergers for galaxy evolution.

10. Course completion methods

The course is completed by handing in written problem sets every two weeks. The problem sets consist of mathematical galactic dynamics problems that need to be solved. At the end of the course there is a final exam.

11. Prerequisites

Galaxies and Cosmology and Celestial Mechanics. The basic- and intermediate-level courses of Astronomy as well as Analytical Mechanics and FYMM I-II of Theoretical Physics are also strongly recommended.

12. Recommended optional studies

The course is primarily linked together with Galaxy Formation and Evolution. Also Cosmology I-II and observational extragalactic courses could serve as optional studies.

13. Course content

Galactic dynamics is an integral part of modern theoretical astrophysics. The course follows the outline of the second edition of the classic text "Galactic Dynamics" by Binney & Tremaine (2008).

We begin with a general overview of galaxies, their properties and classification followed by a discussion of relaxation and dynamical timescales. After this we discuss potential theory, how to compute the gravitational potential of galaxies and how to describe galaxies using spherical and flattened density distributions. Then orbit theory is discussed, specifically what kinds of orbits are possible in galaxies described by a spherically symmetric, or an axially symmetric potential. This followed by a discussion on numerical orbit integration and a derivation of the collisionless Boltzmann equation.

In the second part of the course we will cover the equilibria of collisionless systems and derive the distribution functions for isotropic spherical systems. We then introduce the Jeans and virial equations and discuss how they can be used to detect black holes and dark matter haloes in galaxies using observations of the kinematics of their stars. Next we discuss the stability of collisionless systems and the dynamics of disk galaxies. This is followed by a discussion on kinetic theory and the thermodynamics of self-gravitating systems. We end the course with a discussion on dynamical friction and its applications and describe the related concepts of galaxy interactions and mergers.

14. Recommended and required literature

Course homepage: https://wiki.helsinki.fi/display/astjourn/Galactic+dynamics

The course will use chapters from the book:

J. Binney, S. Tremaine, Galactic Dynamics, 2nd Ed., Princeton University Press, 2008.

In addition handwritten lecture notes by the lecturer will be provided.

Additional material:

Sparke & Gallagher: Galaxies in the Universe, 2nd Ed., Cambridge Univ Press, 2007.

Bertin: Dynamics of Galaxies, Cambridge Univ Press, 2000.

Binney & Merrifield: Galactic Astronomy, Princeton Univ Press, 1998.

15. Activities and teaching methods in support of learning

Two hours of weekly lectures and written problem sets every two weeks. The problem set session will led by the course assistant and there

the correct solutions will be discussed and presented.

16. Assessment practices and criteria, grading scale

To pass with a grade 1/5 requires 43.3% of the maximum exam points, for the highest grade 5/5 the requirement is 86.7% of the maximum exam points. The maximum points from the final exam is 30 and an additional 6 points can be acquired from the problem sets. Additional points are only awarded for problem set points that exceed the minimum level of one third, which is required in order to have the right to take part in the final exam.

### 17. Teaching language

English