27199 - Dynamics of Stellar Systems

Learning outcomes

Working knowledge of the gravitational phenomena (potential theory, violent relaxation, phase mixing, equilibria, stability, tidal fields, merging, Boltzman and Jeans equations) from open clusters to galaxy clusters scale. Epicyclic theory, introduction to the density wave theory for stellar disks.

Course contents

I] GENERALS
Potential theory and Green fuctions (Cartesian, spherical, and cylindrical coordinates) by means of orthogonal functions. First, second and third Newton theorems. Co-area theorem. Ellipsoidal Coordinates - Gravitational potential of disk galaxies and elliptical galaxies.  Collisionless Boltzmann equation and  Fokker-Planck equation. Jeans equations and the problem of self-consistency.

II] COLLISIONAL SYSTEMS: Gravitational evaporation - gravothermal catastrophe and gravothermal oscillations. Dynamical evolution of globular clusters.    

III] COLLISIONLESS SYSTEMS: Epicyclic approximation and Oort constants. Density waves - Jeans theorem: King models, galaxy models and dark matter halos.

IV] EVOLUTIONARY PHENOMENA: Violent relaxation, phase mixing and gravitational collapse. Tidal fields:  tidal shocks, tidal heating, tidal captures - Dynamical friction - Merging.

Readings/Bibliography

Selected arguments from:

'Dynamics of galaxies' (G. Bertin, Cambridge University Press)
 
'Galactic Dynamics' (J. Binney, S. Tremaine Princeton University Press)

'Galactic Astronomy' (J. Binney, M. Merrifield Princeton  University Press)

'Dynamical evolution of globular clusters' (L. Spitzer Princeton University Press)

'Theory of rotating stars' (J.L. Tassoul, Princeton University Press)

'Lecture notes on stellar dynamics' (L. Ciotti Scuola Normale Superiore Pisa)

Teaching methods

Class lectures, discussion of influential research papers on international journals

Assessment methods

Final oral examination. The examination is 45 minutes long, at the blackboard, organized in 3 sections (each 15 minutes long). In the first part the student illustrates a selected subject (the aim is to verify the presentation abilities of a well studied argument). In the second part the student is asked to solve a simple exercise (test of numerical abilities, and of a back-to-the-envelope estimate). In the third and last part a random argument from the program is discussed (test of the global preparation).

Teaching tools

Lecture notes. Selected chapters from technical books.

Office hours

See the website of Luca Ciotti