Second cycle degree in ASTRONOMY

Campus: PADOVA

Language: English

Teaching period: Second Semester


Number of ECTS credits allocated: 6

Prerequisites: Basic knowledge of Physics, Astronomy, Astrophysics, and Numerical Analysis.
Examination methods: Oral exam.
Course unit contents: 1. OVERVIEW OF THE PROPERTIES OF GALAXIES. Morphology. Photometry. Kinematics. Scaling relations.

2. POTENTIAL THEORY. Gravitational potential. Poisson’s equation. Laplace’s equation. Gauss’ theorem. Potential energy. Potential energy tensor. Spherical systems. Newton’s theorems. Point mass. Homogeneous sphere. Hubble density profile. Power-law density profile. Axisymmetric systems. Logarithmic potential.

3. THE ORBITS OF THE STARS. Costants and integrals of the motion. Surfaces of section. Orbits in a static spherical potential. Orbits in a Keplerian potential. Orbits in a static axisymmetric potential. Motion in the meridional plane. Nearly circular orbits. Epicyclic approximation. Orbits in a two-dimensional non-axisymmetric non-rotating potential. Loop and box orbits. Stable and unstable orbits. Orbits in a two-dimensional non-axisymmetric rotating potential. Jacobi’s integral. Lagrange’s points. Corotation. Families of orbits x1, x2, x3, x4. Introduction to the orbits in a three-dimensional triaxial potential.

4. COLLISIONLESS SYSTEMS. Geometric collisions. Strong collisions. Weak collisions. Crossing time. Relaxation time. Distribution function. Collisionless Boltzmann equation. Continuity equation. Euler’s equation. Jeans’ equations. Applications of the Jeans’ equations. Velocity ellipsoid. Asymmetric drift. Mass density in the Solar neighborhood. Velocity dispersions in spherical systems. Mass-anisotropy degeneracy. Spheroidal systems with isotropic velocity dispersions. Disk heating mechanisms. Virial theorem. Mass-to-light ratio of spherical systems. Rotation of elliptical galaxies. Jeans’ theorem. Density profile from the distribution function. Spherical systems with isotropic velocity dispersion. Polytropes. Plummer’s sphere. Isothermal sphere. Singular isothermal sphere. King’s radius. King’s method to derive the mass-to-light ratio. King’s models. Tidal radius. Concentration parameter. Distribution function from the density profile. Eddington’s equation. Introduction to spherical systems with anisotropic velocity dispersion. Michie’s models.