Skip to article frontmatterSkip to article content
Site not loading correctly?

This may be due to an incorrect BASE_URL configuration. See the MyST Documentation for reference.

Week 4: Dark Matter Halos and Equilibria of Collisionless Systems

Reading

Note: you will need to install galpy on your computer for the numerical exercise. You can do it from your rebound virtual environment with pip install galpy.

Reading questions

  1. What is the difference between collisionless and collisional systems?

  2. (a) What are the relaxation time and dynamical time of a galaxy? (b) How can one argue that galaxies are collisionless, by comparing their two-body relaxation time with the age of the Universe?

  3. (a) What’s the assumption required for dynamical equilibrium, based on the virial theorem? (b) Under this assumption, what is the relation between kinetic and potential energy?

  4. What is the collisionless Boltzmann equation?

  5. What are the Jeans equations, and what applicability do they have for studying astronomical systems of many objects?

  6. How can one physically interpret different values of the orbital anisotropy of a galaxy?

  7. How can astronomical observations and the Jeans equation be used to constrain dark matter halos influences?

Answers to these questions should be submitted to your github repository before class on Monday.

Week 3: Tides, Rotation and Shape; Resonant Perturbations
Week 3 Part 2 Solutions
Week 4: Dark Matter Halos and Equilibria of Collisionless Systems
Week 4 Exercise