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    The Physics of Galaxy Clusters

    Clusters of galaxies are the largest and most recently gravitationally-collapsed objects in the Universe. Hence they provide us the opportunity to study an "ecosystem" - a volume that is a high-density microcosm of the rest of the Universe. Clusters are excellent laboratories for studying the rich astrophysics of baryons and dark matter. At the same time, they are extremely rare events, forming at sites of constructive interference of long waves in the primordial density fluctuations. Hence, they are very sensitive tracers of the growth of structure in the universe and the cosmological parameters governing it, which puts them into focus of constraining the properties of Dark Energy or to test whether our understanding of gravity is complete.

    These lectures will explain how clusters form and grow. We will encounter the rich and interesting astrophysics that governs the physics of dark matter and baryons in clusters. We will see how we can take advantage of these physical processes to observe clusters and deepen our understanding of the underlying fundamental physics. To this end we will frequently use the powerful technique of order of magnitude estimates, a very useful tool for contemporary research in astrophysics. The lectures aim at students who

    • wish to extend and deepen their understanding of theoretical physics;
    • are interested in astronomy and astrophysics; or
    • (intend to) carry out a masters thesis or Ph.D. dissertation on an astronomical or astrophysical subject.

    The lectures will be held in English because they are part of the Masters programme. The lectures take place every Tuesday, 14:15 to 15:45 at the seminar room 28.2.123 in the physics building, Karl-Liebknecht-Strasse 24/25, Potsdam/Golm, starting on October 17, 2017.

    I am currently in the process of writing lecture notes in LaTeX. The (still incomplete) manuscript is available as a PDF file. If you find any typos or mistakes, please drop me a note.


    • Overview and background:
      • What is a galaxy cluster? Insights from observations at various wavelengths
      • Why are clusters interesting?
        Tools for Cosmology and Laboratories for High-Energy and Plasma Astrophysics

    • Evolution of the dark component:
      • When do clusters form? ⇒ statistics and power spectra
      • Where do cluster form? ⇒ non-linear evolution
      • How do clusters form? ⇒ spherical collapse model
      • How many clusters are there? ⇒ Press-Schechter mass function
      • What is the structure of a cluster? ⇒ halo density profiles, virial masses

    • Evolution of the baryonic component:
      • Non-radiative physics
        • Adiabatic Processes and Entropy
        • Basic Conservation Equations
        • Buoyancy Instabilities
        • Vorticity and Turbulence
        • Shocks and jump conditions
        • Entropy generation by accretion and hierarchical merging
        • Scaling relations (ideal and real)

      • Radiative physics
        • Radiative cooling and star formation
        • Energy feedback (supernovae, active galactic nuclei)
        • Transport processes of gas:
          conduction, thermal stability (without and with magnetic fields)

      • Non-thermal processes
        • Origin and transport of magnetic fields, magneto-hydrodynamic turbulence
        • Acceleration of cosmic rays (to first and second order), transport equation

    • Cluster physics informed by different observables:
      • Optical: galaxy properties and virial theorem
        • Transforming galaxy populations: ram pressure, tidal effects, dynamical friction
        • Weighting clusters (1): virial theorem

      • Gravitational lensing
        • Deflection angle, lens equation, Einstein radius, lensing potential
        • Weighting clusters (2): strong and weak cluster lensing

      • X-rays: gastrophysics at high-resolution
        • Weighting clusters (3): hydrostatic equilibrium masses (and biases)
        • Kinematics of shocks and cold fronts
        • Probing kinetic equilibrium with collisionless shocks
        • Width of cold fronts - magnetic draping

      • Sunyaev-Zel'dovich (SZ) effect: the thermal energy content
        • Thermal and kinetic SZ effect
        • Properties and SZ scaling relation, SZ power spectrum

      • Radio halos and relics: watching powerful shocks and plasma physics at work


    1. Introduction to galaxy clusters on Nov 14.

    Homework Assignments

    1. Assignment 1 - Due Nov 28, 2017.
    2. Assignment 2 - Due Dec 19, 2017.
    3. Assignment 3 - Due Feb 6, 2018.


    Unfortunately, there does not exist a perfect book on this topic. Hence I decided to provide lecture notes in LaTeX form that I will finalize throughout the course. Here is a selection of books that I found quite useful if you want to extend your knowledge about processs that we encounter during the lectures:

    • Overview and Review Article:
    • Background on Cosmology:
      • Bartelmann, M.: Lectures on Cosmology
      • Peacock, J.: Cosmological physics, Cambridge University Press.
      • Peebles, P.J.E.: Principles of physical cosmology, Princeton University Press.
      • Padmanabhan, T.: Structure formation in the universe, Cambridge University Press.

    • Theoretical Physics and Astrophysics:
      • Thorne, K.S. & Blandford R.D.: Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics, Caltech lecture notes for download, textbook available from Princeton University Press.
      • Landau L.D. & Lifshitz E.M.: Course of Theoretical Physics, Volumes 1, 2, 5, 6, 8, Butterworth-Heinemann.
      • Shu, F.H.: The Physics of Astrophysics: Gas dynamics, University Science Books.
      • Bartelmann, M.: Theoretical Astrophysics: An Introduction, Wiley-VCH.