Christoph Pfrommer

The Physics of Galaxy Clusters
Clusters of galaxies are the largest and most recently gravitationallycollapsed
objects in the Universe. Hence they provide us the opportunity to study an
"ecosystem"  a volume that is a highdensity 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. Advanced Bachelor students are welcome. The lectures take place every Friday,
9:15am to 11am at the "kleiner Hörsaal" at Philosophenweg 12, starting on October 16,
2015.
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.
Contents:
 Overview and background:
 What is a galaxy cluster? Insights from observations at various wavelengths
 Why are clusters interesting?
Tools for Cosmology and Laboratories for HighEnergy and Plasma Astrophysics
 Evolution of the dark component:
 When do clusters form? ⇒ statistics and power spectra
 Where do cluster form? ⇒ nonlinear evolution
 How do clusters form? ⇒ spherical collapse model
 How many clusters are there? ⇒ PressSchechter mass function
 What is the structure of a cluster? ⇒ halo density profiles, virial masses
 Evolution of the baryonic component:
 Nonradiative 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)
 Nonthermal processes
 Origin and transport of magnetic fields, magnetohydrodynamic 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
 Xrays: gastrophysics at highresolution
 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
 SunyaevZel'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
Homework Assignments
 Assignment 1  Due Nov 20, 2015.
 Assignment 2  Due Dec 11, 2015.
 Assignment 3  Due Jan 29, 2016.
Credit Points:
There won't be exercise classes. Students who wish to obtain credit points are invited to
solve the homework problems and to participate in the final exam. Problem sets will be
assigned every three to four weeks. In the end, there will be an oral or written inclass
exam, depending on the number of participants. A successfull participation of the lectures
is rewarded with two credit points.
Literature:
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, ButterworthHeinemann.
 Shu, F.H.: The Physics of Astrophysics: Gas dynamics, University Science Books.
 Bartelmann, M.: Theoretical Astrophysics: An Introduction, WileyVCH.
