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.
Inperson lecture course
 In this class, we will follow the instructional strategy of a "flipped classroom"
(also called "inverted classroom"), which is a type of blended learning focused on
student engagement and active learning.
 The lecture notes are available as
a PDF file. If you
find any typos or mistakes, please drop me a note.
 There will be weekly reading assignments (see below) and small exercises that help
you to prepare the class for the upcoming week.
 The class will meet in person every Thursday, 16:15 to 17:45 in room 2.28.2.011
(starting October 28, 2021). During the class, we will discuss the topic of the
week, do some order of magnitude problems, and I will show some more lengthy
derivations. Ideally, I would appreciate if you brought a lot of input so that we can
have an active discussion with many questions on our topic of galaxy clusters and
theoretical astrophysics.
Weekly Assignments
 Assignment for lecture 2  due Nov 4, 2021.
 Assignment for lecture 3  due Nov 11, 2021.
 Assignment for lecture 4  due Nov 18, 2021.
 Assignment for lecture 5  due Nov 25, 2021.
 Assignment for lecture 6  due Dec 2, 2021.
 Assignment for lecture 7  due Dec 9, 2021.
 Assignment for lecture 8  due Dec 16, 2021.
 Assignment for lecture 9  due Jan 6, 2022.
 Assignment for lecture 10  due Jan 13, 2022.
 Assignment for lecture 11  due Jan 20, 2022.
 Assignment for lecture 12  due Jan 27, 2022.
 Assignment for lecture 13  due Feb 3, 2022.
 Assignment for lecture 14  due Feb 10, 2022.
 Assignment for lecture 15  due Feb 17, 2022.
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
 Nonthermal radio emission
 Origin and transport of magnetic fields, magnetohydrodynamic turbulence
 Acceleration of cosmic rays (to first and second order), transport equation
 Cluster astrophysics and cosmology:
 Optical: galaxy properties and virial theorem
 Transforming galaxy populations: tidal effects, dynamical friction, ram pressure
 Weighting clusters (1): virial theorem
 Gravitational lensing with clusters
 Deflection angle, lens equation
 Einstein radius, lensing potential
 Weighting clusters (2): strong and weak cluster lensing
 Xray cluster astrophysics at highresolution
 Weighting clusters (3): hydrostatic equilibrium masses (and biases)
 Cluster population and evolution
 Intracluster medium turbulence
 Merger shocks and electron equilibration
 Magnetic draping and cold fronts
 SunyaevZel'dovich (SZ) effect: the thermal energy content
 Thermal, kinetic and relativistic SZ effect
 SZ scaling relation and power spectrum
 SZ effect of AGN bubbles and shocks
 Radio halos and relics: watching shocks and plasma physics at work
 Cluster shocks
 Radio halos and relics
 Radio galaxies and jellyfish tails
 Cluster cosmology
 Cosmological parameter estimates
 How clusters probe cosmology
 Cluster probe the nature of dark matter
Lecture Plan:
 Orders of magnitudes sheet
 Lecture 1: Overview of clusters across wave bands: optical, Xrays, gravitational lensing
 Lecture 2: SunyaevZel'dovich effect, the growth of perturbations, power spectra
 Lecture 3: Hierarchical structure formation, nonlinear evolution, spherical collapse
 Lecture 4: Cluster mass function, halo formation and density profiles
 Lecture 5: Adiabatic processes and entropy, basic conservation equations
 Lecture 6: Buoyancy instabilities, vorticity, turbulence
 Lecture 7: Gravity waves, shocks and jump conditions
 Lecture 8: Turbulent scaling laws, entropy generation by accretion, cluster scaling relations
 Lecture 9: Radiative cooling and heating, feedback by supernovae and AGNs
 Lecture 10: Heat conduction, thermal instability
 Lecture 11: Nonthermal processes, magnetic fields
 Lecture 12: Cosmic rays
 Lecture 13: Optical: galaxy interactions and virial theorem
 Lecture 14: Xray cluster astrophysics and SunyaevZel'dovich effect
 Lecture 15: Radio relics and halos probing shocks and plasma physics, cluster cosmology
 Tutorial: Historical context, superclusters, overview and clarifying questions
Credit Points:
Students who wish to obtain credit points are invited to prepare the lectures by reading
and working through the weekly assigments posted on this web site. Those include
comprehension questions, order of magnitude problems and from time to time quantitative
homework problems. We will discuss the solution to these questions and problems in
class. In the end, there will be an oral exam of 20 to 30 min. 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.
