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.
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, questions on the content (see below) and exercises that help
you to prepare the class for the upcoming week. Please upload your answers to
this moodle
page (reading assignment questions weekly, exercises biweekly).
 The class meets in person every Wednesday, 14:15  15:45 in room 2.28.2.011
(starting October 18, 2023) and the exercises take place every second Thursday,
16:15  17:45 in room 2.24.0.29 (starting October 19, 2023). 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 Oct 24, 202.
 Assignment for lecture 3  due Oct 31, 2023.
 Assignment for lecture 4  due Nov 7, 2023.
 Assignment for lecture 5  due Nov 14, 2023.
 Assignment for lecture 6  due Nov 21, 2023.
 Assignment for lecture 7  due Nov 28, 2023.
 Assignment for lecture 8  due Dec 5, 2023.
 Assignment for lecture 9  due Dec 12, 2023.
 Assignment for lecture 10  due Dec 19, 2023.
 Assignment for lecture 11  due Jan 9, 2024.
 Assignment for lecture 12  due Jan 16, 2024
 Assignment for lecture 13  due Jan 23, 2024.
 Assignment for lecture 14  due Jan 30, 2024.
 Assignment for lecture 15  due Feb 6, 2024.
Exercises
 Exercise 1  due Oct 31, 2023.
 Exercise 2  due Nov 14, 2023.
 Exercise 3  due Nov 28, 2023.
 Exercise 4  due Dec 12, 2023.
 Exercise 5  due Jan 9, 2024.
 Exercise 6  due Jan 23, 2024.
 Exercise 7  due Feb 6, 2024.
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: Shocks and jump conditions

Lecture 8: 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 and doing the
exercises. Those include comprehension questions, order of magnitude problems and
quantitative homework problems. You need to achieve 50% of the points to be admitted to an
oral exam of 20 to 30 min at the end of the lecture course. 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.
