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.
Online course because of the corona pandemics
 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, which should hopefully allow differentiated
learning styles during onlineclass time.
 I will provide you with my lecture notes in LaTeX. The manuscript will be finalized
in the upcoming weeks and is 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 on zoom every Tuesday, 12:15 to 13:45 starting April 21,
2020. Please drop me an email to obtain the zoom code and password! 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. I have never done such an online class
before, so I hope you can provide me with feedback on what works and what does not so
that we can improve together and make this class a success for you!
Weekly Assignments
 Send me an email to get the zoom access code for class on April 21, 2020.
 Assignment for lecture 2  due April 28, 2020.
 Assignment for lecture 3  due May 5, 2020.
 Assignment for lecture 4  due May 12, 2020.
 Assignment for lecture 5  due May 19, 2020.
 Assignment for lecture 6  due May 26, 2020.
 Assignment for lecture 7  due June 2, 2020.
 Assignment for lecture 8  due June 9, 2020.
 Assignment for lecture 9  due June 16, 2020.
 Assignment for lecture 10  due June 23, 2020.
 Assignment for lecture 11  due June 30, 2020.
 Assignment for lecture 12  due July 7, 2020.
 Assignment for lecture 13  due July 21, 2020.
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
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.
