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
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.
In-person 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
- 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.
- Orders of magnitudes sheet
- Lecture 1: Overview of clusters across wave bands: optical, X-rays, gravitational lensing
- Lecture 2: Sunyaev-Zel'dovich effect, the growth of perturbations, power spectra
- Lecture 3: Hierarchical structure formation, non-linear 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: Non-thermal processes, magnetic fields
- Lecture 12: Cosmic rays
- Lecture 13: Optical: galaxy interactions and virial theorem
- Lecture 14: X-ray cluster astrophysics and Sunyaev-Zel'dovich effect
- Lecture 15: Radio relics and halos probing shocks and plasma physics, cluster cosmology
- Tutorial: Historical context, superclusters, overview and clarifying questions
- 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
- Non-thermal radio emission
- Origin and transport of magnetic fields, magneto-hydrodynamic 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
- X-ray cluster astrophysics at high-resolution
- 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
- Sunyaev-Zel'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
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.
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.