Cosmology · Year V · Graduate

8.902 Astrophysics II

Galaxies, cosmology and the growth of structure: how small density ripples grew under gravity, why cold dark matter is needed, the power spectrum, the CMB and the thermal history of dark matter. On this site it supplies the dark matter and structure formation that 8.286 leaves out.

8.902 is a graduate-level course at MIT, usually taken after the bachelor's core (Years I–IV).

Based on MIT OpenCourseWare, Fall 2023 · Prof. Mark Vogelsberger · Course on OCW

Themes

Galaxies

What galaxies look like, how stars move in them, and how they evolve chemically.

Lectures 1, 2, 3, 4, 5, 6, 7, 8, 9

Cosmology

The cosmological principle, the expanding universe and inflation, from the astrophysicist's side.

Lectures 10, 11, 12

Structure formation

How tiny density ripples grow by gravity, why cold dark matter is needed, and how structure is measured.

Lectures 13, 14, 15, 16

The CMB and the early universe

CMB anisotropies, the thermal history of dark matter, nucleosynthesis and the Lyman-alpha forest.

Lectures 17, 18, 19, 20, 21

Lectures (5 of 21 with pages so far)

Lecture 1Key Observations of GalaxiesMIT ↗
Page not written yet
Lecture 2Structure of GalaxiesMIT ↗
Page not written yet
Lecture 3Galaxy RelaxationMIT ↗
Page not written yet
Lecture 4Potential-Density Pairs and OrbitsMIT ↗
Page not written yet
Lecture 5EpicyclesMIT ↗
Page not written yet
Lecture 6Phase-Space Distribution FunctionMIT ↗
Page not written yet
Lecture 7Stability CriteriaMIT ↗
Page not written yet
Lecture 8Stellar and Chemical EvolutionMIT ↗
Page not written yet
Lecture 9G-dwarf Problem and Active GalaxiesMIT ↗
Page not written yet
Lecture 10Cosmological Principle and DynamicsMIT ↗
Page not written yet
Lecture 11Observational CosmologyMIT ↗
Page not written yet
Lecture 12InflationMIT ↗
Page not written yet
Lecture 13Linear Perturbation TheoryMIT ↗
- How small ripples grow — linear perturbation theoryAdd a small density contrast δ to the smooth expanding universe and follow it with the equations of fluid dynamics and gravity. Ripples larger than the Jeans length grow — in proportion to a in the matter era and a² in the radiation era — while smaller ones just oscillate.
Lecture 14Perturbation Growth and Dark Matter vs Baryonic GrowthMIT ↗
- Why structure formation needs cold dark matterOrdinary matter can only start to clump after recombination, and growing in proportion to a from 10⁻⁵ it would reach only about 10⁻² today. Cold dark matter, untouched by radiation pressure and with almost no Jeans mass, gets a head start — and baryons then fall into its wells.
Lecture 15Power SpectrumMIT ↗
- Measuring structure — the power spectrum and the correlation functionThe density field is described statistically. Its power spectrum P(k) says how much fluctuation there is on each scale, and the two-point correlation function ξ(r) — its Fourier transform — says how strongly galaxies cluster. Requiring every mode to enter the horizon with the same strength gives the scale-invariant (Harrison–Zel'dovich) spectrum P ∝ k (n ≈ 1), which the stagnation of early-entering modes bends over at small scales.
Lecture 16Spherical Collapse and the Mass FunctionMIT ↗
- When ripples collapse — the spherical collapse modelLinear theory breaks down once δ approaches 1. Following a single overdense sphere in an Einstein–de Sitter universe shows it expands, turns around and collapses; it has collapsed when the linear theory would give δ ≈ 1.69, and the virialised halo ends up about 178 times denser than the background.
- How many halos? — the Press–Schechter mass functionSmooth the Gaussian density field on the scale of a mass M and ask what fraction of space has a linear density contrast above δ_c ≈ 1.69. Press and Schechter identified that fraction with the mass in halos heavier than M; differentiating it (and fixing a famous factor of two) gives the number of halos of each mass at each redshift.
Lecture 17Anisotropies in the CMBMIT ↗
Page not written yet
Lecture 18Cosmology with the CMBMIT ↗
Page not written yet
Lecture 19Thermal History of Dark MatterMIT ↗
- Where dark matter comes from — freeze-out, hot and coldIn the hot early universe dark matter particles were created and annihilated in equilibrium. As the universe cooled and expanded, annihilations stopped — freeze-out — leaving a fixed relic abundance. Whether the particles were still relativistic then decides between hot dark matter, which erases small structures by free-streaming, and cold dark matter, which builds structure from the bottom up.
Lecture 20Big Bang NucleosynthesisMIT ↗
Page not written yet
Lecture 21Lyman-Alpha ForestMIT ↗
Page not written yet

Note: Source is the course's written lecture notes (one PDF per lecture, numbered equations), not video transcripts. Pages are written lecture by lecture where they add to the cosmology programme; galaxy-dynamics lectures 1–9 are lower priority.