An Introduction to Theoretical Astrophysics
Oral Examination
Preparation Dossier
Reverse-engineered exam strategy · core derivations · scaling relations
order-of-magnitude estimates · mock oral examinations
Module PH2080 — 5 CP, summer semester 2026
Format 30-minute oral examination
Scope gravitating systems, stellar structure, compact objects,
hydrodynamics & shocks, radiative transfer, equations of state
Method predictive reconstruction of examiner style & expectations
A self-study dossier. Worked derivations are complete and untruncated; numerical estimates are carried out explicitly so
they can be reproduced under exam conditions. Symbols “J” and “S” in the mock examinations denote examiner and
student respectively.
,Theoretical Astrophysics — Oral Preparation PH2080 (2026s)
Contents
1 How to use this dossier 3
2 Part I — Reverse-engineering the examination 3
2.1 The 30-minute format, decoded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Probability-ranked topic map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 The master keys: concepts that connect every chapter . . . . . . . . . . . . . . . . . . 5
2.4 Formulas to own cold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.5 Janka’s questioning behaviour and follow-up patterns . . . . . . . . . . . . . . . . . . 6
3 Part II — Core physics by learning outcome 7
3.1 Cosmic structures and their characteristic numbers . . . . . . . . . . . . . . . . . . . 7
3.2 Gravitating dynamics and the virial theorem . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.1 Two-body problem and Kepler . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.2 The virial theorem — derivation . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.3 Timescales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.4 Gravitational instability: the Jeans scale . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Mass determination and dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3.1 Flat rotation curves and the dark halo . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 The equations of stellar structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4.1 Hydrostatic equilibrium — derivation and the central-pressure estimate . . . 10
3.4.2 The stellar virial theorem and Kelvin–Helmholtz contraction . . . . . . . . . . 11
3.5 Degenerate matter, white dwarfs and the Chandrasekhar mass . . . . . . . . . . . . . 11
3.5.1 Why degeneracy pressure exists and why it is temperature-independent . . . 11
3.5.2 The two pressure laws — scaling derivation . . . . . . . . . . . . . . . . . . . 11
3.5.3 White-dwarf mass–radius relation . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5.4 The Chandrasekhar mass — full derivation . . . . . . . . . . . . . . . . . . . . 12
3.5.5 Stability and the role of γ = 4/3 . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.6 Stellar evolution and scaling relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.6.1 The mass–luminosity relation — derivation . . . . . . . . . . . . . . . . . . . . 13
3.6.2 Main-sequence lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.7 Accretion physics and the Eddington luminosity . . . . . . . . . . . . . . . . . . . . . 13
3.7.1 Accretion luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.7.2 The Eddington luminosity — derivation . . . . . . . . . . . . . . . . . . . . . . 14
3.8 Hydrodynamics, shocks, discontinuities and the Sedov solution . . . . . . . . . . . . 14
3.8.1 The Euler equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.8.2 Discontinuities: shocks versus contact discontinuities . . . . . . . . . . . . . . 15
3.8.3 Strong-shock jump conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.8.4 Why shocks form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1
, Theoretical Astrophysics — Oral Preparation PH2080 (2026s)
3.8.5 The Sedov–Taylor blast wave — dimensional derivation . . . . . . . . . . . . 15
3.9 Radiative transfer, the diffusion approximation and radiation pressure . . . . . . . . 16
3.9.1 The transfer equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.9.2 Deriving the diffusion equation — two routes . . . . . . . . . . . . . . . . . . 16
3.9.3 Radiation pressure and the gas/radiation balance . . . . . . . . . . . . . . . . 17
3.10 Equations of state, degenerate matter and astrophysical plasmas . . . . . . . . . . . . 17
3.10.1 The four pressure sources and the ρ–T plane . . . . . . . . . . . . . . . . . . . 17
3.10.2 Astrophysical plasmas and the mean molecular weight . . . . . . . . . . . . . 17
3.10.3 Neutrinos in dense, hot matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Part III — Mock Oral Examinations 18
5 Part IV — High-Yield Compilation 25
5.1 Topics ranked by probability of appearing . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2 Most likely questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3 Formulas to know cold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.4 Conceptual traps (consolidated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.5 Examiner follow-ups that recur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6 Part V — The Ultimate 30-Minute Simulation 28
2
Oral Examination
Preparation Dossier
Reverse-engineered exam strategy · core derivations · scaling relations
order-of-magnitude estimates · mock oral examinations
Module PH2080 — 5 CP, summer semester 2026
Format 30-minute oral examination
Scope gravitating systems, stellar structure, compact objects,
hydrodynamics & shocks, radiative transfer, equations of state
Method predictive reconstruction of examiner style & expectations
A self-study dossier. Worked derivations are complete and untruncated; numerical estimates are carried out explicitly so
they can be reproduced under exam conditions. Symbols “J” and “S” in the mock examinations denote examiner and
student respectively.
,Theoretical Astrophysics — Oral Preparation PH2080 (2026s)
Contents
1 How to use this dossier 3
2 Part I — Reverse-engineering the examination 3
2.1 The 30-minute format, decoded . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Probability-ranked topic map . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 The master keys: concepts that connect every chapter . . . . . . . . . . . . . . . . . . 5
2.4 Formulas to own cold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.5 Janka’s questioning behaviour and follow-up patterns . . . . . . . . . . . . . . . . . . 6
3 Part II — Core physics by learning outcome 7
3.1 Cosmic structures and their characteristic numbers . . . . . . . . . . . . . . . . . . . 7
3.2 Gravitating dynamics and the virial theorem . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.1 Two-body problem and Kepler . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.2 The virial theorem — derivation . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.3 Timescales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2.4 Gravitational instability: the Jeans scale . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Mass determination and dark matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3.1 Flat rotation curves and the dark halo . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 The equations of stellar structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4.1 Hydrostatic equilibrium — derivation and the central-pressure estimate . . . 10
3.4.2 The stellar virial theorem and Kelvin–Helmholtz contraction . . . . . . . . . . 11
3.5 Degenerate matter, white dwarfs and the Chandrasekhar mass . . . . . . . . . . . . . 11
3.5.1 Why degeneracy pressure exists and why it is temperature-independent . . . 11
3.5.2 The two pressure laws — scaling derivation . . . . . . . . . . . . . . . . . . . 11
3.5.3 White-dwarf mass–radius relation . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.5.4 The Chandrasekhar mass — full derivation . . . . . . . . . . . . . . . . . . . . 12
3.5.5 Stability and the role of γ = 4/3 . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3.6 Stellar evolution and scaling relations . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.6.1 The mass–luminosity relation — derivation . . . . . . . . . . . . . . . . . . . . 13
3.6.2 Main-sequence lifetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.7 Accretion physics and the Eddington luminosity . . . . . . . . . . . . . . . . . . . . . 13
3.7.1 Accretion luminosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.7.2 The Eddington luminosity — derivation . . . . . . . . . . . . . . . . . . . . . . 14
3.8 Hydrodynamics, shocks, discontinuities and the Sedov solution . . . . . . . . . . . . 14
3.8.1 The Euler equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.8.2 Discontinuities: shocks versus contact discontinuities . . . . . . . . . . . . . . 15
3.8.3 Strong-shock jump conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.8.4 Why shocks form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1
, Theoretical Astrophysics — Oral Preparation PH2080 (2026s)
3.8.5 The Sedov–Taylor blast wave — dimensional derivation . . . . . . . . . . . . 15
3.9 Radiative transfer, the diffusion approximation and radiation pressure . . . . . . . . 16
3.9.1 The transfer equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.9.2 Deriving the diffusion equation — two routes . . . . . . . . . . . . . . . . . . 16
3.9.3 Radiation pressure and the gas/radiation balance . . . . . . . . . . . . . . . . 17
3.10 Equations of state, degenerate matter and astrophysical plasmas . . . . . . . . . . . . 17
3.10.1 The four pressure sources and the ρ–T plane . . . . . . . . . . . . . . . . . . . 17
3.10.2 Astrophysical plasmas and the mean molecular weight . . . . . . . . . . . . . 17
3.10.3 Neutrinos in dense, hot matter . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4 Part III — Mock Oral Examinations 18
5 Part IV — High-Yield Compilation 25
5.1 Topics ranked by probability of appearing . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2 Most likely questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3 Formulas to know cold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.4 Conceptual traps (consolidated) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
5.5 Examiner follow-ups that recur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6 Part V — The Ultimate 30-Minute Simulation 28
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