TÄHT7040 Stellar structure and evolution 8 ECTS
Organised by
Person in charge
Seppo Mattila, Sergey Tsygankov
Planned organizing times
Period(s) I II III IV
2016–2017 X X
Preceding studies

Learning outcomes

At the end of the course, students should be able to:
outline the main observed properties of stars as well as their masses;
use the equation of hydrostatic equilibrium to estimate the core properties of stars;
calculate the dynamical, thermal, and nuclear timescales of stars;
write down the four ordinary differential equations of stellar structure and their boundary conditions;
describe the main nuclear reactions that power high and low mass stars;
demonstrate a basic understanding of energy transport, sources of pressure;
outline the principles of evolution of high and low mass stars from the main sequence to the final stages;
explain how ages of stellar clusters can be measured from HR diagrams;
calculate the Jeans mass and describe the process of star formation;
explain the difference between degenerate and ideal gas;
describe the physics of compact stars and derive the mass-radius relationship for white dwarfs;
discuss the terminal stages of stellar evolution;
describe the main characteristics of different types of supernovae;
apply quantum and classical mechanics, and thermal physics to stellar systems;
describe the main difference between single and binary star evolution;
explain how to measure stellar masses in binary systems;
describe the main characteristics of different classes of white dwarf binary systems;
describe the relation between radio and X-ray pulsars;
develop self-study skills;
solve problems on topics in the syllabus.


Stellar properties, luminosities, masses, temperatures, spectral classes and the HR diagram.
Dimensional analysis: hydrostatic equilibrium, virial theorem, characteristic timescales.
Fundamental equations of stellar structure. Stellar equilibrium. Theory of polytropes.
Thermodynamic properties of matter: ideal gas with radiation, degenerate electron and neutron gases.
Nuclear reactions: mass excess, binding energy, Coulomb barrier, quantum tunneling, Gamow peak, cross-sections and reaction rates. Nucleosynthesis.
Energy transport. Opacity of stellar matter. Convection.
Instabilities and stellar pulsations, the period-luminosity relation, the k-mechanism and the partially ionized regions, Cepheids and RR Lyrae.
Phases of stellar evolution: proto-star, Main Sequence and post-Main Sequence.
Evolution of low-mass stars. AGB stars, planetary nebulae, and formation of white dwarfs.
White dwarf properties, the Chandrasekhar mass, thermonuclear explosions of white dwarfs as Type Ia supernovae.
Evolution of massive stars, supernovae, formation of neutron stars and black holes, gamma-ray bursts. Binary stars, measuring stellar masses.
Cataclysmic variables, polars, intermediate polars.
Low- and high-mass X-ray binaries. Evolution of binary stars.
Radio pulsars, accreting millisecond pulsars, X-ray pulsars.
Stellar-mass black holes in the nearby Universe.
The course contains a number of demanding computer exercises.

Teaching methods

Teaching method Contact Online
Lectures 40 h 0 h
Seminar 16 h 0 h

Homework and computer tasks

Teaching language


Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Participation in classroom work
  • In English
Written exam
  • In English

Minimum 50% of exercises, 50% of computer tasks and the final exam.

Evaluation and evaluation criteria

Numeric 0-5.
Exercises and computer tasks constitute 30% and the exam 70% of the final score.

Recommended year of study

4. year autumn
5. year autumn

MSc-degree students, year 1 or 2

Study materials

Lecture notes.
1. Phillips, A.C.: The Physics of Stars, Manchester Physics Series, 1999
2. Padmanabhan, T.: Theoretical astrophysics, Vol. II: Stars and Stellar Systems, 2001
3. Tayler, R.J.: The Stars: their Structure and Evolution, CUP 1994 (paperback in 2011)
4. Bowers R.L. and Deeming T. (1984), Astrophysics 1 - Stars, Jones and Bartlett, ISBN 0-86720-018-9
5. Prialnik, D., An Introduction to the Theory of Stellar Structure and Evolution, CUP 2000.
6. Karttunen, H. et al., Fundamental Astronomy (chapters 9, 11, and 12.), Springer Verlag, 1993 (2nd Ed.)             
7. Hansen, C.J. and Kawaler, S.D., Stellar Interiors: Physical Principles, Structure, and Evolution, Springer-Verlag 1994. ISBN 0 387 94138 X
8. Kippenhahn, R. and Weigert, A., Stellar Structure and Evolution, Springer-Verlag 1990.  ISBN 3 540 50211 4 

Belongs to following study modules

Department of Physics and Astronomy
Department of Physics and Astronomy
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Department of Physics and Astronomy
Degree Programme in Physical Sciences
DP in Physics Education Track
Degree Programme in Physical Sciences
DP in Theoretical Physics
Finnish Study Modules