The Final exam will be held on Friday, April 29, 2022, at 9.15-12.15 in L9.

Questions for the exam: [PDF]




an advanced course (10 credits)

at the Space Physics and Astronomy research unit, University of Oulu

The course period: January 10 – April 29, 2022

Lectures take place usually on Monday and Wednesday at 14-16, exercise and practical sessions on Friday at 10-12, see Peppi for detail. However, classes on Friday will only occur when I announce them!

The course is lectured in English

Teacher: Vitaly Neustroev, MA 308, vitaly[-at-]



Course plan:

  • Stellar structure and evolution
  • Radiative processes
  • Stellar photospheres
  • Interstellar Medium
  • etc…

Theoretical and practical considerations will be supplemented with the home exercises which constitute the important part of the course.



Textbook choice for this course is largely a matter of personal taste. I provide below a list of recommended books. Study them in parallel with the lectures.


Compulsory problems (return by the deadline). 5+ sets (30% of the final score).



  • Lecture 1: January 10: Introduction (What is Astrophysics and Theoretical Astrophysics? Astronomical units)
  • Lecture 2: January 12: Stars (Role of stars; Definition; What can we learn from observations? Properties of stars; Stellar timeline)
  • January 14: NO CLASS
  • Lecture 3: January 17: Stars (basic assumptions, mass conservation, hydrostatic equilibrium, virial theorem)
  • Lecture 4: January 19: Stars (Timescales of stellar evolution. Conditions in stellar interiors)
    PDF (Updated on 24.01.2022)
  • January 21: NO CLASS
  • Lecture 5: January 24: Stars (Energy generation. The equation of conservation of energy)
  • Lecture 6: January 26: Basics about radiative transfer (Radiation terms, specific intensity, interaction radiation – matter, parallel-ray radiative transfer equation)
    PDF (Updated on 31.01.2022)
  • January 28: NO CLASS
  • Lecture 7: January 31: Basics about radiative transfer (solution of the parallel-ray RTE, Mean Intensity, Flux, and K-integral, stellar magnitudes)
  • Lecture 8: February 2: Basics about radiative transfer (RTE in plane-parallel atmosphere. The equations of stellar structure and possible ways to solve them. Boundary conditions. Convection and conditions for its occurrence.)
    Compulsory problems: [Set 1] (return by February 9).
  • February 4: NO CLASS
  • Lecture 9: February 7: The equations of stellar structure (equation of state – EOS, stellar opacity)
  • Lecture 10: February 9: Nuclear Energy Production (Basics on nuclear reactions, the binding energy, Quantum tunnelling, Reaction cross-section, the Gamow peak, Nuclear Reaction Rates, Electron shielding)
    PDF (Updated on 14.02.2022)
  • February 11: NO CLASS
  • Lecture 11: February 14: Nuclear reactions in stellar interiors (Energy generation, PP-chains & CNO-cycle, Helium burning, Carbon burning and beyond, iron and heavier elements, Composition changes)
  • Lecture 12: February 16: Solution of the Equations of Stellar Structure (The stellar structure equations and how to solve them? Simple stellar models. Polytropic models. Lane-emden equation. Different relationships for polytropic stars. Chandrasekhar mass. Dynamical stability of stars)
    PDF (Updated on 21.02.2022)
  • February 18: NO CLASS
  • Lecture 13: February 21: Schematic stellar evolution
    Compulsory problems: [Set 2] (return by March 1).
  • Lecture 14: February 23: Star formation
  • February 25: NO CLASS
  • Lecture 15: February 28: Identification of Young Stars. Pre-main sequence star evolution (the Hayashi track and the Henyey track). Main Sequence stars.
    PDF (Updated on 2.03.2022)
  • Lecture 16: March 2: Main Sequence stars (cont). Evolution of low-mass and high-mass stars. The initial mass function.
    PDF (Updated on 19.04.2022)
  • March 4: Mid-term exam
  • Lecture 17: March 14: What is a stellar atmosphere? Why should we care about it? What can we learn from observations?
  • Lecture 18: March 16:Radiative transfer (Radiative transfer equation in plane-parallel atmosphere. Limb darkening), Solution to transfer equation, Eddington-Barbier relation. Grey atmosphere. Radiative equilibrium. The depth dependence of the source function. Eddington approximation. Temperature structure of the grey atmosphere.
  • Lecture 19: March 21: LTE (Maxwellian distribution in velocities, Boltzmann equation, Saha formula).
  • Compulsory problems: [Set 3] (return by March 28).

  • Lecture 20: March 23: Stellar Opacity (Bound-bound, bound-free and free-free absorptions). Negative hydrogen ion H as the sources of opacity.
    PDF (Updated on 28.03.2022)
  • Compulsory problems: [Set 4] (return by March 30).

  • Lecture 21: March 28: Other sources of opacity (He and Metallic absorptions, Scattering, Effect of nongreyness of the temperature structure, Balmer jump).
  • Lecture 22: March 30: Spectral lines (Equivalent Width, FWHM, FWZI, Radial Velocity). Spectral line formation (Einstein coefficients. Natural Line Width, Natural broadening, Doppler broadening).
    PDF * Homework: slide 22
  • Lecture 23: April 4: Spectral line formation (Natural broadening, Doppler broadening, Pressure broadening, Convolution of different broadening processes, Ingis-Teller relation, Rotational and Instrumental broadening).
  • Lecture 24: April 6: Simple line transfer, Schuster-Schwarzschild model, Theory of line formation, Curve of Growth. Scattering in lines, Transfer Equation including lines, The Milne-Eddington model, Residual flux of the line, Absorption and scattering lines, Schuster Mechanism for Line Emission.
  • Lecture 25: April 11: Non-LTE (Statistical equilibrium, Two-level approximation, the line source function, LTE versus non-LTE). Spectral type sequence. Towards the Model Photosphere (Hydrostatic equilibrium, Gas Pressure, Electron Pressure).
  • Compulsory problems: [Set 5] (return by April 20).

  • Lecture 26: April 13: Radiation Pressure. Eddington limit. Measuring temperatures and surface gravities (Direct measurement of radii. Determining teff and surface gravity, Model-independent methods, Model-dependent methods, Atmospheric models, Photometric methods, Spectroscopic methods).
    PDF * Spectral classification
  • Lecture 27: April 20: A short introduction to the Interstellar Medium.
  • Lecture 28: April 22: ISM: Ionized regions. Strömgren Spheres.