an advanced course (10 credits)

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

The course period: January 10 – April 26, 2024

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

The course is lectured in English

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



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.



  • Lecture 1: January 10: Introduction (What is Astrophysics and Theoretical Astrophysics? Astronomical units). Stars (Role of stars; Definition; What can we learn from observations?).
  • Lecture 2: January 11: Stars (Properties of stars; Stellar timeline; basic assumptions, mass conservation, hydrostatic equilibrium).
  • January 15: NO CLASS
  • January 17: NO CLASS
  • Lecture 3: January 18: Stars (Virial theorem. Timescales of stellar evolution. Conditions in stellar interiors).
  • Lecture 4: January 22: Stars (Energy generation. The equation of conservation of energy). Basics about radiative transfer (Specific intensity).
    Compulsory problems: Set 1 (return by January 29).
  • Lecture 5: January 24: Basics about radiative transfer (Radiation terms, specific intensity, interaction radiation – matter, parallel-ray radiative transfer equation, solution of the parallel-ray RTE)
  • January 25: NO CLASS
  • Lecture 6: January 29: Basics about radiative transfer (Mean Intensity, Flux, and K-integral. RTE in plane-parallel atmosphere. The temperature gradient for radiative transport).
  • Lecture 7: January 31: The equations of stellar structure and possible ways to solve them. Boundary conditions. Convection and conditions for its occurrence. Equation of state (EOS).
  • February 1: NO CLASS
  • Lecture 8: February 5: Solution of HW1. Lecture: the equations of stellar structure (EOS, degeneracy pressure, stellar opacity)
  • Lecture 9: February 7: Nuclear Energy Production (Basics on nuclear reactions, the binding energy, Quantum tunnelling, Reaction cross-section, the Gamow peak, Nuclear Reaction Rates, Electron shielding)
    Compulsory problems: Set 2 (return by February 19).
  • Lecture 10: February 12: Nuclear reactions in stellar interiors (Energy generation, PP-chains & CNO-cycle, Helium burning, Carbon burning and beyond, iron and heavier elements, Composition changes)
  • Lecture 11: February 14: 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 15.02.2024)
  • Lecture 12: February 15: Stellar evolution codes. Schematic stellar evolution. Star formation.
    PDF * EZ-Web
  • Lecture 13: February 21: Star formation (cont). Identification of Young Stars. Pre-main sequence star evolution (the Hayashi track and the Henyey track).
  • Lecture 14: February 22: Main Sequence stars. Evolution of low-mass stars.
  • Lecture 15: February 26: Evolution of high-mass stars. The initial mass function. Solution of HW2.
  • February 28: Mid-term exam
  • Lecture 16: February 29: The end point: stellar remnants. White dwarfs, Supernovae, Neutron stars, Black holes.
  • Lecture 17: March 11: What is a stellar atmosphere? Why should we care about it? What can we learn from observations? Radiative transfer (Radiative transfer equation in plane-parallel atmosphere. Limb darkening).
  • Lecture 18: March 13:Limb darkening (cont.), Solution to transfer equation, Eddington-Barbier relation. Grey atmosphere. Radiative equilibrium.
  • Lecture 19: March 18: The depth dependence of the source function. Eddington approximation. Temperature structure of the grey atmosphere. LTE (Maxwellian distribution in velocities, Boltzmann equation, Saha formula).
    PDF (Updated on 21.03.2024)
    Compulsory problems: Set 3 (return by March 25).
  • Lecture 20: March 20: Stellar Opacity (Bound-bound, bound-free and free-free absorptions).
    Compulsory problems: Set 4 (return by April 3).
  • Lecture 21: March 25: Lyman edge and Balmer jump. Negative hydrogen ion H as the sources of opacity. Other sources of opacity (He and Metallic absorptions, Scattering, Effect of nongreyness of the temperature structure, Balmer jump).
  • Lecture 22: March 27: Spectral lines (Equivalent Width, FWHM, FWZI, Radial Velocity). Spectral line formation (Einstein coefficients. Natural Line Width, Natural broadening, Doppler broadening).
    PDF * Homework: slide 192
  • Lecture 23: March 28: Spectral line formation (Convolution of different broadening processes, Pressure broadening, Ingis-Teller relation, Rotational and Instrumental broadening).
  • Lecture 24: April 4: 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 8: Non-LTE (Statistical equilibrium, Two-level approximation, the line source function, LTE versus non-LTE). Spectral type sequence.
    Compulsory problems: Set 5 (return by April 15).
  • Lecture 26: April 10: Towards the Model Photosphere (Hydrostatic equilibrium. Gas and electron pressure). 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 15: A short introduction to the Interstellar Medium (ISM).
  • Lecture 28: April 17: ISM: Interstellar Absorption Lines and DIBs. 21 cm hydrogen line. Ionized regions. Strömgren Spheres.