Course required for degree Diploma in Astrophysics
VII Semester 2+2, VIII Semester 2+2

Subject, Problems and Methods in Stellar Astronomy. Observed Characteristics of Stars. Time Dependence of Characteristics.

Distribution Functions and Some of their Characteristics. Univariate and Multivariate Distributions. Transformation of Variables. Problems in the Statistical Description of the Galactic System. Apparent Magnitude and Absolute Magnitude Distributions. The Total Number of Stars. Integral Equations of Stellar Statistics. Basic Equations in an Absolutely Transparent Medium. The Normal Form. General Solution of the Space Density Function. Analytical and Numerical Methods in Finding the Solution. Interstellar Absorption Low in Continuous and Discontinuous Medium. Effect of Interstellar Absorption on the Space Density Function. Fluctuations of the Apparent Luminosity of the Galactic Field - Basic Equation, the Equation for Moments of the Differential Luminosity Function.

Relationships between Observational and Descriptive Kinematic Characteristics. Transformations of Coordinate Frames. Local Centroid and Residual Velocities. Local Solar Motion in the Galaxy - Determination of the Motion Elements from Radial Velocities, Determination of the Solar Apex from Annual Proper Motions. Statistical Parallaxes. Tau and Nu Components of Annual Proper Motions. Mean Annual Parallaxes from Tau and Nu Components. Residual Velocity Distribution - Spherical Distribution, Two Star Stream Hypothesis, Ellipsoidal Distribution. Quadratic Form Transformation. Determination of the Velocity Ellipsoid from Observations. Local Field of Centroid Velocities - the Helmholtz Theorem for Stellar Systems. Plane-Parallel Motion. Determination of the Plane-Parallel Motion from Observations - Radial Velocity Method and Annual Proper Motion Method. Galactic Rotation. Asymmetry of Stellar Motions. General Formulae of Galactic Rotation. Local Field of the Barotropic Rotation of the Centroid. The Interpretation of Oort's Formulae. Dynamical Interpretation of the Rotation Parameters. Dynamical Constants of the Galaxy. Analysis of Oort Coefficients.

Modelling of Gravitational Systems. Basic and Perturbative Forces. Cumulative Effect of Perturbative Forces. Relaxation. Statistical Stellar Dynamics. Phase Density Function. Basic Equation of Stellar Dynamics, Jeans' Theorem. General Solution of the Basic Equation. Direct Problem of Stationary Systems. Quasiergodic Systems. Asymmetric Potential. Systems with Rotating Symmetry. Systems with Spherical Symmetry. Elements of Ellipsoidal Dynamics for Stationary Systems. Theoretical Velocity Ellipsoid. Potential Function. Comparison with Observations. Quasiintegrals. Stellar Orbits in the Galactic Disk. Epicyclical Approximation. Stability of Circular Orbits. Stability of Stellar Condensations. The Virial Theorem and Application to Stellar Systems. Stellar Hydrodynamics. Moment Equations in Generalized Coordinates. Interpretation of the Velocity Asymmetry.

Populations and Sub-Systems. The Central Region - the Stellar Bulge with a Gaseous Disk. The Core. The Disk - Stars in the Galactic Disk, Open Clusters, Associations, Grouping of Young Stars, Interstellar Medium. Spiral Structure. Vertical Structure of the Disk. The Halo - Stars in the Halo, Globular Clusters. Quasistationary Models of the Galaxy. Polytropic Models. Rotation Curve and Mass of the Galaxy. The Schmidt Model. Other Models. The Dark Matter.

Analysis of Small Perturbations - Mode Method and Method of Integral Transformations. Instability of Interstellar Medium - Linearization of Basic Equations, the Jeans Instability Criterion. Character of Long Wave Evolution. The Density Wave Theory of the Galactic Spiral Structure - Description of Spiral Perturbation, the Model of the Infinitely Thin Disk, Resonances, Velocity Field of Spiral Waves. Asymptotic Solution of Poisson Equation for Small Perturbations. Stability of Gaseous Disks. Stability of Stellar Disks. Group Velocity of Spiral Waves. Theoretical Models and Observations.

EXERCISES. Computational Exercises.

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