Prague Relativistic Astrophysics

Lydia Stofanova, Katerina Jarkovska

Lydia Stofanova: Coherent dusty and gaseous structures near the Galactic centre

Abstract. Sagittarius A*, a compact source in the centre of the Milky Way, is the nearest supermassive black hole (SMBH) in our cosmic neighbourhood, where various astrophysical processes take place. In consequence, variety of structures emerge near the Galactic centre and bow shocks that are closely studied in this work represent an example of them. The introductory part of this thesis is a brief review of the history of the Galactic centre research and its discovery in radio wavelengths. The main body of the thesis is focused on a simplified model of the bow-shock structures that are generated by stars moving supersonically with respect to the ambient medium. We discuss how these structures vary along the orbit. To this end, we consider four different models: (a) without the presence of any gaseous medium emerging from or accreting onto the SMBH, (b) taking an outflow from the SMBH into account, (c) the case of an inflow onto the SMBH, and finally (d) the combined model involving both an outflow and an inflow at the same time. We discuss symmetries of each model (or lack of them) and we find that the model considering the ambient medium at rest appears symmetrical with respect to the pericentre passage. The combined model manifests itself as the most asymmetrical one of them all. We show profiles for the tangential velocity in the shell and the mass surface density of the bow-shock shell along the stellar orbit for all considered models.

Katerina Jarkovska: Annihilation and creation operators in Lie algebra theory and physics

Abstract. We show the use of the theory of Lie algebras, especially their oscillator realizations, in the context of quantum mechanics. One can construct oscillator realizations from matrix realizations. In the case of symplectic and special orthogonal algebra, we demonstrate an alternative method of obtaining oscillator realizations from symmetric or exterior power of a vector space of annihilation and creation bosonic or fermionic operators. We find Lie algebra of polynomials of degree at most two in phase space of a mechanical system, which form the semidirect product of the Heisenberg algebra and symplectic algebra. It is shown that a classical system with Hamiltonian function in this algebra can be quantized by two equivalent representations - Schrödinger or Bargmann-Fock representation. The second mentioned representation generates the same operators of symplectic algebra as we got from their previous formal construction from symmetric power of a vector space of bosonic operators. Quantization is demonstrated on the bosonic harmonic oscillator. We use the similarities between bosonic and fermionic oscillator realizations to define the fermionic harmonic oscillator. Some properties of spinor representations of special orthogonal algebra are illustrated on its state space.