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In this work, the thermo-acoustic instabilities of a gas turbine model combustor, the so-called SFB606 combustor, are numerically investigated using Large Eddy Simulation (LES) combined with tabulated chemistry and Artificial Thickened Flame (ATF) approach. The main focus is a detailed analysis of the thermo-acoustic cycle and the accompanied equivalence ratio oscillations and their associated convective time delay. In particular, the variations of the thermo-chemical state and flame characteristics over the thermo-acoustic cycle are investigated. For the operating point flame B ($P_{th}=25\,$kW), the burner exhibits thermo-acoustic instabilities with a dominant frequency of 392Hz, the acoustic eigenmode of the inner air inlet duct. These oscillations are accompanied by an equivalence ratio oscillation, which exhibits a convective time delay between the injection in the inner swirler and the flame zone. Two LES, one adiabatic and one accounting for heat losses at the walls by prescribing the wall temperatures from experimental data and Conjugated Heat Transfer (CHT) simulations, are conducted. Results with the enthalpy-dependent table are found to predict the time-averaged flow field in terms of velocity, major species, and temperature with higher accuracy than in the adiabatic case. Further, they indicate, that heat losses should be accounted for to correctly predict the flame position. Subsequently, the thermo-chemical state variations over the thermo-acoustic cycle for the enthalpy-dependant case are analyzed in detail and compared with experimental data in terms of phase-conditioned averaged profiles and conditional averages. An overall good prediction is observed. The results provide a detailed quantitative analysis of the thermo-acoustic feedback mechanism of this burner., Comment: Proceedings of the ASME Turbo Expo 2022 Turbomachinery Technical Conference and Exposition. Volume 3B Combustion, Fuels, and Emissions. Rotterdam, Netherlands. 2022 ASME