The non-linear dynamics of bending instability and vertical structure of a galactic stellar disc embedded into a spherical halo are studied with N-body numerical modelling. Development of the bending instability in stellar galactic disc is considered as the main factor that increases the disc thickness. Correlation between the disc vertical scale height and the halo-to-disc mass ratio is predicted from the simulations. The method of assessment of the spherical-to-disc mass ratio for edge-on spiral galaxies with small bulges is considered. Modelling of eight edge-on galaxies: NGC 891, NGC 4738, NGC 5170, UGC 6080, UGC 7321, UGC 8286, UGC 9422 and UGC 9556 is performed. Parameters of stellar discs, dark haloes and bulges are estimated. The lower limit of the dark-to-luminous mass ratio in our galaxies is of the order of 1 within the limits of their stellar discs. The dark haloes dominate by mass in the galaxies with very thin stellar discs (NGC 5170, UGC 7321 and UGC 8286).
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