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Three-dimensional eccentric discs around Be stars

One-armed oscillation modes in the circumstellar discs of Be stars may explain the cyclical variations in their emission lines. We show that a three-dimensional effect, involving vertical motion and neglected in previous treatments, profoundly influences the dynamics. Using a secular theory of eccentric discs that reduces the problem to a second-order differential equation, we show that confined prograde modes are obtained for all reasonable disc temperatures and stellar rotation rates. We confirm these results using a numerical analysis of the full set of linearized equations for three-dimensional isothermal discs including viscous terms that couple the horizontal motions at different altitudes. In order to make these modes grow, viscous damping must be overcome by an excitation mechanism such as viscous overstability.