Gravitationally focused wind accretion in binary systems consisting of an evolved star with a gaseous envelope and a compact accreting companion is a possible mechanism to explain mass transfer in symbiotic binaries. We study the mass accretion around the secondary caused by the strong wind from the primary late-type component using global three-dimensional hydrodynamic numerical simulations during quiescence and outburst stages. In particular, the dependence of the mass accretion rate on the mass-loss rate, wind parameters and phases of wind outburst development is considered. For a typical wind from an asymptotic giant branch star with a mass-loss rate of 1e-6 Msun/year and wind speeds of 20-50 km/s, the mass transfer through a focused wind results in efficient infall on to the secondary. Accretion rates onto the secondary of 5-20 per cent of the mass-loss from the primary are obtained during quiescence and outburst periods where the wind velocity and mass-loss rates are varied, about 20-50 per cent larger than in the standard Bondi-Hoyle-Lyttleton approximation. This mechanism could be an important method for explaining observed accretion luminosities and periodic modulations in the accretion rates for a broad range of interacting binary systems.
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