We study numerically the quasi‐spherical accretion of matter on to a compact object (neutron star or black hole). Anisotropic x‐ray luminosity, powered by mass accretion, heats the accreting gas through Compton scattering. When the gas temperature increases above the local escape temperature, part of the accreting gas will flow outwards as a result of the action of buoyancy force. The direction of the outflow coincides with the maximum of the x‐ray luminosity. The depth of outflow is correlated with the energy of x‐ray quanta. In spite of its quantum nature, Compton heating markedly affects the gas, forcing the matter outflow at x‐ray luminosities as small as three or four orders of magnitude less than the Eddington limit. The phenomenon of hot gas outflow takes place in the case of accretion on to a wind‐fed x‐ray source in a wide binary with massive OB or Be‐star. We propose a new spin‐down mechanism for accreting neutron stars that explains the existence of a number of long‐period (p∼100–1000 s) x‐ray pulsars in these binaries. The spin‐down is a result of efficient angular‐momentum transfer from the rotating magnetosphere of the accreting star to an outflowing stream, when the outflow forms so deep as to capture the magnetic‐field lines from the rotating magnetosphere. The balance between angular‐momentum gain by accreting gas and loss by outflow matter takes place at a particular value of the equilibrium spin period (peq∼100–1000 s). ©1994 American Institute of Physics.