On the absence of winds in advection-dominated accretion flows

We show that recently published assertions that advection-dominated accretion flows (ADAFs) require the presence of strong winds are unfounded because they assume that low radiative efficiency in flows accreting at low rates on to black holes implies vanishing radial energy and angular momentum fluxes through the flow (which is also formulated in terms of the 'Bernoulli function' being positive). This, however, is a property only of self-similar solutions which are an inadequate representation of global accretion flows. We recall general properties of accretion flows on to black holes and show that such, necessarily transonic, flows may have either d positive or negative Bernoulli function depending on the flow viscosity. Flows with low viscosities (alpha less than or equal to 0.1 in the alpha-viscosity model) have a negative Bernoulli function. Without exception, all 2D and 1D numerical models of low-viscosity flows constructed to date experience no significant outflows. At high viscosities the presence of outflows depends on the assumed viscosity, on the equation of state and on the outer boundary condition. The positive sign of the Bernoulli function invoked in this context is irrelevant to the presence of outflows. As an illustration, we recall 2D numerical models with moderate viscosity that have positive values of the Bernoulli function and experience no outflows. ADAFs, therefore, do not differ from this point of view from thin Keplerian discs: they may have, but they do not have to have, strong winds.