Jesús A. Toalá, Emilio Tejeda, Diego A. Vasquez-Torres

Wind accretion in binary systems is commonly described using the Bondi-Hoyle-Lyttleton (BHL) formalism. However, its standard implementation fails in the slow-wind regime, where the wind velocity of the donor star ($v_\mathrm{w}$) is comparable to or smaller than the orbital velocity of the accretor ($v_\mathrm{o}$). Tejeda & Toalá recently proposed a geometrical correction to the BHL formalism that accounts for the wind aberration caused by the binary's orbital motion, which tilts the accretion cylinder and reduces its effective cross-section. Here we present a suite of smoothed particle hydrodynamic simulations performed with PHANTOM to test wind accretion in binary systems operating in this slow-wind regime. We explore circular configurations and directly measure mass accretion efficiencies from the simulations. Our results confirm that the standard BHL prescription systematically overestimates accretion rates for $v_\mathrm{w}/v_\mathrm{o} < 1$, while the geometrically corrected model reproduces the simulated efficiencies with remarkable accuracy. A key finding is that the velocity relevant for accretion estimates is not the value derived from the unperturbed stellar wind, but the local gas velocity measured upstream of the accretor. The gravitational potential of the accretor perturbs the flow, altering the effective relative velocity and modifying the accretion efficiency, particularly for compact orbits. These results provide strong numerical support for the geometrically corrected framework and establish a physically motivated basis for modeling wind-fed accretion in interacting binaries, including symbiotic systems.