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We carry out a numerical experiment of ejecting winds in a massive collidingwind binary system, and quantifying the accretion onto the secondary star underdifferent primary mass loss rates. We set a binary system comprising a LuminousBlue Variable (LBV) as the primary and a Wolf-Rayet (WR) star as the secondary,and vary the mass loss rate of the LBV to obtain different values of windmomentum ratio $\eta$. Our simulations include two sets of cases: one where thestars are stationary, and one that includes the orbital motion. As $\eta$decreases the colliding wind structure moves closer to the secondary. We findthat for $\eta \lesssim 0.05$ the accretion threshold is reached and clumpswhich originate by instabilities are accreted onto the secondary. For eachvalue of $\eta$ we calculate the mass accretion rate and identify differentregions in the $\dot{M}_{\rm acc}$ - $\eta$ diagram. For $0.001 \lesssim \eta\lesssim 0.05$ the accretion is sub- Bondi-Hoyle-Lyttleton (BHL) and theaverage accretion rate satisfies the power-law $\dot{M}_{\rm acc} \propto\eta^{-1.73}$ for static stars. The accretion is not continuous but ratherchanges from sporadic to a larger duty cycle as $\eta$ decreases. For$\eta\lesssim0.001$ the accretion becomes continuous in time and the accretionrate is BHL, up to a factor of 0.4--0.8. The simulations that include theorbital motion give qualitatively similar results, with the steeper power law$\dot{M}_{\rm acc} \propto \eta^{-1.86}$ for the sub-BHL region and lower$\eta$ as an accretion threshold.

Accretion in massive colliding wind binaries and the effect of wind momentum ratio