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

We carry out a numerical experiment of ejecting winds in a massive colliding wind binary system, and quantifying the accretion onto the secondary star under different primary mass loss rates. We set a binary system comprising a Luminous Blue 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 wind momentum ratio $\eta$. Our simulations include two sets of cases: one where the stars are stationary, and one that includes the orbital motion. As $\eta$ decreases the colliding wind structure moves closer to the secondary. We find that for $\eta \lesssim 0.05$ the accretion threshold is reached and clumps which originate by instabilities are accreted onto the secondary. For each value of $\eta$ we calculate the mass accretion rate and identify different regions 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 the average accretion rate satisfies the power-law $\dot{M}_{\rm acc} \propto \eta^{-1.73}$ for static stars. The accretion is not continuous but rather changes from sporadic to a larger duty cycle as $\eta$ decreases. For $\eta\lesssim0.001$ the accretion becomes continuous in time and the accretion rate is BHL, up to a factor of 0.4--0.8. The simulations that include the orbital 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.