There are important but unresolved processes in the standard formation scenarios of double compact star binaries (DCBs; BH-BH, BH-NS, NS-NS systems), such as mass transfer and the common envelope (CE) phase. We analyze the effects of different assumptions on key physical processes and binary initial conditions on massive star binary evolution with binary population synthesis (BPS), including a survey of proposed prescriptions for the mass transfer ($rm q_{rm cr}$) and the binding energy parameter ($lambda$) in the CE phase. We find that $rm q_{rm cr}$ clearly affects the properties of NS-NS systems while $lambda$ has influence on the mass distributions of BH-BH systems. The merger rates of DCBs are increased by efficient CE ejection, which in our prescription is related to the binding energy parameter including all the possible budgets to the energy content. It has been suggested that the difference in the properties of GW150914 and GW151226 may reflect different metallicity. We reproduce their properties with our BPS calculations and find that the property of BH-BH systems at low metallicity is sensitive to $lambda$; the efficient CE ejection leads to a top-heavy mass distribution both for the primary and secondary BHs, which is favored to explain the nature of GW150914. The efficient CE ejection also leads to enhancement of both the BH-BH and NS-NS merger rates to the level consistent with the observational constraints from the detected gravitational wave sources including GW170817.
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