  Rapid binary population synthesis codes are often used to investigate the
evolution of compact-object binaries. They typically rely on analytical fits of
single-star evolutionary tracks and parameterized models for interactive phases
of evolution (e.g., mass-transfer on thermal timescale, determination of
dynamical instability, and common envelope) that are crucial to predict the
fate of binaries. These processes can be more carefully implemented in stellar
structure and evolution codes such as MESA. To assess the impact of such
improvements, we compare binary black hole mergers as predicted in models with
the rapid binary population synthesis code COSMIC to models ran with MESA
simulations through mass transfer and common-envelope treatment. We find that
results significantly differ in terms of formation paths, the orbital periods
and mass ratios of merging binary black holes, and consequently merger rates.
While common-envelope evolution is the dominant formation channel in COSMIC,
stable mass transfer dominates in our MESA models. Depending upon the black
hole donor mass, and mass-transfer and common-envelope physics, at sub-solar
metallicity COSMIC overproduces the number of binary black hole mergers by
factors of 2--35 with a significant fraction of them having merger times orders
of magnitude shorter than the binary black holes formed when using detailed
MESA models. Therefore we find that some binary black hole merger rate
predictions from rapid population syntheses of isolated binaries may be
overestimated by factors of ~5--500. We conclude that the interpretation of
gravitational-wave observations requires the use of detailed treatment of these
interactive binary phases.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics