Understanding the survival and orbital evolution of brown dwarf (BD) companions during the post-main-sequence (MS) evolution of their host stars has become increasingly important, especially following recent discoveries of substellar companions around white dwarfs (WDs). We investigated the long-term evolution and final outcomes of BDs orbiting low-mass MS stars as these evolve into WDs. By comparing forward-modelled populations with observed WD--BD binaries, we tested evolutionary models and predicted the existence of yet-undetected systems. We employed the code Compact Object Mergers: Population Astrophysics and Statistics (COMPAS) to evolve observed MS--BD systems through the post-MS phases of their host stars into the WD stage, tracking orbital changes driven by mass loss, tides, and common-envelope (CE) evolution. Our simulations reproduce a period gap in the distribution of detached WD--BD binaries, consistent with observations. We also identify a boundary separating detached and semi-detached systems in the period-mass diagram at orbital periods of ∼1--2 hours, depending on the BD mass. We predict that a subset of currently known MS--BD binaries will survive post-MS evolution and emerge as detached WD--BD systems, while others will undergo CE evolution and potentially form cataclysmic variables with BD donors. Our results reproduce the observed period gap in WD--BD binaries and provide quantitative predictions for the role of CE efficiency in shaping their distribution. These findings indicate that many WD--BD systems remain undetected, motivating targeted searches using microlensing and high-contrast imaging techniques with next-generation large telescopes.
Chen et al. (Mon,) studied this question.