Blue Large-Amplitude Pulsators (BLAPs) are a recently discovered class of pulsating star, believed to be proto-white dwarfs, produced by mass stripping of a red giant when it has a small helium core. An outstanding question is why the stars in this class of pulsator seem to form two distinct groups by surface gravity, despite predictions that stars in the gap between them should also pulsate. We use a binary population synthesis model to identify potential evolutionary pathways that a star can take to become a BLAP. We find that BLAPs can be produced either through common envelope evolution or Roche lobe overflow, with a Main Sequence star or an evolved compact object being responsible for the envelope stripping. The mass distribution of the inferred population indicates that fewer stars would be expected in the range of masses intermediate to the two known groups of pulsators, suggesting that the lack of observational discoveries in this region may be a result of the underlying population of pre-white dwarf stars. We also consider metallicity variation and find evidence that BLAPs at $Z = 0.010$ (half-Solar) would be pulsationally unstable and may also be more common. Based on this analysis, we expect the Milky Way to host around 12000 BLAPs and we predict the number density of sources expected in future observations such as the Legacy Survey of Space and Time at the Vera Rubin Observatory.
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