On the formation of subdwarf B stars via engulfment of substellar companions I. Conditions for and occurrence of envelope ejection events

The canonical scenario for the formation of subdwarf B (sdB) stars involves the ejection of the progenitor's envelope near the tip of the Red Giant Branch (RGB), concurrent with the onset of core He-burning. While binary interactions are known to dominate sdB formation, the origin of apparently single sdB stars remains uncertain. We investigate the conditions under which an sdB progenitor can eject its envelope through the engulfment of a substellar companion, using an energy balance approach. We simulate the orbital evolution of substellar companions during the subgiant and RGB phases of their host stars (1.2-2.0 M Sun) to determine the onset of engulfment and calculate the energy released during inspiral within the stellar envelope. By comparing this energy with the envelope binding energy and exploring different efficiencies for its deposition, we identify the conditions required for envelope ejection. We then estimate the occurrence of such events using observed population of substellar companions. The engulfment of substellar objects can lead to envelope ejection within a limited region of the mass-semi-major axis parameter space, whose extent depends on the host star's properties and energy transfer efficiency. The minimum companion mass required for ejection increases with decreasing efficiency and increasing stellar mass. As a result, the frequency of envelope ejection is strongly influenced by the distribution of substellar companions, particularly by the paucity of objects in the brown-dwarf desert. The engulfment of low-mass brown dwarfs and massive planets during the late RGB can provide sufficient energy to eject the stellar envelope, which could ultimately lead to the formation of sdB stars. Our results define the region of parameter space where this mechanism is energetically possible and provide a guide for future multidimensional hydrodynamical simulations.