The Birth of Minor-Body Populations in the $β$ Pictoris System I: The First 25 Myr
The discovery of the third known giant planet, $β$ Pic d, offers a new opportunity to investigate how planet-disk interactions build the minor-body architecture of the young Beta Pictoris system. We study the formation and redistribution of scattered-disk objects, falling evaporating bodies, a proto-Oort-cloud population, transitional interstellar objects, and interstellar objects. Using $N$-body simulations, we evolve a primordial planetesimal disk extending from 0.5 to 1000 au for 25 Myr under the perturbations of $β$ Pic b, c, and d, together with reconstructed stellar encounters from Gaia DR3. The resulting evolution is strongly radius-dependent. The planets efficiently restructure the inner disk, while the outermost primordial population remains largely unchanged beyond $325$ au. $β$ Pic c remains the main driver of the star-grazing population, showing that the falling-evaporating-body pathway persists after the inclusion of $β$ Pic d. At larger radii, $β$ Pic b and d dominate planetary scattering and produce a surviving disk edge near 50 au, consistent with the observed debris-disk truncation. Over 25 Myr, $8.74\%$ of the initial disk enters the scattered-disk population, $2.04\%$ reaches the proto-Oort-cloud region, and $6.44\%$ becomes unbound. Planetary stirring also generates a transient one-armed spiral among particles originating at $\sim60$-150 au, overlapping part of the observed "Cat's Tail" and the radial location of the prominent CO clump near 85 au. The reconstructed stellar encounters included here produce only weak perturbations, although the encounter catalog is complete only over the first ~2.5 Myr of the present epoch. The early evolution of the Beta Pictoris minor-body system is therefore dominated by its planetary architecture, offering a view of distinct minor-body populations while they are still being formed and redistributed.