Tidal Debris Candidates from the $\omega$ Centauri Accretion Event and its Role in Building Up the Milky Way Halo

We identify stellar tidal debris from the $\omega$ Centauri ($\omega$ Cen) system among field stars in the APOGEE survey via chemical tagging using a neural network trained on APOGEE observations of the $\omega$ Cen core. We find a total of 463 $\omega$ Cen debris candidates have a probability $P>0.8$ of sharing common patterns in their chemical abundances across a range of individual elements or element combinations, including [C+N], O, Mg, Al, Si, Ca, Ni, and Fe. Some debris candidates show prograde or retrograde disk-like kinematics, but most show kinematics consistent with the accreted halo, showing high radial actions, $J_R$, values. We find that a sample of Gaia-Sausage-Enceladus (GES) members are chemically distinct from the $\omega$ Cen core, suggesting that $\omega$ Cen is associated to an independent merger event shaping the Milky Way halo. However, a connection between GSE and $\omega$ Cen cannot be ruled out. A detailed comparison with $N$-body simulations indicates that the $\omega$ Cen progenitor was a massive dwarf galaxy ($\gtrsim {10}^8{M}_{\odot }$). The existence of a metal-poor high-$\alpha$ chemically homogeneous halo debris is also reported.