Stirred, not shaken: Dislodging $ω$ Centauri from the Sausage galaxy through bar resonances
We test the idea proposed by Laporte \& Orkney that $ω$ Centauri ($ω$Cen) is the central nuclear star cluster of the Gaia-Sausage-Enceladus galaxy (GSE) which got dislodged by the bar. We run a series of simulations in time-evolving bar potentials with present-day pattern speeds within Portail et al's $Ω_{b}=39\pm3.5\,\rm{km\,s^{-1}\,kpc^{-1}}$ and rate of slow-down $\dotΩ_{\rm b}= 4.5 \pm 1.4 \,\rm{km \,s^{-1}\,kpc^{-1}\, Gyr^{-1}}$ to study how bar resonances modulate the angular momentum and energies of both GSE-debris and $ω$Cen's location in $(E,L_{z})$ space. We find that the retrograde $3:2$ resonance is capable of inflicting changes of $ΔE\approx0.4\times10^{5}\,\rm{km^{2}\, s^{-2}}$, $ΔL_{z}\approx0.3-0.5\times10^{3}\, \rm{km \, s^{-1}\, kpc^{-1}}$ within timescales of $Δt\approx 0.5-1\,\rm{Gyr}$, well within the bar's lifespan $t_{\rm{bar}}\approx10-8\,\rm{Gyr}$. These results are independent of the choice of potential or modelling. We uncover a sample of N-rich stars with metallicities $-2.0<[\rm{Fe/H}]<-1.0$ and aluminium enrichments consistent with $ω$Cen. In ($E,L_{z}$) space, the map reveals a corridor of trailing N-rich stars clustered about the region connecting $ω$Cen to the GSE's debris centroid, matching $ω$Cen's past predicted track. This provides the best evidence yet that $ω$Cen is the nuclear star cluster of the GSE. Using M54 and $ω$Cen's chemistry we show that neither first nor second generations follow general galaxy-wide scale chemical enrichment trends. This is empirical evidence that GC chemical trends are a cluster-scale physics problem, not a galaxy-wide one.