The accretion history of the Milky Way V. The kinematics of most globular clusters trace the merger epochs
Several studies have associated globular clusters (GCs) with former Galactic accretion events by comparing their positions in the energy-angular momentum ($E$-$L_z$) plane, an approach further supported by similarities in their age-metallicity relations. However, recent merger simulations suggest that GCs initially associated with the Gaia-Sausage-Enceladus (GSE) disc may have lost their orbital energy and thus may not reliably trace this accretion event. We extend this framework by considering three N-body simulations of the Milky Way-GSE merger with different initial masses, mass ratios, and gas content. In addition to GCs belonging to the GSE disc progenitor, we accounted for GCs in its halo and, in gas-rich models, a population of GCs formed during the Milky Way-GSE merger. We confirm that most GCs originating in the disc have lost a significant part of their orbital energy during repeated passages through the dense disc medium, and we conjecture that associated tidal shocks may have destroyed many of them. In contrast, GCs from the halo and GCs formed during the merger have largely retained their orbital energy, which remains comparable to that of GSE stars even up to 9 Gyr after the completion of the merger. By using a more realistic GC population and GSE modelling, we find that most GCs linked to GSE can be associated with Milky Way accretion events in the $E$-$L_z$ plane, which supports previous observational associations based on a combination of energy-angular momentum and age-metallicity relations.