2025MNRAS.541..494B

The dominant processes by which galaxies replenish their cold gas reservoirs remain disputed, especially in massive galaxies. Stellar-gas kinematic misalignments offer an opportunity to study these replenishment processes. However, observed distributions of these misalignments conflict with current models of gas replenishment in early-type galaxies, with longer relaxation time-scales suggested as a possible solution. We use the EAGLE simulation to explore the relaxation of unstable misaligned gas in galaxies with masses of $M_{*}\geqslant \mathrm{10^{9.5}}$ M$_\odot$ in the range $0< z< 1$. We extract misalignments from formation to relaxation providing a sample of $\sim 3200$ relaxations. We find relaxation time-scales tend to be of short-duration, with median lifetimes of $\sim 0.5$ Gyr, though with a notable population of unstable misalignments lasting $\gtrsim 1$ Gyr. Relaxation time distributions show a log-linear relationship, with $\approx 20~{{\ \rm per\ cent}}$ of unstable misalignments persisting for $\gtrsim 3$ torquing times. Long-lived unstable misalignments are predominantly found in galaxies with higher stellar masses, lower star-forming gas fractions, higher ongoing gas inflow, and in galaxies that reside in the centres of dense environments. Mergers only cause $\approx 10~{{\ \rm per\ cent}}$ of unstable misalignments among galaxies at $z< 0.35$, and $\approx$21 per cent at $0.35< c z< 1.0$ in EAGLE. We conclude that, at least in EAGLE, unstable kinematic misalignments are not predominantly driven by gas-rich minor mergers at any redshift probed. Additionally, processes that significantly extend relaxation times are not dominant in the galaxy population. Instead, we see a diverse formation pathway for misalignments such as through hot halo cooling.