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We study the present-day rotational velocity (Vrot) and velocity dispersion (σ) profiles of the globular cluster (GC) systems in a sample of 50 lenticular (S0) galaxies from the E-MOSAICS galaxy formation simulations. We find that $82{{\ \rm per\ cent}}$ of the galaxies have GCs that are rotating along the photometric major axis of the galaxy (aligned), while the remaining $18{{\ \rm per\ cent}}$ of the galaxies do not (misaligned). This is generally consistent with the observations from the SLUGGS survey. For the aligned galaxies, classified as peaked and outwardly decreasing ($49{{\ \rm per\ cent}}$), flat ($24{{\ \rm per\ cent}}$), and increasing ($27{{\ \rm per\ cent}}$) based on the Vrot/σ profiles out to large radii, we do not find any clear correlation between these present-day Vrot/σ profiles of the GCs and the past merger histories of the S0 galaxies, unlike in previous simulations of galaxy stars. For just over half of the misaligned galaxies, we find that the GC misalignment is the result of a major merger within the last $10\, \mathrm{Gyr}$ so that the ex-situ GCs are misaligned by an angle between 0° (co-rotation) and 180° (counter-rotation), with respect to the in situ GCs, depending on the orbital configurationmore »of the merging galaxies. For the remaining misaligned galaxies, we suggest that the in situ metal-poor GCs, formed at early times, have undergone more frequent kinematic perturbations than the in situ metal-rich GCs. We also find that the GCs accreted early and the in situ GCs are predominantly located within 0.2 virial radii (R200) from the centre of galaxies in 3D phase-space diagrams.

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ABSTRACT It has been proposed that S0 galaxies are either fading spirals or the result of galaxy mergers. The relative contribution of each pathway and the environments in which they occur remain unknown. Here, we investigate stellar and gas kinematics of 219 S0s in the SAMI Survey to look for signs of multiple formation pathways occurring across the full range of environments. We identify a large range of rotational support in their stellar kinematics, which correspond to ranges in their physical structure. We find that pressure-supported S0s with v/σ below 0.5 tend to be more compact and feature misaligned stellar and gas components, suggesting an external origin for their gas. We postulate that these S0s are consistent with being formed through a merger process. Meanwhile, comparisons of ellipticity, stellar mass, and Sérsic index distributions with spiral galaxies show that the rotationally supported S0s with v/σ above 0.5 are more consistent with a faded spiral origin. In addition, a simulated merger pathway involving a compact elliptical and gas-rich satellite results in an S0 that lies within the pressure-supported group. We conclude that two S0 formation pathways are active, with mergers dominating in isolated galaxies and small groups, and the faded spiralmore »pathway being most prominent in large groups ($10^{13}\lt \rm {M_{halo}}\lt 10^{14}$).« less