The distribution of globular clusters in kinematic spaces does not trace the accretion history of the host galaxy

Context. Reconstructing how all the stellar components of the Galaxy formed and assembled over time by studying the properties of the stars that form it is the aim of Galactic archaeology. Thanks to the launch of the ESA Gaia astrometric mission and the development of many spectroscopic surveys in recent years, we are for the first time in the position to delve into the layers of the past of the Galaxy. Globular clusters play a fundamental role in this research field since they are among the oldest stellar systems in the MW and thus bear witness to its entire past. Aims. As a natural result of galaxy formation, globular clusters did not necessarily all form in the Galaxy itself. Indeed, a fraction of them could have been formed in satellite galaxies accreted by the Milky Way over time. In recent years, there have been several attempts to constrain the nature of clusters (accreted or formed in the Milky Way itself) through the analysis of kinematic spaces, such as the E - L-z, L-perp - L-z, eccentricity - L-z, and the action space, as well as attempts to reconstruct the properties of the accretion events experienced by the Milky Way through time from this kind of analysis. This work aims to test a widely used assumption about the clustering of the accreted populations of globular clusters in the integrals of motions space. Methods. In this paper we analyse a set of dissipationless N-body simulations that reproduce the accretion of one or two satellites with their globular cluster population on a Milky Way-type galaxy. Results. Our results demonstrate that a significant overlap between accreted and 'kinematically heated' in situ globular clusters is expected in kinematic spaces for mergers with mass ratios of 1:10. In contrast with the standard assumptions made in the literature so far, we find that accreted globular clusters do not show dynamical coherence, that is, they do not cluster in kinematic spaces. In addition, we show that globular clusters can also be found in regions dominated by stars that have a different origin (i.e. a different progenitor). This casts doubt on the association between clusters and field stars that is generally made in the literature and is used to assign them to a common origin. By means of Gaussian mixture models, we demonstrate that the overlap of clusters is not only a projection effect on specific planes but is also found when the whole set of kinematic properties (i.e. E, L-z, L-perp, eccentricity, radial, and vertical actions) is taken into account. Overall, our findings severely question the recovered accretion history of the Milky Way based on the phase-space clustering of the globular cluster population.