  Three-body interactions can eject stars from the core of a globular cluster,
causing them to enter the Galactic halo as extra-tidal stars. While finding
extra-tidal stars is imperative for understanding cluster evolution, connecting
isolated extra-tidal field stars back to their birth cluster is extremely
difficult. In this work, we present a new methodology consisting of
high-dimensional data analysis and a particle spray code to identify
extra-tidal stars of any Galactic globular cluster using M3 as a case study.
Using the t-Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold
Approximation and Projection (UMAP) machine learning dimensionality reduction
algorithms, we first identify a set of 103 extra-tidal candidates in the APOGEE
DR17 data catalogue with chemical abundances similar to M3 stars. To confirm
each candidate's extra-tidal nature, we introduce corespray - a new
Python-based three-body particle spray code that simulates extra-tidal stars
for any Galactic globular cluster. Using Gaia EDR3 proper motions and APOGEE
DR17 radial velocities, we apply multivariate Gaussian modelling and an extreme
deconvolution to identify the extra-tidal candidates that are more likely to be
associated with a distribution of corespray-simulated M3 extra-tidal stars than
the field. Through these methods, we identify 10 new high-probability
extra-tidal stars produced via three-body interactions in M3. We also explore
whether any of our extra-tidal candidates are consistent with being ejected
from M3 through different dynamical processes. Future applications of corespray
will yield better understandings of core dynamics, star formation histories and
binary fractions in globular clusters.
