The structural and kinematical properties of NGC 5634, a globular cluster associated with the Sagittarius dwarf galaxy?

Abstract: We investigate the origin of NGC 5634 through a comprehensive analysis of its morphology, kinematics and dynamics. Utilizing data from the DESI Legacy Survey, we refined its fundamental parameters (age t = 12.8 +/- 0.3 Gyr, metallicity [Fe/H] = -1.8 +/- 0.1 dex, distance modulus dm = 17.0 +/- 0.1 mag) and constructed matched-filter template based on the combination of these parameters to search for extra-tidal structures. However, no significant features were detected above a 3 sigma signal-to-noise threshold, which limits our ability to further investigate the association between NGC 5634 and the Sagittarius (Sgr) stream based on morphological evidence. Incorporating GAIA data, we further examine the orbital path of NGC 5634. We found that its orbit only briefly intersects with the Sgr stream and diverges significantly over long-term integrations. This behavior contrasts with that of confirmed Sgr-associated clusters, whose orbits remain closely aligned with the stream throughout their orbital evolution. Additionally, NGC 5634 exhibits a relatively shorter semi-major axis and smaller apocenter and pericenter distances compared to Sgr clusters. These orbital characteristics are more consistent with clusters associated with the Gaia-Sausage-Enceladus (GSE) or the Helmi streams. From a dynamical perspective, in the Lz-E space, NGC 5634 is also distinctly different from Sgr clusters and aligns more closely with the GSE and Helmi regions. Taken together, these findings do not support a strong connection between NGC 5634 and the Sgr dSph, but instead suggest a potential association with another progenitor system, such as GSE or Helmi stream. Nevertheless, further evidence is needed to definitively establish its origin.