Robust ellipticity measurements of 29 Galactic globular clusters

Abstract

Globular clusters (GCs) exhibit varying degrees of flattening (ellipticity), which may provide insight into their internal dynamics and evolution histories. Commonly used methods to measure ellipticity, such as ellipse fitting of density contours and principal component analysis, often produce biased results, especially for clusters that are nearly round or have few observable stars. Using a combination of ground-based and space-based photometry, we investigate the shapes of 29 Galactic GCs. To that end, we test two commonly used methods: an ellipse fit to a kernel density profile and a principal component analysis. We find that both methods suffer from bias arising when the number of stars is small or the cluster is close to round. To solve this issue, we develop a robust method to measure the ellipticity of GCs, test it extensively on mock data, and apply it to the 29 Milky Way GCs in our sample. Using the $V/\sigma$ diagram used in the isotropic oblate rotator framework, we examine potential causes for the flattening, including rotation and velocity anisotropy. For ten clusters: NGC~104, NGC~1261, NGC~2808, NGC 3201, NGC 5286, NGC 5904, NGC 5986, NGC 6205, NGC 6341, and NGC 7078 we identify a very good agreement between the rotation angle and semi-minor axis of the ellipse, further corroborating the findings that rotation is the main driver of the ellipticity. The $V/\sigma$ diagram reveals that velocity anisotropy or tides could also be important in shaping the GCs. The robust method developed provides reliable measurements of the ellipticity of GCs, emphasising the importance of taking into account the flattening in theoretical models and simulations. It also offers a promising way to investigate the shapes of multiple stellar populations within GCs, where only small samples are usually available.