On the relationship between the ellipticity of Galactic globular clusters and their X-ray luminosity

We examine the dependence of the ellipticity of globular clusters in the Milky Way on their X-ray luminosity using two modern catalogs and combine them with optical and X-ray data from the literature. Kolmogorov-Smirnov tests applied across multiple subsets reveal statistically significant differences in the ellipticity distributions when both $L_{\mathrm{X}}$ and optical luminosity are considered. Two X-ray luminosity thresholds, $L_{\mathrm{X}}^{\ast }(M_{\mathrm{V}}=-7)={10}^{33.05}$ erg/s and $L_{\mathrm{X}}^{\ast }(M_{\mathrm{V}}=-7)={10}^{32.01}$ erg/s, yield the most reliable distinction. In contrast to earlier findings based solely on optical data, our results demonstrate that globular clusters with the highest X-ray luminosity tend to have higher ellipticity on average.