Ellipticities of Galaxy Cluster Halos from Halo-Shear-Shear Correlations

We report the first detection of the halo ellipticities of galaxy clusters by applying the halo-shear-shear correlations (HSSC), without the necessity of major axis determination. We use the Fourier\_Quad shear catalog based on the Hyper Suprime-Cam Survey and the group catalog from the DESI Legacy Surveys for the measurement of group/cluster lensing and HSSC. Our analysis includes the off-centering effects. We obtain the average projected ellipticity of dark matter halos with mass $13.5 < {\rm log} (M_G h/ M_\odot) < 14.5$ within 1.3 virial radius to be $0.48^{+0.12}_{-0.19}$. We divide the sample into two groups based on mass and redshift, and we find that halos with higher mass tend to exhibit increased ellipticity. We also reveal that high-richness halos have larger ellipticities, confirming the physical picture from numerical simulation that high-richiness halos have a dynamical youth and more active mass accretion phase.