Statistical Isotropy Violations in CMB Temperature Anisotropy: Analysis Using Minimal Bipolar Spherical Harmonics

In this work, we present a follow-up to our previous work where the concept of minimal Bipolar spherical harmonics (mBipoSH) functions was introduced as a natural basis for studying angular correlations in the non-statistical isotropic (nSI) Cosmic Microwave Background (CMB) sky. In this study, we extend the formalism of mBipoSH functions and apply it to analyze two sources of statistical isotropy (SI) violation-cosmic hemispherical asymmetry (CHA) and non-circular (NC) beam shapes. We present the analytical expression for mBipoSH functions and plot the corresponding angular correlation functions for these cases, addressing the $L=1$ and $L=2$ multipole statistical isotropy violations within the BipoSH basis. Our results confirm the effectiveness of the proposed approach, as it successfully captures and explains the observed angular correlations in the CMB sky.