Cosmic Strings-induced CMB anisotropies in light of Weighted Morphology

Motivated by the morphological measures in assessing the geometrical and topological properties of a generic cosmological stochastic field, we propose an extension of the weighted morphological measures, specifically the $n$th conditional moments of derivative (cmd-$n$). This criterion assigns a distinct weight to each excursion set point based on the associated field. We apply the cmd-$n$ on the Cosmic Microwave Background (CMB) to identify the cosmic string networks (CSs) through their unique Gott-Kaiser-Stebbins effect on the temperature anisotropies. We also formulate the perturbative expansion of cmd-$n$ for the weak non-Gaussian regime up to $\mathcal{O}(\sigma_0^3)$. We propose a comprehensive pipeline designed to analyze the morphological properties of string-induced CMB maps within the flat sky approximation. To evaluate the robustness of our proposed criteria, we employ string-induced high-resolution flat-sky CMB simulated patches of $7.2$ deg$^2$ size with a resolution of $0.42$ arc-minutes. Our results demonstrate that the minimum detectable value of cosmic string tension is $G\mu\gtrsim 1.9\times 10^{-7}$ when a noise-free map is analyzed with normalized cmd-$n$. Whereas for the ACT, CMB-S4, and Planck-like experiments at 95.45\% confidence level, the normalized cmd-$n$ can distinguish the CSs network for $G\mu\gtrsim2.9 \times 10^{-7}$, $G\mu\gtrsim 2.4\times 10^{-7}$ and $G\mu\gtrsim 5.8\times 10^{-7}$, respectively. The normalized cmd-$n$ exhibits a significantly enhanced capability in detecting CSs relative to the Minkowski Functionals.