Galaxy clusters morphology with Zernike polynomials: the first application on $\mathit{\text{Planck}}$ Compton parameter maps

The study of the morphology of 2D projected maps of galaxy clusters is a suitable approach to infer, from real data, the dynamical state of those systems. We recently developed a new method to recover the morphological features in galaxy cluster maps which consists of an analytical modelling through the Zernike polynomials. After the first validation of this approach on a set of high-resolution mock maps of the Compton parameter, $y$, from hydrodynamically simulated galaxy clusters in THE THREE HUNDRED project, we apply the Zernike modelling on $y$-maps of local ($z<0.1$) galaxy clusters observed by the $Planck$ satellite. With a single parameter collecting the main information of the Zernike modelling, we classify their morphology. A set of mock $Planck$-like $y$-maps, generated from THE THREE HUNDRED clusters, is also used to validate our indicator with a proper dynamical state classification. This approach allows us to test the efficiency of the Zernike morphological modelling in evaluating the dynamical population in the real $Planck$ sample.