Alessandro Ignesti, Francesca Loi, Antonino Marasco, Benedetta Vulcani, Bianca M. Poggianti, Christoph Pfrommer, Marco Gullieuszik, Alessia Moretti, Paolo Serra, Stephanie Tonnesen, Rory Smith, Cecilia Bacchini, Marc A. W. Verheijen, Myriam Gitti, Anna Wolter, Koshy George, Yara Jaffe, Rosita Paladino, Giorgia Peluso, Mario Radovich, Augusto E. Lassen, Neven Tomicic, Peter Kamphuis

All gas-rich galaxies in cluster environments are expected to experience ram-pressure stripping from the intra-cluster medium. However, only a fraction of these develop ongoing star-formation in their stripped tail, becoming the so-called ``jellyfish'' galaxies. In this work we provide observational evidence that magnetic fields can signal differences in the extraplanar star formation and explore what are the physical conditions that lead to the formation of a jellyfish galaxy. We first focus on JO147, a jellyfish galaxy that features weak star formation activity in its tail. Using MeerKAT radio continuum observations, we discover polarized emission only in a small fraction of its tail, with an average fraction of $~10\%$, and a low Mach number $\mathcal{M}=1.3-1.6$, which suggests a possible association between magnetic field draping, shock-compression of the gas, and extraplanar star formation activity. Then, we test this scenario in a sample of 17 jellyfish galaxies from the GASP project. We combine dynamical models for their orbits within the host clusters with realistic cluster temperature profiles to infer their Mach number, and we find a positive correlation between it and the star formation activity in their tail. We conclude that supersonic motion is a necessary condition for triggering star formation in the stripped tails of jellyfish galaxies. Our findings provide empirical evidence that the critical factor preventing the stripped gas evaporation is the shock compression induced by the supersonic motion through the cluster. This process likely enhances the magnetic field surrounding the galaxy and the properties of the stripped material.