Title: The rise and fall of the anomalous microwave emission from extragalactic star-forming regions

Abstract: We investigate the impact of anomalous microwave emission (AME) on the radio-millimeter spectral energy distribution for three typical interstellar medium (ISM) conditions surrounding star-forming regions-cold neutral medium, warm neutral medium, and photodissociation regions-by comparing the emissivities of three major contributors: free-free, thermal dust emission, and AME. In particular, for spinning nanoparticles (i.e., potential carriers of AME), we consider a known grain destruction mechanism due to a centrifugal force from spin-up processes caused by collisions between dust grains and supersonic neutral streams in a magnetized shock (C-shock). We demonstrate that, if the ISM in a magnetic field is impacted by a C-shock developed by a supernova explosion in the early phase of massive star formation (≲10 Myr), AME can be significantly or almost entirely suppressed relative to free-free and thermal dust continuum emission if the grain tensile strength is small enough. This study may shed light on explaining the rare observations of AME from extragalactic star-forming regions preferentially observed from massive star clusters and suggest a scenario of "the rise and fall of AME" in accordance with the temporal evolution of star-forming regions.