  We study parametric instability of compact axion dark matter structures
decaying to radiophotons. Corresponding objects - Bose (axion) stars, their
clusters, and clouds of diffuse axions - form abundantly in the
postinflationary Peccei-Quinn scenario. We develop general description of
parametric resonance incorporating finite-volume effects, backreaction, axion
velocities and their (in)coherence. With additional coarse-graining, our
formalism reproduces kinetic equation for virialized axions interacting with
photons. We derive conditions for the parametric instability in each of the
above objects, as well as in collapsing axion stars, evaluate photon resonance
modes and their growth exponents. As a by-product, we calculate stimulated
emission of Bose stars and diffuse axions, arguing that the former can give
larger contribution into the radiobackground. In the case of QCD axions, the
Bose stars glow and collapsing stars radioburst if the axion-photon coupling
exceeds the original KSVZ value by two orders of magnitude. The latter
constraint is alleviated for several nearby axion stars in resonance and absent
for axion-like particles. Our results show that the parametric effect may
reveal itself in observations, from FRB to excess radiobackground.
