### Spectral signatures of compact sources in the inverse Compton catastrophe limit

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The inverse Compton catastrophe is defined as a dramatic rise in the luminosity of inverse Compton scattered photons. It is described by a non-linear loop of radiative processes that sets in for high values of the electron compactness and is responsible for the efficient transfer of energy from electrons to photons, predominantly through inverse Compton scatterings. We search for the conditions that drive a magnetized non-thermal source to the inverse Compton catastrophe regime and study its multi-wavelength (MW) photon spectrum. We develop a generic analytical framework and use numerical calculations as a backup to the analytical predictions. We find that the escaping radiation from a source in the Compton catastrophe regime bears some unique features. The MW photon spectrum is a broken power law with a break at $\sim m_e c^2$ due to the onset of the Klein-Nishina suppression. The spectral index below the break energy depends on the electron and magnetic compactnesses logarithmically, while it is independent of the electron power-law index ($s$). The maximum radiating power emerges typically in the $\gamma$-ray regime, at energies $\sim m_e c^2$ ($\sim \gamma_{\max} m_e c^2$ ) for $s>2$ ($s\lesssim 2$), where $\gamma_{\max}$ is the maximum Lorentz factor of the injected electron distribution. We apply the principles of the inverse Compton catastrophe to blazars and $\gamma$-ray bursts using the analytical framework we developed, and show how these can be used to impose robust constraints on the source parameters.