Removing outbursts from multiwavelength light curves of the blazar Mrk~421, we construct outburstless time series for this system. A model-independent power spectrum light curve analysis in the optical, hard X-ray and gamma-rays for this outburstless state and also the full light-curves, show clear evidence for a periodicity of ~ 310 days across all wavelengths studied. A subsequent full maximum likelihood analysis fitting an eclipse model confirms a periodicity of 310 pm 1 days. The power spectrum of the signal in the outburstless state of the source does not follow a flicker noise behaviour and so, the system producing it is not self-organised. This and the fact that the periodicity is better defined in the outburstless state, strongly suggests that it is not produced by any internal physical processes associated to the central engine. The simplest physical mechanism to which this periodicity could be ascribed is a dynamical effect produced by an orbiting supermassive black hole companion eclipsing the central engine. Interestingly, the optimal eclipse model infers a brightness enhancement of (136.4 pm 20 )%, suggesting an eclipse resulting in a gravitational lensing brightening. Consisting with this interpretation, the eclipse occurs for only ( 9.7 pm 0.2)% of the orbital period.
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