Multi-wavelength (X-ray to radio) monitoring of Young Stellar Objects (YSOs) can provide important information about physical processes at the stellar surface, in the stellar corona, and/or in the inner circumstellar disk regions. While coronal processes should mainly cause variations in the X-ray and radio bands, accretion processes may be traced by time-correlated variability in the X-ray and optical/infrared bands. Several multi-wavelength studies have been successfully performed for field stars and approx. 1-10 Myr old T Tauri stars, but so far no such study succeeded in detecting simultaneous X-ray to radio variability in extremely young objects like class I and class 0 protostars. Here we present the first simultaneous X-ray, radio, near-infrared, and optical monitoring of YSOs, targeting the Coronet cluster in the Corona Australis star-forming region, which harbors at least one class 0 protostar, several class I objects, numerous T Tauri stars, and a few Herbig AeBe stars. [...] Seven objects are detected simultaneously in the X-ray, radio, and optical/infrared bands; they constitute our core sample. While most of these sources exhibit clear variability in the X-ray regime and several also display optical/infrared variability, none of them shows significant radio variability on the timescales probed. We also do not find any case of clearly time-correlated optical/infrared and X-ray variability. [...] The absence of time-correlated multi-wavelength variability suggests that there is no direct link between the X-ray and optical/infrared emission and supports the notion that accretion is not an important source for the X-ray emission of these YSOs. No significant radio variability was found on timescales of days.
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