Young stars exhibit variability due to changes in the gas accretion rate onto them, an effect that should be quite significant in the early stages of their formation. As protostars are embedded within their natal cloud, this variability may only be inferred through long wavelength observations. We perform radiative transfer simulations of young stellar objects (YSOs) formed in hydrodynamical simulations, varying the structure and luminosity properties in order to estimate the long-wavelength, sub-mm and mm, variations of their flux. We find that the flux increase due to an outburst event depends on the protostellar structure and is more prominent at sub-mm wavelengths than at mm wavelengths; e.g. a factor of 40 increase in the luminosity of the young protostar leads to a flux increase of a factor of 10 at 250 micron but only a factor of 2.5 at 1.3 mm. We find that the interstellar radiation field dilutes the flux increase but that this effect may be avoided if resolution permits the monitoring of the inner regions of a YSO, where the heating is primarily due to protostellar radiation. We also confirm that the bolometric temperature and luminosity of outbursting protostars may result in an incorrect classification of their evolutionary stage.

MNRAS accepted, 8 pages, 9 figures