We study the evaporation and condensation of CO and CO_2 during the embedded stages of low-mass star formation by using numerical simulations. We focus on the effect of luminosity bursts, similar in magnitude to FUors and EXors, on the gas-phase abundance of CO and CO_2 in the protostellar disk and infalling envelope. The evolution of a young protostar and its environment is followed based on hydrodynamical models using the thin-disk approximation, coupled with a stellar evolution code and phase transformations of CO and CO_2. The accretion and associated luminosity bursts in our model are caused by disk gravitational fragmentation followed by quick migration of the fragments onto the forming protostar. We found that bursts with luminosity on the order of 100-200 L_sun can evaporate CO ices in part of the envelope. The typical freeze-out time of the gas-phase CO onto dust grains in the envelope (a few kyr) is much longer than the burst duration (100-200 yr). This results in an increased abundance of the gas-phase CO in the envelope long after the system has returned into a quiescent stage. In contrast, luminosity bursts can evaporate CO_2 ices only in the disk, where the freeze-out time of the gas-phase CO_2 is comparable to the burst duration. We thus confirm that luminosity bursts can leave long-lasting traces in the abundance of gas-phase CO in the infalling envelope, enabling the detection of recent bursts as suggested by previous semi-analytical studies.
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