The conversion factor $alpha_{rm CO}$ from the observable CO(1-0) luminosity to the mass of molecular gas is known to vary between isolated galaxies and some mergers, but the underlying reasons are not clearly understood. Thus, the value(s) of $alpha_{rm CO}$ to be adopted remain highly uncertain. To provide better constraints, we apply the large velocity gradient method to a series of hydrodynamical simulations of galaxies and derive the evolution of $alpha_{rm CO}$. We report significant variations of $alpha_{rm CO}$, and identify three distinct regimes: disk galaxies, starbursts and post-burst phases. We show that estimating the star formation rate over 20 Myr smooths out some of these differences, but still maintains a distinction between disks and starbursts. We find a tighter correlation of $alpha_{rm CO}$ with the gas depletion time than with star formation rate, yet with deviations induced by the transitions to and from the starburst episodes. We conclude that $alpha_{rm CO}$ fluctuates because of both the feedback energy and the velocity dispersion. Identifying the phase of an interaction by classical means (e.g. morphology, luminosity) could then help selecting the relevant conversion factor to be used and get more accurate estimates of the molecular masses of galaxies.
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