How fast do young star clusters expel their natal gas? Estimating the upper limit of the gas expulsion time-scale

Formation of massive stars within embedded star clusters starts a complex interplay between their feedback, inflowing gas, and stellar dynamics, which often includes close stellar encounters. Hydrodynamical simulations usually resort to substantial simplifications to model embedded clusters. Here, we address the simplification which approximates the whole star cluster by a single sink particle, which completely neglects the internal stellar dynamics. In order to model the internal stellar dynamics, we implement a Hermite predictor-corrector integration scheme to the hydrodynamic code FLASH. As we illustrate by a suite of tests, this integrator significantly outperforms the current leap-frog scheme, and it is able to follow the dynamics of small compact stellar systems without the necessity to soften the gravitational potential. We find that resolving individual massive stars instead of representing the whole cluster by a single energetic source has a profound influence on the gas component: for clusters of mass less than $\approx3 \times 10^3 \, \mathrm{M}_{\odot }$ , it slows gas expulsion by a factor of ≈5 to $\approx 1 \, \mathrm{Myr}$ , and it results in substantially more complex gas structures. With increasing cluster mass (up to $\approx 3\times 10^3 \, \mathrm{M}_{\odot }$ ), the gas expulsion time-scale slightly decreases. However, more massive clusters ( $\gtrsim 5\times 10^3 \, \mathrm{M}_{\odot }$ ) are unable to clear their natal gas with photoionizing radiation and stellar winds only if they form with a star formation efficiency (SFE) of 1/3. This implies that the more massive clusters are either cleared with another feedback mechanism or they form with an SFE higher than 1/3.