Young massive clusters (YMCs) are the most intense regions of star formation in galaxies. Formulating a model for YMC formation while at the same time meeting the constraints from observations is, however, highly challenging. We show that forming YMCs requires clouds with densities ≳ 100 cm−3 to collide with high velocities (≳ 20 km s−1). We present the first simulations which, starting from moderate cloud densities of ∼100 cm−3, are able to convert a large amount of mass into stars over a time period of around 1 Myr, to produce dense massive clusters similar to those observed. Such conditions are commonplace in more extreme environments, where YMCs are common, but atypical for our Galaxy, where YMCs are rare.

We present Ekster, a new method for simulating star clusters from birth in a live galaxy simulation that combines the smoothed-particle hydrodynamics (SPH) method Phantom with the N-body method PeTar. With Ekster, it becomes possible to simulate individual stars in a simulation with only moderately high resolution for the gas, allowing us to study whole sections of a galaxy rather than be restricted to individual clouds. We use this method to simulate star and star cluster formation in spiral arms, investigating massive GMCs and spiral arm regions with lower mass clouds, from two galaxy models with different spiral potentials. After selecting these regions from pre-run galaxy simulations, we re-sample the particles to obtain a higher resolution. We then re-simulate these regions for 3 Myr to study where and how star clusters form. We analyse the early evolution of the embedded star clusters in these regions. We find that the massive GMC regions, which are more common with stronger spiral arms, form more massive clusters than the sections of spiral arms containing lower mass clouds. Clusters form both by accreting gas and by merging with other proto-clusters, the latter happening more frequently in the denser GMC regions.

Young massive clusters (YMCs) are recently formed astronomical objects with unusually high star formation rates. We propose the collision of giant molecular clouds (GMCs) as a likely formation mechanism of YMCs, consistent with the YMC conveyor-belt formation mode concluded by other authors. We conducted smoothed particle hydrodynamical simulations of cloud-cloud collisions and explored the effect of the clouds’ collision speed, initial cloud density, and the level of cloud turbulence on the global star formation rate and the properties of the clusters formed from the collision. We show that greater collision speed, greater initial cloud density and lower turbulence increase the overall star formation rate and produce clusters with greater cluster mass. In general, collisions with relative velocity ≳ 25 km s−1, initial cloud density ≳ 250 cm−3, and turbulence of ≈2.5 km s−1 can produce massive clusters with properties resembling the observed Milky Way YMCs.

Modelling star formation and resolving individual stars in numerical simulations of molecular clouds and galaxies is highly challenging. Simulations on very small scales can be sufficiently well resolved to consistently follow the formation of individual stars, whilst on larger scales sinks that have masses sufficient to fully sample the IMF can be converted into realistic stellar populations. However, as yet, these methods do not work for intermediate scale resolutions whereby sinks are more massive compared to individual stars but do not fully sample the IMF. In this paper, we introduce the grouped star formation prescription, whereby sinks are first grouped according to their positions, velocities, and ages, then stars are formed by sampling the IMF using the mass of the groups. We test our grouped star formation method in simulations of various physical scales, from sub-parsec to kilo-parsec, and from static isolated clouds to colliding clouds. With suitable grouping parameters, this star formation prescription can form stars that follow the IMF and approximately mimic the original stellar distribution and velocity dispersion. Each group has properties that are consistent with a star-forming region. We show that our grouped star formation prescription is robust and can be adapted in simulations with varying physical scales and resolution. Such methods are likely to become more important as galactic or even cosmological scale simulations begin to probe sub-parsec scales.

To form stars in hydrodynamical simulations, we introduce the grouped star formation prescription to convert the grouped sink particles into stars that follow the IMF. We show that this method is robust in different physical scales. Such methods to form stars are likely to become more important as galactic or even cosmological scale simulations begin to probe sub-parsec scales.