We present a new implementation of star formation in cosmological simulations, by considering star clusters as a unit of star formation. Cluster particles grow in mass over several million years at the rate determined by local gas properties, with high time resolution. The particle growth is terminated by its own energy and momentum feedback on the interstellar medium. We test this implementation for Milky Way-sized galaxies at high redshift, by comparing the properties of model clusters with observations of young star clusters. We find that the cluster initial mass function is best described by a Schechter function rather than a single power law. In agreement with observations, at low masses the logarithmic slope is α ≈ 1.8 − 2, while the cutoff at high mass scales with the star formation rate. A related trend is a positive correlation between the surface density of star formation rate and fraction of stars contained in massive clusters. Both trends indicate that the formation of massive star clusters is preferred during bursts of star formation. These bursts are often associated with major merger events. We also find that the median timescale for cluster formation ranges from 0.5 to 4 Myr and decreases systematically with increasing star formation efficiency. Local variations in the gas density and cluster accretion rate naturally lead to the scatter of the overall formation efficiency by an order of magnitude, even when the instantaneous efficiency is kept constant. Comparison of the formation timescale with the observed age spread of young star clusters provides an additional important constraint on the modeling of star formation and feedback schemes.

We present a study of a star formation prescription in which star formation efficiency depends on local gas density and turbulent velocity dispersion, as suggested by direct simulations of SF in turbulent giant molecular clouds (GMCs). We test the model using a simulation of an isolated Milky Way-sized galaxy with a selfconsistent treatment of turbulence on unresolved scales. We show that this prescription predicts a wide variation of local star formation efficiency per free-fall time, ff ∼ 0.1 − 10%, and gas depletion time, t dep ∼ 0.1 − 10 Gyr. In addition, it predicts an effective density threshold for star formation due to suppression of ff in warm diffuse gas stabilized by thermal pressure. We show that the model predicts star formation rates in agreement with observations from the scales of individual star-forming regions to the kiloparsec scales. This agreement is nontrivial, as the model was not tuned in any way and the predicted star formation rates on all scales are determined by the distribution of the GMC-scale densities and turbulent velocities σ in the cold gas within the galaxy, which is shaped by galactic dynamics. The broad agreement of the star formation prescription calibrated in the GMCscale simulations with observations, both gives credence to such simulations and promises to put star formation modeling in galaxy formation simulations on a much firmer theoretical footing.

Using an isolated Milky Way-mass galaxy simulation, we compare results from 9 state-of-the-art gravitohydrodynamics codes widely used in the numerical community. We utilize the infrastructure we have built for the AGORA High-resolution Galaxy Simulations Comparison Project. This includes the common disk initial conditions, common physics models (e.g., radiative cooling and UV background by the standardized package GRACKLE) and common analysis toolkit yt, all of which are publicly available. Subgrid physics models such as Jeans pressure floor, star formation, supernova feedback energy, and metal production are carefully constrained across code platforms. With numerical accuracy that resolves the disk scale height, we find that the codes overall agree well with one another in many dimensions including: gas and stellar surface densities, rotation curves, velocity dispersions, density and temperature distribution functions, disk vertical heights, stellar clumps, star formation rates, and Kennicutt-Schmidt relations. Quantities such as velocity dispersions are very robust (agreement within a few tens of percent at all radii) while measures like newly-2 J. KIM ET AL. FOR THE AGORA COLLABORATION formed stellar clump mass functions show more significant variation (difference by up to a factor of ∼3). Systematic differences exist, for example, between mesh-based and particle-based codes in the low density region, and between more diffusive and less diffusive schemes in the high density tail of the density distribution. Yet intrinsic code differences are generally small compared to the variations in numerical implementations of the common subgrid physics such as supernova feedback. Our experiment reassures that, if adequately designed in accordance with our proposed common parameters, results of a modern high-resolution galaxy formation simulation are more sensitive to input physics than to intrinsic differences in numerical schemes.

We present a model that explains why galaxies form stars on a time scale significantly longer than the time scales of processes governing the evolution of interstellar gas. We show that gas evolves from a nonstar-forming to a star-forming state on a relatively short time scale and thus the rate of this evolution does not limit the star formation rate. Instead, the star formation rate is limited because only a small fraction of star-forming gas is converted into stars before star-forming regions are dispersed by feedback and dynamical processes. Thus, gas cycles into and out of star-forming state multiple times, which results in a long time scale on which galaxies convert gas into stars. Our model does not rely on the assumption of equilibrium and can be used to interpret trends of depletion times with the properties of observed galaxies and the parameters of star formation and feedback recipes in simulations. In particular, the model explains how feedback selfregulates the star formation rate in simulations and makes it insensitive to the local star formation efficiency. We illustrate our model using the results of an isolated L * -sized galaxy simulation that reproduces the observed Kennicutt-Schmidt relation for both molecular and atomic gas. Interestingly, the relation for molecular gas is almost linear on kiloparsec scales, although a nonlinear relation is adopted in simulation cells. We discuss how a linear relation emerges from non-self-similar scaling of the gas density PDF with the average gas surface density.

Using a suite of isolated L galaxy simulations, we show that global depletion times and star-forming gas mass fractions in simulated galaxies exhibit systematic and well-defined trends as a function of the local star formation efficiency per freefall time, ff , strength of stellar feedback, and star formation threshold. We demonstrate that these trends can be reproduced and explained by a simple physical model of global star formation in galaxies. Our model is based on mass conservation and the idea of gas cycling between star-forming and non-star-forming states on certain characteristic time scales under the influence of dynamical and feedback processes. Both the simulation results and our model predictions exhibit two limiting regimes with rather different dependencies of global galactic properties on the local parameters. When ff is small and feedback is inefficient, the total star-forming mass fraction, f sf , is independent of ff and the global depletion time, τ dep , scales inversely with ff . When ff is large or feedback is very efficient, these trends are reversed: f sf ∝ −1 ff and τ dep is independent of ff but scales linearly with the feedback strength. We also compare our results with the observed depletion times and mass fractions of star-forming and molecular gas and show that they provide complementary constraints on ff and the feedback strength. We show that useful constraints on ff can also be obtained using measurements of the depletion time and its scatter on different spatial scales.