Star Cluster Formation in Cosmological Simulations. II. Effects of Star Formation Efficiency and Stellar Feedback

The implementation of star formation and stellar feedback in cosmological simulations plays a critical role in shaping galaxy properties. In the first paper of the series, we presented a new method to model star formation as a collection of star clusters. In this paper, we improve the algorithm by eliminating accretion gaps, boosting momentum feedback, and introducing a subgrid initial bound fraction, $f_i$, that distinguishes cluster mass from stellar particle mass. We perform a suite of simulations with different star formation efficiency per freefall time $\epsilon_{\rm ff}$ and supernova momentum feedback intensity $f_{\rm boost}$. We find that the star formation history of a Milky Way-sized galaxy is sensitive to $f_{\rm boost}$, which allows us to constrain its value, $f_{\rm boost}\approx5$, in the current simulation setup. Changing $\epsilon_{\rm ff}$ from a few percent to 200\% has little effect on global galaxy properties. However, on smaller scales, the properties of star clusters are very sensitive to $\epsilon_{\rm ff}$. We find that $f_i$ increases with $\epsilon_{\rm ff}$ and cluster mass. Through the dependence on $f_i$, the shape of the cluster initial mass function varies strongly with $\epsilon_{\rm ff}$. The fraction of clustered star formation and maximum cluster mass increase with the star formation rate surface density, with the normalization of both relations dependent on $\epsilon_{\rm ff}$. The cluster formation timescale systematically decreases with increasing $\epsilon_{\rm ff}$. Local variations in the gas accretion history lead to a 0.25~dex scatter for the integral cluster formation efficiency. Joint constraints from all the observables prefer the runs that produce a median integral efficiency of 16\%.