Toward First-Principle Simulations of Galaxy Formation: I. How Should We Choose Star-Formation Criteria in High-Resolution Simulations of Disk Galaxies?

Abstract

We performed three-dimensional $N$-body/SPH simulations to study how mass resolution and other model parameters, such as the star-formation efficiency parameter, $C_*$ and the threshold density for star formation, $n_{\rm th}$ affect structures of the galactic gaseous/stellar disk. We employed $10^6$–$10^7$ particles to resolve a cold ($T \lt$ 100 K) and dense ($n_{\rm H} \gt$ 100 cm$^{-3}$) phase as well as diffuse, hot phases. We found that structures of the interstellar medium (ISM) and the distribution of young stars were sensitive to the assumed values of $n_{\rm th}$. High-$n_{\rm th}$ models with $n_{\rm th} =$ 100 cm$^{-3}$ yielded clumpy multi-phase features in the ISM. Young stars were distributed in a thin disk, of which the half-mass scale height was 10–30 pc. In low-$n_{\rm th}$ models with $n_{\rm th} =$ 0.1 cm$^{-3}$, which is usually employed in cosmological galaxy-formation simulations, the gas disk appears to be smoother and the stellar disk is found to be several-times thicker than the high-$n_{\rm th}$ models. A high-resolution simulation with high-$n_{\rm th}$ is necessary to reproduce the complex structure of the gas disk. The global star-formation properties of galaxies, such as the star-formation history, in low-$n_{\rm th}$ models are similar to those in high-$n_{\rm th}$ models when we tune the value of $C_*$ so that they reproduce the observed relation between the surface gas density and the surface star-formation rate density. We however emphasize that high-$n_{\rm th}$ models automatically reproduce the relation, regardless of the values of $C_*$. The ISM structure, phase distribution and distributions of young star-forming regions are quite similar in runs with different values of $C_*$. We found that the timescale of the flow from the reservoir ($n_{\rm H} \sim$ 1 cm$^{-3}$ ) to the star-forming regions ($n_{\rm H} \gtrsim 100$ cm$^{-3}$ ) is about five-times as long as the local dynamical time, and this evolution timescale is independent of the value of $C_*$. The use of a high-$n_{\rm th}$ criterion for star formation in high-resolution simulations makes numerical models fairy insensitive to the modeling of star formation.