The efficiency per free-fall time as a ratio of the Star Formation Rate to the gas-infall rate in collapsing cores: dependence on the core definition, accretion, and radial structure

Abstract

A parameter used to characterise star formation activity in MCs is the efficiency per free-fall time, $\hat{I}{\mu }_{\mathrm{ff}}$, although commonly referred to as an efficiency, it is formally the ratio between the star formation rate (SFR) and the gas-infall rate. Here we numerically study the collapse of cores and define $\hat{I}{\mu }_{\mathrm{ff}}\equiv ⟨{\dot{M}}_{\star }⟩/(M_{\mathrm{core}}/\ddot{I}{„}_{\mathrm{ff}})$, where $⟨{\dot{M}}_{\star }⟩$ is the average SFR, $M_{\mathrm{core}}$ is the gas mass within the core (as the gas cells above a density threshold), and $\ddot{I}{„}_{\mathrm{ff}}$ is the free-fall time of the core gas. We perform simplified numerical experiments of the gravitational collapse of an isolated core, varying the initial mean number density ($n_0=100$ and $1000\mathrm{c}{\mathrm{m}}^{-3}$) and adopting closed/open BCs to (dis)allow fresh gas accretion into the domain. The simulations start with a slight central Gaussian overdensity that evolved into a power-law profile, $n\propto r^{-p}$ with $p\to 2$. As the collapse proceeds, a sink particle forms in the center of the core. We find that both the BCs and the adopted core definition modify the measured core properties and, consequently, the inferred $\hat{I}{\mu }_{\mathrm{ff}}$. Low-density models have less mass available, and their accretion histories are therefore much more sensitive to the choice of BCs, while high-density runs, with their larger mass reservoirs, maintain similar accretion histories regardless of the BCs. In all models, after sink formation, $\hat{I}{\mu }_{\mathrm{ff}}$ rises and then remains relatively stable while accretion continues to replenish the core's mass, but increases once the gas reservoir is exhausted. Somewhat counterintuitively, $\hat{I}{\mu }_{\mathrm{ff}}$ is higher in the low-mass cores, since the larger gas infall rates onto the high-mass cores compensate for their higher SFR. We conclude that the inferred $\hat{I}{\mu }_{\mathrm{ff}}$ depends sensitively on both the adopted core definition and external mass supply

10 pages, 5 figures