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

A parameter used to characterise star formation activity in MCs is the efficiency per free-fall time, epsilon 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 epsilon ff/(M core /tau ff), where is the average SFR, M core is the gas mass within the core (as the gas cells above a density threshold), and tau 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 cm-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 proportional to r-p with p to2. 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 epsilon 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, epsilon 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, epsilon 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 epsilon ff depends sensitively on both the adopted core definition and external mass supply