Fabián Quesada-Zúñiga

arXiv2026

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, $ε_{\rm ff}$, 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 $ε_{\rm ff}\equiv\langle\dot{M}_\star\rangle/(M_{\rm core}/τ_{\rm ff})$, where $\langle\dot{M}_\star\rangle$ is the average SFR, $M_{\rm core}$ is the gas mass within the core (as the gas cells above a density threshold), and $τ_{\rm ff}$ 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 $1000~\rm cm^{-3}$) 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, $n\propto r^{-p}$ 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 $ε_{\rm ff}$. 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, $ε_{\rm ff}$ 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, $ε_{\rm ff}$ 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 $ε_{\rm ff}$ depends sensitively on both the adopted core definition and external mass supply

astro-ph.SR↗

arXiv2025

Gravity or turbulence? VII. The Schmidt-Kennicutt law, the star formation efficiency, and the mass density of clusters from gravitational collapse rather than turbulent support

We explore the Schmidt-Kennicutt (SK) relations and the star formation efficiency per free-fall time ($ε_{\rm ff}$), mirroring observational studies, in numerical simulations of filamentary molecular clouds undergoing gravitational contraction. We find that (a)~collapsing clouds accurately replicate the observed SK relations for galactic clouds and (b)~$ε_{\rm ff}$ is small and constant in space and in time, with values similar to those found in local clouds. We propose that this constancy arises from the similar radial scaling of the free-fall time ($τ_{\rm ff}$) and the internal mass in density structures with spherically-averaged density profiles near $r^{-2}$. We additionally show that (c)~the star formation rate (SFR) increases rapidly in time; (d)~the low values of $ε_{\rm ff}$ result from evaluating $τ_{\rm ff}$ and the characteristic star-formation time scale over different time intervals, combined with the increasing SFR, and (e)~the fact that star clusters are significantly denser than the gas clumps from which they form is a natural consequence of the rapidly increasing SFR, the continuous replenishment of the star-forming gas by the accretion flow, and the near $r^{-2}$ density profile induced by the collapse. Finally, we argue that interpreting $ε_{\rm ff}$ as an efficiency is problematic since it is not bounded by unity, and because the gas mass in clouds evolves. Instead, we propose that viewing $ε_{\rm ff}$ as the ratio of the actual SFR to the gas free-fall rate. In summary, our results show that the SK relation, the low values of $ε_{\rm ff}$, and the mass density of stellar clusters arise naturally from gravitational contraction.

astro-ph.GA↗