Determining Star Formation Thresholds from Observations

Abstract

Most gas in giant molecular clouds is relatively low-density and forms star inefficiently, converting only a small fraction of its mass to stars per dynamical time. However, star formation models generally predict the existence of a threshold density above which the process is efficient and most mass collapses to stars on a dynamical timescale. A number of authors have proposed observational techniques to search for a threshold density above which star formation is efficient, but it is unclear which of these techniques, if any, are reliable. In this paper we use detailed simulations of turbulent, magnetised star-forming clouds, including stellar radiation and outflow feedback, to investigate whether it is possible to recover star formation thresholds using current observational techniques. Using mock observations of the simulations at realistic resolutions, we show that plots of projected star formation efficiency per free-fall time ff can detect the presence of a threshold, but that the resolutions typical of current dust emission or absorption surveys are insufficient to determine its value. In contrast, proposed alternative diagnostics based on a change in the slope of the gas surface density versus star formation rate surface density (Kennicutt-Schmidt relation) or on the correlation between young stellar object counts and gas mass as a function of density are ineffective at detecting thresholds even when they are present. The signatures in these diagnostics sometimes taken as indicative of a threshold in observations, which we generally reproduce in our mock observations, do not prove to correspond to real physical features in the 3D gas distribution. 1 As discussed in the Krumholz et al. (2019) review, the amount of spread about this average is a subject of current debate; Krumholz et al. argue that the weight of evidence favours a relatively small spread of ≈ 0.3 dex, but some authors argue for larger spreads of 1 dex.

Where’s the Dust?: The Deepening Anomaly of Microwave Emission in NGC 4725 B

“…In these simulations, ò ff is small at low densities. As mass flows rapidly into higher-density regions within the cloud, ò ff approaches unity (Khullar et al 2019) with little time spent at intermediate densities. Therefore, the ò ff derived for NGC 4725 B may suggest that this object is being observed in a short-lived phase of its evolution.…”

The Single-Cloud Star Formation Relation

“…We construct this Figure following the method of ref. 28 , whereby we vary the contour level as shown in Figure 1, and within each contour we measure ff = SFR/( gas / ff ), where the values of SFR, gas , and ff are the values within the contour. The Figure shows how ff varies with mean gas column density within the corresponding contour Σ gas .…”

“…Variation of the free-fall efficiency ( ff ) with Σ gas for our sample of clouds. The uncertainties in ff are computed by assuming a Poisson distribution on the number of protostars 28 . The median of the logarithm of ff (−1.59, see Table 1) is shown by a black dashed line.…”

“…We propagated the uncertainties in column density to estimate uncertainties in derived Σ gas . For the uncertainty in the number of protostars enclosed by each N (H 2 ) contour, we assume Poissonian errors so the error on N PS is √ N PS (Khullar et al 2019), and propagate this to obtain the uncertainty in Σ SFR . Finally, Hu et al (2021) shows that the assumption of a uniform, spherical region that we use to estimate t ff is likely responsible for adding a scatter of ∼0.2 dex.…”

“…To demonstrate that the correlations seen in Figure 2b are not just an artifact created by comparing two quantities that are inversely proportional to the area, we further examine the value of ff as a function of column density for each of our clouds in Figure 3. We construct this figure following the method of Khullar et al (2019), whereby we vary the contour level as shown in Figure 1 Note that t ff ∝ A 3/4 , while Σ gas ∝ A −1 , so if the correlation shown in Figure 2b were primarily due to the fact that both axes depend similarly on area, then in Figure 3 we would expect to find…”