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Register a new userOn the Appearance of Thresholds in the Dynamical Model of Star Formation
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Bruce G. Elmegreen
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The Kennicutt-Schmidt (KS) relationship between the surface density of the star formation rate (SFR) and the gas surface density has three distinct power laws that may result from one model in which gas collapses at a fixed fraction of the dynamical rate. The power law slope is 1 when the observed gas has a characteristic density for detection, 1.5 for total gas when the thickness is about constant as in the main disks of galaxies, and 2 for total gas when the thickness is regulated by self-gravity and the velocity dispersion is about constant, as in the outer parts of spirals, dwarf irregulars, and giant molecular clouds. The observed scaling of the star formation efficiency (SFR per unit CO) with the dense gas fraction (HCN/CO) is derived from the KS relationship when one tracer (HCN) is on the linear part and the other (CO) is on the 1.5 part. Observations of a threshold density or column density with a constant SFR per unit gas mass above the threshold are proposed to be selection effects, as are observations of star formation in only the dense parts of clouds. The model allows a derivation of all three KS relations using the probability distribution function of density with no thresholds for star formation. Failed galaxies and systems with sub-KS SFRs are predicted to have gas that is dominated by an equilibrium warm phase where the thermal Jeans length exceeds the Toomre length. A squared relation is predicted for molecular gas-dominated young galaxies.
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We aim at understanding the massive star formation (MSF) limit $m(r) = 870 M_{odot} (r/pc)^{1.33}$ in the mass-size space of molecular structures recently proposed by Kauffmann & Pillai (2010). As a first step, we build on the hypothesis of a volume density threshold for overall star formation and the model of Parmentier (2011) to establish the mass-radius relations of molecular clumps containing given masses of star-forming gas. Specifically, we relate the mass $m_{clump}$, radius $r_{clump}$ and density profile slope $-p$ of molecular clumps which contain a mass $m_{th}$ of gas denser than a volume density threshold $rho_{th}$. In a second step, we use the relation between the mass of embedded-clusters and the mass of their most-massive star to estimate the minimum mass of star-forming gas needed to form a $10,M_{odot}$ star. Assuming a star formation efficiency of $SFE simeq 0.30$, this gives $m_{th,crit} simeq 150 M_{odot}$. In a third step, we demonstrate that, for sensible choices of the clump density index ($p simeq 1.7$) and of the cluster formation density threshold ($n_{th} simeq 10^4,cm^{-3}$), the line of constant $m_{th,crit} simeq 150 M_{odot}$ in the mass-radius space of molecular structures equates with the MSF limit for spatial scales larger than 0.3,pc. Hence, the observationally inferred MSF limit of Kauffmann & Pillai is consistent with a threshold in star-forming gas mass beyond which the star-forming gas reservoir is large enough to allow the formation of massive stars. For radii smaller than 0.3,pc, the MSF limit is shown to be consistent with the formation of a $10,M_{odot}$ star out of its individual pre-stellar core of density threshold $n_{th} simeq 10^5,cm^{-3}$. The inferred density thresholds for the formation of star clusters and individual stars within star clusters match those previously suggested in the literature.
Young massive clusters (YMCs) are usually accompanied by lower-mass clusters and unbound stars with a total mass equal to several tens times the mass of the YMC. If this was also true when globular clusters (GCs) formed, then their cosmic density implies that most star formation before redshift ~2 made a GC that lasted until today. Star-forming regions had to change after this time for the modern universe to be making very few YMCs. Here we consider the conditions needed for the formation of a ~10^6 Msun cluster. These include a star formation rate inside each independent region that exceeds ~1 Msun/yr to sample the cluster mass function up to such a high mass, and a star formation rate per unit area of Sigma_SFR ~ 1 Msun/kpc^2/yr to get the required high gas surface density from the Kennicutt-Schmidt relation, and therefore the required high pressure from the weight of the gas. High pressures are implied by the virial theorem at cluster densities. The ratio of these two quantities gives the area of a GC-forming region, ~1 kpc^2, and the young stellar mass converted to a cloud mass gives the typical gas surface density of 500-1000 Msun/pc^2 Observations of star-forming clumps in young galaxies are consistent with these numbers, suggesting they formed todays GCs. Observations of the cluster cut-off mass in local galaxies agree with the maximum mass calculated from Sigma_SFR. Metal-poor stellar populations in local dwarf irregular galaxies confirm the dominant role of GC formation in building their young disks.
To make predictions for the existence of ``dark galaxies, it is necessary to understand what determines whether a gas cloud will form stars. Star formation thresholds are generally explained in terms of the Toomre criterion for gravitational instability. I contrast this theory with the thermo-gravitational instability hypothesis of Schaye (2004), in which star formation is triggered by the formation of a cold gas phase and which predicts a nearly constant surface density threshold. I argue that although the Toomre analysis is useful for the global stability of disc galaxies, it relies on assumptions that break down in the outer regions, where star formation thresholds are observed. The thermo-gravitational instability hypothesis can account for a number of observed phenomena, some of which were thought to be unrelated to star formation thresholds.
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 $epsilon_{rm ff}$ 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.
We use cosmological hydrodynamical galaxy formation simulations from the NIHAO project to investigate the response of cold dark matter (CDM) haloes to baryonic processes. Previous work has shown that the halo response is primarily a function of the ratio between galaxy stellar mass and total virial mass, and the density threshold above which gas is eligible to form stars, $n [{rm cm}^{-3}]$. At low $n$ all simulations in the literature agree that dwarf galaxy haloes are cuspy, but at high $nge 100$ there is no consensus. We trace halo contraction in dwarf galaxies with $nge 100$ reported in some previous simulations to insufficient spatial resolution. Provided the adopted star formation threshold is appropriate for the resolution of the simulation, we show that the halo response is remarkably stable for $nge 5$, up to the highest star formation threshold that we test, $n=500$. This free parameter can be calibrated using the observed clustering of young stars. Simulations with low thresholds $nle 1$ predict clustering that is too weak, while simulations with high star formation thresholds $nge 5$, are consistent with the observed clustering. Finally, we test the CDM predictions against the circular velocities of nearby dwarf galaxies. Low thresholds predict velocities that are too high, while simulations with $nsim 10$ provide a good match to the observations. We thus conclude that the CDM model provides a good description of the structure of galaxies on kpc scales provided the effects of baryons are properly captured.
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