On the Appearance of Thresholds in the Dynamical Model of Star Formation

Abstract

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.

The MALATANG Survey: The LGAS–LIR Correlation on Sub-kiloparsec Scale in Six Nearby Star-forming Galaxies as Traced by HCN J = 4 → 3 and HCO+ J = 4 → 3

“…In contrast, a slope of unity relates Σ SFR and H 2 S for normal and dwarf galaxies (Schruba 2013). However, the slope steepens for the SFR H 2 S S -relation if we expand the sample to include galaxies with extreme starbursts, such as luminous infrared galaxies (LIRGs, L L L 10 10 11 IR 12  <   ) and ultraluminous infrared galaxies (ULIRGs, L L 10 IR 12   ), which is evident from both observations (e.g., Gao & Solomon 2004b;Daddi et al 2010;Liu et al 2015b) and theoretical predictions (e.g., Krumholz & McKee 2005;Elmegreen 2015Elmegreen , 2018. In addition, a breakdown of the KS law is found at giant molecular cloud (GMC) scales of a few tens of parsecs (e.g., Onodera et al 2010;Nguyen-Luong et al 2016), which is attributed to the dynamical evolution of GMCs and the drift of young clusters from their GMCs.…”

The Kennicutt–Schmidt Law and Gas Scale Height in Luminous and Ultraluminous Infrared Galaxies

“…The timescale is then the collapse time at that selected density, i.e., a constant. In contrast, the total gas should have a continuum of densities that widely participates in a gravity-driven condensation into dense clouds (Elmegreen 2015(Elmegreen , 2018. If the average density increases with Σ SFR , then the KS slope will be steeper than linear, such as 1.4 in the observations by Kennicutt (1998), de los Reyes & Kennicutt (2019), and others.…”

The Density Gradient Inside Molecular-gas Clumps as a Booster of Their Star Formation Activity

“…(ii) it is unclear which fraction of their YSOs clouds actually form in their dense gas as the existence of a gas density threshold for star formation remains debated (Parmentier 2016(Parmentier , 2017Elmegreen 2018); (iii) p is unknown in the number density regime beyond the resolution limit of the observations, i.e. > 5 · 10 4 cm −3 (Kainulainen et al 2014); (iv) the observed YSO census measures the past star formation history and, therefore, results from the cloud and clump structures prevailing before the time t of the observations; presentlyobserved structures, as quantified by the observed steepness p, drive the present and forthcoming star formation rate.…”