A Universal, Turbulence-Regulated Star Formation Law: From Milky Way Clouds to High-Redshift Disk and Starburst Galaxies

Abstract

Whilst the star formation rate (SFR) of molecular clouds and galaxies is key in understanding galaxy evolution, the physical processes which determine the SFR remain unclear. This uncertainty about the underlying physics has resulted in various different star formation laws, all having substantial intrinsic scatter. Extending upon previous works that define the column density of star formation (Σ SFR ) by the gas column density (Σ gas ), we develop a new universal star formation (SF) law based on the multi-freefall prescription of gas. This new SF law relies predominantly on the probability density function (PDF) and on the sonic Mach number of the turbulence in the star-forming clouds. By doing so we derive a relation where the star formation rate (SFR) correlates with the molecular gas mass per multi-freefall time, whereas previous models had used the average, single-freefall time. We define a new quantity called maximum (multi-freefall) gas consumption rate (MGCR) and show that the actual SFR is only about 0.4% of this maximum possible SFR, confirming the observed low efficiency of star formation. We show that placing observations in this new framework (Σ SFR vs. MGCR) yields a significantly improved correlation with 3-4 times reduced scatter compared to previous SF laws and a goodness-of-fit parameter R 2 = 0.97. By inverting our new relationship, we provide sonic Mach number predictions for kpc-scale observations of Local Group galaxies as well as unresolved observations of local and high-redshift disk and starburst galaxies that do not have independent, reliable estimates for the turbulent cloud Mach number.

The Link Between Turbulence, Magnetic Fields, Filaments, and Star Formation in the Central Molecular Zone Cloud G0.253+0.016

“…The density PDF is a key ingredient for theoretical models of the SFR and efficiency (Krumholz & McKee 2005;Elmegreen 2008;Padoan & Nordlund 2011;Federrath 2013;Padoan et al 2014;Salim et al 2015), for predicting bound star cluster formation (Kruijssen 2012), and for the initial mass function of stars (Padoan & Nordlund 2002;Hennebelle & Chabrier 2008Veltchev et al 2011;Donkov et al 2012;Hopkins 2012Hopkins , 2013aChabrier et al 2014). It is supersonic, magnetized turbulence that determines the density PDF and, in particular, its standard deviation (Padoan et al 1997b;Federrath et al 2008b;Padoan & Nordlund 2011;Price et al 2011;Konstandin et al 2012;Burkhart & Lazarian 2012;Molina et al 2012;Federrath & Banerjee 2015;Nolan et al 2015).…”

A dynamical model for gas flows, star formation and nuclear winds in galactic centres

“…This expression has all the properties we desire: ff → 1 as αvir → 0, ff = 0.01 at αvir = 1, and ff declines exponentially as αvir rises. While the value of ff is tightly constrained by observations to lie near our fiducial choice (e.g., Krumholz & Tan 2007;Krumholz, Dekel & McKee 2012;Federrath 2013;Krumholz 2014;Evans, Heiderman & Vutisalchavakul 2014;Salim, Federrath & Kewley 2015;Heyer et al 2016), we also consider the effects of varying ff,0 . Before moving on we note that, although we have phrased our star formation rate as a function of αvir, the virial ratio in our models is closely related to the Toomre Q of the gas.…”

The Physical Origin of Long Gas Depletion Times in Galaxies

“…A number of useful global star formation frameworks and models have been developed over the last three decades (e.g., Wyse & Silk 1989;Silk 1997;Tan 2000;Elmegreen 2002;Krumholz & McKee 2005;Li et al 2005;Krumholz & Thompson 2007;Saitoh et al 2008;Krumholz et al 2009b;Silk & Norman 2009;Ostriker et al 2010;Ostriker & Shetty 2011;Renaud et al 2012;Faucher-Giguère et al 2013;Federrath 2013;Elmegreen 2015;Salim et al 2015). Many of these models consider the physical processes shaping the form of the KSR while treating its normalization as a flexible constant.…”