The Star Formation Rate of Supersonic Magnetohydrodynamic Turbulence

Abstract

This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magnetohydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, α vir , the rms sonic Mach number, M S,0 , and the ratio of mean gas pressure to mean magnetic pressure, β 0 . The SFR is predicted to decrease with increasing α vir (stronger turbulence relative to gravity), to increase with increasing M S,0 (for constant values of α vir ), and to depend weakly on β 0 for values typical of star forming regions (M S,0 ≈ 4-20 and β 0 ≈ 1-20). In the unrealistic limit of β 0 → ∞, that is in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvénic turbulence). In this non-magnetized limit, our definition of the critical density for star formation has the same dependence on α vir , and almost the same dependence on M S,0 , as in the model of Krumholz and McKee, although our physical derivation does not rely on the concepts of local turbulent pressure and sonic scale. However, our model predicts a different dependence of the SFR on α vir and M S,0 than the model of Krumholz and McKee. The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations are shown to agree very well with the theoretical predictions. A physical model of the SFR is needed for a realistic implementation of the star formation feedback in simulations of galaxy formation, and to retrieve the correct morphological and chemical evolution of galaxies. The new star formation law derived in this paper is suitable for such applications.

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).…”

“…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 high-density power-law tail can develop as a consequence of gravitational contraction of the dense cores in a cloud (Klessen 2000;Federrath et al 2008aFederrath et al , 2011bKritsuk et al 2011;Federrath & Klessen 2013;Girichidis et al 2014).…”

GMC Collisions as Triggers of Star Formation. II. 3D Turbulent, Magnetized Simulations

“…Magnetic fields (e.g., Mouschovias 2001;Crutcher 2012;Li et al 2014, p. 101) and turbulence (e.g., Krumholz & McKee 2005;Padoan & Nordlund 2011;Federrath & Klessen 2012;Padoan et al 2014, p. 77) are both likely to be more important in influencing the gravitational stability of molecular gas and thus the regulation of star formation.…”

The distribution of density in supersonic turbulence

“…These are crucial for star-formation applications and directly observable in the ISM. However, although there are certain wellestablished results-most importantly the density variance-Mach number relation: that the density distribution is approximately lognormal with a variance that increases with Mach number (Passot & Vázquez-Semadeni 1998;Price et al 2011;Padoan & Nordlund 2011;Molina et al 2012;Federrath & Banerjee 2015;Pan et al 2016)-we lack detailed understanding of many important issues. For example, the power spectrum of density and its variation with Mach number is not well understood (Kim & Ryu 2005;Kritsuk et al 2007;Kowal et al 2007;Konstandin et al 2016).…”