THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS

By Christoph Federrath, Ralf Klessen. 2012

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The role of turbulence and magnetic fields is studied for star formation in molecular clouds. We derive and compare six theoretical models for the star formation rate (SFR)—the Krumholz & McKee (KM), Padoan & Nordlund (PN), and Hennebelle & Chabrier (HC) models, and three multi-freefall versions of these, suggested by HC—all based on integrals over the log-normal distribution of turbulent gas. We extend all theories to include magnetic fields and show that the SFR depends on four basic parameters: (1) virial parameter αvir; (2) sonic Mach number ; (3) turbulent forcing parameter b, which is a measure for the fraction of energy driven in compressive modes; and (4) plasma with the Alfvén Mach number . We compare all six theories with MHD simulations, covering cloud masses of 300 to 4 × 106 M☉ and Mach numbers –50 and –∞, with solenoidal (b = 1/3), mixed (b = 0.4), and compressive turbulent (b = 1) forcings. We find that the SFR increases by a factor of four between and 50 for compressive turbulent forcing and αvir ∼ 1. Comparing forcing parameters, we see that the SFR is more than 10 times higher with compressive than solenoidal forcing for simulations. The SFR and fragmentation are both reduced by a factor of two in strongly magnetized, trans-Alfvénic turbulence compared to hydrodynamic turbulence. All simulations are fit simultaneously by the multi-freefall KM and multi-freefall PN theories within a factor of two over two orders of magnitude in SFR. The simulated SFRs cover the range and correlation of SFR column density with gas column density observed in Galactic clouds, and agree well for star formation efficiencies SFE = 1%–10% and local efficiencies ϵ = 0.3–0.7 due to feedback. We conclude that the SFR is primarily controlled by interstellar turbulence, with a secondary effect coming from magnetic fields.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/3ff9c0e2f4cc602ad5859c9792099c9f3924ee0d

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Citations in the corpus

Star formation rates and efficiencies in the Galactic Centre (2017, methodology): “Shown in table 1 of Federrath & Klessen (2012) are the several definitions for the critical density for collapse, xcrit, and resultant solution to the integral of the density probability distribution function (equation 5).”
Fluctuating feedback-regulated escape fraction of ionizing radiation in low-mass, high-redshift galaxies (2017, methodology): “The exact formulae are given in Federrath & Klessen (2012), using their multi-scale model based on Padoan & Nordlund (2011), coined ‘multi-ff PN’ model.”
On the universality of supersonic turbulence (2013, background): “…the rate of star formation triggered by gas compression in shocks (Krumholz & McKee 2005; Hennebelle & Chabrier 2011; Padoan & Nordlund 2011; Federrath & Klessen 2012), affects the star formation efficiency (Elmegreen 2008; Federrath & Klessen 2013; Kainulainen, Federrath & Henning 2013),…”
Inefficient star formation through turbulence, magnetic fields and feedback (2015, methodology): “The top circle is a purely hydrodynamical simulation and the bottom circle included a magnetic field, yielding a reduction of the SFR by about a factor of 2–3, consistent with Wang et al. (2010), Padoan & Nordlund (2011), Padoan et al. (2012), Federrath & Klessen (2012) and this work.”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, methodology): “The exact order-unity coefficient is calibrated from higher-resolution simulations of collapsing clouds/cores (see Padoan et al. 2012; Federrath & Klessen 2012), but our results are insensitive to variations.”
Before the first supernova: combined effects of H II regions and winds on molecular clouds (2014, unknown): “Numerous recent studies (e.g Price & Bate 2009; Wang et al. 2010; Vázquez-Semadeni et al. 2011; Padoan & Nordlund 2011; Peters et al. 2011; Federrath & Klessen 2012; Myers et al. 2014) have found that the support provided at intermediate and large scales by magnetic fields slows star formation…”
Relativistic jet feedback in high-redshift galaxies – I. Dynamics (2016, background): “The mass in the swept- up shell is seen to have significantly high-velocity dispersion indicating the existence of strong turbulent motions, which can significantly affect star formation (Krumholz & McKee 2005; Federrath & Klessen 2012).”
On the diversity and statistical properties of protostellar discs (2018, background): “Magnetic pressure support can slow down the star formation rate by factors of 2–3 compared to hydrodynamical calculations (Price & Bate 2008, 2009; Wang et al. 2010; Padoan & Nordlund 2011; Federrath & Klessen 2012; Myers et al. 2014; Federrath 2015), but its affect on disc properties is unclear.”
A unified model for galactic discs: star formation, turbulence driving, and mass transport (2017, background): “These small-scale relations, while theoretically motivated, can be checked directly against numerical simulations of self-gravitating turbulence, and the agreement is generally good (e.g. Padoan & Nordlund 2011; Federrath & Klessen 2012; Padoan et al. 2014).”
STAR FORMATION RELATIONS IN NEARBY MOLECULAR CLOUDS (2014, background): “Federrath & Klessen (2012) also focus on the remaining scatter in the Heiderman et al. (2010) data, which is indeed substantial.”
A sub-parsec resolution simulation of the Milky Way: global structure of the interstellar medium and properties of molecular clouds (2013, background): “…al. 2013), recent works showed that turbulence is the most important factor, while magnetic fields have a more moderate but still significant influence on the star formation efficiency and the dense gas mass fraction (Padoan & Nordlund 2011; Federrath & Klessen 2012, 2013; Kainulainen et al. 2013).”
xCOLD GASS: The Complete IRAM 30 m Legacy Survey of Molecular Gas for Galaxy Evolution Studies (2017, background): “…the CGM down to star formation efficiency at the smallest of scales suggest that “whole cloud” theories for star formation (e.g. Krumholz & McKee 2005; Federrath & Klessen 2012) may have to also take into account the larger scale environment that regulates the availability of gas on small scales.”
Cloud-scale Molecular Gas Properties in 15 Nearby Galaxies (2018, background): “Theoretical works by McKee & Zweibel (1992), Krumholz & McKee (2005), Padoan & Nordlund (2011), Federrath & Klessen (2012), Kruijssen (2012), Krumholz et al. (2012), Hennebelle & Chabrier (2013), and Padoan et al. (2017) predict that αvir plays an important role in determining the ability of a…”
On the universality of interstellar filaments: theory meets simulations and observations (2015, unknown): “Based on this, the sonic scale is explicitly defined as (see Equation (22) in Federrath & Klessen 2012), λsonic = L [ cs σV ( 1 + β−1 )1/2]2 , (4) where L, σV , cs and β are the cloud scale, the velocity dispersion on the cloud scale, the sound speed, and the ratio of thermal to magnetic pressure,…”
The SPHINX Cosmological Simulations of the First Billion Years: the Impact of Binary Stars on Reionization★ (2018, methodology): “…Jeans length is unresolved, i.e. λJ, turb < x, where x is the finest cell width and the turbulent Jeans length is given by (Bonazzola et al. 1987; Federrath & Klessen 2012) λJ,turb = πσ 2gas + √ 36πc2s G x 2ρ + π2σ 4gas 6Gρ x , (2) where σ gas is the gas velocity dispersion over neighbour cells…”
Global hierarchical collapse in molecular clouds. Towards a comprehensive scenario (2019, methodology): “…of the free-fall time for the thresh- MNRAS 000, 1–41 (0000) old (e.g., Krumholz & McKee 2005; Padoan & Nordlund 2011; Hennebelle & Chabrier 2011; Federrath & Klessen 2012; Zamora-Avilés, Vázquez-Semadeni & Coĺın 2012; Völschow et al. 2017; Burkhart 2018), so that the stars formed by the…”