The Stellar Initial Mass Function from Turbulent Fragmentation

By P. Padoan, Åke Nordlund. 2000

810 citations recorded by the source corpus.

The morphology and kinematics of molecular clouds (MCs) are best explained as the consequence of supersonic turbulence. Supersonic turbulence fragments MCs into dense sheets, filaments, and cores and large low-density "voids," via the action of highly radiative shocks. We refer to this process as turbulent fragmentation. In this work we derive the mass distribution of gravitationally unstable cores generated by the process of turbulent fragmentation. The mass distribution above 1 M☉ depends primarily on the power spectrum of the turbulent flow and on the jump conditions for isothermal shocks in a magnetized gas. For a power spectrum index β = 1.74, consistent with Larson's velocity dispersion-size relation as well as with new numerical and analytic results on supersonic turbulence, we obtain a power-law mass distribution of dense cores with a slope equal to 3/(4 - β) = 1.33, consistent with the slope of the stellar initial mass function (IMF). Below 1 M☉, the mass distribution flattens and turns around at a fraction of 1 M☉, as observed for the stellar IMF in a number of stellar clusters, because only the densest cores are gravitationally unstable. The mass distribution at low masses is determined by the probability distribution of the gas density, which is known to be approximately lognormal for an isothermal turbulent gas. The intermittent nature of the turbulent density distribution is thus responsible for the existence of a significant number of small collapsing cores, even of substellar mass. Since turbulent fragmentation is unavoidable in supersonically turbulent molecular clouds, and given the success of the present model in predicting the observed shape of the stellar IMF, we conclude that turbulent fragmentation is essential to the origin of the stellar IMF.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/5fbda7db4306f71b54539517178bf072b6de26d6

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Citations in the corpus

The First Stars (2003, background): “Recent hydrodynamical simulations of the collapse and fragmentation of turbulent molecular cloud cores (e.g., Padoan & Nordlund 2002, Bate et al. 2003) illustrate the highly dynamic and chaotic nature of the star formation process.2 The metal-rich chemistry, magnetohydrodynamics, and radiative…”
The Mass Distribution and Lifetime of Prestellar Cores in Perseus, Serpens, and Ophiuchus (2008, background): “For example, we found in Paper III that the predicted dependence of CMD shape on the turbulent mach number (Ballesteros-Paredes et al. 2006; Padoan & Nordlund 2002) does not agree with observations.”
The Birth of High-Mass Stars: Accretion and/or Mergers? (2005, background): “The origin of the initial mass function (IMF) has been extensively debated in the lit- erature (e.g. Larson 2005; Mac Low & Klessen 2004; Padoan & Nordlund 2002; Kroupa 2001, 2002; Elmegreen 2000; Bonnell et al. 1997, 2004).”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, background): “…Jeans mass” (the actual characteristic mass of structures) depends on turbulence, not on the sound speed, in a super-sonically turbulent medium (see e.g. Padoan & Nordlund 2002; Hennebelle & Chabrier 2008; Hopkins 2012b,a, 2013d,c,b; Hopkins & Christiansen 2013; Guszejnov & Hopkins 2015, 2016).”
THE INTERSTELLAR MEDIUM IN DISTANT STAR-FORMING GALAXIES: TURBULENT PRESSURE, FRAGMENTATION, AND CLOUD SCALING RELATIONS IN A DENSE GAS DISK AT z = 2.3 (2011, methodology): “While this has been widely used in numerical simulations (e.g. Padoan & Nordlund 2002), and analytical models of turbulence-regulated star-formation in individual molecular clouds and gaseous galactic disks (e.g. Krumholz & McKee 2005), it does not represent a realistic ISM.”
Molecular Clouds in the Milky Way (2015, positive): “…on cloud structure, it is the shape and width of the volume density PDFs of molecular clouds that are used in analytical theories of star formation to predict star-formation rates and the mass distribution of newborn stars (Padoan & Nordlund 2002, Krumholz & McKee 2005, Hennebelle & Chabrier 2008).”
Importance of the Initial Conditions for Star Formation - I. Cloud Evolution and Morphology (2010, methodology): “A comparison with analytic models of the IMF (e.g. Padoan & Nordlund 2002; Hennebelle & Chabrier 2008) is planned in a future contribution.”
Dusty Star Forming Galaxies at High Redshift (2014, background): “Similarly, nearly every model for the origin and potential variations in the IMF depend on the physical properties of the molecular ISM on small scales (e.g. Krumholz, 2011b; Hopkins, 2013; Padoan and Nordlund, 2002; Narayanan and Davé, 2012, 2013).”
THE STELLAR INITIAL MASS FUNCTION IN EARLY-TYPE GALAXIES FROM ABSORPTION LINE SPECTROSCOPY. II. RESULTS (2012, background): “…by the Jeans mass (e.g., Larson 1998, 2005), by feedback from protostars (Silk 1995; Adams & Fatuzzo 1996; Krumholz 2011), or by the distribution of densities in a supersonically turbulent interstellar medium (Padoan et al. 1997; Padoan & Nordlund 2002; Hennebelle & Chabrier 2008; Hopkins 2012a,b).”
STAR FORMATION IN DISK GALAXIES. I. FORMATION AND EVOLUTION OF GIANT MOLECULAR CLOUDS VIA GRAVITATIONAL INSTABILITY AND CLOUD COLLISIONS (2008, methodology): “Following the empirical relation σ2PDF = ln[1+(3M2/4)] derived from analysis of simulations of isothermal, non-self-gravitating supersonic turbulence (Padoan, Nordlund & Jones 1997, Padoan & Nordlund 2002, Krumholz & McKee 2005), where M is the 1D Mach number, we estimate M = 8.5.”
Star formation through gravitational collapse and competitive accretion (2006, background): “Turbulent fragmentation has also been suggested as an alternative mechanism whereby the masses of stars are determined by the size and densities of turbulent shocks (Padoan & Nordlund 2002).”
Toward Understanding Massive Star Formation (2007, background): “This means that supersonic turbulence rapidly produces localized compressed pockets of gas, some of which remain gravitationally bound and provide the initial conditions for collapse (Padoan & Nordlund 2002; Klessen et al. 2005).”
Two Regimes of Turbulent Fragmentation and the Stellar Initial Mass Function from Primordial to Present-Day Star Formation (2007, methodology): “This coincidence suggests that the process of turbulent fragmentationmay play amajor role in the origin of the stellar IMF (Padoan & Nordlund 2002), with only minor effects due to gravitational fragmentation, accretion, or merging.”