The origin of the initial mass function and its dependence on the mean Jeans mass in molecular clouds

By Matthew R. Bate, Ian A. Bonnell. 2004

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We investigate the dependence of stellar properties on the mean thermal Jeans mass in molecular clouds. We compare the results from the two largest hydrodynamical simulations of star formation to resolve the fragmentation process down to the opacity limit, the first of which was reported by Bate, Bonnell & Bromm. The initial conditions of the two calculations are identical except for the radii of the clouds, which are chosen so that the mean densities and mean thermal Jeans masses of the clouds differ by factors of 9 and 3, respectively. We find that the denser cloud, with the lower mean thermal Jeans mass, produces a higher proportion of brown dwarfs and has a lower characteristic (median) mass of the stars and brown dwarfs. This dependence of the initial mass function (IMF) on the density of the cloud may explain the observation that the Taurus star-forming region appears to be deficient in brown dwarfs when compared with the Orion Trapezium cluster. The new calculation also produces wide binaries (separations >20 au), one of which is a wide binary brown dwarf system. Based on the hydrodynamical calculations, we develop a simple accretion/ejection model for the origin of the IMF. In the model, all stars and brown dwarfs begin with the same mass (set by the opacity limit for fragmentation) and grow in mass until their accretion is terminated stochastically by their ejection from the cloud through dynamically interactions. The model predicts that the main variation of the IMF in different star-forming environments should be in the location of the peak (due to variations in the mean thermal Jeans mass of the cloud) and in the substellar regime. However, the slope of the IMF at high masses may depend on the dispersion in the accretion rates of protostars. Ke yw ords: accretion, accretion discs ‐ hydrodynamics ‐ binaries: general ‐ stars: formation ‐ stars: low-mass, brown dwarfs ‐ stars: luminosity function, mass function.

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Citations in the corpus

THE PALOMAR/KECK ADAPTIVE OPTICS SURVEY OF YOUNG SOLAR ANALOGS: EVIDENCE FOR A UNIVERSAL COMPANION MASS FUNCTION (2008, methodology): “Based on results from three-dimensional smoothed particle hydrodynamic simulations, Bate et al. (2002) and Bate & Bonnell (2005) estimate that the opacity limit for gravo-turbulent fragmentation may be as low as 3–10 MJup.”
Theory of Star Formation (2007, background): “Bate, Bonnell, & Bromm (2003) and Bate & Bonnell (2005) analyzed the results of SPH decaying-turbulence simulations with a switch from isothermal to T ∝ ρ0.”
ERRATUM: “THE LUMINOSITY AND MASS FUNCTIONS OF LOW-MASS STARS IN THE GALACTIC DISK. II. THE FIELD” (2010, AJ, 139, 2679) (2010, methodology): “An alternative model to turbulent fragmentation is accretion and ejection (Bate & Bonnell 2005).”
The Formation and Early Evolution of Low-Mass Stars and Brown Dwarfs (2012, background): “Some of these objects are ejected through dynamical interactions with other companions or nearby stars (Bate & Bonnell 2005; Bate, Bonnell & Bromm 2002, 2003; Goodwin & Whitworth 2007; Offner, Klein & McKee 2008; Offner et al. 2009; Rice et al. 2003; Shen et al. 2010; Stamatellos, Hubber &…”
The Gemini Deep Planet Survey (2007, result): “The competitive accretion and ejection mechanism that was proposed initially to explain the formation of BDs (Reipurth & Clarke 2001) could also form planetary mass companions on large orbits, as suggested by the results of recent simulations by Bate & Bonnell (2005).”
Runaway collisions in young star clusters - II. Numerical results (2005, background): “The pioneering SPH/N-body simulations of very early cluster evolution could only handle up to a few hundred stars (Bonnell et al. 2004; Bate & Bonnell 2005).”
Toward Understanding Massive Star Formation (2007, background): “How general this random accretion model is and how it relates to the competitive accretion model above needs to be further explored (cf. Bate & Bonnell 2005).”
A CORRELATION BETWEEN SURFACE DENSITIES OF YOUNG STELLAR OBJECTS AND GAS IN EIGHT NEARBY MOLECULAR CLOUDS (2011, background): “…natal cloud material is needed to understand the nature of the distributed component, constrain models of star formation in molecular clouds, and ascertain the underlying physics that determine the density and rate of star formation (e.g. Bate & Bonnell 2005; Krumholz & Tan 2007; Myers 2009a).”
Thermal physics, cloud geometry and the stellar initial mass function (2005, background): “…simulations of isothermal collapse and fragmentation have shown that the number of bound fragments formed is generally similar to the number of Jeans masses present initially (e.g. Larson 1978; Monaghan & Lattanzio 1991; Klessen et al. 1998; Klessen 2001; Bate et al. 2003; Bate & Bonnell 2005).”
The Stellar IMF, Core Mass Function, & The Last-Crossing Distribution (2012, background): “This is a well-established result from both analytic work and numerical simulations (see e.g. Klessen & Burkert 2000, 2001; Bate & Bonnell 2005), and is true even if the gas is not isothermal (although our sub-sonic extrapolation is questionable in this case; see Larson 1985, 2005; Jappsen et al.…”
THE EFFECTS OF RADIATIVE TRANSFER ON LOW-MASS STAR FORMATION (2009, methodology): “These brown dwarf size objects are commonly produced in simulations that do not include a merger criterion, typically in larger numbers than are observed in the stellar IMF (e.g., Bate et al. 2003; Bate & Bonnell 2005; Bate 2009a).”
Evidence for top-heavy stellar initial mass functions with increasing density and decreasing metallicity (2012, background): “The Jeans-mass (MJ ∝ ρ−1/2T 3/2) is higher for denser (Larson 1998; Bate & Bonnell 2005; Bonnell et al. 2006) and warmer gas (Klessen et al. 2007) such that a higher average mass for stars is expected when favourable conditions are met.”
Stellar, brown dwarf and multiple star properties from a radiation hydrodynamical simulation of star cluster formation (2011, methodology): “This method was also used for the radiation hydrodynamical calculations presented by Bate (2009c), which were radiation hydrodynamical versions of the earlier barotropic calculations published by Bate et al. (2003) and Bate & Bonnell (2005).”
The importance of radiative feedback for the stellar initial mass function (2008, methodology): “…was similar to the initial mean Jeans mass of the cloud (Klessen et al. 1998; Klessen & Burkert 2000, 2001; Klessen 2001; Bate, Bonnell & Bromm 2003) and that variations in the initial Jeans mass led to corresponding variations in the characteristic mass of the IMF (Bate & Bonnell 2005; Bate 2005).”
ANALYTICAL THEORY FOR THE INITIAL MASS FUNCTION. II. PROPERTIES OF THE FLOW (2009, methodology): “…purely thermal support lead to too steep an IMF at large masses (Padoan et al. 2007), while simulations which use sink particles and include by definition the turbulent support with a Kolmogorov-like power spectrum index obtain the proper Salpeter slope (e.g. Klessen 2001, Bate & Bonnell 2005).”
Stellar, brown dwarf and multiple star properties from hydrodynamical simulations of star cluster formation (2008, background): “Furthermore, there are currently many models that have been proposed for the origin of the IMF (see the recent review, Bonnell, Larson & Zinnecker 2007 or the introduction of Bate & Bonnell 2005).”
The effect of magnetic fields on star cluster formation (2008, background): “…mass stars are simply those which have been quickly ejected from multiple systems and thus have only a short accretion history (Bate et al. 2002; Bate & Bonnell 2005), whereas higher mass stars are those which form and remain at the bottom f deep potential wells and build up their mass through…”
The stellar and sub-stellar IMF of simple and composite populations (2011, background): “11.1 and 12): There are two broad theoretical ansatzes for the origin of stellar masses: The Jeans-Mass Ansatz: According to the Jeans-mass argument (e.g. Jeans 1902, Larson 1998, Bate & Bonnell 2005, Bonnell et al. 2006, Eq.”