ANALYTICAL THEORY FOR THE INITIAL MASS FUNCTION. II. PROPERTIES OF THE FLOW

By P. Hennebelle, G. Chabrier. 2009

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Recently, Hennebelle and Chabrier derived an analytical theory for the mass spectrum of non-self-gravitating clumps associated with overdensities in molecular clouds and for the initial mass function (IMF) of gravitationally bound prestellar cores, as produced by the turbulent collapse of the cloud. In this companion paper, we examine the effects of the nonisothermality of the flow, of the turbulence forcing and of local fluctuation of the velocity dispersion, on the mass function. In particular, we investigate the influence of a polytropic equation of state (eos) and of the effective adiabatic exponent γ and find that it has a drastic influence on the low-mass part of the IMF. We also consider a barotropic eos (i.e., a piecewise polytropic eos) that mimics the thermal behavior of the molecular gas and compare the prediction of our theory with the results of numerical simulations and with the observationally derived IMF, for cloud parameters which satisfy Larson-type relations. We find that for clouds whose density is, at all scales, almost an order of magnitude larger than the density inferred for the CO clumps in the Galaxy, a good agreement is obtained between the theory and the observed IMF, suggesting that star formation preferentially occurs in high-density environments. We derive an analytical expression for the IMF which generalizes the expression previously obtained for the isothermal case. This easy-to-implement analytical IMF should serve as a template to compare observational or numerical results with the theory.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/19b4eaf4e09fd4dbed41539c4f7b192ba016590f

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Citations in the corpus

The density variance–Mach number relation in supersonic turbulence – I. Isothermal, magnetized gas (2012, background): “…primarily established (Press & Schechter 1974), to star formation and theories of the initial mass function or the core mass function (e.g. Fleck 1982; Zinnecker 1984; Padoan, Nordlund & Jones 1997; Klessen & Burkert 2000; Li et al. 2004; Hennebelle & Chabrier 2008, 2009; Padoan & Nordlund 2011).”
ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, background): “The density PDF of the turbulent gas is a key for analytic models of the core and stellar initial mass functions (Padoan & Nordlund 2002; Hennebelle & Chabrier 2008, 2009; Elmegreen 2011; Veltchev et al. 2011; Donkov et al. 2012; Parravano et al. 2012; Hopkins 2012c,a), the Kennicutt-Schmidt…”
A NEW JEANS RESOLUTION CRITERION FOR (M)HD SIMULATIONS OF SELF-GRAVITATING GAS: APPLICATION TO MAGNETIC FIELD AMPLIFICATION BY GRAVITY-DRIVEN TURBULENCE (2011, background): “Moreover, the PDF is an essential ingredient for models of star formation (e.g., Padoan & Nordlund 2002; Krumholz & McKee 2005; Hennebelle & Chabrier 2008, 2009) and the gas distribution in galaxies (e.g., Tassis 2007; Krumholz et al. 2009).”
LIMITING ACCRETION ONTO MASSIVE STARS BY FRAGMENTATION-INDUCED STARVATION (2010, background): “Arguments to explain the core mass distribution generally rely on the statistical properties of turbulence (Klessen 2001; Padoan & Nordlund 2002; Hennebelle & Chabrier 2008, 2009), which generate structures with a pure powerlaw mass spectrum.”
MODELING COLLAPSE AND ACCRETION IN TURBULENT GAS CLOUDS: IMPLEMENTATION AND COMPARISON OF SINK PARTICLES IN AMR AND SPH (2010, background): “…core and stellar initial mass functions (e.g., Klessen et al. 1998; Klessen 2001; Kroupa 2001; Padoan & Nordlund 2002; Chabrier 2003; Mac Low & Klessen 2004; Elmegreen & Scalo 2004; Larson 2005; Bonnell & Bate 2006; McKee & Ostriker 2007; Krumholz & Bonnell 2007; Hennebelle & Chabrier 2008, 2009).”
ERRATUM: “THE LUMINOSITY AND MASS FUNCTIONS OF LOW-MASS STARS IN THE GALACTIC DISK. II. THE FIELD” (2010, AJ, 139, 2679) (2010, background): “In particular, the high-mass IMF is regulated by the power spectrum of the turbulent flows (Padoan & Nordlund 2002; Hennebelle & Chabrier 2009) and is probably affected by the coagulation of less massive cores, while the flatter, low-mass distribution can be linked to the dispersions in gas density…”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, methodology): “The full HC model for SFRff is based on the mass spectrum of gravitationally bound structures, as derived in Hennebelle & Chabrier (2008, 2009): N (M) = d(N/V ) dM ∝ − 1 M ds dM exp(s) p(s) , (33) which is essentially Equation (6) in Hennebelle & Chabrier (2011), except for the freefall time factor.”
RADIATION-HYDRODYNAMIC SIMULATIONS OF THE FORMATION OF ORION-LIKE STAR CLUSTERS. II. THE INITIAL MASS FUNCTION FROM WINDS, TURBULENCE, AND RADIATION (2012, background): “…in the litera- 11 ture about whether massive stars form from distinct massive protostellar cores (Padoan 1995; Padoan & Nordlund 2002; McKee & Tan 2002, 2003; Krumholz et al. 2007a; Hennebelle & Teyssier 2008; Hennebelle & Chabrier 2009), or whether all stars are born from cores with masses .”
Collapse, outflows and fragmentation of massive, turbulent and magnetized prestellar barotropic cores (2011, unknown): “Although performing a quantitative analysis of the fragment distribution (e.g. Hennebelle & Chabrier 2008, 2009) seems difficult at this stage, the decrease of the fragmentation with magnetic intensity seems to be attributable to two different processes, as already discussed.”
A census of dense cores in the Aquila cloud complex: SPIRE/PACS observations from the Herschel Gould Belt survey (2015, background): “…timescale problem raised by Clark et al. (2007) is not a serious issue in the context of the gravoturbulent theory of the CMF/IMF proposed by Hennebelle & Chabrier (2009), because the mass of cores corresponds to the turbulent Jeans mass in this theory and the free-fall time has only a…”
The stellar and sub-stellar IMF of simple and composite populations (2011, background): “Such conditions are very rare in typical turbulent molecular clouds that have Mach numbers ∼ 6 (Hennebelle & Chabrier 2008, 2009).”
Physical Processes in the Interstellar Medium (2014, background): “This was later extended by Hennebelle & Chabrier (2008, 2009, 2013).”
The Stellar IMF, Core Mass Function, & The Last-Crossing Distribution (2012, background): “…already noted that our predictions are much more sensitive to the turbulent spectrum, and our simplifying assumption that the gas is isothermal, while introducing negligible corrections at R> Rsonic, can have large effects on CMF in the substellar (R Rsonic) regime (see Hennebelle & Chabrier 2009).”