Analytical Theory for the Initial Mass Function: CO Clumps and Prestellar Cores

By P. Hennebelle, G. Chabrier. 2008

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We derive an analytical theory of the prestellar core initial mass function (IMF) based on an extension of the Press-Schechter statistical formalism. Our approach relies on the general concept of the gravothermal and gravoturbulent collapse of a molecular cloud, with a selection criterion based on the thermal or turbulent Jeans mass, which yields the derivation of the mass spectrum of self-gravitating objects in a quiescent or a turbulent environment. The same formalism also yields the mass spectrum of non-self-gravitating clumps produced in supersonic flows. The mass spectrum of the self-gravitating cores reproduces well the observed IMF. The theory predicts that the shape of the IMF results from two competing contributions, namely, a power law at large scales and an exponential cutoff (lognormal form) centered around the characteristic mass for gravitational collapse. The cutoff exists both in the case of thermal or turbulent collapse, provided that the underlying density field has a lognormal distribution. Whereas pure thermal collapse produces a power-law tail steeper than the Salpeter value, dN/dlog M ∝ M−x with x ≃ 1.35, the latter is recovered exactly for the (three-dimensional) value of the spectral index of the velocity power spectrum, n ≃ 3.8, found in observations and in numerical simulations of isothermal supersonic turbulence. Indeed, the theory predicts that x = (n + 1)/(2n − 4) for self-gravitating structures and x = 2 − n′/3 for non-self-gravitating structures, where n′ is the power spectrum index of log ρ . We show that, whereas supersonic turbulence promotes the formation of both massive stars and brown dwarfs, it has an overall negative impact on star formation, decreasing the star formation efficiency. This theory provides a novel theoretical foundation to understand the origin of the IMF and provides useful guidance to numerical simulations exploring star formation, while making testable predictions.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/d11edfc4afcd61c43d3340d4cca5215bb66496d0

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Citations in the corpus

A sub-parsec resolution simulation of the Milky Way: global structure of the interstellar medium and properties of molecular clouds (2013, background): “10 and already noted by several authors (e.g. Klessen 2000; Hennebelle & Chabrier 2008; Vázquez-Semadeni et al. 2008; Audit & Hennebelle 2010).”
THE STAR FORMATION RATE OF SUPERSONIC MAGNETOHYDRODYNAMIC TURBULENCE (2009, background): “…turbulent pressure support; Krumholz & McKee (2005) defined the critical density for star formation based on the local turbulent pressure support of a Bonnor-Ebert sphere; Hennebelle & Chabrier (2008) proposed that the Salpeter stellar IMF is the result of the local turbulent pressure support.”
ANALYTICAL STAR FORMATION RATE FROM GRAVOTURBULENT FRAGMENTATION (2011, methodology): “In this Letter, we derive a SFR, based on our IMF analytical theory (Hennebelle & Chabrier 2008-HC08, 2009-HC09, Chabrier & Hennebelle 2011), and show that (i) this theory yields SFR values in good agreement with observations, (ii) there is no a priori density threshold for star formation; instead,…”
Dusty Star Forming Galaxies at High Redshift (2014, background): “Some are able to motivate physical origins for bottom light IMFs in heavily star-forming systems (e.g. Narayanan andDavé, 2012, 2013), while others argue for a bottom-heavy IMF in starbursts (e.g. Hennebelle and Chabrier, 2008; Hopkins, 2012; Krumholz, 2011a).”
The Density Probability Distribution in Compressible Isothermal Turbulence: Solenoidal versus Compressive Forcing (2008, background): “For instance, Padoan & Nordlund (2002) and Hennebelle & Chabrier (2008) relate the density PDF to the core mass function (CMF) and stellar initial mass function (IMF).”
Dynamic star formation in the massive DR21 filament (2010, background): “Cores are then formed by ’gravoturbulent fragmentation’ (Klessen et al. 2005, Hennebelle & Chabrier 2008), which characterizes a hierarchy of smaller and smaller entities.”
Collapse, outflows and fragmentation of massive, turbulent and magnetized prestellar barotropic cores (2011, neutral): “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.”
The Formation and Early Evolution of Low-Mass Stars and Brown Dwarfs (2012, background): “Turbulent compression and fragmentation of gas in a molecular cloud produces collapsing cores over a wide range of masses (Elmegreen 2011, Hennebelle & Chabrier 2008, Padoan & Nordlund 2002, 2004).”
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).”
AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS (2014, result): “16, from which we selected the GPs KOI-889b (Hébrard et al. 2013) and WASP-18b (Maxted et al. 2013) and the following BDs: Corot-3b (Deleuil et al. 2008), Corot-15b (Bouchy et al. 2011b), WASP-30b (Anderson et al. 2011), KOI205b (Dı́az et al. 2013), Kepler-39b (Bouchy et al. 2011a), and LHS-6343c (”
Accretion-driven turbulence as universal process: galaxies, molecular clouds, and protostellar disks (2009, background): “…often follows a power law dN/dM ∝ Mα with a slope of α ≈ −1.7 (see, e.g. Heithausen et al. 1998, for the observations; or Klessen 2001; Ballesteros-Paredes et al. 2006; or Hennebelle & Audit 2007, Page 3 of 18 for numerical simulations; and Hennebelle & Chabrier 2008, for analytical arguments).”
The Stellar IMF, Core Mass Function, & The Last-Crossing Distribution (2012, methodology): “Hennebelle & Chabrier (2008) (HC08) attempted to derive the stellar IMF as a consequence of lognormal density fluctuations in a turbulent medium, using an argument similar to Press & Schechter (1974) for Gaussian random fields.”
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).”
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).”
Turbulent molecular clouds (2012, methodology): “…as entities which cross first the requested self-gravitating barrier have a mass spectrum which is slightly shallower than M−2 while the condensations defined by the last crossing of the barrier have a mass spectrum almost identical to that by Hennebelle & Chabrier (2008) except at large masses.”
THE STELLAR INITIAL MASS FUNCTION IN EARLY-TYPE GALAXIES FROM ABSORPTION LINE SPECTROSCOPY. II. RESULTS (2012, background): “Hennebelle & Chabrier 2008; Hopkins 2012a,b).”
A comparison between grid and particle methods on the statistics of driven, supersonic, isothermal turbulence (2010, background): “2006; Dib et al. 2008) and possibly the mass distribution of stars themselves, i.e., the Initial Mass Function (IMF) (Padoan et al.1997; Padoan & Nordlund 2002; Hennebelle & Chabrier 2008).”
On the universality of supersonic turbulence (2013, background): “…2011; Federrath & Klessen 2012), affects the star formation efficiency (Elmegreen 2008; Federrath & Klessen 2013; Kainulainen, Federrath & Henning 2013), and determines the mass distribution of stars when they are born (Padoan & Nordlund 2002; Hennebelle & Chabrier 2008, 2013; Hopkins 2013a).”