The Stellar IMF, Core Mass Function, & The Last-Crossing Distribution

By P. Hopkins. 2012

142 citations recorded by the source corpus.

Hennebelle & Chabrier 2008 (HC08) attempted to derive the stellar IMF as a consequence of turbulent density fluctuations, using an argument similar to Press & Schechter 1974 for Gaussian random fields. Like that example, however, this solution does not resolve the 'cloud in cloud' problem; it also does not extend to large scales that dominate the velocity/density fluctuations. In principle, these can change the results at the order-of-magnitude level. Here, we use the results from Hopkins 2011 (H11) to generalize the excursion set formalism and derive the exact solution in this regime. We argue that the stellar IMF and core mass function (CMF) should be associated with the last-crossing distribution, i.e. the mass spectrum of bound objects defined on the smallest scale on which they are self-gravitating. This differs from the first-crossing distribution (mass function on the largest self-gravitating scale) which is defined cosmologically and which H11 show corresponds to the GMC mass function in disks. We derive an analytic equation for the last-crossing distribution that can be used for an arbitrary collapse threshold in ISM and cosmological studies. With this, we show that the same model that predicts the GMC mass function and large-scale structure of galaxy disks also predicts the CMF (and by extrapolation IMF) in good agreement with observations. The only adjustable parameter in the model is the turbulent velocity power spectrum, which in the range p~5/3-2 gives similar results. We also use this to justify why the approximate solution in HC08 is reasonable (up to a normalization) over the CMF/IMF mass range; however there are significant corrections at intermediate and high masses. We discuss how the exact solutions here can be embedded into time-dependent models that follow density fluctuations, fragmentation, successive generations of star formation.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/8ef44eae69d2e976e79ee5b978a4d6a5c27c6741

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Citations in the corpus

THE STELLAR INITIAL MASS FUNCTION IN EARLY-TYPE GALAXIES FROM ABSORPTION LINE SPECTROSCOPY. II. RESULTS (2012, background): “Hennebelle & Chabrier 2008; Hopkins 2012a,b).”
ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS (2012, background): “…(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 relation (Krumholz & McKee 2005; Tassis 2007), the SFE (Elmegreen 2008), and the SFR (Krumholz & McKee 2005;…”
FIRE-2 simulations: physics versus numerics in galaxy formation (2017, background): “…repeatedly shown that almost all star formation occurs in the largest GMC complexes in galaxies (see Evans 1999; Rosolowsky et al. 2003; Blitz & Rosolowsky 2005; Bolatto et al. 2008; Elmegreen 2007; Tasker & Tan 2009; Feldmann & Gnedin 2011; Murray 2011; Harper-Clark & Murray 2011; Hopkins 2012a).”
What controls star formation in the central 500 pc of the Galaxy (2013, methodology): “For core massesM ∼ 1 M⊙ (i.e. stellar massesM ∼ 0.5 M⊙) and a Mach number ofM ∼ 100, Hopkins (2012) predicts a steepened mass spectrum with a slope ofβ ∼ 3.”
THE STELLAR INITIAL MASS FUNCTION OF ULTRA-FAINT DWARF GALAXIES: EVIDENCE FOR IMF VARIATIONS WITH GALACTIC ENVIRONMENT (2013, background): “…properties of the stellar birth cloud such as the gas density, metallicity, or turbulent velocity (e.g.,; Larson 2005; Bate 2009; Myers et al. 2011; Marks et al. 2012; Hopkins 2012), however, IMF observations are largely invariant within the Milky Way (Bochanski et al. 2010; Covey et al. 2008).”
Turbulent molecular clouds (2012, background): “4.3.2) and that of the largest selfgravitating clumps obtained by Hopkins (2012b) are both power-laws with very similar exponents.”
THE STAR FORMATION RATE OF TURBULENT MAGNETIZED CLOUDS: COMPARING THEORY, SIMULATIONS, AND OBSERVATIONS (2012, background): “…(IMF) (Padoan & Nordlund 2002; Hennebelle & Chabrier 2008, 2009; Elmegreen 2011; Veltchev et al. 2011; Donkov et al. 2012; Parravano et al. 2012; Hopkins 2012), the Kennicutt-Schmidt relation (Krumholz & McKee 2005; Tassis 2007), the SFE (Elmegreen 2008), and the SFR (Krumholz & McKee 2005;…”
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).”