Clump mass function at an early stage of molecular cloud evolution – II. Galactic cloud complexes

MNRAS 432, 3495–3507 (2013) doi:10.1093/mnras/stt699 Advance Access publication 2013 May 16 Clump mass function at an early stage of molecular cloud evolution – II. Galactic cloud complexes Todor V. Veltchev,1,2‹ Sava Donkov3 and Ralf S. Klessen2 1 University of Sofia, Faculty of Physics, 5 James Bourchier Blvd., BG-1164 Sofia, Bulgaria 2 Universität Heidelberg, Zentrum für Astronomie, Institut für Theoretische Astrophysik, Albert-Überle-Str. 2, D-69120 Heidelberg, Germany 3 Department of Applied Physics, Technical University, 8 Kliment Ohridski Blvd., BG-1000 Sofia, Bulgaria Accepted 2013 April 22. Received 2013 April 22; in original form 2012 September 20 ABSTRACT Key words: turbulence – methods: statistical – ISM: clouds – ISM: structure. 1 I N T RO D U C T I O N Dense clumps in molecular clouds (MCs) are typical sites of star formation as they are often associated with young stellar objects. Their origin can be sought in the early epoch of cloud evolution when supersonic turbulence creates sets of condensations in the cold, mainly molecular gas. Recent numerical simulations indicate that their mean densities, sizes and masses vary in ranges 102 –104 cm−3 , 0.04–1 pc and 0.1–103 M , respectively (VázquezSemadeni et al. 2007; Banerjee et al. 2009; Shetty et al. 2010), in consistency with extensive observational data about MC clumps (e.g. Bergin & Tafalla 2007). Clump morphology is also diverse: from filamentary to compact, quasi-spherical shapes (Hennebelle et al. 2008). Gravitational stability analysis shows that some clumps are subject to further contraction and collapse and eventually give birth to single stars or stellar clusters. Numerous individual clumps were initially identified on maps of molecular line emissions which trace different density regimes in MCs: 12 CO (n ∼ 102 cm−3 ), 13 CO and C18 O (n ∼ 103 cm−3 ), CS (J = 1–0) and H13 CO+ (J = 1–0) (n  104 cm−3 ). Such surveys were performed in nearby (at distances <500 pc) Galactic cloud complexes like Orion A (Tatematsu et al. 1993), Orion B (Kramer et al. 1998), Taurus (Onishi et al. 1996), Ophiuchus (Tachihara, Mizuno & Fukui 2000), Lupus (Hara et al. 1999) and many others. Some of these results on the physical parameters of clumps were included in the statistical study of Tachihara et al. (2002), who  E-mail: considered a sample of nine Galactic star-forming regions. In the last decade, further intensive research of MCs by use of some highdensity tracers like H13 CO+ (J = 1–0) (Onishi et al. 2002; Ikeda, Sunada & Kitamura 2007; Ikeda, Kitamura & Sunada 2009) as well of dust continuum (Johnstone et al. 2001; Kerton et al. 2001; Reid & Wilson 2005, 2006a; Johnstone, Matthews & Mitchell 2006; Di Francesco et al. 2010), and dust extinction (e.g. Alves, Lombardi & Lada 2007) observations allowed for more precise mapping of cloud structure. Some clumps originally found on emission maps were further decomposed, and more compact (typical sizes 0.2 pc), very dense (n  105 cm−3 ) and probably collapsing clumps were delineated. Some authors call such objects ‘dense cores’; hereafter, we label them simply cores. It is suggested that cores eventually form stars (Bergin & Tafalla 2007) and thus the study of their mass function (CMF) will enable a better understanding of the physical origin of the stellar initial mass function (IMF) and its possible variations. Indeed, numerous dust continuum and dust extinction observations demonstrate that the CMF resembles the IMF in its shape when fitted by a single-powerlaw (Testi & Sargent 1998; Johnstone et al. 2001), a combination of two-power-law (Motte, André & Neri 1998; Motte & André 2001; Johnstone et al. 2006; Nutter & Ward-Thompson 2007) or a lognormal function (Stanke et al. 2006; Enoch et al. 2008; Könyves et al. 2010). It therefore has been proposed that the IMF is a direct product of the CMF and a uniform star formation efficiency (Alves et al. 2007). Yet it is still unclear how the CMF originates from the mass distribution of the initially formed MC clumps. The clump mass function (ClMF), as derived from molecular line emission surveys  C 2013 The Authors Published by Oxford University Press on behalf of the Royal Astronomical Society The statistical approach for derivation of the clump mass function (ClMF) developed by Donkov, Veltchev & Klessen is put to observational test through comparison with mass distributions of clumps from molecular emission and dust continuum maps of Galactic cloud complexes, obtained by various authors. The results indicate gravitational boundedness of the dominant clump population, with or without taking into account the contribution of their thermal and magnetic energy. The ClMF can be presented by combination of two-power-law functions separated by a characteristic mass from about ten to hundreds of solar masses. The slope of the intermediate-mass ClMF is shallow and nearly constant (−0.25   IM  −0.55) while the high-mass part is fitted by models that imply gravitationally unstable clumps and exhibit slopes in a broader range (−0.9   IM  −1.6), centred at the value of the stellar initial mass function ( HM  −1.3). 3496 T. V. Veltchev, S. Donkov and R. S. Klessen tion 4 contains a discussion on the applicability and the restrictions of our approach to predict the observational ClMF and envisions its possible extensions. Our conclusions are summarized in Section 5. 2 S T RU C T U R E A N D C lM F O F A N I N D I V I D UA L CLOUD 2.1 Physical framework of the model Our statistical model for clump description is presented in detail in DVK11 (sections 2 and 3) and Paper I (section 2). Its main assumptions can be summarized as follows. (i) Scaling laws within the turbulent cloud. We consider fully developed supersonic turbulence that implies homogeneous and isotropic stochastic medium with a fractal structure and well-defined scaling laws of turbulent velocity, mean density and mean magnetic field. Turbulent flows create density structures at any scale in the inertial range Lmax  L  Lmin through a cascade possibly driven by the very process of cloud formation (Klessen & Hennebelle 2010). We estimate the upper limit Lmax = 20 pc adopting a typical size of giant MC ∼50 pc as an injection scale and taking in view that the largest scale of the turbulence inertial range is about a factor of 3 less (Padoan et al. 2006; Kritsuk et al. 2007). The lower limit Lmin is imposed above the actual end of the inertial range from the construction of our model: the sizes l of all clumps generated at a given scale L must be within the inertial range and are typically an order of magnitude less than L. Various observations show that the inertial range spans at least three orders of magnitude, i.e. the size of the smallest generated object lmin must be about 0.02 pc. We consider mainly molecular and isothermal gas with temperatures T = 10–20 K. Requiring supersonic medium at all fractal scales and by use of a typical vel (...truncated)