Flow-driven cloud formation and fragmentation: results from Eulerian and Lagrangian simulations

Fabian Heitsch 0 1 2 Thorsten Naab 0 4 Stefanie Walch 0 3 0 Universita ts Sternwarte Mu nchen , Scheinerstr. 1, D-81679 Mu nchen , Germany 1 Department of Astronomy, University of Michigan , 500 Church St, Ann Arbor, MI 48109-1042 , USA 2 Department of Physics and Astronomy, UNC Chapel Hill , 120 E Cameron St, Chapel Hill, NC 27599-3255 , USA 3 School of Physics and Astronomy, Cardiff University , 5 The Parade, Cardiff CF24 3AA 4 Max Planck Institut fu r Astrophysik , Karl-Schwarzschild-Str. 1, 85741 Garching , Germany A B S T R A C T The fragmentation of shocked flows in a thermally bistable medium provides a natural mechanism to form turbulent cold clouds as precursors to molecular clouds. Yet because of the large density and temperature differences and the range of dynamical scales involved, following this process with numerical simulations is challenging. We compare two-dimensional simulations of flow-driven cloud formation without self-gravity, using the Lagrangian smoothed particle hydrodynamics (SPH) code VINE and the Eulerian grid code PROTEUS. Results are qualitatively similar for both methods, yet the variable spatial resolution of the SPH method leads to smaller fragments and thinner filaments, rendering the overall morphologies different. Thermal and hydrodynamical instabilities lead to rapid cooling and fragmentation into cold clumps with temperatures below 300 K. For clumps more massive than 1 M pc1, the clump mass function has an average slope of 0.8. The internal velocity dispersion of the clumps is nearly an order of magnitude smaller than their relative motion, rendering it subsonic with respect to the internal sound speed of the clumps but supersonic as seen by an external observer. For the SPH simulations most of the cold gas resides at temperatures below 100 K, while the grid-based models show an additional, substantial component between 100 and 300 K. Independent of the numerical method, our models confirm that converging flows of warm neutral gas fragment rapidly and form high-density, low-temperature clumps as possible seeds for star formation. - The highly filamentary morphology of molecular clouds (MCs) and their observed non-thermal linewidths (Falgarone & Phillips 1990; Williams, Blitz & McKee 2000) point to MCs being highly dynamical objects. Observational evidence suggests that star formation in local MCs such as Taurus is rapid once molecular gas is available and that the parental clouds are short-lived (Elmegreen 2000; Hartmann, Ballesteros-Paredes & Bergin 2001; Hartmann 2003). The dynamical, or turbulent, nature of MCs is assumed to play a crucial role in the process of star formation via turbulent fragmentation (Larson 1981; Mac Low & Klessen 2004, see also BallesterosParedes 2006, for a summary of the effects and interpretation of turbulence in MCs). E-mail: (FH); (TN); (SW) Because of the rapid onset of star formation, the cloud formation process needs to provide the MC with the observed turbulence and substructure. Moreover, global geometry and gravity considerations mandate that this substructure be non-linear (Burkert & Hartmann 2004), i.e. a physical process is needed that can imprint non-linear density perturbations in the protocloud during its formation. These requirements have led to the scenario of flow-driven cloud formation, where MCs are assembled by large-scale converging flows of atomic hydrogen corresponding to the warm neutral medium (Ballesteros-Paredes, Hartmann & Vazquez-Semadeni 1999; Hartmann et al. 2001; Hartmann 2003; see also Elmegreen 1993, 2000). The rapid fragmentation is driven by a combination of strong thermal and dynamical instabilities, dominated by the thermal instability [TI; Field 1965; see also Heitsch, Hartmann & Burkert 2008b for a discussion of time-scales]. Large-scale gas flows are ubiquitous in the Galaxy. They might be driven locally by supernova explosions (Elmegreen & Lada 1977; McCray & Kafatos 1987; Nigra et al. 2008) or globally by shear motions in the Galactic disc, global gravitational instabilities (Yang et al. 2007), gas infall from the halo (Mirabel 1982; Lacey & Fall 1985), interactions with the central bar (Roberts, Huntley & van Albada 1979; Combes & Gerin 1985) or satellite galaxies. On extragalactic scales collisions of galactic discs trigger gas flows, shocks and starbursts (Mihos & Hernquist 1996; Naab, Jesseit & Burkert 2006; Karl et al. 2010). High-resolution simulations in two (Audit & Hennebelle 2005; Heitsch et al. 2005, 2006; Hennebelle & Audit 2007; Hennebelle, Audit & Miville-Deschenes 2007) and three dimensions (VazquezSemadeni et al. 2006, 2007; Heitsch et al. 2008a; Hennebelle et al. 2008; Banerjee et al. 2009) have demonstrated that the flow-driven formation of clouds is indeed a natural and elegant way to provide the clouds with the observed turbulence and substructure. Except for Vazquez-Semadeni et al. (2007), the above authors used various grid-based methods. However, due to the high-density contrast and the strong TI in the intermediate-temperature regime between 300 < T < 5000 K, the spatial scales of the forming cold filaments and clumps shrink dramatically. This problem becomes even more severe with gravity acting upon the cold regions. Due to its Lagrangian nature, the strength of smoothed particle hydrodynamics (SPH; e.g. Monaghan 1992) resides in its capability to follow fluid flows at arbitrary spatial resolution. In particular, dissipative properties of SPH methods do not depend on the geometry or direction, which can cause issues for grid-based methods without physical dissipation control (Rampp, Mueller & Ruffert 1998). SPH has been used to model the interstellar medium on all scales, from planet formation (e.g. Mayer et al. 2002), formation of protostellar discs from rotating and turbulent cores (Walch et al. 2009, 2010), formation of stars and cores (Klessen 1997; Bate, Bonnell & Bromm 2003), ionization feedback from massive stars (Bisbas et al. 2009; Gritschneder et al. 2009, 2010), formation of MCs in galactic discs (Dobbs, Bonnell & Pringle 2006; Dobbs & Bonnell 2007; Dobbs et al. 2008) and galaxy evolution (Hernquist & Katz 1989; Steinmetz 1996; Springel 2000; Naab et al. 2006, 2007) to large-scale simulation of galaxy formation (e.g. Springel & Hernquist 2003). VazquezSemadeni et al. (2007) presented models of flow-driven MC formation using SPH. However, SPH has its own inherent limitations, among others a limited mass resolution and spatially varying dissipative properties. Hence, the question remains whether SPH and grid-based methods give similar results for a specific astrophysical problem and what the method-intrinsic differences are. Nagamine et al. (2005) showed for cosmological applications that both approaches give statistically similar results, and Klessen, Heitsch & Mac Low (2000) concluded the same for models of self-gravitatingdriven turbulence in a periodic box of isothermal gas, although Kitsionas et al. (2009) show (...truncated)