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# The formation of filamentary bundles in turbulent molecular clouds

Abstract

The classical picture of a star-forming filament is a near-equilibrium structure, with collapse dependent on its gravitational criticality. Recent observations have complicated this picture, revealing filaments as a mess of apparently interacting subfilaments, with transsonic internal velocity dispersions and mildly supersonic intra-subfilament dispersions. How structures like this form is unresolved. Here we study the velocity structure of filamentary regions in a simulation of a turbulent molecular cloud. We present two main findings: first, the observed complex velocity features in filaments arise naturally in self gravitating hydrodynamic simulations of turbulent clouds without the need for magnetic or other effects. Second, a region that is filamentary only in projection and is in fact made of spatially distinct features can displays these same velocity characteristics. The fact that these disjoint structures can masquerade as coherent filaments in both projection and velocity diagnostics highlights the need to continue developing sophisticated filamentary analysis techniques for star formation observations.

# Introduction

Observations with the Herschel satellite have revealed that the backbone of molecular clouds is a compex network of connecting and interacting filaments (e.g. André et al., 2010; Molinari et al., 2010; Arzoumanian et al., 2011; Schneider et al., 2012). The dynamics of this web of dense molecular gas not only determines the evolution and stability of molecular clouds, but also regulates their condensation into stars. Molecular cloud cores and single low-mass stars are almost always found in filaments, often aligned like pearls on a string (Hartmann, 2002; Lada et al., 2008; André et al., 2010). This can be interpreted as a result of the gravitational instability of a supercritical filamentary section (Inutsuka et al., 1997; Hacar et al., 2011). Where filaments intersect, more massive hubs form (Myers, 2009; Myers, 2013) that later on could become the progenitors of star clusters.

Lada et al. (2010) (see also e.g. Enoch et al., 2007) demonstrated that the fraction of gas in the dense molecular web is of order 10 percent of the total molecular mass. Interestingly, the mass fraction of protostars to dense ($$n > 10^4$$ cm$$^{-3}$$) molecular gas is also a constant of the same order. Burkert et al. (2013) showed that this requires new filamentary segments to continuously form from the diffuse intra-filament medium on a gravitational collapse timescale.

Classically, gas filaments have been treated as cylinders of gas in hydrostatic equilibrium (Ostriker, 1964; Fischera et al., 2012; Recchi et al., 2013). It is not clear, however, how such quiescent structures could form in the turbulent environment of a molecular cloud (e.g. Klessen et al., 2010; Heitsch, 2013). In addition, millimeter line studies indicate that filaments have intrinsic, super-thermal linewidths (Arzoumanian et al., 2013).

More recently, observations by Hacar et al. (2013) revealed that filaments are often compact bundles of thin spaghetti-like subfilaments. They presented observations of a prominent filamentary feature in Taurus, dominated by the L1495 cloud (Lynds, 1962) and several dark patches (Barnard, 1927). They observed the region in the moderate density tracer C$$^{18}$$O, obtaining spectra along a $$\sim 10$$ pc length of the region. Analysing the richest $$\sim 3$$ pc section of the filament in the resultant position–position–velocity space, they found the intriguing result that the gas along the ridge is organized in velocity-coherent filamentary structures, with typical lengths $$\sim0.5$$ pc. Each filament is internally subsonic or transsonic, though the collection of filaments is characterised by a mildly supersonic interfilamentary dispersion of $$\sim 0.5$$ km s$$^{-1}$$. They describe the collection of velocity detections as “elongated groups that lie at different ‘heights’ (velocities) and present smooth and often oscillatory patterns”. Multiple velocity components along a single line of sight have also been observed in Serpens South (Tanaka et al., 2013); this feature may therefore be common for many young star forming sites.

The complexity of Hacar et al.’s position–position–velocity data, exemplified by their figure 9, invites theoretical and numerical exploration. In particular the apparent organization of filaments into bundles tends to bring to mind magnetic fields or other relatively complex physics. In this Letter we explore whether this velocity signal is present in simulated molecular clouds with a more minimal set of physics, including only gravity and hydrodynamic forces acting on the initial turbulence.

# The simulation

We simulated a 10 pc periodic cube of a molecular cloud, beginning from fully developed isothermal turbulent initial conditions. We generated the turbulent initial conditions using version 4.2 of the ATHENA code (Gardiner et al., 2005; Gardiner et al., 2008; Stone et al., 2008; Stone et al., 2009). The turbulent driving was technically similar to that of Lemaster et al. (2009). Briefly, on a $$1024^{3}$$ grid with domain length 1 we applied divergence-free velocity perturbations at every timestep to an initially uniform medium. The perturbations had a Gaussian random distribution with a Fourier power spectrum $$\left | d {\bf v}_{k}^{2} \right | \propto k^{-2}$$, for wavenumbers $$2 < k/2 \pi < 4$$. Similarly to, e.g., Federrath (2013), turbulence on smaller length scales was generated self-consistently from the large scale driving. The driving continued until the box reached a saturated state at a Mach number $$\mathcal{M}$$ of roughly 8. During this driving stage we did not include gravitational forces.

At this point we scaled the box to a physical size $$S = 10$$ pc, mean number density $$n = 100$$ cm$$^{-3}$$ at mean molecular weight $$\mu=2.33$$ (giving a total gas mass $$\sim5700$$ M$$_{\sun}$$), and a constant sound speed $$c_s$$ = 0.2 km s$$^{-1}$$. After turning off the forcing and turning on self gravity, we turned the simulation over to the adaptive mesh refinement (AMR) code RAMSES (Teyssier, 2002). The $$1024^{3}$$ base grid was maintained along with 4 steps of adaptive refinement (i.e. a maximum effective resolution of $$16384^{3}$$), with each level of refinement triggered when the local Jeans length became shorter than 32 grid cells (Federrath et al., 2011; Truelove et al., 1997).

Regions collapsing beyond this point were replaced by sink particles, using the sink implementation described in Dubois et al. (2010), which largely follows the implementation of Krumholz et al. (2004). The salient points of this implementation are that regions exceeding the Truelove density limit on the finest level of refinement and that are collapsing along all directions are replaced by sink particles. The sinks accrete gas in a momentum conserving fashion from a region 4 cells in radius ($$\sim0.01$$ pc) at the local Bondi-Hoyle rate in that region. While the sinks are addressed in this paper, we can approximate the integrated star (rather, sink) formation efficiency as the fraction of the total mass in sinks at some time.

We integrated the box through $$\sim2.1$$ Myr of self gravitating evolution. Following Kritsuk et al. (2007)’s definition of the turbulent turnover time in a box , $$T_{turb} = S/(2 c_s \mathcal{M})$$, we have $$T_{turb} \sim 3$$ Myr. The free-fall time $$T_{ff} = [3\pi / (32 G \rho)]^{1/2}$$, at the mean density of the simulation, is also roughly 3 Myr. In this paper we focus on moderately dense gas, with $$10^3 < n/{\rm cm}^{-3} < 10^{4.5}$$; at these densities we have $$0.2 \lesssim T_{ff} / \rm{Myr} \lesssim 1.1$$. After 1 Myr the global structure of the simulated box is thus still dominated by the initial turbulence, while the denser gas has had time to become organized by self gravity.