Small-scale Intermittency of the Dissipation of

Submillimeter Astrophysics and Technology: A Symposium Honoring Thomas G. Phillips c 2009 ASP Conference Series, Vol. 417, ! D. C. Lis, J. E. Vaillancourt, P. F. Goldsmith, T. A. Bell, N. Z. Scoville, and J. Zmuidzinas, eds.

Small-scale Intermittency of the Dissipation of Interstellar Turbulence E. Falgarone,1 P. Hily-Blant,2 and J. Pety1,3 Abstract. Molecular clouds are turbulent flows with comparable turbulent and magnetic internal energy densities at large scales. Jointly, turbulence and magnetic fields balance their self-gravity. Hence, dissipation of turbulence or decoupling of matter from magnetic fields are critical processes in the early steps of star formation in molecular clouds. Turbulence is known to be intermittent in space and time in laboratory and atmospheric flows. Interstellar turbulence may be intermittent as well, with characteristics modified by compressibility and magnetic fields. We report here the results of a two-decade effort, shared with T. G. Phillips and several others, to find and characterize the rare and tiny regions where turbulent dissipation is concentrated in molecular clouds. These appear to be organized into thin parsec-scale coherent structures of intense velocityshears in the three translucent fields where they have been sought. The values of velocity-shears found at the milliparsec-scale are large, up to 800 km s−1 pc−1 , and suggest dissipation rates that are locally several orders of magnitude above average. The short timescales (or large gas accelerations) involved, ∼ 3×103 yr, are commensurate to many inelastic collision timescales in gas of moderate density. Thus, gas dynamics in these structures not only affect chemistry, with even a possible causal relation between intense velocity-shears and molecule formation in the cold neutral medium, but also modify the coupling of the gas to dust grains and to magnetic fields. These results open a new window on turbulent dissipation, its impact on small-scale gas dynamics and its role in the formation of dense cores in molecular clouds.

1

Introduction

The first observations of the CO rotational lines in molecular clouds revealed that the emitting gas was very cold (Penzias et al. 1972), immediately raising the puzzle of the origin of their suprathermal widths. Large-scale infall motions would have been a possible explanation since, according to their density, low temperature and estimated mass, molecular clouds appeared gravitationally unstable. But molecular clouds in free fall would have produced far too large star formation rates. The origin of the CO suprathermal linewidths was then proposed to be small-scale turbulence (Zuckerman & Evans 1974). This in turn raised the problem of the accompanying rapid turbulent dissipation. More than thirty years later, the nature and properties of turbulence in molecular clouds, 1 LERMA/LRA, Ecole Normale Supérieure & Observatoire de Paris, CNRS UMR 8112, Paris, France 2

LAOG, Université Joseph Fourier, CNRS UMR 5571, Grenoble, France

3

IRAM, Grenoble, France

243

244

Falgarone, Hily-Blant, and Pety

and in the interstellar medium (ISM) at large, are still a highly debated and controversial issue in spite of dedicated efforts on observational and numerical grounds. This is due in part to the huge range of scales separating those of the energy injection(s) at the Galaxy scale (up to tens of kpc) from those where it is dissipated, presumably below the milliparsec scale. It is also due to the fact that the ISM is compressible, magnetized and multi-phase. Unraveling the properties of interstellar turbulence is essential though because turbulence and magnetic fields are the main support of molecular clouds against their self-gravity. Turbulent dissipation is therefore a key process among all those eventually leading to star formation (see the reviews of Elmegreen & Scalo 2004; Scalo & Elmegreen 2004). In molecular clouds, turbulence is observed to be highly supersonic with respect to the cold gas. It is thus expected to dissipate in shocks in a cloud crossing time, ≈ a few 10 Myr, for giant molecular clouds of 100 pc with internal velocity dispersion of a few km s−1 . Numerical experiments show that magnetic fields do not significantly slow the dissipation down (Mac Low et al. 1998). This is even the basis of the turbulent models of star formation — one of the two current scenarios of low-mass star formation — in which self-gravitating entities form in the shock-compressed layers of supersonic turbulence. Yet, whether turbulent dissipation occurs primarily in compressive (curl-free) or in solenoidal (divergencefree) modes in molecular clouds is still an open issue. In their hydrodynamical simulations of midly compressible turbulence, Porter et al. (2002) show that the compressible component of the velocity field is weaker than its solenoidal counterpart by a factor ∼ 3, independent of the nature of the driving process (compressible or solenoidal) and Vestuto et al. (2003) find that the energy fraction in the solenoidal modes is dominant and increases with the magnetic field intensity in compressible magneto-hydrodynamical (MHD) turbulence. These numerical experiments are still far from approaching the ISM conditions but they suggest that turbulent dissipation may occur primarily in solenoidal modes, i.e. without direct gas compression. One ideal target to study turbulent dissipation is the diffuse molecular gas because it is highly turbulent and it is the gas component in which dense cores form, with less turbulent energy density than their environment. Intense turbulent dissipation is therefore expected to take place in that component of molecular clouds. The word “diffuse” here comprises all material in the neutral ISM at large that is not in dense cores or star forming regions i.e. whose total hydrogen column density is less than a few ∼ 1021 cm−2 . This includes the mixture of cold and warm neutral medium (CNM and WNM), the edges of molecular cloud complexes (often called translucent gas) and the high latitude clouds. Moreover, the diffuse gas component, as defined above, comprises the bulk of the mass of molecular clouds, at the 30 pc scale. Goldsmith et al. (2008) find that half the mass of the Taurus-Auriga-Perseus complex lies in regions having H2 column density below 2.1 × 1021 cm−2 and that the probability of finding a young star increases only in pixels of column density larger than 6 × 1021 cm−2 . The precursors of dense cores are therefore likely buried in the diffuse neutral ISM that builds up the bulk of molecular cloud masses. Turbulent dissipation may also provide the missing important clues to the so-called “outstanding mysteries” raised by the observations of diffuse molecular gas (see the review of Snow & McCall 2006): the ubiquitous small scale

Small-scale Intermittency of Interstellar Turbulence

245

Figure 1. A record of the square of the velocity (time or space) derivative measured in the turbulent wake of a cylinder (Sreenivasan et al. 1989). This signal can be viewed as the rate of dissipation of turbulent kinetic energy. The rare largest excursions are more frequent than they would be if the signal were Gaussian.

structure, down to AU-scales (Heiles 2007), the large fluctuations of thermal pressure (Jenkins & Tripp 2001, 2007), the remarkable molecular richness found in this hostile medium weakly protected from UV radiation (e.g. Liszt & Lucas 1998), a richness that even the most sophisticated chemical models driven by UV photons fail to reproduce. 2

Intermittency of Interstellar Turbulence: Two Early Conjectures

For half a century now, turbulence in laboratory and atmospheric flows has been recognized to be intermittent i.e. the smaller the scale, the larger the spatiotemporal velocity fluctuations at that scale, relative to their average (Landau & Lifchitz 1959; Kolmogorov 1962). Turbulent energy is not transferred homogeneously from scale to scale so that, unlike the large scales, the active small scales are not space-filling. The statistical properties of the velocity fluctuations have been widely studied theoretically and experimentally in laboratory and atmospheric flows (see the review by Anselmet et al. 2001). In particular, the statistics of velocity derivative signals are non-Gaussian, with large departures from the average more frequent than for a Gaussian distribution (see an illustration in Fig. 1). This property is at the origin of the non-Gaussian probability density functions (pdf) of the dissipation rate ǫ ∝ Σ(∂j ui + ∂i uj )2 and rate-of-strain Sij = ∂j ui + ∂i uj in incompressible flows, with a departure from a Gaussian more pronounced at small scales. Note that the velocity pdfs are Gaussian. In the late 1980’s, as studies of interstellar cloud turbulence developed, an interesting challenge emerged: searching for signatures of intermittency in the turbulence of molecular clouds because it was foreseeable that singularities in the turbulent dissipation rate would have measurable consequences on cloud structure and evolution. The 10.4 m antenna of the Caltech Submillimeter Observatory (CSO) was in its commissioning phase. Weak and broad wings of

246


Figure 2. Left: Maps of the 12 CO(2-1) emission of a 2 pc field in the Polaris Flare integrated over two velocity ranges: [−6, −3.5] (blue) and [−3.5, −0.5] km s−1 (red). The pixel size (11′′ ) is 7.5 mpc at the distance (d = 150 pc) of the source. Right: Space-velocity cut perpendicular to the interface between the two velocity components. The variations of the line CVI (thick squares) and width (thin squares) are shown (in red and blue, respectively, in the electronic version). The maximum velocity-shear at offset 450 arcseconds is ∼ 40 km s−1 pc−1 . From HF09.

unknown origin were being discovered in 12 CO lines observed with sufficiently high signal-to-noise ratio in regions far from star formation. Two conjectures were then made: (1) these broad CO linewings trace the intermittency of turbulence in molecular clouds (Falgarone & Phillips 1990) and (2) the fractal dimension of cloud edges, measured in the 12 CO(2-1) line at the CSO, is related to the scaling law of turbulence (Falgarone et al. 1991). It took about two decades to put these statements on firmer observational and theoretical ground, where they seem to stand now. 3

Instrumental, Observational, and Theoretical Challenges

The authors of these conjectures did not foresee then how long the road ahead would be. Many properties of intermittency were not known at that time, in particular the existence of coherent structures of intense shear, vorticity, rate of strain, ... (“The sinews of turbulence”; Moffatt et al. 1994), the clustering of these coherent structures, the inertial range intermittency (Moisy & Jiménez 2004) and the strong coupling between scales i.e. small-scale intermittency is more pronounced in turbulent fields where large-scale shear is larger (Mininni et al. 2006). These properties are now helpful in this research field. Moreover, identifying regions of intermittency in interstellar turbulence requires large homogeneous statistical samples of the velocity field, a prerequisite almost unobtainable at that time. The instrumental challenges have been overcome through the years, thanks to several developments at IRAM and CSO. Array receivers, on-the-fly mode for observations combined with frequency-switching and low-noise receivers have led


247

to the discovery of rarer and rarer events, down to a probability density ∼ 10−5 in the most recent 12 CO maps. Small scales, accessible only to interferometers, have been detected as long and thin coherent structures, rather than isolated clumps, once mosaicing with an interferometer has been feasible. Theoretical challenges have been overcome as well. One of the observables available to build two-point statistics of the velocity field in diffuse and translucent gas is the line Centroid Velocity (CV) of the CO lines, used as a substitute for the velocity. It had to be demonstrated that CV increments (CVI) between two positions in the plane-of-the-sky (pos) could be used to study some facets of the two-point statistics of the velocity field in diffuse molecular clouds, and, in particular, that extrema of CVIs in translucent molecular gas trace intense velocity-shears1 (Lis et al. 1996; Miville-Deschênes et al. 2003; Levrier 2004; Esquivel & Lazarian 2005). Only recently has a large ensemble of observational results allowed progress along the above lines. They are presented in what follows. 4

Parsec-scale Observations: Increasing the Dynamic Range

A first set of results dates back to 1998 when elongated structures, uncorrelated with any other emission, were found in the 12 CO wing-emission of small nearby fields harbouring low-mass dense cores (Falgarone et al. 1998). Statistics of the velocity field were built on these small samples, and one much larger obtained at the CSO. Non-Gaussian pdfs of line-CVI were found. This property was proposed to be a signature of the space-time intermittency of the velocity field (Pety & Falgarone 2003). Maps only a few times larger have opened the route to more reliable statistical studies and allowed the thermal and chemical characterization of the regions contributing to the non-Gaussian tails of the pdfs: large HCO+ abundances were inferred from HCO+ (1–0) line observations (Falgarone et al. 2006) and gas temperatures larger than in the bulk of the gas were derived from multitransition analyses of CO isotopologues (Hily-Blant & Falgarone 2007). The most recent maps, obtained with the IRAM-30 m/HERA array receiver, operating in the on-the-fly and frequency-switching mapping mode, contain up to ∼ 105 independent spectra of homogeneous samples of turbulence. An example is shown in Figure 2 (left) that displays the 12 CO(2-1) emission of a translucent (or diffuse) molecular region (the total hydrogen column density corresponds to Av = 0.6 to 0.8 mag only) located in the Polaris Flare (Hily-Blant & Falgarone 2009, hereafter HF09). The two velocity components barely overlap in projection and share a narrow interface over ∼ 1 pc. The position-velocity cut (Fig. 2, right) shows that the centroid velocity varies by ∼ 2 km s−1 over ∼ 0.05 pc (red curve) across this interface providing an intense velocity-shear of 40 km s−1 pc−1 , far larger than the average value of 1 km s−1 pc−1 of molecular clouds at the parsecscale (Goldsmith & Arquilla 1985). The CVI-pdfs in that field have the anticipated non-Gaussian tails that increase as the lag over which the increment is measured decreases (Fig. 3, left). 1 Velocity-shear is used rather than velocity-gradient because the observations provide crossderivatives of the velocity field (i.e. the displacement measured in the pos is perpendicular to the line-of-sight (los) velocity).

248


Figure 3. Left: Normalized pdfs of Centroid Velocity Increments measured over variable lags, expressed in units of 15 arcsec (upper right corners). The Gaussians of same dispersion σ(δCl ) (given in km s−1 at the bottom of each panel) are also drawn. Note that a probability of 10−5 is reached in the most extreme bins. Right: Locus of the positions populating the non-Gaussian tails of the pdf for a lag 60 arcseconds. The scale of the wedge is expressed in km s−1 . Two crosses mark the positions of the two low-mass dense cores in the field (Heithausen et al. 2002). The rectangle is the area observed with the PdBI. From HF09.

Figure 4. Comparison of the E-CVIs structure (contours) with the 12 CO(21) line integrated intensity (left) and the spatial distribution of the blue 12 CO(2-1) linewing (right). The line integrated intensities in the wedges are in K km s−1 . From HF09.


249

The locus of the CVI extrema (the E-CVIs) that build the non-Gaussian tails of the pdfs is a narrow structure (∼ 0.03 pc thick) more than a parsec long (Fig. 3, right). This structure is defined on the basis of velocity only. It does not trace any peculiar density, nor column density, structure as shown in Figure 4 (left). It does follow the intense-velocity shear mentioned above and it is reassuring that the statistical method finds what is straightforward to find in the data. What was unexpected, in turn, is that this structure follows the distribution of the broad 12 CO linewings in the field (Fig. 4, right). 12 CO line centroids (the line 1st moments) are therefore sensitive to broad line-wings in diffuse molecular gas. The statistics of CVIs therefore provide valid tracers of large local velocity excursions in translucent molecular gas where radiative trapping is moderate. Finally, the two low-mass dense cores in the field lie at one tip of the E-CVIs locus (Fig. 3, right), suggesting a causal link between the E-CVI structure and the presence of the cores. A similar analysis has been performed in a cloud edge of the Perseus-TaurusAuriga giant molecular complex. The field has the same total hydrogen column density as that in the Polaris Flare, but is less turbulent (twice as small a rms velocity dispersion at the parsec-scale). The CVI-pdfs show departures from a Gaussian distribution with amplitude 2.5 times smaller than in the Polaris Flare and the E-CVI structure is remarkably straight and parallel to the local projection of the magnetic field measured by Heiles (2000). This ensemble of properties, (i) the increasing departure of CVI-pdfs from a Gaussian distribution as the scale decreases, (ii) the coherent structures of ECVIs and (iii) the link between the large-scale properties of turbulence and the magnitude of the small-scale E-CVIs, suggests that the 12 CO E-CVIs trace the intermittency of turbulence in translucent molecular clouds. Their coincidence with the broad 12 CO linewings may be seen as the first observational proof of the conjecture of Falgarone & Phillips (1990).

5

Milliparsec-scale Observations: Approaching the Dissipation Scale

A step beyond is provided by IRAM Plateau de Bure Interferometer (IRAMPdBI) observations of the field located on one branch of the E-CVI structure shown in Figure 3 (right). A mosaic of 13 fields covers the area in the 12 CO(1–0) line with a resolution of ∼ 4′′ or 3 mpc (Falgarone et al. 2009, hereafter FPH09). The interferometer data uncover not one, but eight weak and elongated structures with thickness as small as ≈ 3 mpc (600 AU) and length up to 70 mpc. These are not filaments because once merged with short-spacings data, the PdBIstructures appear to be the sharp edges of extended CO velocity components. Moreover, six out of eight, form pairs of quasi-parallel structures at different velocities. This cannot be due to chance alignment that would have a probability of at most 2 × 10−8 . The velocity-shears estimated for the three pairs, not corrected for projection effects, include the largest values ever measured in non-star-forming regions, up to 780 km s−1 pc−1 (see Fig. 5). Two velocity components separated by 3.5 km s−1 , i.e. about the rms velocity dispersion of the CNM (Haud & Kalberla 2007), therefore share an interface as thin as 7 mpc with no shock signature nor large density enhancement.

250


Figure 5. Position-velocity diagrams across the pair of structures with largest velocity-shear. Left: Cut across the PdBI data cube. Right: Same across the PdBI data cube merged with short spacings data from the IRAM30 m telescope. The intensities in the wedges are in Kelvin.

FPH09 argue that, because the extended CO velocity components have sharp edges and because the small overlap of the pairs of velocity components has to be preserved for any viewing angle (an edge-on viewing would ensure little or null overlap but is unlikely), they have to be thin sheets of CO emission. In other words, the only way to prevent shadowing of the pairs at different velocities under any viewing angle is that these CO components are thin sheets, not 3D-volumes. The same reasoning applies to the geometry of the large-shear detected in the single dish data (Fig. 2). The edges detected by the PdBI mark a discontinuity, at the milliparsec scale, between a detected CO-rich component flowing out of the region of largeshear and a gas flowing into it, undetected in the 12 CO(1–0) line, presumably the CNM (see the sharp transitions at ∼ −1.7 km s−1 and −4.7 km s−1 in Fig. 5, right). These may be the first directly-detected manifestations of the intermittency of interstellar turbulent dissipation. The large velocity-shears reveal an intense straining field, generating a local dissipation rate much larger than average, acting as a source of CO molecules (see Section 7). The milliparsec scale shear-structures have been detected only where they have been sought, and it is presently unknown whether they would exist everywhere along the structure of Figure 3. Now, many surfaces in turbulent flows, in particular those of iso-dissipation, have been shown to be fractal with a dimension D = 2 + ξ where ξ is the scaling exponent of the velocity structure function (ξ = 1/3 in Kolmogorov turbulence) (Sreenivasan et al. 1989). If, as it seems to be the case, CO molecules form in the regions of intense turbulent dissipation in diffuse molecular gas, it is not surprising that their spatial distribution be a fractal structure of dimension 1.3 in projection. This result supports the second conjecture (Falgarone et al.


251

Figure 6. Size-linewidth relation for a large sample of 12 CO(1–0) structures taken in the literature (see references in FPH09) to which are added: the single-dish data of the small isolated structures of Heithausen (2002, 2006) (solid triangles), PdBI data within one of them (Heithausen 2004) (open triangles), a polygon that limits those of Sakamoto & Sunada (2003) and the eight PdBI structures discussed here (solid squares). The 4 large empty symbols without error bars show where the pairs of PdBI-structures would be if not resolved spatially. The straight lines show the slopes 1/3 and 1/2 for comparison.

1991) linking the fractal distribution of CO emission in cloud edges to the power spectrum of turbulence. 6

Comparison with other Data Sets

These findings broaden the perspective on the presence of small-scale CO structures in diffuse and translucent molecular clouds. Isolated CO features have been found in the high latitude sky (Heithausen 2002, 2006) with bright substructures seen in PdBI observations (Heithausen 2004). The sub-structures, although analysed as clumps by the author, are not randomly scattered in the field but form two elongated patterns, reminiscent for their thickness and length of what is found in FPH09, providing a velocity shear of 180 km s−1 pc−1 . Sakamoto & Sunada (2003) have discovered a number of CO small-scale structures in the edges of the Taurus molecular cloud. Their main characteristics are their large line-width and their sudden appearance and disappearance within 0.03 to 0.1 pc. Interestingly, the authors propose that their small-scale CO structures pinpoint CO molecule-forming regions, driven by the thermal instability in the turbulent diffuse ISM. All these data are plotted in Figure 6 with a large sample of 12 CO(1–0) structures taken in the literature. Above 0.1 pc, a power law 1/2 ∆vN T ≈ 1 km s−1 lpc , although with a large scatter, is a good description of the data set. Below 0.1 pc, in turn, the small-scale data significantly depart from that power law by a large factor and it cannot be due to projection effects. The

252


Figure 7. Comparison of observed column densities of HCO+ and OH in diffuse molecular gas (black symbols) (Liszt & Lucas 1998) with (left) PDR models at different densities and (right) models of turbulent dissipation regions (TDR) for the same densities (Godard et al. 2009). Along each curve, the main free parameter, the rate-of-strain, increases from a = 10−11 s−1 (top-right) to a = 3 × 10−10 s−1 (bottom-left).

departure is the largest for the pairs of PdBI-structures, as they would appear if they were not resolved spatially i.e. as structures anomalously broad in velocity with respect to their size. The increased scatter of velocity-widths of the structures below 0.1 pc down to 1 mpc may be seen as another manifestation of the intermittency of turbulence in translucent molecular gas.

7

Eighteen Years Later: New Openings to the Future

Structures carrying most of the properties of the intermittency of turbulence have been identified in nearby translucent molecular gas. They appear as regions of intense velocity-shears when los and pos projections allow their detection. These are as large as ∼ 800 km s−1 pc−1 , almost three orders of magnitude larger than the cloud average value at the parsec scale. They do not appear to be shocks because no post-shock gas has been detected. These structures follow the locus of broad CO linewings and tend to be parallel to the magnetic field. If viewed as the sites of enhanced turbulent dissipation, whatever the actual physical process, and assuming that turbulent dissipation scales as the square of the velocity-shear, a significant fraction of the turbulent energy at the parsec scale is dissipated in less than a few percent of the volume. The coherent velocity-structure found in the Polaris Flare couples scales of 7 mpc (or less) to > 2 pc and it is the first time that such a velocity-structure is detected in the ISM. The timescales associated to the largest velocity-shears are short, τ ∼ 3 × 103 yr, which also suggests large gas accelerations. Many processes, inoperative on large scales (e.g. decoupling of ions and neutrals, of small dust grains and gas) are therefore anticipated to be dominant at small scales in diffuse gas. This is by far the main difficulty faced by direct numerical simulations (DNS) trying to model interstellar turbulence: not only the range of scales to be coupled is huge, but also the dominant processes and the physics to be described change with scale (e.g. the fluid approximation becomes marginally invalid at the 10 AU scale).


253

This is why, to understand the origin of the unexpected chemical richness of the diffuse ISM, models of the chemical and thermal evolution of a fluid particle trapped in a dissipation burst rely on analytical solutions of the Helmholtz equation for the vorticity evolution (Joulain et al. 1998; Godard et al. 2009). A magnetized Burgers vortex is computed in which the dissipation is due to (i) molecular viscosity in the layers of large-shear at the vortex boundary, and (ii) ion-neutral friction in the inner layers. The two main independent parameters of the model are the rate-of-strain a due to the large scales of the ambient turbulence that stretch the vortex tube and the gas density. Chemical routes comprising highly endothermic reactions, inoperative in cold gas, are opened: the output of this warm chemistry are abundances of CO, CH+ , HCO+ , CN, H2 O, ... significantly larger than those produced in photodissociation regions (PDR) models and closer to those observed in high latitude clouds (e.g. Liszt & Lucas 1998). An illustration is given in Figure 7. It shows that the agreement of the TDR models with the data is better for intermittent structures driven by a small rate-of-strain, which are also those in which the dissipation is dominated by ion-neutral friction rather than viscous dissipation. Further chemical probes of such a turbulence-driven chemistry are the large CH+ abundances inferred in diffuse molecular gas from the detection of 13 CH+ (1–0) in absorption against bright star forming regions at the CSO (Falgarone et al., in prep.; see Lis et al., this volume). Last, the intense cooling radiation in the rotationally excited H2 lines predicted to be emitted by the myriads of tiny regions of turbulent dissipation has been detected in the galactic diffuse medium by ISO-SWS (Falgarone et al. 2005) and more recently by Spitzer/IRS. All the above seem to preclude detailed comparisons of cloud small-scale properties with predictions from numerical simulations in a near future and might explain why molecular clouds, as observed, have a larger Quantity-of-Structure than cubes produced by DNS of supersonic or MHD turbulence (Levrier et al. 2006). However, the largest millimeter-line maps of local molecular clouds have a dynamic range between 250 and 1000 (covering scales 0.008–2 pc, HF09; and 0.035–25 pc, Goldsmith et al. 2008) comparable to that of DNS of interstellar turbulence. Confrontations of the statistical properties of the observed and computed velocity fields may be achieved over a range of scales far enough from the dissipation scale. For instance, computations of high-order (> 3) structure functions of CVIs are now possible, allowing to explore the statistics of rare events of increasing magnitude. The role of the driving scales can be explored, clarifying why the statistics of supersonic turbulence can mimic incompressible statistics at small scale (Porter et al. 2002; Vestuto et al. 2003; Mininni et al. 2006; Federrath et al. 2009). In conclusion, the coherent velocity-structures that carry the properties of intermittency of interstellar turbulence tap the turbulent non-thermal energy of the medium into a set of dissipation processes activated at small-scale that significantly modify the gas equation-of-state over time scales shorter than a few 103 yr, and trigger cooling and condensation. The existence of such a structure in the Polaris Flare with two low-mass dense cores at its tip may not be due to chance: there seems to exist a time-sequence along this structure, from a soft velocity-shear in the NW to thinner multiple structures of more intense velocityshear in the SE, up to the dense cores themselves. The complex coupled processes

254


involved in this evolution, including the role and morphology of the magnetic field are yet to be described. Acknowledgments. EF is most grateful to T. G. Phillips for his supportive enthusiasm at entering a field (interstellar turbulence) that he had not touched before, and for his generous allocation of CSO telescope time, during its commissioning phase, to disclose the fractal and thermal properties of apparently featureless cloud edges and more recently, dedicated to the risky observations of the 13 CH+ (1–0) absorption lines at 830 GHz. References Anselmet, F., Antonia, R. A., & Danaila, L. 2001, Planetary & Space Sciences, 49, 1177 Elmegreen, B. G. & Scalo, J. 2004, ARA&A, 42, 211 Esquivel, A. & Lazarian, A. 2005, ApJ, 631, 320 Falgarone, E. & Phillips, T. G. 1990, ApJ, 359, 344 Falgarone, E., Phillips, T. G., & Walker, C. K. 1991, ApJ, 378, 186 Falgarone, E., Panis, J.-F., Heithausen, A., et al. 1998, A&A, 331, 669 Falgarone, E., Verstraete, L., Pineau des Forêts, G., & Hily-Blant, P. 2005, A&A, 433, 997 Falgarone, E., Pineau des Forêts, G., Hily-Blant, P., & Schilke, P. 2006, A&A, 452, 511 Falgarone, E., Pety, J., & Hily-Blant, P. 2009, A&A, accepted (FPH09) Federrath, C., Duval, J., Klessen, R. S., et al. 2009, arXiv0905.1060F Godard, B., Falgarone, E., & Pineau des Forêts, G. 2009, A&A, 495, 847 Goldsmith, P. F. & Arquilla, R. 1985, in Protostars and Planets II, ed. D. C. Black & M. S. Matthews, 137–149 Goldsmith, P. F., Heyer, M., Narayanan, G., et al. 2008, ApJ, 680, 428 Haud, U. & Kalberla, P.M.W. 2007, A&A, 466, 555 Heiles, C. 2000, AJ, 119, 923 Heiles, C. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 365, SINS - Small Ionized and Neutral Structures in the Diffuse Interstellar Medium, ed. M. Haverkorn & W. M. Goss, 3–11 Heithausen, A. 2002, A&A, 393, L41 Heithausen, A. 2004, ApJ, 606, L13 Heithausen, A. 2006, A&A, 450, 193 Heithausen, A., Bertoldi, F., & Bensch, F. 2002, A&A, 383, 591 Hily-Blant, P. & Falgarone, E. 2007, A&A, 469, 173 Hily-Blant, P., Falgarone, E., & Pety, J. 2008, A&A, 481, 367 Hily-Blant, P. & Falgarone, E., 2009, A&A, 500, L29 (HF09) Jenkins, E. B. & Tripp, T. M. 2001, ApJS, 137, 297 Jenkins, E. B. & Tripp, T. M. 2007, in Astronomical Society of the Pacific Conference Series, Vol. 365, SINS - Small Ionized and Neutral Structures in the Diffuse Interstellar Medium, ed. M. Haverkorn & W. M. Goss, 51–58 Joulain, K., Falgarone, E., Pineau des Forêts, G. P., & Flower, D. 1998, A&A, 340, 241 Kolmogorov, A. N. 1962, J. Fluid Mech., 13, 82 Landau, L. E. & Lifchitz, E. M. 1959, Fluid Mechanics, Pergamon Press, Oxford Levrier, F. 2004, A&A, 421, 387 Levrier, F., Falgarone, E., & Viallefond, F. 2006, A&A, 456, 205 Lis, D. C., Pety, J., Phillips, T. G., & Falgarone, E. 1996, ApJ, 463, 623 Liszt, H. S. & Lucas, R. 1998, A&A, 339, 561 Mac Low, M.-M., Klessen, R. S., Burkert, A., & Smith, M. D. 1998, Phys. Rev. Letters, 80, 2754 Mac Low, M.-M. & Klessen, R. S. 2004, Reviews of Modern Physics, 76, 125 Mininni, P. D., Alexakis, A., & Pouquet, A. 2006, Phys. Rev. E, 74, 6303


255

Miville-Deschênes, M.-A., Levrier, F., & Falgarone, E. 2003, ApJ, 593, 831 Moffatt, H. K., Kida, S., & Ohkitani, K. 1994, Journal of Fluid Mechanics, 259, 241 Moisy, F. & Jiménez, J. 2004, Journal of Fluid Mechanics, 513, 111 Penzias, A. A., Solomon, P. M., Jefferts, K. B., & Wilson, R. W., 1972, ApJ, 174, L43 Pety, J. & Falgarone, E. 2003, A&A, 412, 417 Porter, D. H., Pouquet, A., & Woodward, P. R. 2002, Phys. Rev. E, 66, 026301 Sakamoto, S. & Sunada, K. 2003, ApJ, 594, 340 Scalo, J. & Elmegreen, B. G. 2004, ARA&A, 42, 275 Snow, T. P. & McCall, B. J. 2006, ARA&A, 44, 367 Sreenivasan, K. R., Ramshankar, R., & Méneveau, C. 1989, Proc. R. Soc. Lond. A, 421, 79 Vestuto, J. G., Ostriker, E. C., & Stone, J. M. 2003, ApJ, 590, 858 Zuckerman, B. & Evans, N. J. 1974, ApJ, 192, L149