E. Falgarone et al.: Extreme velocity-shears and CO on milliparsec sca<strong>le</strong> 367<strong>tel</strong>-<strong>00726959</strong>, version 1 - 31 Aug 2012numerical simulations of incompressib<strong>le</strong> and compressib<strong>le</strong> turbu<strong>le</strong>nce,and the TDR chemical model of Godard et al. (2009).The fact that the most dissipative structures appear to belayers of intense strain-rate is consistent with recent resultsof numerical simulations of incompressib<strong>le</strong> turbu<strong>le</strong>nce at highReynolds number (Moisy & Jiménez 2004) and laboratory experiments(Ganapathisubramani et al. 2008). These regions arenot randomly distributed and form inertial-range clusters (Moisy& Jiménez 2004) or develop at the boundaries regions of high<strong>le</strong>vel of vorticity (i.e. vortex tubes) (Ganapathisubramani et al.2008). Coupling between small-sca<strong>le</strong> statistics of the velocityfield and the properties of the large-sca<strong>le</strong> flows is also c<strong>le</strong>arlyprobed in the high-Re numerical simulations of Mininni et al.(2006): correlations are observed between large-sca<strong>le</strong> shear andsmall-sca<strong>le</strong> intermittency.In compressib<strong>le</strong> turbu<strong>le</strong>nce, the fact that the most dissipativestructures are shear-layers is not expected. Yet, in their hydrodynamicalsimulations of mildly compressib<strong>le</strong> turbu<strong>le</strong>nce, Porteret al. (2002) show that the compressib<strong>le</strong> component of the velocityfield is weaker than its so<strong>le</strong>noidal counterpart by a factor ∼3,independent of the nature of the driving process (compressib<strong>le</strong> orso<strong>le</strong>noidal) and Vestuto et al. (2003) find that the energy fractionin the so<strong>le</strong>noidal modes is dominant and increases with the magneticfield intensity in compressib<strong>le</strong> magneto-hydrodynamical(MHD) turbu<strong>le</strong>nce. These numerical experiments are still farfrom approaching the ISM conditions but they suggest that turbu<strong>le</strong>ntdissipation may occur primarily in so<strong>le</strong>noidal modes,i.e. without direct gas compression, and that the properties ofthe small sca<strong>le</strong>s are coup<strong>le</strong>d to the large-sca<strong>le</strong>s.In the TDR models of Godard et al. (2009), the chemical enrichmentof the CNM is driven by high gas temperatures and enhancedion-neutral drift, without density enhancement. The temperatureincrease is due to viscous dissipation in the layers oflargest velocity-shears at the boundaries of coherent vortices 4 .The large ion-neutral drift occurs in the layers of largest rotationalvelocity in which ions and magnetic fields decoup<strong>le</strong> fromneutrals. These two dissipative processes trigger endothermicchemical reactions, blocked at the low temperature of the CNM.Enrichments consistent with observations are obtained for turbu<strong>le</strong>ntrates-of-strain a = 10 −11 s −1 induced by large sca<strong>le</strong> turbu<strong>le</strong>nceand for modera<strong>tel</strong>y dense gas (n H < 200 cm −3 )characteristicof the CNM. There is no direct determination of therates-of-strain generated by turbu<strong>le</strong>nce in the CNM. We notehowever that the largest observed velocity-shear (Tab<strong>le</strong> 3) corresponds,if the projected quantities provide reasonab<strong>le</strong> estimates,to a comparab<strong>le</strong> rate-of-strain. The range of observed CO columndensities from N(CO) = 10 14 to 1.6 × 10 15 cm −2 can bereproduced by intense velocity-shears occurring in gas of density100 to 200 cm −3 . In this framework, the energy sourcetapped to enrich the medium in mo<strong>le</strong>cu<strong>le</strong>s is the supersonic turbu<strong>le</strong>nceof the CNM.The association between the large observed velocity-shearsand local enhanced dissipation rate is therefore supported notonly by the earlier works presented in the Introduction but alsoby a quantitative agreement between the TDR chemical modelsand the present observational results. We cannot ru<strong>le</strong> out howevera contribution of low-velocity C-shocks to the turbu<strong>le</strong>nt dissipation.If they propagate in the CNM, they are not visib<strong>le</strong> in theCO lines. Such shocks are not yet reliably model<strong>le</strong>d (Hily-Blantet al., in preparation).4 The “sinews of turbu<strong>le</strong>nce” put forward by Moffatt et al. (1994) thatlink large-sca<strong>le</strong> strain and small-sca<strong>le</strong> vorticity.8. Conclusions and perspectivesIRAM-PdBI observations of a mosaic of 13 fields in the turbu<strong>le</strong>ntenvironment of a low-mass dense core have disclosedsmall and weak 12 CO(1−0) structures in translucent mo<strong>le</strong>culargas. They are straight and elongated structures but they are notfilaments because, once merged with short-spacings data, thePdBI-structures appear as the sharp edges of larger-sca<strong>le</strong> structures.Their thickness is as small as ≈3 mpc (600 AU), and their<strong>le</strong>ngth, up to 70 mpc, is only limited by the size of the mosaic.Their CO column density is a well determined quantity for theexcitation conditions found at larger sca<strong>le</strong> and is in the rangeN(CO) = 10 14 to 10 15 cm −2 .TheirH 2 density, estimated inseveral ways, including the continuum emission of the brighteststructure, does not exceed a few 10 3 cm −3 . Their well-distributedorientations can be followed in the larger-sca<strong>le</strong> environment ofthe field. Six of them form three pairs of quasi-paral<strong>le</strong>l structures,physically related. The velocity-shears estimated for thethree pairs include the largest ever measured in non-star-formingclouds (up to 780 km s −1 pc −1 ).The PdBI-structures are therefore not isolated and are theedges of so-cal<strong>le</strong>d SEE(D)S for sharp-edged extended (doub<strong>le</strong>)structures. We show that the SEE(D)S are thin layers of CO-richgas and that their sharp edges pinpoint a small-sca<strong>le</strong> dynamicalprocess, at the origin of the CO contrast detected by the PdBI.We propose that the SEE(D)S are the outcomes of the chemica<strong>le</strong>nrichment driven by intense dissipation occurring in largevelocity-shears and that they are CO-rich layers swept along bythe straining field of CNM turbu<strong>le</strong>nce.The present work is the first detection of mpc-sca<strong>le</strong> intensevelocity-shears belonging to a parsec-sca<strong>le</strong> shear. The large departurefrom average of the kinematic properties of these structures,confirms that they are a manifestation of the small-sca<strong>le</strong>intermittency of turbu<strong>le</strong>nce in this high latitude field, a propertyalready established on statistical grounds (HF09). The values ofthe velocity-shears (or rate-of-strain) provide a quantitative constrainton the dissipation rate that can be compared to chemicalmodels. The link between the turbu<strong>le</strong>nt dissipation in the diffusegas and the dense core observed in the vicinity of the PdBI mosaic(Fig. 1) still remains to be established.Last, we would like to stress that sub-structure still exists inthese mpc-sca<strong>le</strong> structures of the diffuse ISM and that the nextgeneration of interferometers (e.g. ALMA) should be ab<strong>le</strong> to observegas at the dissipation sca<strong>le</strong> of turbu<strong>le</strong>nce (that is still unknown)or at <strong>le</strong>ast observe the effects on the ISM (temperature,excitation, mo<strong>le</strong>cular abundances) of the huge re<strong>le</strong>ase of energyexpected to occur there.Acknow<strong>le</strong>dgements. We thank the IRAM staff at Plateau de Bure and Grenob<strong>le</strong>for their support during the observations. E.F. is most grateful to Michael Dumke,Emmanuel Dartois, Anne Dutrey and Stéphane Guilloteau for their help duringthe early stages of the data reduction. E.F. also acknow<strong>le</strong>dges the stimulantdiscussions over the years with E. Ostriker, P. Hennebel<strong>le</strong>, A. Lazarian, B. G.Elmegreen, M. M. Mac-Low, E. Vasquez-Semadeni and many others that cannotbe listed here. We thank J. Scalo, our (formerly anonymous) referee, forhis dedicated efforts at making us write our observational paper accessib<strong>le</strong> tonumericists.Appendix A: Noise <strong>le</strong>vel in the mosaicMosaic noise is inhomogeneous due to primary beam correction.This is shown in Fig. A.1. The 13-field mosaic produces a largearea with uniform noise <strong>le</strong>vel. Only at the edge of the mosaicdoes it increase sharply due to the primary beam correction (thecontour shown are at a 2−4 sigma <strong>le</strong>vel, 1 sigma being measuredat the map center on a channel devoided of signal).
368 E. Falgarone et al.: Extreme velocity-shears and CO on milliparsec sca<strong>le</strong><strong>tel</strong>-<strong>00726959</strong>, version 1 - 31 Aug 2012Fig. A.1. Map of the noise <strong>le</strong>vel in K km s −1 over the 13-field mosaic.Appendix B: The size-linewidth scaling lawMo<strong>le</strong>cular cloud parameters have long been determined as thoseof three-dimensional structures isolated in the four-dimensionalspace of the mo<strong>le</strong>cular line data sets T L (x,y,v z ), the line brightnesstemperature being a function of position in the pos (twocoordinates x,y), and one spectral dimension, the projected velocityon the los direction v z . In this 4D space, 3D structuresare isolated following different methods (Stutzki & Guesten1990; Williams et al. 1994; Falgarone & Perault 1987; Loren1989; Falgarone et al. 1992). The size and linewidth of thelarge number of clouds displayed in Fig. 10 have been obtainedby using published values, corrected in several cases toallow the size and linewidth obey the same definitions in allthe samp<strong>le</strong>s (see Falgarone 1998). The structures are identifiedin 12 CO(1−0) mo<strong>le</strong>cular line surveys of the central partsof the Galaxy (stars, Dame et al. 1986; open triang<strong>le</strong>s Solomonet al. 1987) and of the third quadrant (open hexagons, Mayet al. 1997), in the Rosette (crosses) and Madda<strong>le</strong>na (opensquares) mo<strong>le</strong>cular clouds (Williams et al. 1994), in non-starformingclouds (solid triang<strong>le</strong>s, Falgarone & Perault 1987; solidsquares, Falgarone et al. 1992; tripods, Lemme et al. 1995), inρ Ophiuchus (solid hexagons, Loren 1989) and in a high latitudecloud (starred triang<strong>le</strong>s, Heithausen et al. 1998).ReferencesAnselmet, F., Antonia, R. A., & Danaila, L. 2001, Planet. 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