Sonic Scale Research Articles

Turbulence and Accretion: A High-resolution Study of the B5 Filaments

High-resolution observations of the Perseus B5 “core” have previously revealed that this subsonic region actually consists of several filaments that are likely in the process of forming a quadruple stellar system. Since subsonic filaments are thought to be produced at the ∼0.1 pc sonic scale by turbulent compression, a detailed kinematic study is crucial to test such a scenario in the context of core and star formation. Here we present a detailed kinematic follow-up study of the B5 filaments at a 0.009 pc resolution using the VLA and GBT combined observations fitted with multicomponent spectral models. Using precisely identified filament spines, we find a remarkable resemblance between the averaged width profiles of each filament and Plummer-like functions, with filaments possessing FWHM widths of ∼0.03 pc. The velocity dispersion profiles of the filaments also show decreasing trends toward the filament spines. Moreover, the velocity gradient field in B5 appears to be locally well ordered (∼0.04 pc) but globally complex, with kinematic behaviors suggestive of inhomogeneous turbulent accretion onto filaments and longitudinal flows toward a local overdensity along one of the filaments.

PENAMBAHAN SISTEM KOMPUTERISASI PADA UNIVERSAL TESTING MACHINE DI JURUSAN TEKNIK MESIN POLITEKNIK NEGERI MALANG

Rafik Djoenaidi, Andri Setiawan, Marthania Putri Indrayati ,. 2021. "Addition of Computerized Systems to Universal Testing Machines in the Department of Mechanical Engineering, State Polytechnic of Malang".
 
 Tensile testing equipment is an educational laboratory facility that is very important in supporting and supporting the teaching and learning process in the laboratory, especially the Tensile testing machine in the Polynema Mechanical Engineering department still uses manual reading of test results, along with the development of technology, currently the Tensile testing machine will equipped with digitalization tools and integrated into the computer with data acquisition.
 
 Tensile test equipment is an educational laboratory facility that is very important in supporting and supporting the teaching and learning process in the laboratory, especially the Tensile testing machine in the Polynema Mechanical Engineering department still uses reading test results manually, along with the development of technology, the current Tensile test machine will equipped with a digitizing device and integrated into a computer with data acquisition. The output of this tensile test is in the form of a tensile force table (F), elongation (ΔL), stress, strain and stress strain graph. The method for recording tensile force data (F) is done by connecting directly using a sonic scale type sp-320 and integrating it into a computer with data acquisition so that it can display a graph..
 
 Keywords: Tensile test equipment, data acquisition, Sonic Scale

Turbulent Properties in Star-forming Molecular Clouds Down to the Sonic Scale. II. Investigating the Relation between Turbulence and Star-forming Environments in Molecular Clouds

Abstract We investigate the effect of star formation on turbulence in the Orion A and Ophiuchus clouds using principal component analysis (PCA). We measure the properties of turbulence by applying PCA on the spectral maps in 13CO, C18O, HCO+ J = 1–0, and CS J = 2–1. First, the scaling relations derived from PCA of the 13CO maps show that the velocity difference (δv) for a given spatial scale (L) is the highest in the integral-shaped filament (ISF) and L1688, where the most active star formation occurs in the two clouds. The δv increases with the number density and total bolometric luminosity of the protostars in the subregions. Second, in the ISF and L1688 regions, the δv of C18O, HCO+, and CS are generally higher than that of 13CO, which implies that the dense gas is more turbulent than the diffuse gas in the star-forming regions; stars form in dense gas, and dynamical activities associated with star formation, such as jets and outflows, can provide energy into the surrounding gas to enhance turbulent motions.

The sonic scale of interstellar turbulence

Understanding the physics of turbulence is crucial for many applications, including weather, industry, and astrophysics. In the interstellar medium (ISM), supersonic turbulence plays a crucial role in controlling the gas density and velocity structure, and ultimately the birth of stars. Here we present a simulation of interstellar turbulence with a grid resolution of 10048^3 cells that allows us to determine the position and width of the sonic scale (l_s) - the transition from supersonic to subsonic turbulence. The simulation simultaneously resolves the supersonic and subsonic cascade, v(l) ~ l^p, where we measure p_sup = 0.49 +/- 0.01 and p_sub = 0.39 +/- 0.02, respectively. We find that l_s agrees with the relation l_s / L = phi_s Mach^(-1/p_sup), where Mach is the three-dimensional Mach number, and L is either the driving scale of turbulence or the diameter of a molecular cloud. If L is the driving scale, we measure phi_s = 0.42 (+0.12) (-0.09), primarily because of the separation between the driving scale and the start of the supersonic cascade. For a supersonic cascade extending beyond the cloud scale, we get phi_s = 0.91 (+0.25) (-0.20). In both cases, phi_s < 1, because we find that the supersonic cascade transitions smoothly to the subsonic cascade over a factor of 3 in scale, instead of a sharp transition. Our measurements provide quantitative input for turbulence-regulated models of filament structure and star formation in molecular clouds.

Compressible Turbulence in the Interstellar Medium: New Insights from a High-resolution Supersonic Turbulence Simulation

Abstract The role of supersonic turbulence in structuring the interstellar medium (ISM) remains an unsettled question. Here, this problem is investigated using a new exact law of compressible isothermal hydrodynamic turbulence, which involves two-point correlations in physical space. The new law is shown to have a compact expression that contains a single flux term reminiscent of the incompressible case and a source term with a simple expression whose sign is given by the divergence of the velocity. The law is then used to investigate the properties of such a turbulence at integral Mach number 4 produced by a massive numerical simulation with a grid resolution of points. The flux (resp. source) term was found to have positive (resp. negative) contribution to the total energy cascade rate, which is interpreted as a direct cascade amplified by compression, while their sum is constant in the inertial range. Using a local (in space) analysis it is shown that the source is mainly driven by filamentary structures in which the flux is negligible. Taking positive defined correlations reveals the existence of different turbulent regimes separated by the sonic scale, which determines the scale over which the nonnegligible source modifies the scaling of the flux. Our study provides new insight into the dynamics and structures of supersonic interstellar turbulence.

The role of the sonic scale in the growth of magnetic field in compressible turbulence

ABSTRACT We study the growth of small fluctuations of magnetic field in supersonic turbulence, the small-scale dynamo. The growth is due to the smallest and fastest turbulent eddies above the resistive scale. We observe that for supersonic turbulence these eddies are localized below the sonic scale ls, defined as the scale where the typical velocity of the turbulent eddies equals the speed of sound, and are therefore effectively incompressible. All previous studies have ignored the existence of the sonic scale and consequently treated the entire inertial range as made up of compressible eddies. However, at large Mach numbers ls is much smaller than the integral scale of the turbulence so the fastest growing mode of the magnetic field belongs to small-scale incompressible turbulence. We determine this mode and the associated growth rate numerically with the aid of a white noise in time model of turbulence whose approximate validity for the description of the Navier–Stokes turbulence is explained. For that purpose, we introduce a new non-dimensional number Rsm that we name the magnetosonic Reynolds number that describes the division of the magnetic field amplification range between small-scale incompressible eddies and large-scale supersonic ones. We show that indeed, as Rsm grows (which means that the incompressible eddies occupy a larger portion of the magnetic field amplification range) the growth rate of the fastest growing mode increases, while the spatial distribution of the growing magnetic field shifts to smaller scales. Our result implies the existence of small-scale dynamo for compressible homogeneous turbulence.

THE LINK BETWEEN TURBULENCE, MAGNETIC FIELDS, FILAMENTS, AND STAR FORMATION IN THE CENTRAL MOLECULAR ZONE CLOUD G0.253+0.016

ABSTRACT Star formation is primarily controlled by the interplay between gravity, turbulence, and magnetic fields. However, the turbulence and magnetic fields in molecular clouds near the Galactic center may differ substantially compared to spiral-arm clouds. Here we determine the physical parameters of the central molecular zone (CMZ) cloud G0.253+0.016, its turbulence, magnetic field, and filamentary structure. Using column density maps based on dust-continuum emission observations with ALMA+Herschel, we identify filaments and show that at least one dense core is located along them. We measure the filament width and the sonic scale of the turbulence, and find . A strong velocity gradient is seen in the HNCO intensity-weighted velocity maps obtained with ALMA+Mopra. The gradient is likely caused by large-scale shearing of G0.253+0.016, producing a wide double-peaked velocity probability distribution function (PDF). After subtracting the gradient to isolate the turbulent motions, we find a nearly Gaussian velocity PDF typical for turbulence. We measure the total and turbulent velocity dispersion, and , respectively. Using magnetohydrodynamical turbulence simulations, we find that G0.253+0.016's turbulent magnetic field is only of the ordered field component. Combining these measurements, we reconstruct the dominant turbulence driving mode in G0.253+0.016 and find a driving parameter of , indicating solenoidal (divergence-free) driving. We compare this to spiral-arm clouds, which typically have a significant compressive (curl-free) driving component ( ). Motivated by previous reports of strong shearing motions in the CMZ, we speculate that shear causes the solenoidal driving in G0.253+0.016 and show that this reduces the star-formation rate by a factor of 6.9 compared to typical nearby clouds.

On the universality of interstellar filaments: theory meets simulations and observations

Filaments are ubiquitous in the universe. Recent observations have revealed that stars and star clusters form preferentially along dense filaments. Understanding the formation and properties of filaments is therefore a crucial step in understanding star formation. Here we perform three-dimensional high-resolution magnetohydrodynamical simulations that follow the evolution of molecular clouds and the formation of filaments and stars. We apply a filament detection algorithm and compare simulations with different combinations of physical ingredients: gravity, turbulence, magnetic fields and jet/outflow feedback. We find that gravity-only simulations produce significantly narrower filament profiles than observed, while simulations that include turbulence produce realistic filament properties. For these turbulence simulations, we find a remarkably universal filament width of 0.10 +/- 0.02 pc, which is independent of the star formation history of the clouds. We derive a theoretical model that provides a physical explanation for this characteristic filament width, based on the sonic scale (lambda_sonic) of molecular cloud turbulence. Our derivation provides lambda_sonic as a function of the cloud diameter L, the velocity dispersion sigma_v, the gas sound speed c_s, and the ratio of thermal to magnetic pressure, plasma beta. For typical cloud conditions in the Milky Way spiral arms, we find lambda_sonic = 0.04-0.16 pc, in excellent agreement with the filament width of 0.05-0.15 pc from observations. Consistent with the theoretical model assumptions, we find that the velocity dispersion inside the filaments is subsonic and supersonic outside. We further explain the observed p=2 scaling of the filament density profile, rho ~ r^(-p) with the collision of two planar shocks forming a filament at their intersection.

Mapping the core mass function to the initial mass function

It has been shown that fragmentation within self-gravitating, turbulent molecular clouds ("turbulent fragmentation") can naturally explain the observed properties of protostellar cores, including the core mass function (CMF). Here, we extend recently-developed analytic models for turbulent fragmentation to follow the time-dependent hierarchical fragmentation of self-gravitating cores, until they reach effectively infinite density (and form stars). We show that turbulent fragmentation robustly predicts two key features of the IMF. First, a high-mass power-law scaling very close to the Salpeter slope, which is a generic consequence of the scale-free nature of turbulence and self-gravity. We predict the IMF slope (-2.3) is slightly steeper then the CMF slope (-2.1), owing to the slower collapse and easier fragmentation of large cores. Second, a turnover mass, which is set by a combination of the CMF turnover mass (a couple solar masses, determined by the `sonic scale' of galactic turbulence, and so weakly dependent on galaxy properties), and the equation of state (EOS). A "soft" EOS with polytropic index $\gamma<1.0$ predicts that the IMF slope becomes "shallow" below the sonic scale, but fails to produce the full turnover observed. An EOS which becomes "stiff" at sufficiently low surface densities $\Sigma_{\rm gas} \sim 5000\,M_{\odot}\,{\rm pc^{-2}}$, and/or models where each collapsing core is able to heat and effectively stiffen the EOS of a modest mass ($\sim 0.02\,M_{\odot}$) of surrounding gas, are able to reproduce the observed turnover. Such features are likely a consequence of more detailed chemistry and radiative feedback.

Load tests on drilled shaft foundations in moderately strong to strong limestone

AbstractThree drilled shaft foundations (DSFs) were constructed in moderately strong to strong limestone at the Siloam Springs Arkansas Test Site (SSATS). The embedment lengths within the limestone were 3·0, 1·5 and 2·1 m for the DSFs with diameters of 1·2, 1·8 and 1·2 m, respectively. The DSFs were instrumented to facilitate cross-hole sonic logging testing and full scale load testing using bidirectional load cells (BLCs). Lessons learned from construction included the: (1) proper concrete pouring techniques; (2) ability to retrofit improperly installed telltale instrumentation; and (3) influence of rock socket length within moderately strong to strong limestone. Recommended design, construction and testing techniques in moderately strong to strong limestone are presented. Based on the full scale testing, t–z model recommendations for weathered limestone and moderately strong to strong limestone are presented and discussed. Comparisons between measured unit side resistance and current design recommendati...

A supersonic turbulence origin of Larson's laws

We revisit the origin of Larson's scaling laws describing the structure and kinematics of molecular clouds. Our analysis is based on recent observational measurements and data from a suite of six simulations of the interstellar medium, including effects of self-gravity, turbulence, magnetic field, and multiphase thermodynamics. Simulations of isothermal supersonic turbulence reproduce observed slopes in linewidth-size and mass-size relations. Whether or not self-gravity is included, the linewidth-size relation remains the same. The mass-size relation, instead, substantially flattens below the sonic scale, as prestellar cores start to form. Our multiphase models with magnetic field and domain size 200 pc reproduce both scaling and normalization of the first Larson law. The simulations support a turbulent interpretation of Larson's relations. This interpretation implies that: (i) the slopes of linewidth-size and mass-size correlations are determined by the inertial cascade; (ii) none of the three Larson laws is fundamental; (iii) instead, if one is known, the other two follow from scale invariance of the kinetic energy transfer rate. It does not imply that gravity is dynamically unimportant. The self-similarity of structure established by the turbulence breaks in star-forming clouds due to the development of gravitational instability in the vicinity of the sonic scale. The instability leads to the formation of prestellar cores with the characteristic mass set by the sonic scale. The high-end slope of the core mass function predicted by the scaling relations is consistent with the Salpeter power-law index.

A general theory of turbulent fragmentation

We develop an analytic framework to understand fragmentation in turbulent, self-gravitating media. Previously, we showed some properties of turbulence can be predicted with the excursion-set formalism. Here, we generalize to fully time-dependent gravo-turbulent fragmentation & collapse. We show that turbulent systems are always gravitationally unstable (in a probabilistic sense). The fragmentation mass spectra, size/mass relations, correlation functions, range of scales over which fragmentation occurs, & time-dependent rates of fragmentation are predictable. We show how this depends on bulk turbulent properties (Mach numbers & power spectra). We also generalize to include rotation, complicated equations of state, collapsing/expanding backgrounds, magnetic fields, intermittency, & non-normal statistics. We derive how fragmentation is suppressed with 'stiffer' equations of state or different driving mechanisms. Suppression appears at an 'effective sonic scale' where Mach(R,rho)~1. Gas becomes stable below this scale for polytropic gamma>4/3, but fragmentation still occurs on larger scales. The scale-free nature of turbulence and gravity generically drives mass spectra and correlation functions towards universal shapes, with weak dependence on many properties of the media. Correlated fluctuation structures, non-Gaussian density distributions, & intermittency have surprisingly small effects on the fragmentation process. This is because fragmentation cascades on small scales are 'frozen in' when large-scale modes push the 'parent' region above the collapse threshold; though they collapse, their statistics are only weakly modified by the collapse process. With thermal support, structure develops 'top-down' in time via fragmentation cascades; but strong rotational support reverses this to 'bottom-up' growth via mergers & introduces a maximal instability scale distinct from the Toomre scale.

ON THE STAR FORMATION EFFICIENCY OF TURBULENT MAGNETIZED CLOUDS

We study the star formation efficiency (SFE) in simulations and observations of turbulent, magnetized, molecular clouds. We find that the probability density functions (PDFs) of the density and the column density in our simulations with solenoidal, mixed, and compressive forcing of the turbulence, sonic Mach numbers of 3-50, and magnetic fields in the super- to the trans-Alfvenic regime, all develop power-law tails of flattening slope with increasing SFE. The high-density tails of the PDFs are consistent with equivalent radial density profiles, rho ~ r^(-kappa) with kappa ~ 1.5-2.5, in agreement with observations. Studying velocity-size scalings, we find that all the simulations are consistent with the observed v ~ l^(1/2) scaling of supersonic turbulence, and seem to approach Kolmogorov turbulence with v ~ l^(1/3) below the sonic scale. The velocity-size scaling is, however, largely independent of the SFE. In contrast, the density-size and column density-size scalings are highly sensitive to star formation. We find that the power-law slope alpha of the density power spectrum, P(rho,k) ~ k^alpha, or equivalently the Delta-variance spectrum of column density, DV(Sigma,l) ~ l^(-alpha), switches sign from alpha < 0 for SFE ~ 0 to alpha > 0 when star formation proceeds (SFE > 0). We provide a relation to compute the SFE from a measurement of alpha. Studying the literature, we find values ranging from alpha = -1.6 to +1.6 in observations covering scales from the large-scale atomic medium, over cold molecular clouds, down to dense star-forming cores. From those alpha values, we infer SFEs and find good agreement with independent measurements based on young stellar object (YSO) counts, where available. Our SFE-alpha relation provides an independent estimate of the SFE based on the column density map of a cloud alone, without requiring a priori knowledge of star-formation activity or YSO counts.

Characterizing interstellar filaments withHerschelin IC 5146

We provide a first look at the results of the Herschel Gould Belt survey toward the IC5146 molecular cloud and present a preliminary analysis of the filamentary structure in this region. The column density map, derived from our 70-500 micron Herschel data, reveals a complex network of filaments, and confirms that these filaments are the main birth sites of prestellar cores. We analyze the column density profiles of 27 filaments and show that the underlying radial density profiles fall off as r^{-1.5} to r^{-2.5} at large radii. Our main result is that the filaments seem to be characterized by a narrow distribution of widths having a median value of 0.10 +- 0.03 pc, which is in stark contrast to a much broader distribution of central Jeans lengths. This characteristic width of ~0.1 pc corresponds to within a factor of ~2 to the sonic scale below which interstellar turbulence becomes subsonic in diffuse gas, supporting the argument that the filaments may form as a result of the dissipation of large-scale turbulence.

The link between molecular cloud structure and turbulence

We aim to better understand how the spatial structure of molecular clouds is governed by turbulence. For that, we study the large-scale spatial distribution of low density molecular gas and search for characteristic length scales. We employ a 35 square degrees 13CO 1-0 molecular line survey of Cygnus X and visual extinction (A_V) maps of 17 Galactic clouds to analyse the spatial structure using the Delta-variance method. This sample contains a large variety of different molecular cloud types with different star forming activity. The Delta-variance spectra obtained from the A_V maps show differences between low-mass star-forming (SF) clouds and massive giant molecular clouds (GMC) in terms of shape of the spectrum and its power-law exponent beta. Low-mass SF clouds have a double-peak structure with characteristic size scales around 1 pc (though with a large scatter around this value) and 4 pc. GMCs show no characteristic scale in the A_V-maps, which can partly be ascribed to a distance effect due to a larger line-of-sight (LOS) confusion. The Delta-variance for Cygnus, determined from the 13CO survey, shows characteristic scales at 4 pc and 40 pc, either reflecting the filament structure and large-scale turbulence forcing or - for the 4 pc scale - the scale below which the 13CO 1-0 line becomes optically thick. Though there are different processes that can introduce characteristic scales, i.e. geometry, decaying turbulence the transition scale from supersonic to subsonic turbulence (the sonic scale), line-of-sight effects and energy injection due to expanding supernova shells, outflows, HII-regions, and the relative contribution of these effects strongly varies from cloud to cloud, it is remarkable that the resulting turbulent structure of molecular clouds shows similar characteristics.

THE STAR FORMATION RATE OF SUPERSONIC MAGNETOHYDRODYNAMIC TURBULENCE

This work presents a new physical model of the star formation rate (SFR), verified with an unprecedented set of large numerical simulations of driven, supersonic, self-gravitating, magneto-hydrodynamic (MHD) turbulence, where collapsing cores are captured with accreting sink particles. The model depends on the relative importance of gravitational, turbulent, magnetic, and thermal energies, expressed through the virial parameter, alpha_vir, the rms sonic Mach number, M_S,0, and the ratio of mean gas pressure to mean magnetic pressure, beta_0. The SFR is predicted to decrease with increasing alpha_vir (stronger turbulence relative to gravity), to increase with increasing M_S,0 (for constant values of alpha_vir), and to depend weakly on beta_0 for values typical of star forming regions (M_S,0 ~ 4-20 and beta_0 ~ 1-20). In the unrealistic limit of beta_0 -> infinity, that is in the complete absence of a magnetic field, the SFR increases approximately by a factor of three, which shows the importance of magnetic fields in the star formation process, even when they are relatively weak (super-Alfvenic turbulence). In this non-magnetized limit, our definition of the critical density for star formation has the same dependence on alpha_vir, and almost the same dependence on M_S,0, as in the model of Krumholz and McKee, although our physical derivation does not rely on the concepts of local turbulent pressure and sonic scale. However, our model predicts a different dependence of the SFR on alpha_vir and M_S,0 than the model of Krumholz and McKee. The star-formation simulations used to test the model result in an approximately constant SFR, after an initial transient phase. Both the value of the SFR and its dependence on the virial parameter found in the simulations are shown to agree very well with the theoretical predictions.

Comparing the statistics of interstellar turbulence in simulations and observations

<i>Context. <i/>Density and velocity fluctuations on virtually all scales observed with modern telescopes show that molecular clouds (MCs) are turbulent. The forcing and structural characteristics of this turbulence are, however, still poorly understood.<i>Aims. <i/>To shed light on this subject, we study two limiting cases of turbulence forcing in numerical experiments: solenoidal (divergence-free) forcing and compressive (curl-free) forcing, and compare our results to observations.<i>Methods. <i/>We solve the equations of hydrodynamics on grids with up to 1024<sup>3<sup/> cells for purely solenoidal and purely compressive forcing. Eleven lower-resolution models with different forcing mixtures are also analysed.<i>Results. <i/>Using Fourier spectra and <i>Δ<i/>-variance, we find velocity dispersion-size relations consistent with observations and independent numerical simulations, irrespective of the type of forcing. However, compressive forcing yields stronger compression at the same rms Mach number than solenoidal forcing, resulting in a three times larger standard deviation of volumetric and column density probability distributions (PDFs). We compare our results to different characterisations of several observed regions, and find evidence of different forcing functions. Column density PDFs in the Perseus MC suggest the presence of a mainly compressive forcing agent within a shell, driven by a massive star. Although the PDFs are close to log-normal, they have non-Gaussian skewness and kurtosis caused by intermittency. Centroid velocity increments measured in the Polaris Flare on intermediate scales agree with solenoidal forcing on that scale. However, <i>Δ<i/>-variance analysis of the column density in the Polaris Flare suggests that turbulence is driven on large scales, with a significant compressive component on the forcing scale. This indicates that, although likely driven with mostly compressive modes on large scales, turbulence can behave like solenoidal turbulence on smaller scales. Principal component analysis of G216-2.5 and most of the Rosette MC agree with solenoidal forcing, but the interior of an ionised shell within the Rosette MC displays clear signatures of compressive forcing.<i>Conclusions. <i/>The strong dependence of the density PDF on the type of forcing must be taken into account in any theory using the PDF to predict properties of star formation. We supply a quantitative description of this dependence. We find that different observed regions show evidence of different mixtures of compressive and solenoidal forcing, with more compressive forcing occurring primarily in swept-up shells. Finally, we emphasise the role of the sonic scale for protostellar core formation, because core formation close to the sonic scale would naturally explain the observed subsonic velocity dispersions of protostellar cores.

Fracture characterization at multiple scales using borehole images, sonic logs, and walkaround vertical seismic profile

We present a quantitative forward-modeling methodology to link and interpret several measurements relevant to mechanical properties of fractures such as borehole images, sonic anisotropy logs, and borehole seismic anisotropy. The analysis is applied to a case study from a north African tight gas field using data from a vertical well. Two studies are conducted independently using the same geological fracture data to model fracture-induced anisotropy. In the first study, we use the orientation of the natural and drilling-induced fractures interpreted on the image log to model the azimuthal fracture-induced anisotropy at the sonic scale. The mechanical effects of natural and drilling-induced fractures are treated using different compliance parameters for each fracture type. We show that modeled sonic fast shear azimuths could be biased by the presence of noncompliant fractures in each fracture type, and we propose an empirical selection criterion to reject noncompliant fractures prior to compliance estimation. Then, we estimate the fracture compliances and confirm that natural open fractures have larger compliances than drilling-induced fractures. In the second study, we apply interpreted borehole images toward modeling of the azimuthal vertical seismic profile (VSP) attributes as a function of source azimuthal position. Natural fractures inside a window of height, h, and located at depth, d, are included, and several volume sizes and positions (i.e., h and d) are considered. We find a good agreement between modeled and observed transverse-over-radial displacement trends using natural fractures within windows located at the depth of the VSP receiver, and having window heights on the order of one to two VSP shear wavelengths.

Turbulent Gas Flows in the Rosette and G216‐2.5 Molecular Clouds: Assessing Turbulent Fragmentation Descriptions of Star Formation

The role of turbulent fragmentation in regulating the efficiency of star formation in interstellar clouds is examined from new wide-field imaging of 12CO and 13CO J = 1-0 emission from the Rosette and G216-2.5 molecular clouds. The Rosette molecular cloud is a typical star-forming giant molecular cloud, and G215-2.5 is a massive molecular cloud with no OB stars and very little low-mass star formation. The properties of the turbulent gas flow are derived from the set of eigenvectors and eigenimages generated by principal component analysis (PCA) of the spectroscopic data cubes. While the two clouds represent quite divergent states of star formation activity, the velocity structure functions for both clouds are similar. The sonic scale, λS, defined as the spatial scale at which turbulent velocity fluctuations are equivalent to the local sound speed, and the turbulent Mach number evaluated at 1 pc, M1 pc, are derived for an ensemble of clouds including the Rosette and G216-2.5 regions that span a large range in star formation activity. We find no evidence for the positive correlations between these quantities and the star formation efficiency that are predicted by turbulent fragmentation models. A correlation does exist between the star formation efficiency and the sonic scale for a subset of clouds with LFIR/M(H2) > 1 that are generating young stellar clusters. Turbulent fragmentation must play a limited and nonexclusive role in determining the yield of stellar masses within interstellar clouds.

A Holistic Scenario of Turbulent Molecular Cloud Evolution and Control of the Star Formation Efficiency: First Tests

We compile a holistic scenario for molecular cloud (MC) evolution and control of the star formation efficiency (SFE) and present a first set of numerical tests of it. A lossy compressible cascade can generate density fluctuations and further turbulence at small scales from large-scale motions, implying that the turbulence in MCs may originate from the compressions that form them. Below a sonic scale λs, turbulence cannot induce any further subfragmentation nor can it be a dominant support agent against gravity. Since progressively smaller density peaks contain progressively smaller fractions of the mass, we expect the SFE to decrease with decreasing λs, at least when the cloud is globally supported by turbulence. Our numerical experiments confirm this prediction. We also find that the collapsed mass fraction in the simulations always saturates below 100% efficiency. This may be due to the decreased mean density of the leftover interclump medium, which in real clouds (not confined to a box) should then be more easily dispersed, marking the death of the cloud. We identify two different functional dependences (modes) of the SFE on λs, which roughly correspond to globally supported and unsupported cases. Globally supported runs with most of the turbulent energy at the largest scales have similar SFEs to those of unsupported runs, providing numerical evidence of the dual role of turbulence, whereby turbulence, besides providing support, induces collapse at smaller scales through its large-scale modes. We tentatively suggest that these modes may correspond to the clustered and isolated modes of star formation, although here they are seen to form part of a continuum rather than being separate modes. Finally, we compare with previous proposals that the relevant parameter is the energy injection scale.