Shocked Clouds Research Articles

2FHL J0826.1–4500: Discovery of a Possible Shock–Cloud Interaction on the Western Edge of the Vela Supernova Remnant

Abstract We report on the investigation of a very high-energy, Galactic γ-ray source recently discovered at >50 GeV using the Large Area Telescope on board Fermi. This object, 2FHL J0826.1−4500, displays one of the hardest >50 GeV spectra (photon index Γ γ ∼ 1.6) in the 2FHL catalog, and a follow-up observation with XMM-Newton has uncovered diffuse, soft thermal emission at the position of the γ-ray source. A detailed analysis of the available multi-wavelength data shows that this source is located on the western edge of the Vela supernova remnant (SNR): the observations and the modeling of the spectral energy distribution support a scenario where this γ-ray source is the byproduct of the interaction between the SNR shock and a neutral hydrogen cloud. If confirmed, this shock–cloud interaction would make 2FHL J0826.1−4500 a promising candidate for efficient particle acceleration.

Triggering Collapse of the Presolar Dense Cloud Core and Injecting Short-lived Radioisotopes with a Shock Wave. VI. Protostar and Protoplanetary Disk Formation

Abstract Cosmochemical evaluations of the initial meteoritical abundance of the short-lived radioisotope (SLRI) 26Al have remained fairly constant since 1976, while estimates for the initial abundance of the SLRI 60Fe have varied widely recently. At the high end of this range, 60Fe initial abundances have seemed to require 60Fe nucleosynthesis in a core-collapse supernova, followed by incorporation into primitive meteoritical components within ∼1 Myr. This paper continues the detailed exploration of this classical scenario, using models of the self-gravitational collapse of molecular cloud cores that have been struck by suitable shock fronts, leading to the injection of shock front gas into the collapsing cloud through Rayleigh–Taylor fingers formed at the shock–cloud interface. As before, these models are calculated using the FLASH three-dimensional, adaptive mesh refinement, gravitational hydrodynamical code. While the previous models used FLASH 2.5, the new models employ FLASH 4.3, which allows sink particles to be introduced to represent the newly formed protostellar object. Sink particles permit the models to be pushed forward farther in time to the phase where a ∼1 M ⊙ protostar has formed, orbited by a rotating protoplanetary disk. These models are thus able to define what type of target cloud core is necessary for the supernova triggering scenario to produce a plausible scheme for the injection of SLRIs into the presolar cloud core: a ∼3 M ⊙ cloud core rotating at a rate of ∼3 × 10−14 rad s−1 or higher.

Shocked Interstellar Clouds and Dust Grain Destruction in the LMC Supernova Remnant N132D

Abstract From integral field data we extract the optical spectra of 20 shocked clouds in the supernova remnant N132D in the Large Magellanic Cloud (LMC). Using self-consistent shock modeling, we derive the shock velocity, pre-shock cloud density, and shock ram pressure in these clouds. We show that the [Fe x] and [Fe xiv] emission arises in faster, partially radiative shocks moving through the lower-density gas near the periphery of the clouds. In these shocks dust has been effectively destroyed, while in the slower cloud shocks the dust destruction is incomplete until the recombination zone of the shock has been reached. These dense interstellar clouds provide a sampling of the general interstellar medium (ISM) of the LMC. Our shock analysis allows us to make a new determination of the ISM chemical composition in N, O, Ne, S, Cl, and Ar, and to obtain accurate estimates of the fraction of refractory grains destroyed. From the derived cloud shock parameters, we estimate cloud masses and show that the clouds previously existed as typical self-gravitating Bonnor–Ebert spheres into which converging cloud shocks are now being driven.

Spatially resolved spectroscopy of non-thermal X-rays in RX J1713.7−3946 with Chandra

Abstract The young shell-type supernova remnant (SNR) RX J1713.7−3946 has been studied as a suitable target to test the SNR paradigm for the origin of Galactic cosmic rays. We present a spatially resolved spectroscopy of the non-thermal X-ray emission in RX J1713.7−3946 with Chandra. In order to obtain X-ray properties of the filamentary structures and their surrounding regions, we divide the southeastern (SE), southwestern (SW), and northwestern (NW) parts of the SNR into subregions on the typical order of several 10" and extract spectra from each subregion. Their photon indices are significantly different among the subregions, with a range of 1.8 < Γ < 3. In the SE part, the clear filaments are harder (Γ ∼ 2.0) than the surrounding regions. This is a common feature often observed in young SNRs and naturally interpreted as a consequence of synchrotron cooling. On the other hand, the bright filamentary regions do not necessarily coincide with the hardest regions in the SW and NW parts. We also find the SW filamentary region is relatively rather soft (Γ ∼ 2.7). In addition, we find that hard regions with photon indices of 2.0–2.2 exist around the bright emission although the hard regions lie in the downstream region and the bright emission does not appear to be the blast wave shock front. Both the aforementioned characteristic regions in SW are located close to peaks of the interstellar gas. We discuss possible origins of the spatial variation of the photon indices, paying particular attention to the shock–cloud interactions.

Chemical evolution of the gas in C-type shocks in dark clouds

A magnetohydrodynamic model of a steady, transverse C-type shock in a dense molecular cloud is presented. A complete gas-grain chemical network is taken into account: the gas-phase chemistry, the adsorption of gas species on dust grains, various desorption mechanisms, the grain surface chemistry, the ion neutralization on dust grains, the sputtering of grain mantles. The population densities of energy levels of ions CI, CII and OI and molecules H$_2$, CO, H$_2$O are computed in parallel with the dynamical and chemical rate equations. The large velocity gradient approximation is used in the line radiative transfer calculations. The simulations consist of two steps: (i) modelling of the chemical and thermal evolution of a static molecular cloud and (ii) shock simulations. A comparison is made with the results of publicly available models of similar physical systems. The focus of the paper is on the chemical processing of gas material and ice mantles of dust grains by the shock. Sputtering of ice mantles takes place in the shock region close to the temperature peak of the neutral gas. At high shock speeds, molecules ejected from ice mantles are effectively destroyed in hot gas, and their survival time is low - of the order of dozens of years. After a passage of high-speed C-type shock, a zone of high abundance of atomic hydrogen appears in the cooling postshock gas that triggers formation of complex organic species such as methanol. It is shown that abundances of some complex organic molecules (COMs) in the postshock region can be much higher than in the preshock gas. These results are important for interpretation of observations of COMs in protostellar outflows.

HCN J = 4–3, HNC J = 1–0, H13CN J = 1–0, and HC3N J = 10–9 Maps of the Galactic Center Region. I. Spatially Resolved Measurements of Physical Conditions and Chemical Composition

Abstract This supplement paper presents the maps of HCN J = 4–3, HNC J = 1–0, J = 1–0, and HC3N J = 10–9 for the Galactic central molecular zone (CMZ), which have been obtained using the Atacama Submillimeter Telescope Experiment and Nobeyama Radio Observatory 45 m telescope. Three-dimensional maps (2D in space and 1D in velocity) of the gas kinetic temperature (T kin), hydrogen volume density ( ), and fractional abundances of eight molecules (HCN, HNC, , HCO+, , SiO, CS, and ) have been constructed from our and archival data. We have developed a method with hierarchical Bayesian inference for this analysis, which has successfully suppressed the artificial correlations among the parameters created by systematic errors due to the deficiency in the simple one-zone excitation analysis and the calibration uncertainty. The typical values of T kin and are and , respectively, and the presence of an additional cold, low-density component is also indicated. The distribution of high-temperature regions is poorly correlated with known active star-forming regions, while a few of them coincide with shocked clouds. Principal component analysis has identified two distinct groups in the eight analyzed molecules: one group with large PC1 and PC2 scores, and the other with a large T kin dependence, which could be explained using two regimes of shock chemistry with fast ( ) and slow ( ) velocity shocks, respectively. This supports the idea that the mechanical sputtering of dust grains and the mechanical heating play primary roles in the chemical and thermal processes in CMZ clouds.

Role of pseudo-turbulent stresses in shocked particle clouds and construction of surrogate models for closure

Macroscale models of shock–particle interactions require closure terms for unresolved solid–fluid momentum and energy transfer. These comprise the effects of mean as well as fluctuating fluid-phase velocity fields in the particle cloud. Mean drag and Reynolds stress equivalent terms (also known as pseudo-turbulent terms) appear in the macroscale equations. Closure laws for the pseudo-turbulent terms are constructed in this work from ensembles of high-fidelity mesoscale simulations. The computations are performed over a wide range of Mach numbers (M) and particle volume fractions ( $$\phi )$$ and are used to explicitly compute the pseudo-turbulent stresses from the Favre average of the velocity fluctuations in the flow field. The computed stresses are then used as inputs to a Modified Bayesian Kriging method to generate surrogate models. The surrogates can be used as closure models for the pseudo-turbulent terms in macroscale computations of shock–particle interactions. It is found that the kinetic energy associated with the velocity fluctuations is comparable to that of the mean flow—especially for increasing M and $$\phi $$ . This work is a first attempt to quantify and evaluate the effect of velocity fluctuations for problems of shock–particle interactions.

A comparison of shock–cloud and wind–cloud interactions: effect of increased cloud density contrast on cloud evolution

The similarities, or otherwise, of a shock or wind interacting with a cloud of density contras t$ \chi = 10$ were explored in a previous paper. Here, we investigate such interactions with clouds of higher density contrast. We compare the adiabatic hydrodynamic interaction of a Mach 10 shock with a spherical cloud of $\chi = 10^{3}$ with that of a cloud embedded in a wind with identical parameters to the post-shock flow. We find that initially there are only minor morphological differences between the shock-cloud and wind-cloud interactions, compared to when $\chi = 10$. However, once the transmitted shock exits the cloud, the development of a turbulent wake and fragmentation of the cloud differs between the two simulations. On increasing the wind Mach number, we note the development of a thin, smooth tail of cloud material, which is then disrupted by the fragmentation of the cloud core and subsequent `mass-loading' of the flow. We find that the normalized cloud mixing time ($t_{mix}$) is shorter at higher $\chi$. However, a strong Mach number dependence on tmix and the normalized cloud drag time, $t'_{drag}$, is not observed. Mach-number-dependent values of $t_{mix}$ and $t'_{drag}$ from comparable shock-cloud interactions converge towards the Mach-number-independent time-scales of the wind-cloud simulations. We find that high $\chi$ clouds can be accelerated up to 80-90 per cent of the wind velocity and travel large distances before being significantly mixed. However, complete mixing is not achieved in our simulations and at late times the flow remains perturbed.

High-energy radiation from collisions of high-velocity clouds and the Galactic disc

High-velocity clouds (HVCs) are interstellar clouds of atomic hydrogen that do not partake of the Galactic rotation and have velocities of a several hundred kilometers per second. A considerable number of these clouds are falling down towards the Galactic disk. HVCs form large and massive complexes, so their collisions with the disk must release a great amount of energy into the interstellar medium. The cloud-disk interaction produces two shocks, one propagates through the cloud and the other through the disk; the properties of these shocks depend mainly on the cloud velocity and the disk-cloud density ratio. In this work we study the conditions necessary for these shocks to accelerate particles by diffusive shock acceleration and the produced non-thermal radiation. We analyze particle acceleration in both the cloud and disk shocks. Solving a time-dependent 2-D transport equation for both relativistic electrons and protons we obtain particle distributions and non-thermal spectral energy distributions. In a shocked cloud significant synchrotron radio emission is produced along with soft gamma rays. In the case of acceleration in the shocked disk, the non-thermal radiation is stronger; the gamma rays, of leptonic origin, might be detectable with current instruments. A large number of protons are injected into the Galactic interstellar medium, and locally exceed the cosmic-ray background. We conclude that under adequate conditions the contribution from HVC-disk collisions to the galactic population of relativistic particles and the associated extended non-thermal radiation might be important.

Simultaneous observation of cavitation collapse and shock wave formation in cavitating jet

In this study, the mechanism of cavitation erosion in the cavitating jet discharging from a cavitator nozzle into a still water environment was examined through simultaneous observations of cloud collapse behavior and shock wave formation with and without wall. The simultaneous observations of the cloud collapse and shock wave formation were conducted by time-resolved shadowgraph and laser schlieren methods, respectively, while the impulsive signal on the wall was synchronously detected by an acceleration sensor. The time-resolved shadowgraph and laser schlieren images indicated that some shock waves were occurred at the instant of cloud collapse during the periodic behavior of the cavitating jet, which results in the impulsive forces on the wall. To a large extent, the shock waves originated from the near-wall region, and they induced the impulsive forces on the wall; in the case without wall, shock wave formation was observed in a similar distance from the nozzle with a broad distribution from the origin along the jet centerline. These results indicate that the cavitating-jet erosion occurs due to the cloud collapse near the wall, where some shock waves are generated and results in the erosion of the wall.

The formation of massive molecular filaments and massive stars triggered by a magnetohydrodynamic shock wave

Abstract Recent observations suggest an that intensive molecular cloud collision can trigger massive star/cluster formation. The most important physical process caused by the collision is a shock compression. In this paper, the influence of a shock wave on the evolution of a molecular cloud is studied numerically by using isothermal magnetohydrodynamics simulations with the effect of self-gravity. Adaptive mesh refinement and sink particle techniques are used to follow the long-time evolution of the shocked cloud. We find that the shock compression of a turbulent inhomogeneous molecular cloud creates massive filaments, which lie perpendicularly to the background magnetic field, as we have pointed out in a previous paper. The massive filament shows global collapse along the filament, which feeds a sink particle located at the collapse center. We observe a high accretion rate $\dot{M}_{\rm acc}> 10^{-4}\, M_{\odot }\:$yr−1 that is high enough to allow the formation of even O-type stars. The most massive sink particle achieves M > 50 M$_{\odot }$ in a few times 105 yr after the onset of the filament collapse.

Numerical Simulations of Supernova Remnant Evolution in a Cloudy Interstellar Medium

Abstract The mixed morphology class of supernova remnants has centrally peaked X-ray emission along with a shell-like morphology in radio emission. White & Long proposed that these remnants are evolving in a cloudy medium wherein the clouds are evaporated via thermal conduction once being overrun by the expanding shock. Their analytical model made detailed predictions regarding temperature, density, and emission profiles as well as shock evolution. We present numerical hydrodynamical models in 2D and 3D including thermal conduction, testing the White & Long model and presenting results for the evolution and emission from remnants evolving in a cloudy medium. We find that, while certain general results of the White & Long model hold, such as the way the remnants expand and the flattening of the X-ray surface brightness distribution, in detail there are substantial differences. In particular we find that the X-ray luminosity is dominated by emission from shocked cloud gas early on, leading to a bright peak, which then declines and flattens as evaporation becomes more important. In addition, the effects of thermal conduction on the intercloud gas, which is not included in the White & Long model, are important and lead to further flattening of the X-ray brightness profile as well as lower X-ray emission temperatures.

Triggering Collapse of the Presolar Dense Cloud Core and Injecting Short-lived Radioisotopes with a Shock Wave. V. Nonisothermal Collapse Regime

Abstract Recent meteoritical analyses support an initial abundance of the short-lived radioisotope (SLRI) 60Fe that may be high enough to require nucleosynthesis in a core-collapse supernova, followed by rapid incorporation into primitive meteoritical components, rather than a scenario where such isotopes were inherited from a well-mixed region of a giant molecular cloud polluted by a variety of supernovae remnants and massive star winds. This paper continues to explore the former scenario, by calculating three-dimensional, adaptive mesh refinement, hydrodynamical code (FLASH 2.5) models of the self-gravitational, dynamical collapse of a molecular cloud core that has been struck by a thin shock front with a speed of 40 km s−1, leading to the injection of shock front matter into the collapsing cloud through the formation of Rayleigh–Taylor fingers at the shock–cloud intersection. These models extend the previous work into the nonisothermal collapse regime using a polytropic approximation to represent compressional heating in the optically thick protostar. The models show that the injection efficiencies of shock front materials are enhanced compared to previous models, which were not carried into the nonisothermal regime, and so did not reach such high densities. The new models, combined with the recent estimates of initial 60Fe abundances, imply that the supernova triggering and injection scenario remains a plausible explanation for the origin of the SLRIs involved in the formation of our solar system.

A systematic comparison of two-equation Reynolds-averaged Navier–Stokes turbulence models applied to shock–cloud interactions

Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-Averaged Navier-Stokes (RANS) turbulence models, and we implement six models in the Athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.

Shock–Cloud Interaction in the Solar Corona

Abstract Flare-associated coronal shock waves sometimes interact with solar prominences, leading to large-amplitude prominence oscillations (LAPOs). Such prominence activation gives us a unique opportunity to track the time evolution of shock–cloud interaction in cosmic plasmas. Although the dynamics of interstellar shock–cloud interaction has been extensively studied, coronal shock–solar prominence interaction is rarely studied in the context of shock–cloud interaction. Associated with the X5.4 class solar flare that occurred on 2012 March 7, a globally propagated coronal shock wave interacted with a polar prominence, leading to LAPO. In this paper, we studied bulk acceleration and excitation of the internal flow of the shocked prominence using three-dimensional magnetohydrodynamic (MHD) simulations. We studied eight MHD simulation runs, each with different mass density structure of the prominence, and one hydrodynamic simulation run, and we compared the result. In order to compare the observed motion of activated prominence with the corresponding simulation, we also studied prominence activation by injection of a triangular-shaped coronal shock. We found that the prominence is first accelerated mainly by magnetic tension force as well as direct transmission of the shock, and later decelerated mainly by magnetic tension force. The internal flow, on the other hand, is excited during the shock front sweeps through the prominence and damps almost exponentially. We construct a phenomenological model of bulk momentum transfer from the shock to the prominence, which agreed quantitatively with all the simulation results. Based on the phenomenological prominence activation model, we diagnosed physical parameters of the coronal shock wave. The estimated energy of the coronal shock is several percent of the total energy released during the X5.4 flare.

A density-based method with semi-discrete central-upwind schemes for ideal magnetohydrodynamics

In the present work, the central-upwind schemes proposed by Kurganov et al. (SIAM J Sci Comput 23:707–740, 2001) for hydrodynamics are extended and combined with the divergence cleaning method of Dedner (J Comput Phys 175:645–673, 2002) in order to approximate the equations of the ideal magnetohydrodynamics in a finite volume discretization framework with Gaussian integration. To improve the quality of the solution, the Van Leer interpolation scheme is used. The accuracy and the robustness of the obtained solver are demonstrated through numerical simulations of benchmark problems such as the Brio–Wu shock tube problem, the Orszag–Tang vortex problem and the 2D cloud–shock interaction problem.

A high-order positivity-preserving single-stage single-step method for the ideal magnetohydrodynamic equations

We propose a high-order finite difference weighted ENO (WENO) method for the ideal magnetohydrodynamics (MHD) equations. The proposed method is single-stage (i.e., it has no internal stages to store), single-step (i.e., it has no time history that needs to be stored), maintains a discrete divergence-free condition on the magnetic field, and has the capacity to preserve the positivity of the density and pressure. To accomplish this, we use a Taylor discretization of the Picard integral formulation (PIF) of the finite difference WENO method proposed in Christlieb et al. (2015) [23] , where the focus is on a high-order discretization of the fluxes (as opposed to the conserved variables). We use the version where fluxes are expanded to third-order accuracy in time, and for the fluid variables space is discretized using the classical fifth-order finite difference WENO discretization. We use constrained transport in order to obtain divergence-free magnetic fields, which means that we simultaneously evolve the magnetohydrodynamic (that has an evolution equation for the magnetic field) and magnetic potential equations alongside each other, and set the magnetic field to be the (discrete) curl of the magnetic potential after each time step. In this work, we compute these derivatives to fourth-order accuracy. In order to retain a single-stage, single-step method, we develop a novel Lax–Wendroff discretization for the evolution of the magnetic potential, where we start with technology used for Hamilton–Jacobi equations in order to construct a non-oscillatory magnetic field. The end result is an algorithm that is similar to our previous work Christlieb et al. (2014) [8] , but this time the time stepping is replaced through a Taylor method with the addition of a positivity-preserving limiter. Finally, positivity preservation is realized by introducing a parameterized flux limiter that considers a linear combination of high and low-order numerical fluxes. The choice of the free parameter is then given in such a way that the fluxes are limited towards the low-order solver until positivity is attained. Given the lack of additional degrees of freedom in the system, this positivity limiter lacks energy conservation where the limiter turns on. However, this ingredient can be dropped for problems where the pressure does not become negative. We present two and three dimensional numerical results for several standard test problems including a smooth Alfvén wave (to verify formal order of accuracy), shock tube problems (to test the shock-capturing ability of the scheme), Orszag–Tang, and cloud shock interactions. These results assert the robustness and verify the high-order of accuracy of the proposed scheme.

TRIGGERING COLLAPSE OF THE PRESOLAR DENSE CLOUD CORE AND INJECTING SHORT-LIVED RADIOISOTOPES WITH A SHOCK WAVE. IV. EFFECTS OF ROTATIONAL AXIS ORIENTATION

Both astronomical observations of the interaction of Type II supernova remnants (SNR) with dense interstellar clouds as well as cosmochemical studies of the abundances of daughter products of short-lived radioisotopes (SLRIs) formed by supernova nucleosynthesis support the hypothesis that the Solar Systems SLRIs may have been derived from a supernova. This paper continues a series devoted to examining whether such a shock wave could have triggered the dynamical collapse of a dense, presolar cloud core and simultaneously injected sufficient abundances of SLRIs to explain the cosmochemical evidence. Here we examine the effects of shock waves striking clouds whose spin axes are oriented perpendicular, rather than parallel, to the direction of propagation of the shock front. The models start with 2.2 solar mass cloud cores and shock speeds of 20 or 40 km/sec. Central protostars and protoplanetary disks form in all models, though with disk spin axes aligned somewhat randomly. The disks derive most of their angular momentum not from the initial cloud rotation, but from the Rayleigh-Taylor fingers that also inject shock wave SLRIs. Injection efficiencies, fi, the fraction of the incident shock wave material injected into the collapsing cloud core, are 0.04 - 0.1 in these models, similar to when the rotation axis is parallel to the shock propagation direction. Evidently altering the rotation axis orientation has only a minor effect on the outcome, strengthening the case for this scenario as an explanation for the Solar Systems SLRIs.

EVIDENCE OF THE SOLAR EUV HOT CHANNEL AS A MAGNETIC FLUX ROPE FROM REMOTE-SENSING AND IN SITU OBSERVATIONS

Hot channels (HCs), high temperature erupting structures in the lower corona of the Sun, have been proposed as a proxy of magnetic flux ropes (MFRs) since their initial discovery. However, it is difficult to make definitive proof given the fact that there is no direct measurement of magnetic field in the corona. An alternative way is to use the magnetic field measurement in the solar wind from in-situ instruments. On 2012 July 12, an HC was observed prior to and during a coronal mass ejection (CME) by the AIA high-temperature images. The HC is invisible in the EUVI low-temperature images, which only show the cooler leading front (LF). However, both the LF and an ejecta can be observed in the coronagraphic images. These are consistent with the high temperature and high density of the HC and support that the ejecta is the erupted HC. In the meanwhile, the associated CME shock was identified ahead of the ejecta and the sheath through the COR2 images, and the corresponding ICME was detected by \textit{ACE}, showing the shock, sheath and magnetic cloud (MC) sequentially, which agrees with the coronagraphic observations. Further, the MC contained a low-ionization-state center and a high-ionization-state shell, consistent with the pre-existing HC observation and its growth through magnetic reconnection. All of these observations support that the MC detected near the Earth is the counterpart of the erupted HC in the corona for this event. Therefore, our study provides strong observational evidence of the HC as an MFR.

EVIDENCE FOR DECAY OF TURBULENCE BY MHD SHOCKS IN THE ISM VIA CO EMISSION

We utilize observations of sub-millimeter rotational transitions of CO from a Herschel Cycle 2 open time program ("COPS", PI: J. Green) to identify previously predicted turbulent dissipation by magnetohydrodynamic (MHD) shocks in molecular clouds. We find evidence of the shocks expected for dissipation of MHD turbulence in material not associated with any protostar. Two models fit about equally well: model 1 has a density of 10$^{3}$ cm$^{-3}$, a shock velocity of 3 km s$^{-1}$, and a magnetic field strength of 4 ${\mu}$G; model 2 has a density of 10$^{3.5}$ cm$^{-3}$, a shock velocity of $2$ km s$^{-1}$, and a magnetic field strength of 8 $\mu$G. Timescales for decay of turbulence in this region are comparable to crossing times. Transitions of CO up to $J$ of 8, observed close to active sites of star formation, but not within outflows, can trace turbulent dissipation of shocks stirred by formation processes. Although the transitions are difficult to detect at individual positions, our Herschel-SPIRE survey of protostars provides a grid of spatially-distributed spectra within molecular clouds. We averaged all spatial positions away from known outflows near seven protostars. We find significant agreement with predictions of models of turbulent dissipation in slightly denser (10$^{3.5}$ cm$^{-3}$) material with a stronger magnetic field (24 $\mu$G) than in the general molecular cloud.