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Register a new userSupernova Driving. I. The Origin of Molecular Cloud Turbulence
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Turbulence is ubiquitous in molecular clouds (MCs), but its origin is still unclear because MCs are usually assumed to live longer than the turbulence dissipation time. Interstellar medium (ISM) turbulence is likely driven by SN explosions, but it has never been demonstrated that SN explosions can establish and maintain a turbulent cascade inside MCs consistent with the observations. In this work, we carry out a simulation of SN-driven turbulence in a volume of (250 pc)$^3$, specifically designed to test if SN driving alone can be responsible for the observed turbulence inside MCs. We find that SN driving establishes a velocity scaling consistent with the usual scaling laws of supersonic turbulence, suggesting that previous idealized simulations of MC turbulence, driven with a random, large-scale volume force, were correctly adopted as appropriate models for MC turbulence, despite the artificial driving. We also find that the same scaling laws extend to the interior of MCs, and that the velocity-size relation of the MCs selected from our simulation is consistent with that of MCs from the Outer-Galaxy Survey, the largest MC sample available. The mass-size relation and the mass and size probability distributions also compare successfully with those of the Outer Galaxy Survey. Finally, we show that MC turbulence is super-Alfv{e}nic with respect to both the mean and rms magnetic-field strength. We conclude that MC structure and dynamics are the natural result of SN-driven turbulence.
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The compressibility of molecular cloud (MC) turbulence plays a crucial role in star formation models, because it controls the amplitude and distribution of density fluctuations. The relation between the compressive ratio (the ratio of powers in compressive and solenoidal motions) and the statistics of turbulence has been previously studied systematically only in idealized simulations with random external forces. In this work, we analyze a simulation of large-scale turbulence (250 pc) driven by supernova (SN) explosions that has been shown to yield realistic MC properties. We demonstrate that SN driving results in MC turbulence with a broad lognormal distribution of the compressive ratio, with a mean value $approx 0.3$, lower than the equilibrium value of $approx 0.5$ found in the inertial range of isothermal simulations with random solenoidal driving. We also find that the compressibility of the turbulence is not noticeably affected by gravity, nor are the mean cloud radial (expansion or contraction) and solid-body rotation velocities. Furthermore, the clouds follow a general relation between the rms density and the rms Mach number similar to that of supersonic isothermal turbulence, though with a large scatter, and their average gas density PDF is described well by a lognormal distribution, with the addition of a high-density power-law tail when self-gravity is included.
We present a comparison of molecular clouds (MCs) from a simulation of supernova-driven interstellar medium (ISM) turbulence with real MCs from the Outer Galaxy Survey. The radiative transfer calculations to compute synthetic CO spectra are carried out assuming the CO relative abundance depends only on gas density, according to four different models. Synthetic MCs are selected above a threshold brightness temperature value, $T_{rm B,min}=1.4$ K, of the $J=1-0$ $^{12}$CO line, generating 16 synthetic catalogs (four different spatial resolutions and four CO abundance models), each containing up to several thousands MCs. The comparison with the observations focuses on the mass and size distributions and on the velocity-size and mass-size Larson relations. The mass and size distributions are found to be consistent with the observations, with no significant variations with spatial resolution or chemical model, except in the case of the unrealistic model with constant CO abundance. The velocity-size relation is slightly too steep for some of the models, while the mass-size relation is a bit too shallow for all models only at a spatial resolution $dxapprox 1$ pc. The normalizations of the Larson relations show a clear dependence on spatial resolution, for both the synthetic and the real MCs. The comparison of the velocity-size normalization suggests that the SN rate in the Perseus arm is approximately 70% or less of the rate adopted in the simulation. Overall, the realistic properties of the synthetic clouds confirm that supernova-driven turbulence can explain the origin and dynamics of MCs.
We compute the star formation rate (SFR) in molecular clouds (MCs) that originate {it ab initio} in a new, higher-resolution simulation of supernova-driven turbulence. Because of the large number of well-resolved clouds with self-consistent boundary and initial conditions, we obtain a large range of cloud physical parameters with realistic statistical distributions, an unprecedented sample of star-forming regions to test SFR models and to interpret observational surveys. We confirm the dependence of the SFR per free-fall time, $SFR_{rm ff}$, on the virial parameter, $alpha_{rm vir}$, found in previous simulations, and compare a revised version of our turbulent fragmentation model with the numerical results. The dependences on Mach number, ${cal M}$, gas to magnetic pressure ratio, $beta$, and compressive to solenoidal power ratio, $chi$ at fixed $alpha_{rm vir}$ are not well constrained, because of random scatter due to time and cloud-to-cloud variations in $SFR_{rm ff}$. We find that $SFR_{rm ff}$ in MCs can take any value in the range $0 le SFR_{rm ff} lesssim 0.2$, and its probability distribution peaks at a value $SFR_{rm ff}approx 0.025$, consistent with observations. The values of $SFR_{rm ff}$ and the scatter in the $SFR_{rm ff}$--$alpha_{rm vir}$ relation are consistent with recent measurements in nearby MCs and in clouds near the Galactic center. Although not explicitly modeled by the theory, the scatter is consistent with the physical assumptions of our revised model and may also result in part from a lack of statistical equilibrium of the turbulence, due to the transient nature of MCs.
We analyze hydrodynamic simulations of turbulent, star-forming molecular clouds that are post-processed with the photo-dissociation region astrochemistry code 3D-PDR. We investigate the sensitivity of 15 commonly applied turbulence statistics to post-processing assumptions, namely variations in gas temperature, abundance and external radiation field. We produce synthetic $^{12}$CO(1-0) and CI($^{3}$P$_{1}$-$^{3}$P$_{0}$) observations and examine how the variations influence the resulting emission distributions. To characterize differences between the datasets, we perform statistical measurements, identify diagnostics sensitive to our chemistry parameters, and quantify the statistic responses by using a variety of distance metrics. We find that multiple turbulent statistics are sensitive not only to the chemical complexity but also to the strength of the background radiation field. The statistics with meaningful responses include principal component analysis, spatial power spectrum and bicoherence. A few of the statistics, such as the velocity coordinate spectrum, are primarily sensitive to the type of tracer being utilized, while others, like the delta-variance, strongly respond to the background radiation field. Collectively, these findings indicate that more realistic chemistry impacts the responses of turbulent statistics and is necessary for accurate statistical comparisons between models and observed molecular clouds.
I review recent numerical and analytical work on the feedback from both low- and high-mass cluster stars into their gasoeus environment. The main conclusions are that i) outflow driving appears capable of maintaing the turbulence in parsec-sized clumps and retarding their collapse from the free-fall rate, although there exist regions within molecular clouds, and even some examples of whole clouds, which are not actively forming stars, yet are just as turbulent, so that a more universal turbulence-driving mechanism is needed; ii) outflow-driven turbulence exhibits specific spectral features that can be tested observationally; iii) feedback plays an important role in reducing the star formation rate; iv) nevertheless, numerical simulations suggest that feedback cannot completely prevent a net contracting motion of clouds and clumps. Therefore, an appealing source for driving the turbulence everywhere in GMCs is the accretion from the environment, at all scales. In this case, feedbacks most important role may be to prevent a fraction of the gas nearest to newly formed stars from actually reaching them, thus reducing the star formation efficiency.
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