arXiv subjects

M. -M. Mac Low

Publications and source records attributed to M. -M. Mac Low.

36 records · Page 2Linked to original sources

arXiv2009

Modelling CO formation in the turbulent interstellar medium

We present results from high-resolution three-dimensional simulations of turbulent interstellar gas that self-consistently follow its coupled thermal, chemical and dynamical evolution, with a particular focus on the formation and destruction of H2 and CO. We quantify the formation timescales for H2 and CO in physical conditions corresponding to those found in nearby giant molecular clouds, and show that both species form rapidly, with chemical timescales that are comparable to the dynamical timescale of the gas. We also investigate the spatial distributions of H2 and CO, and how they relate to the underlying gas distribution. We show that H2 is a good tracer of the gas distribution, but that the relationship between CO abundance and gas density is more complex. The CO abundance is not well-correlated with either the gas number density n or the visual extinction A_V: both have a large influence on the CO abundance, but the inhomogeneous nature of the density field produced by the turbulence means that n and A_V are only poorly correlated. There is a large scatter in A_V, and hence CO abundance, for gas with any particular density, and similarly a large scatter in density and CO abundance for gas with any particular visual extinction. This will have important consequences for the interpretation of the CO emission observed from real molecular clouds. Finally, we also examine the temperature structure of the simulated gas. We show that the molecular gas is not isothermal. Most of it has a temperature in the range of 10--20 K, but there is also a significant fraction of warmer gas, located in low-extinction regions where photoelectric heating remains effective.

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arXiv2009

Algorithmic comparisons of decaying, isothermal, supersonic turbulence

Contradicting results have been reported in the literature with respect to the performance of the numerical techniques employed for the study of supersonic turbulence. We aim at characterising the performance of different particle-based and grid-based techniques on the modelling of decaying supersonic turbulence. Four different grid codes (ENZO, FLASH, TVD, ZEUS) and three different SPH codes (GADGET, PHANTOM, VINE) are compared. We additionally analysed two calculations denoted as PHANTOM A and PHANTOM B using two different implementations of artificial viscosity. Our analysis indicates that grid codes tend to be less dissipative than SPH codes, though details of the techniques used can make large differences in both cases. For example, the Morris & Monaghan viscosity implementation for SPH results in less dissipation (PHANTOM B and VINE versus GADGET and PHANTOM A). For grid codes, using a smaller diffusion parameter leads to less dissipation, but results in a larger bottleneck effect (our ENZO versus FLASH runs). As a general result, we find that by using a similar number of resolution elements N for each spatial direction means that all codes (both grid-based and particle-based) show encouraging similarity of all statistical quantities for isotropic supersonic turbulence on spatial scales k<N/32 (all scales resolved by more than 32 grid cells), while scales smaller than that are significantly affected by the specific implementation of the algorithm for solving the equations of hydrodynamics. At comparable numerical resolution, the SPH runs were on average about ten times more computationally intensive than the grid runs, although with variations of up to a factor of ten between the different SPH runs and between the different grid runs. (abridged)

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arXiv2009

What is Driving the HI Velocity Dispersion?

We explore what dominant physical mechanism sets the kinetic energy contained in neutral, atomic (HI) gas. We compare the HI line widths predicted from turbulence driven by supernova (SN) explosions and magneto-rotational instability (MRI) to direct observations in 11 disk galaxies. We use high-quality maps of the HI mass surface density and line width, obtained by the THINGS survey. We show that all sample galaxies exhibit a systematic radial decline in the HI line width, which appears to be a generic property of HI disks and also implies a radial decline in kinetic energy density of HI. At a galactocentric radius of r25 there is a characteristic value of the HI velocity dispersion of $10\pm2$ \kms. Inside this radius, galaxies show HI line widths above the thermal value expected from a warm HI component, implying that turbulence drivers must be responsible for maintaining this line width. Therefore, we compare maps of HI kinetic energy to maps of the star formation rate (SFR) and to predictions for energy generated by MRI. We find a positive correlation between kinetic energy of HI and SFR. For a given turbulence dissipation timescale we can estimate the energy input required to maintain the observed kinetic energy. The SN rate implied by the observed recent SFR is sufficient to maintain the observed velocity dispersion, if the SN feedback efficiency is at least ε_SN\simeq0.1. Beyond r25, this efficiency would have to increase to unrealistic values, $ε>1$, suggesting that mechanical energy from young stars does not supply most energy in outer disks. On the other hand, both thermal broadening and turbulence driven by MRI can produce the velocity dispersions and kinetic energies that we observe in this regime.

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arXiv2009

Star Formation at Very Low Metallicity. V. The Greater Importance of Initial Conditions Compared to Metallicity Thresholds

The formation of the first stars out of metal-free gas appears to result in stars at least an order of magnitude more massive than in the present-day case. We here consider what controls the transition from a primordial to a modern initial mass function. It has been proposed that this occurs when effective metal line cooling occurs at a metallicity threshold of Z/Z_sun > 10^{-3.5}. We study the influence of low levels of metal enrichment on the cooling and collapse of initially ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations with particle splitting. Our initial conditions represent protogalaxies forming within a previously ionized H ii region that has not yet had time to cool and recombine. These differ considerably from those used in simulations predicting a metallicity threshold, where the gas was initially cold and only partially ionized. In the centrally condensed potential that we study here, a wide variety of initial conditions for the gas yield a monolithic central collapse. Our models show no fragmentation during collapse to number densities as high as 10^5 cm^{-3}, for metallicities reaching as high as 10^{-1} Z_sun in one rotating case, far above the threshold suggested by previous work. Rotation allows for the formation of gravitationally stable gas disks over large fractions of the local Hubble time. Turbulence slows the growth of the central density slightly, but both spherically symmetric and turbulent initial conditions collapse and form a single sink particle. We therefore argue that fragmentation at moderate density depends on the initial conditions for star formation more than on the metal abundances present.

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arXiv2008

Geometrically Derived Timescales for Star Formation in Spiral Galaxies

We estimate a characteristic timescale for star formation in the spiral arms of disk galaxies, going from atomic hydrogen (HI) to dust-enshrouded massive stars. Drawing on high-resolution HI data from The HI Nearby Galaxy Survey and 24$μ$m images from the Spitzer Infrared Nearby Galaxies Survey we measure the average angular offset between the HI and 24$μ$m emissivity peaks as a function of radius, for a sample of 14 nearby disk galaxies. We model these offsets assuming an instantaneous kinematic pattern speed, $Ω_p$, and a timescale, t(HI-->24$μ$m), for the characteristic time span between the dense \hi phase and the formation of massive stars that heat the surrounding dust. Fitting for $Ω_p$ and t(HI-->24$μ$m), we find that the radial dependence of the observed angular offset (of the \hi and 24$μ$m emission) is consistent with this simple prescription; the resulting corotation radii of the spiral patterns are typically $R_{cor}\simeq 2.7 R_{s}$, consistent with independent estimates. The resulting values of t(HI-->24$μ$m) for the sample are in the range 1--4 Myr. We have explored the possible impact of non-circular gas motions on the estimate of t(HI-->24$μ$m) and have found it to be substantially less than a factor of 2. This implies that a short timescale for the most intense phase of the ensuing star formation in spiral arms, and implies a considerable fraction of molecular clouds exist only for a few Myr before forming stars. However, our analysis does not preclude that some molecular clouds persist considerably longer. If much of the star formation in spiral arms occurs within this short interval t(HI-->24$μ$m), then star formation must be inefficient, in order to avoid the short-term depletion of the gas reservoir.

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arXiv2007

Diffuse interstellar medium and the formation of molecular clouds

(Abridged) The formation of molecular clouds (MCs) from the diffuse interstellar gas appears to be a necessary step for star formation, as young stars invariably occur within them. However, the mechanisms controlling the formation of MCs remain controversial. In this contribution, we focus on their formation in compressive flows driven by interstellar turbulence and large-scale gravitational instability. Turbulent compression driven by supernovae appears insufficient to explain the bulk of cloud and star formation. Rather, gravity must be important at all scales, driving the compressive flows that form both clouds and cores. Cooling and thermal instability allow the formation of dense gas out of moderate, transonic compressions in the warm diffuse gas, and drive turbulence into the dense clouds. MCs may be produced by an overshoot beyond the thermal-pressure equilibrium between the cold and warm phases of atomic gas, caused by some combination of the ram pressure of compression and the self-gravity of the compressed gas. In this case, properties of the clouds such as their mass, mass-to-magnetic flux ratio, and total kinetic and gravitational energies are in general time-variable quantities. MCs may never enter a quasi-equilibrium or virial equilibrium state but rather continuously collapse to stars.

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arXiv2007

The Influence of Metallicity on Star Formation in Protogalaxies

In cold dark matter cosmological models, the first stars to form are believed to do so within small protogalaxies. We wish to understand how the evolution of these early protogalaxies changes once the gas forming them has been enriched with small quantities of heavy elements, which are produced and dispersed into the intergalactic medium by the first supernovae. Our initial conditions represent protogalaxies forming within a fossil H II region, a previously ionized region that has not yet had time to cool and recombine. We study the influence of low levels of metal enrichment on the cooling and collapse of ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics (SPH) simulations that incorporate the effects of the appropriate chemical and thermal processes. Our previous simulations demonstrated that for metallicities Z < 0.001 Z_sun, metal line cooling alters the density and temperature evolution of the gas by less than 1% compared to the metal-free case at densities below 1 cm-3) and temperatures above 2000 K. Here, we present the results of high-resolution simulations using particle splitting to improve resolution in regions of interest. These simulations allow us to address the question of whether there is a critical metallicity above which fine structure cooling from metals allows efficient fragmentation to occur, producing an initial mass function (IMF) resembling the local Salpeter IMF, rather than only high-mass stars.

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arXiv2007

Star formation at very low metallicity. II: On the insignificance of metal-line cooling during the early stages of gravitational collapse

We study the influence of low levels of metal enrichment on the cooling and collapse of ionized gas in small protogalactic halos using three-dimensional, smoothed particle hydrodynamics simulations. Our initial conditions represent protogalaxies forming within a fossil HII region -- a previously ionized HII region which has not yet had time to cool and recombine. Prior to cosmological reionization, such regions should be relatively common, since the characteristic lifetimes of the likely ionizing sources are significantly shorter than a Hubble time. We show that in these regions, H_2 is the dominant and most effective coolant, and that it is the amount of H_2 formed that determines whether or not the gas can collapse and form stars. At the low metallicities (Z < 10^{-3} Z_sun) thought to be associated with the transition from population III to early population II star formation, metal line cooling has an almost negligible effect on the evolution of low density gas, altering the density and temperature evolution of the gas by less than 1% compared to the metal-free case at densities below 1 cm^{-3} and temperatures above 2000 K. Although there is evidence that metal line cooling becomes more effective at higher density, we find no significant differences in behaviour from the metal-free case at any density below our sink particle creation threshold at n = 500 cm^{-3}. Increasing the metallicity also increases the importance of metal line cooling, but it does not significantly affect the dynamical evolution of the low density gas until Z = 0.1 Z_sun. This result holds regardless of whether or not an ultraviolet background is present.

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arXiv2007

Simulating the formation of molecular clouds. II. Rapid formation from turbulent initial conditions

(Abridged). In this paper, we present results from a large set of numerical simulations that demonstrate that H2 formation occurs rapidly in turbulent gas. Starting with purely atomic hydrogen, large quantities of molecular hydrogen can be produced on timescales of 1 -- 2 Myr, given turbulent velocity dispersions and magnetic field strengths consistent with observations. Moreover, as our simulations underestimate the effectiveness of H2 self-shielding and dust absorption, we can be confident that the molecular fractions that we compute are strong lower limits on the true values. The formation of large quantities of H2 on the timescale required by rapid cloud formation models therefore appears to be entirely plausible. We also investigate the density and temperature distributions of gas in our model clouds. We show that the density probability distribution function is approximately log-normal, with a dispersion that agrees well with the prediction of Padoan, Nordlund & Jones (1997). The temperature distribution is similar to that of a polytrope, with an effective polytropic index gamma_eff \simeq 0.8, although at low gas densities, the scatter of the actual gas temperature around this mean value is considerable, and the polytropic approximation does not capture the full range of behaviour of the gas.

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arXiv2007

Simulating the formation of molecular clouds. I. Slow formation by gravitational collapse from static initial conditions

We study the formation of H2 in the ISM, using a modified version of the astrophysical magnetohydrodynamical code ZEUS-MP that includes a non-equilibrium treatment of the formation and destruction of H2. We examine two different approximations to treat the shielding of H2 against photodissociation: a local approximation, which gives us a solid lower bound on the amount of shielding, and a method based on ray-tracing that is considerably more accurate in some circumstances but that produces results that are harder to clearly interpret. Either approximation allows one to perform three-dimensional high-resolution simulations of cloud formation with only modest computational resources. We also include a detailed treatment of the thermal behaviour of the gas. In this paper, we focus on the problem of molecular cloud formation in gravitationally unstable, initially static gas. We show that in these conditions, and for initial densities consistent with those observed in the cold, neutral atomic phase of the interstellar medium, H2 formation occurs on a timescale t > 10 Myr, comparable to or longer than the gravitational free-fall timescale of the cloud. We also show that the collapsing gas very quickly reaches thermal equilibrium and that the equation of state of the gas is generally softer than isothermal. Finally, we demonstrate that although these results show little sensitivity to variations in most of our simulation parameters, they are highly sensitive to the assumed initial density n_i. Reducing n_i significantly increases the cloud formation timescale and decreases the amount of hydrogen ultimately converted to H2. (Abridged).

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arXiv2006

Simulating Radiating and Magnetized Flows in Multi-Dimensions with ZEUS-MP

This paper describes ZEUS-MP, a multi-physics, massively parallel, message- passing implementation of the ZEUS code. ZEUS-MP differs significantly from the ZEUS-2D code, the ZEUS-3D code, and an early "version 1" of ZEUS-MP distributed publicly in 1999. ZEUS-MP offers an MHD algorithm better suited for multidimensional flows than the ZEUS-2D module by virtue of modifications to the Method of Characteristics scheme first suggested by Hawley and Stone (1995), and is shown to compare quite favorably to the TVD scheme described by Ryu et. al (1998). ZEUS-MP is the first publicly-available ZEUS code to allow the advection of multiple chemical (or nuclear) species. Radiation hydrodynamic simulations are enabled via an implicit flux-limited radiation diffusion (FLD) module. The hydrodynamic, MHD, and FLD modules may be used in one, two, or three space dimensions. Self gravity may be included either through the assumption of a GM/r potential or a solution of Poisson's equation using one of three linear solver packages (conjugate-gradient, multigrid, and FFT) provided for that purpose. Point-mass potentials are also supported. Because ZEUS-MP is designed for simulations on parallel computing platforms, considerable attention is paid to the parallel performance characteristics of each module. Strong-scaling tests involving pure hydrodynamics (with and without self-gravity), MHD, and RHD are performed in which large problems (256^3 zones) are distributed among as many as 1024 processors of an IBM SP3. Parallel efficiency is a strong function of the amount of communication required between processors in a given algorithm, but all modules are shown to scale well on up to 1024 processors for the chosen fixed problem size.

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arXiv2006

Molecular Cloud Turbulence and Star Formation

We review the properties of turbulent molecular clouds (MCs), focusing on the physical processes that influence star formation (SF). MC formation appears to occur during large-scale compression of the diffuse ISM driven by supernovae, magnetorotational instability, or gravitational instability in galactic disks of stars and gas. The compressions generate turbulence that can accelerate molecule production and produce the observed morphology. We then review the properties of MC turbulence, including density enhancements observed as clumps and cores, magnetic field structure, driving scales, the relation to observed scaling relations, and the interaction with gas thermodynamics. We argue that MC cores are dynamical, not quasistatic, objects with relatively short lifetimes not exceeding a few megayears. We review their morphology, magnetic fields, density and velocity profiles, and virial budget. Next, we discuss how MC turbulence controls SF. On global scales turbulence prevents monolithic collapse of the clouds; on small scales it promotes local collapse. We discuss its effects on the SF efficiency, and critically examine the possible relation between the clump mass distribution and the initial mass function, and then turn to the redistribution of angular momentum during collapse and how it determines the multiplicity of stellar systems. Finally, we discuss the importance of dynamical interactions between protostars in dense clusters, and the effect of the ionization and winds from those protostars on the surrounding cloud. We conclude that the interaction of self-gravity and turbulence controls MC formation and behavior, as well as the core and star formation processes within them.

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arXiv2006

Hydrodynamical simulations of the decay of high-speed molecular turbulence. II. Divergence from isothermality

A roughly constant temperature over a wide range of densities is maintained in molecular clouds through radiative heating and cooling. An isothermal equation of state is therefore frequently employed in molecular cloud simulations. However, the dynamical processes in molecular clouds include shock waves, expansion waves, cooling induced collapse and baroclinic vorticity, all incompatible with the assumption of a purely isothermal flow. Here, we incorporate an energy equation including all the important heating and cooling rates and a simple chemical network into simulations of three-dimensional, hydrodynamic, decaying turbulence. This allows us to test the accuracy of the isothermal assumption by directly comparing a model run with the modified energy equation to an isothermal model. We compute an extreme case in which the initial turbulence is sufficiently strong to dissociate much of the gas and alter the specific heat ratio. The molecules then reform as the turbulence weakens. We track the true specific heat ratio as well as its effective value. We analyse power spectra, vorticity and shock structures, and discuss scaling laws for decaying turbulence. We derive some limitations to the isothermal approximation for simulations of the interstellar medium using simple projection techniques. Overall, even given the extreme conditions, we find that an isothermal flow provides an adequate physical and observational description of many properties. The main exceptions revealed here concern behaviour directly related to the high temperature zones behind the shock waves.

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arXiv2004

Stellar Mass Spectra from Non-Isothermal Gravoturbulent Fragmentation

(abridged version) Identifying the processes that determine the initial mass function of stars (IMF) is a fundamental problem in star formation theory. One of the major uncertainties is the exact chemical state of the star forming gas and its influence on the dynamical evolution. Most simulations of star forming clusters use an isothermal equation of state (EOS). We address these issues and study the effect of a piecewise polytropic EOS on the formation of stellar clusters in turbulent, self-gravitating molecular clouds. We increase the polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we vary from from 4.3x10^4 cm^-3 to 4.3x10^7 cm^-3. The change of thermodynamic state at n_c selects a characteristic mass scale for fragmentation M_ch, which we relate to the peak of the observed IMF. We find a relation M_ch ~ n_c^-0.5, supporting the idea that the distribution of stellar masses largely depends on the thermodynamic state of the star-forming gas.

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arXiv2004

Cosmological Feedback from High-Redshift Dwarf Galaxies

We model how repeated supernova explosions in high-redshift dwarf starburst galaxies drive superbubbles and winds out of the galaxies. We compute the efficiencies of metal and mass ejection and energy transport from the galactic potentials, including the effect of cosmological infall of external gas. The starburst bubbles quickly blow out of small, high-redshift, galactic disks, but must compete with the ram pressure of the infalling gas to escape into intergalactic space. We show that the assumed efficiency of the star formation rate dominates the bubble evolution and the metal, mass, and energy feedback efficiencies. With star formation efficiency f*=0.01, the ram pressure of infall can confine the bubbles around high-redshift dwarf galaxies with circular velocities v_c>52 km/s. We can expect high metal and mass ejection efficiencies, and moderate energy transport efficiencies in halos with v_c~30-50 km/s and f*~0.01 as well as in halos with v_c~100 km/s and f*>>0.01. Such haloes collapse successively from 1-2 sigma peaks in LambdaCDM Gaussian density perturbations as time progresses. These dwarf galaxies can probably enrich low and high-density regions of intergalactic space with metals to 10^-3-10^-2 Zsun as they collapse at z~8 and z<5 respectively. They also may be able to provide adequate turbulent energy to prevent the collapse of other nearby halos, as well as to significantly broaden Lyman-alpha absorption lines to v_rms~20-40 km/s. We compute the timescales for the next starbursts if gas freely falls back after a starburst, and find that, for star formation efficiencies as low as f*<0.01, the next starburst should occur in less than half the Hubble time at the collapse redshift. This suggests that episodic star formation may be ubiquitous in dwarf galaxies.

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arXiv2003

Modification of Projected Velocity Power Spectra by Density Inhomogeneities in Compressible Supersonic Turbulence

(Modified) The scaling of velocity fluctuation, dv, as a function of spatial scale L in molecular clouds can be measured from size-linewidth relations, principal component analysis, or line centroid variation. Differing values of the power law index of the scaling relation dv = L^(g3D) in 3D are given by these different methods: the first two give g3D=0.5, while line centroid analysis gives g3D=0. This discrepancy has previously not been fully appreciated, as the variation of projected velocity line centroid fluctuations (dv_{lc} = L^(g2D)) is indeed described, in 2D, by g2D=0.5. However, if projection smoothing is accounted for, this implies that g3D=0. We suggest that a resolution of this discrepancy can be achieved by accounting for the effect of density inhomogeneity on the observed g2D obtained from velocity line centroid analysis. Numerical simulations of compressible turbulence are used to show that the effect of density inhomogeneity statistically reverses the effect of projection smoothing in the case of driven turbulence so that velocity line centroid analysis does indeed predict that g2D=g3D=0.5. Using our numerical results we can restore consistency between line centroid analysis, principal component analysis and size-linewidth relations, and we derive g3D=0.5, corresponding to shock-dominated (Burgers) turbulence. We find that this consistency requires that molecular clouds are continually driven on large scales or are only recently formed.

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arXiv2001

Magnetic Field Diagnostics Based on Far-Infrared Polarimetry: Tests Using Numerical Simulations

The dynamical state of star-forming molecular clouds cannot be understood without determining the structure and strength of their magnetic fields. Measurements of polarized far-infrared radiation from thermally aligned dust grains are used to map the orientation of the field and estimate its strength, but the accuracy of the results has remained in doubt. In order to assess the reliability of this method, we apply it to simulated far-infrared polarization maps derived from three-dimensional simulations of supersonic magnetohydrodynamical turbulence, and compare the estimated values to the known magnetic field strengths in the simulations. We investigate the effects of limited telescope resolution and self-gravity on the structure of the maps. Limited observational resolution affects the field structure such that small scale variations can be completely suppressed, thus giving the impression of a very homogeneous field. The Chandrasekhar-Fermi method of estimating the mean magnetic field in a turbulent medium is tested, and we suggest an extension to measure the rms field. Both methods yield results within a factor of 2 for field strengths typical of molecular clouds, with the modified version returning more reliable estimates for slightly weaker fields. However, neither method alone works well for very weak fields, missing them by a factor of up to 150. Taking the geometric mean of both methods estimates even the weakest fields accurately within a factor of 2.5. Limited telescope resolution leads to a systematic overestimation of the field strengths for all methods. We discuss the effects responsible for this overestimation and show how to extract information on the underlying (turbulent) power spectrum.

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arXiv2000

Gravitational Collapse in Turbulent Molecular Clouds. II. Magnetohydrodynamical Turbulence

Hydrodynamic supersonic turbulence can only prevent local gravitational collapse if the turbulence is driven on scales smaller than the local Jeans lengths in the densest regions, a very severe requirement (Paper I). Magnetic fields have been suggested to support molecular clouds either magnetostatically or via magnetohydrodynamic (MHD) waves. Whereas the first mechanism would form sheet-like clouds, the second mechanism not only could exert a pressure onto the gas counteracting the gravitational forces, but could lead to a transfer of turbulent kinetic energy down to smaller spatial scales via MHD wave interactions. This turbulent magnetic cascade might provide sufficient energy at small scales to halt local collapse. We test this hypothesis with MHD simulations at resolutions up to 256^3 zones, done with ZEUS-3D. We first derive a resolution criterion for self-gravitating, magnetized gas: in order to prevent collapse of magnetostatically supported regions due to numerical diffusion, the minimum Jeans length must be resolved by four zones. Resolution of MHD waves increases this requirement to roughly six zones. We then find that magnetic fields cannot prevent local collapse unless they provide magnetostatic support. Weaker magnetic fields do somewhat delay collapse and cause it to occur more uniformly across the supported region in comparison to the hydrodynamical case. However, they still cannot prevent local collapse for much longer than a global free-fall time.

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