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Mordecai-Mark Mac Low

Publications and source records attributed to Mordecai-Mark Mac Low.

At least 181 records · Page 10Linked to original sources
arXiv2001

Mixing of Primordial Elements in a Supernova-Driven ISM

In order to understand the time scales for complete mixing in a supernova-driven ISM we used the model of Avillez (2000) to follow the mixing and dispersal of inhomogeneities with different length scales. We included tracer fields to follow the inhomogeneities in kpc-scale simulations with different supernova rates. We find that an initially inhomogeneous ISM still shows local variations and a clumpy distribution on time scales of several hundred Myr. This clumpy structure does not disapear over a time of a few tens of Myr, even if the rate of SNe is increased to ten times the Galactic rate. These local variations occur because, even in the presence of numerical diffusion, gas does not mix quickly between hot and cold regions. The lower limit that we are able to place on the mixing time at the kpc scale is already longer than the time for chemistry to reach local equilibrium in the gas. The simulations also show that the time scale to erase inhomogeneities in the ISM is nearly independent of their length scale over the range 25-500 pc, contrary to what is expected from classical mixing length theory.

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arXiv2001

Column Density Probability Distribution Functions in Turbulent Molecular Clouds: A Comparison between Theory and Observations

The one-point statistics of column density distributions of turbulent molecular cloud models are investigated and compared with observations. In agreement with the observations, the number N of pixels with surface density S is distributed exponentially N(S)=exp(-S/S0) in models of driven compressible supersonic turbulence. However, in contrast to the observations, the exponential slope defined by S0 is not universal but instead depends strongly on the adopted rms Mach number and on the smoothing of the data cube. We demonstrate that this problem can be solved if one restricts the analysis of the surface density distribution to subregions with sizes equal to the correlation length of the flow which turns out to be given by the driving scale. In this case, the column density distributions are universal with a slope that is in excellent agreement with the observations and independent of the Mach number or smoothing. The observed molecular clouds therefore are coherent structures with sizes of order their correlation lengths. Turbulence inside these clouds must be driven on the largest scales, if at all. Numerical models of turbulent molecular clouds have to be restricted to cubes with sizes similar to the correlation lengthscale in order to be compared with observations. Our results imply that turbulence is generated on scales that are much larger that the Jeans length. In this case, gravitational collapse cannot be suppressed and star formation should start in molecular clouds within a dynamical timescale after their formation.

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arXiv2001

The Distribution of Pressures in a Supernova-Driven Interstellar Medium

Observations have suggested substantial departures from pressure equilibrium in the interstellar medium (ISM) in the plane of the Galaxy, even on scales under 50 pc. Nevertheless, multi-phase models of the ISM assume at least locally isobaric gas. The pressure then determines the density reached by gas cooling to stable thermal equilibrium. We use two different sets of numerical models of the ISM to examine the consequences of supernova driving for interstellar pressures. The first set of models is hydrodynamical, and uses adaptive mesh refinement to allow computation of a 1 x 1 x 20 kpc section of a stratified galactic disk. The second set of models is magnetohydrodynamical, using an independent code framework, and examines a 200 pc cubed periodic domain threaded by magnetic fields. Both of these models show broad pressure distributions with roughly log-normal functional forms produced by both shocks and rarefaction waves, rather than the power-law distributions predicted by previous work, with rather sharp thermal pressure gradients. The width of the distribution of the logs of pressure in gas with log T < 3.9 is proportional to the rms Mach number in that gas, while the distribution in hotter gas is broader, but not so broad as would be predicted by the Mach numbers in that gas. Individual parcels of gas reach widely varying points on the thermal equilibrium curve: no unique set of phases is found, but rather a dynamically-determined continuum of densities and temperatures. Furthermore, a substantial fraction of the gas remains entirely out of thermal equilibrium. Our results appear consistent with observations of interstellar pressures, and suggest that the pressures observed in molecular clouds may be due to ram pressure rather than gravitational confinement.

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arXiv2001

Mushroom-Shaped Structures as Tracers of Buoyant Flow in the Galactic Disk

Recent HI emission observations of the Southern Galactic hemisphere have revealed a mushroom-like structure extending from z=-70 to -450 pc, composed of a stem and a cap. Similar structures occur in three-dimensional simulations of a dynamic galactic disk driven by isolated and clustered supernovae. Using these simulations, we show that hot gas in the Galactic disk that is not evacuated through chimneys expands into the cooler gas of the thick disk, forming mushroom-shaped structures. This new class of objects traces buoyant flow of hot gas into the thick disk.

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arXiv2000

Clustered vs. Isolated Star Formation

I argue that star formation is controlled by supersonic turbulence, drawing for support on a number of 3D hydrodynamical and MHD simulations as well as theoretical arguments. Clustered star formation appears to be a natural result of a lack of turbulent support, while isolated star formation is a signpost of global turbulent support.

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arXiv2000

The distribution of shock waves in driven supersonic turbulence

Supersonic turbulence generates distributions of shock waves. Here, we analyse the shock waves in three-dimensional numerical simulations of uniformly driven supersonic turbulence, with and without magnetohydrodynamics and self-gravity. We can identify the nature of the turbulence by measuring the distribution of the shock strengths. We find that uniformly driven turbulence possesses a power law distribution of fast shocks with the number of shocks inversely proportional to the square root of the shock jump speed. A tail of high speed shocks steeper than Gaussian results from the random superposition of driving waves which decay rapidly. The energy is dissipated by a small range of fast shocks. These results contrast with the exponential distribution and slow shock dissipation associated with decaying turbulence. A strong magnetic field enhances the shock number transverse to the field direction at the expense of parallel shocks. A simulation with self-gravity demonstrates the development of a number of highly dissipative accretion shocks. Finally, we examine the dynamics to demonstrate how the power-law behaviour arises.

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arXiv2000

The Dynamical Interstellar Medium: Insights from Numerical Models

Numerical models of the dynamical interstellar medium show that interactions between structures such as supernova remnants and superbubbles are more important than the structures themselves in determining the behavior of the ISM. I review the techniques and conclusions of recent global models, focussing on what they tell us about the formation of star-forming giant molecular clouds.

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arXiv2000

The shock waves in decaying supersonic turbulence

We here analyse numerical simulations of supersonic, hypersonic and magnetohydrodynamic turbulence that is free to decay. Our goals are to understand the dynamics of the decay and the characteristic properties of the shock waves produced. This will be useful for interpretation of observations of both motions in molecular clouds and sources of non-thermal radiation. We find that decaying hypersonic turbulence possesses an exponential tail of fast shocks and an exponential decay in time, i.e. the number of shocks is proportional to t exp (-ktv) for shock velocity jump v and mean initial wavenumber k. In contrast to the velocity gradients, the velocity Probability Distribution Function remains Gaussian with a more complex decay law. The energy is dissipated not by fast shocks but by a large number of low Mach number shocks. The power loss peaks near a low-speed turn-over in an exponential distribution. An analytical extension of the mapping closure technique is able to predict the basic decay features. Our analytic description of the distribution of shock strengths should prove useful for direct modeling of observable emission. We note that an exponential distribution of shocks such as we find will, in general, generate very low excitation shock signatures.

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arXiv2000

Gravitational Collapse in Turbulent Molecular Clouds. I. Gasdynamical Turbulence

Observed molecular clouds often appear to have very low star formation efficiencies and lifetimes an order of magnitude longer than their free-fall times. Their support is attributed to the random supersonic motions observed in them. We study the support of molecular clouds against gravitational collapse by supersonic, gas dynamical turbulence using direct numerical simulation. Computations with two different algorithms are compared: a particle-based, Lagrangian method (SPH), and a grid-based, Eulerian, second-order method (ZEUS). The effects of both algorithm and resolution can be studied with this method. We find that, under typical molecular cloud conditions, global collapse can indeed be prevented, but density enhancements caused by strong shocks nevertheless become gravitationally unstable and collapse into dense cores and, presumably, stars. The occurance and efficiency of local collapse decreases as the driving wave length decreases and the driving strength increases. It appears that local collapse can only be prevented entirely with unrealistically short wave length driving, but observed core formation rates can be reproduced with more realistic driving. At high collapse rates, cores are formed on short time scales in coherent structures with high efficiency, while at low collapse rates they are scattered randomly throughout the region and exhibit considerable age spread. We suggest that this naturally explains the observed distinction between isolated and clustered star formation.

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arXiv1999

Is the Plasma Within Bubbles and Superbubbles Hot or Cold?

I review what is known about the temperature of the plasma within stellar wind bubbles and superbubbles. Classical theory suggests that it should be hot, with characteristic temperatures of order a million degrees. This temperature should be set by the balance between heating by the internal termination shocks of the central stellar winds and supernovae, which expand at thousands of km/s, and cooling by conductive evaporation of cold gas off the shell walls. However, if the hot interior gas becomes dense enough due to evaporation or ablation off of interior clouds, it will cool in less than a dynamical time, leading to a cold interior. The observational evidence appears mixed. On the one hand, X-ray emission has been observed from both stellar wind bubbles and superbubbles. On the other hand, no stellar wind bubble or superbubble has yet been observed emitting at the rate predicted by the classical theory: they are either too faint or too bright, by up to an order of magnitude. Alternate explanations have been proposed for the observed emission, including off-center supernova remnants hitting the shell walls of superbubbles, and residual emission from highly-ionized gas out of coronal equilibrium. Furthermore, the structures of post-main sequence stellar wind bubbles, expanding into what are presumably old stellar wind bubbles, appear in at least some cases to show that the bubble interior is cold, not hot. (The classical example of this is NGC 6888.) What is the actual state of bubble and superbubble interiors?

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arXiv1999

MHD Turbulence in Star-Forming Clouds

We review how supersonic turbulence can both prevent and promote the collapse of molecular clouds into stars. First we show that decaying turbulence cannot significantly delay collapse under conditions typical of molecular clouds, regardless of magnetic field strength so long as the fields are not supporting the cloud magnetohydrostatically. Then we review possible drivers and examine simulations of driven supersonic and trans Alfvénic turbulence, finally including the effects of self-gravity. Our preliminary results show that, although turbulence can support regions against gravitational collapse, the strong compressions associated with the required velocities will tend to promote collapse of local condensations.

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arXiv1999

Characterizing the structure of interstellar turbulence

Modeling the structure of molecular clouds depends on good methods to statistically compare simulations with observations in order to constrain the models. Here we characterize a suite of hydrodynamical and magnetohydrodynamical (MHD) simulations of supersonic turbulence using an averaged wavelet transform, the Delta-variance, that has been successfully used to characterize observations. We find that, independent of numerical resolution and dissipation, the only models that produce scale-free, power-law Delta-variance spectra are those with hypersonic Mach numbers above M ~ 4, while slower supersonic turbulence tends to show characteristic scales and produce non-power-law spectra. Magnetic fields have only a minor influence on this tendency, though they tend to reduce the scale-free nature of the turbulence, and increase the transfer of energy from large to small scales. The evolution of the characteristic length scale seen in supersonic turbulence follows exactly the t^{1/2} power-law predicted from recent studies of the kinetic energy decay rate.

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arXiv1999

Giant Outbursts of Luminous Blue Variables and the Formation of the Homunculus Nebula Around eta Carinae

The observed giant outbursts of Luminous Blue Variables (LBVs) may occur when these massive stars approach their Eddington limits. When this happens, they must reach a point where the centrifugal force and the radiative acceleration cancel out gravity at the equator. We call this the Omega-limit. When stars are close to the Omega-limit, strong non-spherical mass loss should occur. This suggests a scenario where a slow and very dense wind, strongly confined to the equatorial plane, is followed by a fast and almost spherical wind. We compute two-dimensional hydrodynamic models of the evolution of the nebula formed from such interacting winds, using parameters consistent with the outburst of eta Carinae in the last century. This outburst gave birth to the Homunculus, the hourglass-shaped inner part of a highly structured circumstellar nebula. Assuming the star was very close to the Omega-limit during outburst, our models produce gas distributions that strongly resemble the Homunculus on large and small scale. This supports the general conjecture that giant outbursts in LBVs occur when they approach the Eddington limit. Our models constrains the average mass loss rate since the outburst to values smaller than the present-day mass loss rate and suggest that eta Car is approaching another outburst. Our models imply that the occurrence of giant LBV outbursts depends on the initial stellar rotation rate, and that the initial angular momentum is as important to the evolution of very massive stars as their initial mass or metallicity.

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arXiv1998

The Interaction of the Disk with the Halo

In this review I focus on how massive stars in the disks of galaxies determine the properties of the ionized, gaseous haloes of star-forming galaxies. I first examine the ionization state of the halo, and conclude that diluted radiation from massive stars, along with a possible secondary heating source such as shocks, appears sufficient to explain the observations. I then look at how single superbubbles evolve, as they must provide one of the main mechanisms for transfer of mass and energy to the halo, as well as opening up lines of sight for ionizing radiation to escape from the disk. Finally, I look at the interactions of superbubbles, as they will rarely evolve in isolation, and describe recent hydrodynamical and MHD simulations of the interstellar medium shaped by multiple superbubbles.

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arXiv1998

The Energy Dissipation Rate of Supersonic, Magnetohydrodynamic Turbulence in Molecular Clouds

Molecular clouds have broad linewidths suggesting turbulent supersonic motions in the clouds. These motions are usually invoked to explain why molecular clouds take much longer than a free-fall time to form stars. It has classically been thought that supersonic hydrodynamical turbulence would dissipate its energy quickly, but that the introduction of strong magnetic fields could maintain these motions. In a previous paper it has been shown, however, that isothermal, compressible, MHD and hydrodynamical turbulence decay at virtually the same rate, requiring that constant driving occur to maintain the observed turbulence. In this paper direct numerical computations of uniformly driven turbulence with the ZEUS astrophysical MHD code are used to derive the absolute value of energy dissipation as a function of the driving wavelength and amplitude. The ratio of the formal decay time of turbulence E_{kin}/\dot{E}_{kin} to the free-fall time of the gas can then be derived as a function of the ratio of driving wavelength to Jeans wavelength and rms Mach number, and shown to be most likely far less than unity, again showing that turbulence in molecular clouds must be constantly and strongly driven. (abridged)

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arXiv1998

Starburst-driven Mass Loss from Dwarf Galaxies: Efficiency and Metal Ejection

We model the effects of repeated supernova explosions from starbursts in dwarf galaxies on the interstellar medium of these galaxies, taking into account the gravitational potential of their dominant dark matter haloes. We explore supernova rates from one every 30,000 yr to one every 3 million yr, equivalent to steady mechanical luminosities of L=0.1-10 x 10^38 ergs/s, occurring in dwarf galaxies with gas masses M_g=10^6 - 10^9 solar masses. We address in detail, both analytically and numerically, the following three questions: 1. When do the supernova ejecta blow out of the disk of the galaxy? 2. When blowout occurs, what fraction of the interstellar gas is blown away, escaping the potential of the galactic halo? 3. What happens to the metals ejected from the massive stars of the starburst? Are they retained or blown away? We give quantitative results for when blowout will or will not occur in galaxies with 10^6 \leq M_g \leq 10^9 solar masses. Surprisingly, we find that the mass ejection efficiency is very low for galaxies with mass M_g \geq 10^7 solar masses. Only galaxies with M_g \leq 10^6 solar masses have their interstellar gas blown away, and then virtually independently of L. On the other hand, metals from the supernova ejecta are accelerated to velocities larger than the escape speed from the galaxy far more easily than the gas. We find that for L_38=1, only about 30% of the metals are retained by a 10^9 solar mass galaxy, and virtually none by smaller galaxies. We discuss the implications of our results for the evolution, metallicity and observational properties of dwarf galaxies.

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arXiv1997

Kinetic Energy Decay Rates of Supersonic and Super-Alfvenic Turbulence in Star-Forming Clouds

We present numerical studies of compressible, decaying turbulence, with and without magnetic fields, with initial rms Alfven and Mach numbers ranging up to five, and apply the results to the question of the support of star-forming interstellar clouds of molecular gas. We find that, in 1D, magnetized turbulence actually decays faster than unmagnetized turbulence. In all the regimes that we have studied 3D turbulence-super-Alfvenic, supersonic, sub-Alfvenic, and subsonic-the kinetic energy decays as (t-t0)^(-x), with 0.85 < x < 1.2. We compared results from two entirely different algorithms in the unmagnetized case, and have performed extensive resolution studies in all cases, reaching resolutions of 256^3 zones or 350,000 particles. We conclude that the observed long lifetimes and supersonic motions in molecular clouds must be due to external driving, as undriven turbulence decays far too fast to explain the observations.

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