arXiv subjects

Mordecai-Mark Mac Low

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

At least 163 records · Page 9Linked to original sources

arXiv2005

Control of Star Formation in Galaxies by Gravitational Instability

We study gravitational instability and consequent star formation in a wide range of isolated disk galaxies, using three-dimensional, smoothed particle hydrodynamics simulations at resolution sufficient to fully resolve gravitational collapse. Stellar feedback is represented by an isothermal equation of state. Absorbing sink particles are inserted in dynamically bound, converging regions with number density $n > 10^3$ cm$^{-3}$ to directly measure the mass of gravitationally collapsing gas available for star formation. Our models quantitatively reproduce not only the observed Schmidt law, but also the observed star formation threshold in disk galaxies. Our results suggest that the dominant physical mechanism determining the star formation rate is just the strength of gravitational instability, with feedback primarily functioning to maintain a roughly constant effective sound speed.

astro-ph↗

arXiv2005

The Distribution of Pressures in a Supernova-Driven Interstellar Medium. I. Magnetized 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 numerical models of the magnetized ISM to examine the consequences of supernova driving for interstellar pressures. In this paper we examine a (200 pc)^3 periodic domain threaded by magnetic fields. Individual parcels of gas at different pressures 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. A substantial fraction of the gas remains entirely out of thermal equilibrium. Our results appear consistent with observations of interstellar pressures. They also suggest that the high pressures observed in molecular clouds may be due to ram pressures in addition to gravitational forces. Much of the gas in our model lies far from equipartition between thermal and magnetic pressures, with ratios ranging from 0.1 to $10^4$ and ratios of uniform to fluctuating magnetic field of 0.5--1. Our models show broad pressure probability distribution functions with log-normal functional forms produced by both shocks and rarefaction waves, rather than power-law distributions produced by isolated supernova remnants. The width of the distribution can be described quantitatively by a formula derived from the work of Padoan, Nordlund, & Jones (1997).

astro-ph↗

arXiv2005

The stellar mass spectrum from non-isothermal gravoturbulent fragmentation

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). However, theoretical predictions and observations suggest that the effective polytropic exponent gamma in the EOS varies with density. 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 using three-dimensional, smoothed particle hydrodynamics simulations. To approximate the results of published predictions of the thermal behavior of collapsing clouds, we increase the polytropic exponent gamma from 0.7 to 1.1 at some chosen density n_c, which we vary. 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. Our investigation generally supports the idea that the distribution of stellar masses depends mainly on the thermodynamic state of the star-forming gas. The thermodynamic state of interstellar gas is a result of the balance between heating and cooling processes, which in turn are determined by fundamental atomic and molecular physics and by chemical abundances. Given the abundances, the derivation of a characteristic stellar mass can thus be based on universal quantities and constants.

astro-ph↗

arXiv2004

Magnetized Turbulence

Several topics in the theory of magnetized turbulence are reviewed with application to star formation and the interstellar medium. The density, pressure, and temperature distribution in a turbulent interstellar medium is described in comparison to a medium dominated by thermal instability. The derivation of the empirical theory for the energy spectrum of hydrodynamic and MHD turbulence is outlined, and comparisons are given to numerical models for the magnetized case. Next discussed is how density fluctuations modify observations of velocity fluctuations in line centroids, coincidentally cancelling the effects of projection smoothing. The analytic description of velocity structure functions as a function of the dimensionality of the dissipative structures is then covered. Finally the question of whether turbulence can support against gravitational collapse is addressed. Turbulence both prevents and promotes collapse, but its net effect is to inhibit collapse, so it does not trigger star formation in any significant sense.

astro-ph↗

arXiv2004

Initial Ionization of Compressible Turbulence

We study the effects of the initial conditions of turbulent molecular clouds on the ionization structure in newly formed H_{ii} regions, using three-dimensional, photon-conserving radiative transfer in a pre-computed density field from three-dimensional compressible turbulence. Our results show that the initial density structure of the gas cloud can play an important role in the resulting structure of the H_{ii} region. The propagation of the ionization fronts, the shape of the resulting H_{ii} region, and the total mass ionized depend on the properties of the turbulent density field. Cuts through the ionized regions generally show ``butterfly'' shapes rather than spherical ones, while emission measure maps are more spherical if the turbulence is driven on scales small compared to the size of the H_{ii} region. The ionization structure can be described by an effective clumping factor $ζ=< n > \cdot < n^2>/< n>^2$, where $n$ is number density of the gas. The larger the value of $ζ$, the less mass is ionized, and the more irregular the H_{ii} region shapes. Because we do not follow dynamics, our results apply only to the early stage of ionization when the speed of the ionization fronts remains much larger than the sound speed of the ionized gas, or Alfvén speed in magnetized clouds if it is larger, so that the dynamical effects can be negligible.

astro-ph↗

arXiv2004

The Influence of Supershells and Galactic Outflows on the Escape of Ionizing Radiation from Dwarf Starburst Galaxies

We study the escape of Lyman continuum radiation from the disks of dwarf starburst galaxies, with and without supershells, by solving the radiation transfer problem of stellar radiation through them. We model disks with Md=10^8-10Msun, with exponential surface density profiles as a function of redshift, and model the of repeated supernova explosions driving supershells out of the disks, using the hydrodynamic simulation code, ZEUS-3D. The amount of star formation is assumed proportional to mass above some density threshold. We vary the threshold to explore the range of star formation efficiencies, f*=0.006, 0.06, and 0.6. We find that the interstellar gas swept up in dense supershells can effectively trap the ionizing photons, before the supershells blow out of the disks. The blow-outs then create galactic outflows, chimneys which allow the photons to escape directly to the intergalactic medium. Our results are consistent with escape fractions of less than 0.1 measured in local dwarf starburst galaxies, because they are likely observed while the starbursts are young, before blow-out. We suggest that high-redshift dwarf starburst galaxies may make a substantial contribution to the UV background radiation with total escape fractions >0.2, as expected if star formation efficiencies >0.06.

astro-ph↗

arXiv2004

Gravoturbulent Star Cluster Formation

Stars form by gravoturbulent fragmentation of interstellar gas clouds. The supersonic turbulence ubiquitously observed in Galactic molecular gas generates strong density fluctuations with gravity taking over in the densest and most massive regions. Collapse sets in to build up stars and star clusters. Turbulence plays a dual role. On global scales it provides support, while at the same time it can promote local collapse. Stellar birth is thus intimately linked to the dynamical behavior of parental gas cloud, which determines when and where protostellar cores form, and how they contract and grow in mass via accretion from the surrounding cloud material to build up stars. Slow, inefficient, isolated star formation is a hallmark of turbulent support, whereas fast, efficient, clustered star formation occurs in its absence. The fact that Galactic molecular clouds are highly filamentary can be explained by a combination of compressional flows and shear. The dynamical evolution of nascent star clusters is very complex. This strongly influences the stellar mass spectrum. The equation of state (EOS) plays a pivotal role in the fragmentation process. Under typical cloud conditions, massive stars form as part of dense clusters. However, for gas with effective polytropic index greater than unity star formation becomes biased towards isolated massive stars, which may be of relevance for understanding Pop III stars.

astro-ph↗

arXiv2003

The Formation of Self-Gravitating Cores in Turbulent Magnetized Clouds

We use ZEUS-MP to perform high resolution, three-dimensional, super-Alfvenic turbulent simulations in order to investigate the role of magnetic fields in self-gravitating core formation within turbulent molecular clouds. Statistical properties of our super-Alfvenic model without gravity agree with previous similar studies. Including self-gravity, our models give the following results. They are consistent with the turbulent fragmentation prediction of the core mass distribution of Padoan & Nordlund. They also confirm that local gravitational collapse is not prevented by magnetohydrodynamic waves driven by turbulent flows, even when the turbulent Jeans mass exceeds the mass in the simulation volume. Comparison of results between 256^3 and 512^3 zone simulations reveals convergence in the collapse rate. Analysis of self-gravitating cores formed in the simulation shows that: (1) All cores formed are magnetically supercritical by at least an order of magnitude. (2) A power law relation between central magnetic field strength and density B_c propto rho_c^{1/2} is observed despite the cores being strongly supercritical. (3) Specific angular momentum j propto R^{3/2} for cores with radius R. (4) Most cores are prolate and triaxial in shape, in agreement with the results of Gammie et al.

astro-ph↗

arXiv2003

Turbulent Structure of the Interstellar Medium

How does turbulence contribute to the formation and structure of the dense interstellar medium (ISM)? Molecular clouds are dense, high-pressure objects. It is usually argued that gravitational confinement causes the high pressures, and that the clouds are (magneto)hydrostaticobjects supported by a balance between magnetic and turbulent pressures and gravity. However, magnetic pressures appear too weak, and MHD turbulent support not only requires driving, but also results in continuing gravitational collapse, as has now been demonstrated in simulations reaching 512^3 zones. Models of supernova-driven, magnetized turbulence readily form transient, high-pressure, dense regions that may form molecular clouds. They are contained not by self-gravity, but by turbulent ram pressures from the larger flow. Apparent virialization may actually be a geometrical effect. Turbulent clouds are unlikely to be in hydrostatic equilibrium, instead either collapsing or expanding, although they may appear well-fit by projected equilibrium Bonnor-Ebert spheres. Collapsing clouds probably form stars efficiently, while expanding ones can still form stars by turbulent compression, but rather inefficiently.

astro-ph↗

arXiv2003

The Turbulent Interstellar Medium: Insights and Questions from Numerical Models

"The purpose of numerical models is not numbers but insight." (Hamming) In the spirit of this adage, and of Don Cox's approach to scientific speaking, we discuss the questions that the latest generation of numerical models of the interstellar medium raise, at least for us. The energy source for the interstellar turbulence is still under discussion. We review the argument for supernovae dominating in star forming regions. Magnetorotational instability has been suggested as a way of coupling disk shear to the turbulent flow. Models make evident that the unstable wavelengths are very long compared to thermally unstable wavelengths, with implications for star formation in the outer galaxy and low surface brightness disks. The perennial question of the factors determining the hot gas filling factor in a SN-driven medium remains open, in particular because of the unexpectedly strong turbulent mixing at the boundaries of hot cavities seen in the models. The formation of molecular clouds in the turbulent flow is also poorly understood. Dense regions suitable for cloud formation clearly form even in the absence of self-gravity, although their ultimate evolution remains to be computed.

astro-ph↗

arXiv2003

Control of star formation by supersonic turbulence

Understanding the formation of stars in galaxies is central to much of modern astrophysics. For several decades it has been thought that stellar birth is primarily controlled by the interplay between gravity and magnetostatic support, modulated by ambipolar diffusion. Recently, however, both observational and numerical work has begun to suggest that support by supersonic turbulence rather than magnetic fields controls star formation. In this review we outline a new theory of star formation relying on the control by turbulence. We demonstrate that although supersonic turbulence can provide global support, it nevertheless produces density enhancements that allow local collapse. Inefficient, isolated star formation is a hallmark of turbulent support, while efficient, clustered star formation occurs in its absence. The consequences of this theory are then explored for both local star formation and galactic scale star formation. (ABSTRACT ABBREVIATED)

astro-ph↗

arXiv2003

Chondrule Formation and Protoplanetary Disk Heating by Current Sheets in Non-Ideal Magnetohydrodynamic Turbulence

We study magnetic field steepening due to ambipolar diffusion (Brandenburg & Zweibel 1994) in protoplanetary disk environments and draw the following conclusions. Current sheets are generated in magnetically active regions of the disk where the ionization fraction is high enough for the magnetorotational instability to operate. In late stages of solar nebula evolution, the surface density is expected to have lowered and dust grains to have gravitationally settled to the midplane. If the local dust-to-gas mass ratio near the midplane is increased above cosmic abundances by factors > 10^3, current sheets reach high enough temperatures to melt millimeter-sized dust grains, and hence may provide the mechanism to form meteoritic chondrules. In addition, these current sheets possibly explain the near-infrared excesses observed in spectral energy distributions (SEDs) of young stellar objects. Direct imaging of protoplanetary disks via a nulling interferometer or, in the future, a multi-band, adaptive optics coronagraph can test this hypothesis.

astro-ph↗

arXiv2002

Turbulence in the Interstellar Medium: Energetics and Driving Mechanisms

Interstellar turbulence is expected to dissipate quickly in the absence of continuous energy input. I examine the energy available for driving the turbulence from six likely mechanisms: magnetorotational instability, gravitational instability, protostellar outflows, H II region expansion, stellar winds, and supernovae. I conclude that supernovae contribute far more energy than the other mechanisms, and so form the most likely drving mechanism.

astro-ph↗

arXiv2002

The Formation of Stellar Clusters in Turbulent Molecular Clouds: Effects of the Equation of State

We study numerically the effect of varying the equation of state (EOS) on the formation of stellar clusters in turbulent molecular clouds. Our results show that the EOS plays an important role in the fragmentation of the clouds, and the determination of the initial mass function (IMF) of the protostellar cores. Fragmentation decreases with increasing adiabatic index $γ$ in the range $0.2 < γ< 1.4$, although the total amount of mass accreted appears to remain roughly constant through that range, resulting in more massive cores at higher $γ$. Fragmentation and collapse ceases entirely for $γ> 1.4$ as expected from analytic arguments. Primordial gas may have effective $γ> 1$, in which case these results may help explain why models of the formation of the first stars produce isolated, massive objects.

astro-ph↗

arXiv2002

MHD Turbulence in Star-Forming Regions and the Interstellar Medium

MHD turbulence plays a central role in the physics of star-forming molecular clouds and the interstellar medium. I here show that MHD turbulence in molecular clouds must be driven to account for the observed supersonic motions in the clouds, as even strongly magnetized turbulence decays quickly. I then show that driven MHD turbulence can globally support gravitationally unstable regions, but local collapse inevitably occurs. Differences in the strength of driving and the gas density may explain the very different rates of star formation observed in different galaxies. The driving mechanism for the turbulence is likely a combination of field supernovae in star-forming sections of galactic disks, and magnetorotational instabilities in outer disks and low surface brightness galaxies. Supernova-driven turbulence has a broad range of pressures with a roughly log-normal distribution. High-pressure, cold regions can be formed even in the absence of self-gravity.

astro-ph↗

arXiv2002

Mixing Time Scales in a Supernova-Driven Interstellar Medium

We study the mixing of chemical species in the interstellar medium (ISM). Recent observations suggest that the distribution of species such as deuterium in the ISM may be far from homogeneous. This raises the question of how long it takes for inhomogeneities to be erased in the ISM, and how this depends on the length scale of the inhomogeneities. We added a tracer field to the three-dimensional, supernova-driven ISM model of Avillez (2000) to study mixing and dispersal in kiloparsec-scale simulations of the ISM with different supernova (SN) rates and different inhomogeneity length scales. We find several surprising results. Classical mixing length theory fails to predict the very weak dependence of mixing time on length scale that we find on scales of 25--500 pc. Derived diffusion coefficients increase exponentially with time, rather than remaining constant. The variance of composition declines exponentially, with a time constant of tens of Myr, so that large differences fade faster than small ones. The time constant depends on the inverse square root of the supernova rate. One major reason for these results is that even with numerical diffusion exceeding physical values, gas does not mix quickly between hot and cold regions.

astro-ph↗

arXiv2002

Hydrodynamical simulations of the decay of high-speed molecular turbulence. I. Dense molecular regions

We present the results from three dimensional hydrodynamical simulations of decaying high-speed turbulence in dense molecular clouds. We compare our results, which include a detailed cooling function, molecular hydrogen chemistry and a limited C and O chemistry, to those previously obtained for decaying isothermal turbulence. After an initial phase of shock formation, power-law decay regimes are uncovered, as in the isothermal case. We find that the turbulence decays faster than in the isothermal case because the average Mach number remains higher, due to the radiative cooling. The total thermal energy, initially raised by the introduction of turbulence, decays only a little slower than the kinetic energy. We discover that molecule reformation, as the fast turbulence decays, is several times faster than that predicted for a non-turbulent medium. This is caused by moderate speed shocks which sweep through a large fraction of the volume, compressing the gas and dust. Through reformation, the molecular density and molecular column appear as complex patterns of filaments, clumps and some diffuse structure. In contrast, the molecular fraction has a wider distribution of highly distorted clumps and copious diffuse structure, so that density and molecular density are almost identically distributed during the reformation phase. We conclude that molecules form in swept-up clumps but effectively mix throughout via subsequent expansions and compressions.

astro-ph↗

arXiv2002

Turbulent Velocity Structure in Molecular Clouds

We compare velocity structure in the Polaris Flare molecular cloud at scales ranging from 0.015 pc to 20 pc to simulations of supersonic hydrodynamic and MHD turbulence computed with the ZEUS MHD code. We use several different statistical methods to compare models and observations. The Delta-variance wavelet transform is most sensitive to characteristic scales and scaling laws, but is limited by a lack of intensity weighting. The scanning-beam size-linewidth relation is more robust with respect to noisy data. Obtaining the global velocity scaling behaviour requires that large-scale trends in the maps not be removed but treated as part of the turbulent cascade. We compare the true velocity PDF in our models to velocity centroids and average line profiles in optically thin lines, and find that the line profiles reflect the true PDF better unless the map size is comparable to the total line-of-sight thickness of the cloud. Comparison of line profiles to velocity centroid PDFs can thus be used to measure the line-of-sight depth of a cloud. The observed density and velocity structure is consistent with supersonic turbulence with a driving scale at or above the size of the molecular cloud and dissipative processes below 0.05 pc. Ambipolar diffusion could explain the dissipation. The velocity PDFs exclude small-scale driving such as that from stellar outflows as a dominant process in the observed region. In the models, large-scale driving is the only process that produces deviations from a Gaussian PDF shape consistent with observations. Strong magnetic fields impose a clear anisotropy on the velocity field, reducing the velocity variance in directions perpendicular to the field. (abridged)

astro-ph↗