An excursion-set model for the structure of giant molecular clouds and the interstellar medium

The interstellar medium (ISM) is governed by supersonic turbulence on a range of scales. We use this simple fact to develop a rigorous excursion-set model for the formation, structure and time evolution of dense gas structures [e.g. giant molecular clouds (GMCs), massive clumps and cores]. Supersonic turbulence drives the density distribution in non-self-gravitating regions to a lognormal with dispersion increasing with Mach number. We generalize this to include scales ≳ h (the disc scale-height), and use it to construct the statistical properties of the density field smoothed on a scale R . We then compare conditions for self-gravitating collapse including thermal, turbulent and rotational (disc shear) support (reducing to the Jeans/Toomre criterion on small/large scales). We show that this becomes a well-defined barrier crossing problem. As such, an exact ‘bound object mass function’ can be derived, from scales of the sonic length to well above the disc Jeans mass. This agrees remarkably well with observed GMC mass functions in the Milky Way and other galaxies, with the only inputs being the total mass and size of the galaxies (to normalize the model). This explains the cut-off of the mass function and its power-law slope (close to, but slightly shallower than, −2). The model also predicts the linewidth–size and size–mass relations of clouds and the dependence of residuals from these relations on mean surface density/pressure, in excellent agreement with observations. We use this to predict the spatial correlation function/clustering of clouds and, by extension, star clusters; these also agree well with observations. We predict the size/mass function of ‘bubbles’ or ‘holes’ in the ISM, and show that this can account for the observed H I hole distribution without requiring any local feedback/heating sources. We generalize the model to construct time-dependent ‘merger/fragmentation trees’ which can be used to follow cloud evolution and construct semi-analytic models for the ISM, GMCs and star-forming populations. We provide explicit recipes to construct these trees. We use a simple example to show that if clouds are not destroyed in ∼1–5 crossing times, then all the ISM mass would be trapped in collapsing objects even if the large-scale turbulent cascade were maintained

A Simple Phenomenological Model for Grain Clustering in Turbulence

We propose a simple model for density fluctuations of aerodynamic grains, embedded in a turbulent, gravitating gas disk. The model combines a calculation for the behavior of a group of grains encountering a single turbulent eddy, with a hierarchical approximation of the eddy statistics. This makes analytic predictions for a range of quantities including: distributions of grain densities, power spectra and correlation functions of fluctuations, and maximum grain densities reached. We predict how these scale as a function of grain drag time t_stop, spatial scale, grain-to-gas mass ratio, strength of turbulence (alpha), and detailed disk properties. We test these against numerical simulations with various turbulence-driving mechanisms. The simulations agree well with the predictions, spanning t_stop*Omega ~ 1e-4 - 10, alpha ~ 1e-10 - 1e-2, and grain-to-gas mass ratio ~0-3. Results from 'turbulent concentration' simulations and laboratory experiments are also predicted as a special case. Vortices on a wide range of scales disperse and concentrate grains hierarchically. For small grains this is most efficient in eddies with turnover time comparable to the stopping time, but fluctuations are also damped by local gas-grain drift. For large grains, shear and gravity lead to a much broader range of eddy scales driving fluctuations, with most power on the largest scales. The grain density distribution has a log-Poisson shape, with fluctuations for large grains up to factors >1000. We provide simple analytic expressions for the predictions, and discuss implications for planetesimal formation, grain growth, and the structure of turbulence.Comment: 23 pages, 10 figures, updated to match accepted version. Text greatly expanded with additional derivations for new regimes, comparison to other analytic grain clustering models, more detailed comparison with experimental dat

A New Public Release of the GIZMO Code

We describe a major update to the public GIZMO code. GIZMO has been used in simulations of cosmology; galaxy and star formation and evolution; black hole accretion and feedback; proto-stellar disk dynamics and planet formation; fluid dynamics and plasma physics; dust-gas dynamics; giant impacts and solid-body interactions; collisionless gravitational dynamics; and more. This release of the public code supports: hydrodynamics (using various mesh-free finite-volume Godunov methods or SPH), ideal and non-ideal MHD, anisotropic conduction and viscosity, radiative cooling and chemistry, star and black hole formation and feedback, sink particles, dust-gas (aero)-dynamics (with or without magnetic fields), elastic/plastic dynamics, arbitrary (gas, stellar, degenerate, solid/liquid material) equations of state, passive scalar/turbulent diffusion, large-eddy and shearing boxes, self-gravity with fully-adaptive force softenings, arbitrary cosmological expansion, and on-the-fly group-finding. It is massively-parallel with hybrid MPI+OpenMP scaling verified up to >1 million threads. The code is extensively documented, with test problems and tutorials provided for these different physics modules.Comment: Brief (2 page) overview. The GIZMO code (with an extensive User Guide, animations, and test problems) is available through http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.html or on the repository at https://bitbucket.org/phopkins/gizmo-publi

Some Stars are Totally Metal: A New Mechanism Driving Dust Across Star-Forming Clouds, and Consequences for Planets, Stars, and Galaxies

Dust grains in neutral gas behave as aerodynamic particles, so they can develop large density fluctuations independent of gas density fluctuations. Specifically, gas turbulence can drive order-of-magnitude 'resonant' fluctuations in the dust on scales where the gas stopping/drag timescale is comparable to the turbulent eddy turnover time. Here we show that for large grains (size >0.1 micron, containing most grain mass) in sufficiently large molecular clouds (radii >1-10 pc, masses >10^4 M_sun), this scale becomes larger than the characteristic sizes of pre-stellar cores (the sonic length), so large fluctuations in the dust-to-gas ratio are imprinted on cores. As a result, star clusters and protostellar disks formed in large clouds should exhibit significant abundance spreads in the elements preferentially found in large grains. This naturally predicts populations of carbon-enhanced stars, certain highly unusual stellar populations observed in nearby open clusters, and may explain the 'UV upturn' in early-type galaxies. It will also dramatically change planet formation in the resulting protostellar disks, by preferentially 'seeding' disks with an enhancement in large carbonaceous or silicate grains. The relevant threshold for this behavior scales simply with cloud densities and temperatures, making straightforward predictions for clusters in starbursts and high-redshift galaxies. Because of the selective sorting by size, this process is not necessarily visible in extinction mapping. We also predict the shape of the abundance distribution -- when these fluctuations occur, a small fraction of the cores may actually be seeded with abundances ~100 times the mean, such that they are almost 'totally metal' (Z~1)! Assuming the cores collapse, these totally metal stars would be rare (1 in 10^4 in clusters where this occurs), but represent a fundamentally new stellar evolution channel.Comment: 16 pages, 5 figures, accepted to ApJ (matches published version). Revised to expand quantitative comparisons with observations, and predictions for stellar properties and planet formatio

GIZMO: A New Class of Accurate, Mesh-Free Hydrodynamic Simulation Methods

We present two new Lagrangian methods for hydrodynamics, in a systematic comparison with moving-mesh, SPH, and stationary (non-moving) grid methods. The new methods are designed to simultaneously capture advantages of both smoothed-particle hydrodynamics (SPH) and grid-based/adaptive mesh refinement (AMR) schemes. They are based on a kernel discretization of the volume coupled to a high-order matrix gradient estimator and a Riemann solver acting over the volume 'overlap.' We implement and test a parallel, second-order version of the method with self-gravity & cosmological integration, in the code GIZMO: this maintains exact mass, energy and momentum conservation; exhibits superior angular momentum conservation compared to all other methods we study; does not require 'artificial diffusion' terms; and allows the fluid elements to move with the flow so resolution is automatically adaptive. We consider a large suite of test problems, and find that on all problems the new methods appear competitive with moving-mesh schemes, with some advantages (particularly in angular momentum conservation), at the cost of enhanced noise. The new methods have many advantages vs. SPH: proper convergence, good capturing of fluid-mixing instabilities, dramatically reduced 'particle noise' & numerical viscosity, more accurate sub-sonic flow evolution, & sharp shock-capturing. Advantages vs. non-moving meshes include: automatic adaptivity, dramatically reduced advection errors & numerical overmixing, velocity-independent errors, accurate coupling to gravity, good angular momentum conservation and elimination of 'grid alignment' effects. We can, for example, follow hundreds of orbits of gaseous disks, while AMR and SPH methods break down in a few orbits. However, fixed meshes minimize 'grid noise.' These differences are important for a range of astrophysical problems.Comment: 57 pages, 33 figures. MNRAS. A public version of the GIZMO code, user's guide, test problem setups, and movies are available at http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm

Variations in the stellar CMF and IMF: from bottom to top

We use a recently developed analytic model for the interstellar medium (ISM) structure from scales of giant molecular clouds (GMCs) through star-forming cores to explore how the pre-stellar core mass function (CMF) and, by extrapolation, stellar initial mass function (IMF) should depend on both local and galactic properties. If the ISM is supersonically turbulent, the statistical properties of the density field follow from the turbulent velocity spectrum, and the excursion set formalism can be applied to analytically calculate the mass function of collapsing cores on the smallest scales on which they are self-gravitating (non-fragmenting). Two parameters determine the model: the disc-scale Mach number M_h (which sets the shape of the CMF) and the absolute velocity/surface density (to assign an absolute scale). We show that, for normal variation in disc properties and gas temperatures in cores in the Milky Way and local galaxies, there is almost no variation in the high-mass behaviour of the CMF/IMF. The slope is always close to Salpeter down to ≲ 1 M_⊙. We predict modest variation in the sub-solar regime, mostly from variation in M_h⁠, but this is consistent with the ∼1σ observed scatter in sub-solar IMFs in local regions. For fixed global (galaxy) properties, there is little variation in shape or ‘upper mass limit’ with parent GMC mass or density. However, in extreme starbursts – ultra-luminous infrared galaxies (ULIRGs) and merging galaxy nuclei – we predict a bottom-heavy CMF. This agrees well with the IMF recently inferred for the centres of Virgo ellipticals, believed to have formed in such a process. The CMF is bottom heavy despite the gas temperature being an order of magnitude larger, because M_h is also much larger. Larger M_h values make the ‘parent’ cloud mass (the turbulent Jeans mass) larger, but promote fragmentation to smaller scales (set by the sonic mass, not the Jeans mass); this shifts the turnover mass and also steepens the slope of the low-mass CMF. The model may also predict a top-heavy CMF for the in situ star formation in the sub-pc disc around Sgr A*, but the relevant input parameters are uncertain