arXiv subjects

Philip F. Hopkins

Publications and source records attributed to Philip F. Hopkins.

At least 307 records · Page 17Linked to original sources

arXiv2016

Reconciling dwarf galaxies with LCDM cosmology: Simulating a realistic population of satellites around a Milky Way-mass galaxy

Low-mass "dwarf" galaxies represent the most significant challenges to the cold dark matter (CDM) model of cosmological structure formation. Because these faint galaxies are (best) observed within the Local Group (LG) of the Milky Way (MW) and Andromeda (M31), understanding their formation in such an environment is critical. We present first results from the Latte Project: the Milky Way on FIRE (Feedback in Realistic Environments). This simulation models the formation of a MW-mass galaxy to z = 0 within LCDM cosmology, including dark matter, gas, and stars at unprecedented resolution: baryon particle mass of 7070 Msun with gas kernel/softening that adapts down to 1 pc (with a median of 25 - 60 pc at z = 0). Latte was simulated using the GIZMO code with a mesh-free method for accurate hydrodynamics and the FIRE-2 model for star formation and explicit feedback within a multi-phase interstellar medium. For the first time, Latte self-consistently resolves the spatial scales corresponding to half-light radii of dwarf galaxies that form around a MW-mass host down to Mstar > 10^5 Msun. Latte's population of dwarf galaxies agrees with the LG across a broad range of properties: (1) distributions of stellar masses and stellar velocity dispersions (dynamical masses), including their joint relation; (2) the mass-metallicity relation; and (3) a diverse range of star-formation histories, including their mass dependence. Thus, Latte produces a realistic population of dwarf galaxies at Mstar > 10^5 Msun that does not suffer from the "missing satellites" or "too big to fail" problems of small-scale structure formation. We conclude that baryonic physics can reconcile observed dwarf galaxies with standard LCDM cosmology.

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arXiv2016

MUFASA: Galaxy Formation Simulations With Meshless Hydrodynamics

We present the MUFASA suite of cosmological hydrodynamic simulations, which employs the GIZMO meshless finite mass (MFM) code including H2-based star formation, nine-element chemical evolution, two-phase kinetic outflows following scalings from the Feedback in Realistic Environments zoom simulations, and evolving halo mass-based quenching. Our fiducial (50 Mpc/h)^3 volume is evolved to z=0 with a quarter billion particles, The predicted galaxy stellar mass functions (GSMF) reproduce observations from z=4-0 to <1.2sigma in cosmic variance, providing an unprecedented match to this key diagnostic. The cosmic star formation history and stellar mass growth show general agreement with data, with a strong archaeological downsizing trend such that dwarf galaxies form the majority of their stars after z~1. We run 25 Mpc/h and 12.5 Mpc/h volumes to z=2 with identical feedback prescriptions, the latter resolving all hydrogen-cooling halos, and the three runs display fair resolution convergence. The specific star formation rates broadly agree with data at z=0, but are underpredicted at z~2 by a factor of three, re-emphasizing a longstanding puzzle in galaxy evolution models. We compare runs using MFM and two flavours of Smoothed Particle Hydrodynamics, and show that the GSMF is sensitive to hydrodynamics methodology at the ~x2 level, which is sub-dominant to choices for parameterising feedback.

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arXiv2016

Forward and backward galaxy evolution in comoving number density space

Galaxy comoving number density is commonly used to forge progenitor/descendant links between observed galaxy populations at different epochs. However, this method breaks down in the presence of galaxy mergers, or when galaxies experience stochastic growth rates. We present a simple analytic framework to treat the physical processes that drive the evolution and diffusion of galaxies within comoving number density space. The evolution in mass rank order of a galaxy population with time is influenced by the galaxy coagulation rate and galaxy "mass rank scatter" rate. We quantify the relative contribution of these two effects to the mass rank order evolution. We show that galaxy coagulation is dominant at lower redshifts and stellar masses, while scattered growth rates dominate the mass rank evolution at higher redshifts and stellar masses. For a galaxy population at $10^{10} M_\odot$, coagulation has been the dominant effect since $z=2.2$, but a galaxy population at $10^{11} M_\odot$ was dominated by mass rank scatter until $z=0.6$. We show that although the forward and backward median number density evolution tracks are asymmetric, the backward median number density evolution can be obtained by convolving the descendant distribution function with progenitor relative abundances. We tabulate fits for the median number density evolution and scatter which can be applied to improve the way galaxy populations are linked in multi-epoch observational datasets.

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arXiv2016

Breathing FIRE: How Stellar Feedback Drives Radial Migration, Rapid Size Fluctuations, and Population Gradients in Low-Mass Galaxies

We examine the effects of stellar feedback and bursty star formation on low-mass galaxies ($M_{\rm star}=2\times10^6-5\times10^{10}{\rm M_{\odot}}$) using the FIRE (Feedback in Realistic Environments) simulations. While previous studies emphasized the impact of feedback on dark matter profiles, we investigate the impact on the stellar component: kinematics, radial migration, size evolution, and population gradients. Feedback-driven outflows/inflows drive significant radial stellar migration over both short and long timescales via two processes: (1) outflowing/infalling gas can remain star-forming, producing young stars that migrate $\sim1{\rm\,kpc}$ within their first $100 {\rm\,Myr}$, and (2) gas outflows/inflows drive strong fluctuations in the global potential, transferring energy to all stars. These processes produce several dramatic effects. First, galaxies' effective radii can fluctuate by factors of $>2$ over $\sim200 {\rm\,Myr}$, and these rapid size fluctuations can account for much of the observed scatter in radius at fixed $M_{\rm star}.$ Second, the cumulative effects of many outflow/infall episodes steadily heat stellar orbits, causing old stars to migrate outward most strongly. This age-dependent radial migration mixes---and even inverts---intrinsic age and metallicity gradients. Thus, the galactic-archaeology approach of calculating radial star-formation histories from stellar populations at $z=0$ can be severely biased. These effects are strongest at $M_{\rm star}\approx10^{7-9.6}{\rm M_{\odot}}$, the same regime where feedback most efficiently cores galaxies. Thus, detailed measurements of stellar kinematics in low-mass galaxies can strongly constrain feedback models and test baryonic solutions to small-scale problems in $Λ$CDM.

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arXiv2016

Binary Stars Can Provide the "Missing Photons" Needed for Reionization

Empirical constraints on reionization require galactic ionizing photon escape fractions fesc>20%, but recent high-resolution radiation-hydrodynamic calculations have consistently found much lower values ~1-5%. While these models include strong stellar feedback and additional processes such as runaway stars, they almost exclusively consider stellar evolution models based on single (isolated) stars, despite the fact that most massive stars are in binaries. We re-visit these calculations, combining radiative transfer and high-resolution cosmological simulations from the Feedback in Realistic Environments (FIRE) project. For the first time, we use a stellar evolution model that includes a physically and observationally motivated treatment of binaries (the BPASS model). Binary mass transfer and mergers enhance the population of massive stars at late times (>3 Myr) after star formation, which in turn strongly enhances the late-time ionizing photon production (especially at low metallicities). These photons are produced after feedback from massive stars has carved escape channels in the ISM, and so efficiently leak out of galaxies. As a result, the time-averaged "effective" escape fraction (ratio of escaped ionizing photons to observed 1500 A photons) increases by factors 4-10, sufficient to explain reionization. While important uncertainties remain, we conclude that binary evolution may be critical for understanding the ionization of the Universe.

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arXiv2016

Gravitational torque-driven black hole growth and feedback in cosmological simulations

We investigate black hole-host galaxy scaling relations in cosmological simulations with a self-consistent black hole growth and feedback model. The sub-grid accretion model captures the key scalings governing angular momentum transport from galactic scales down to parsec scales, while our kinetic feedback implementation enables the injection of outflows with properties chosen to match observed nuclear outflows. We show that "quasar mode" feedback can have a large impact on the thermal properties of the intergalactic medium and the growth of galaxies and massive black holes for kinetic feedback efficiencies as low as 0.1% relative to the bolometric luminosity. Nonetheless, our simulations suggest that the black hole-host scaling relations are only weakly dependent on the effects of black hole feedback on galactic scales, owing to feedback suppressing the growth of galaxies and massive black holes by a similar amount. In contrast, the rate at which gravitational torques feed the central black hole relative to the host galaxy star formation rate governs the slope and normalization of the black hole-host correlations. Our results suggest that a common gas supply regulated by gravitational torques is the primary driver of the observed co-evolution of black holes and galaxies.

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arXiv2016

Star Formation in a Turbulent Framework: From Giant Molecular Clouds to Protostars

Turbulence is thought to be a primary driving force behind the early stages of star formation. In this framework large, self gravitating, turbulent clouds fragment into smaller clouds which in turn fragment into even smaller ones. At the end of this cascade we find the clouds which collapse into protostars. Following this process is extremely challenging numerically due to the large dynamical range so in this paper we propose a semi analytic framework which is able to follow star formation from the largest, giant molecular cloud (GMC) scale, to the final protostellar size scale. Due to the simplicity of the framework it is ideal for theoretical experimentation to explore the principal processes behind different aspects of star formation, at the cost of strong assumptions. The basic version of the model discussed in this paper only contains turbulence, gravity and crude assumptions about feedback, nevertheless it can reproduce the observed core mass function (CMF) and provide the protostellar system mass function (PSMF), which shows a striking resemblance to the observed IMF. Furthermore we find that to produce a universal IMF protostellar feedback must be taken into account otherwise the PSMF peak shows a strong dependence on the background temperature.

astro-ph.SR↗

arXiv2016

Stellar and Quasar Feedback in Concert: Effects on AGN Accretion, Obscuration, and Outflows

We study the interaction of feedback from active galactic nuclei (AGN) and a multi-phase interstellar medium (ISM), in simulations including explicit stellar feedback, multi-phase cooling, accretion-disk winds, and Compton heating. We examine radii ~0.1-100 pc around a black hole (BH), where the accretion rate onto the BH is determined and where AGN-powered winds and radiation couple to the ISM. We conclude: (1) The BH accretion rate is determined by exchange of angular momentum between gas and stars in gravitational instabilities. This produces accretion rates ~0.03-1 Msun/yr, sufficient to power luminous AGN. (2) The gas disk in the galactic nucleus undergoes an initial burst of star formation followed by several Myrs where stellar feedback suppresses the star formation rate (SFR). (3) AGN winds injected at small radii with momentum fluxes ~L/c couple efficiently to the ISM and have dramatic effects on ISM properties within ~100 pc. AGN winds suppress the nuclear SFR by factors ~10-30 and BH accretion rate by factors ~3-30. They increase the outflow rate from the nucleus by factors ~10, consistent with observational evidence for galaxy-scale AGN-driven outflows. (4) With AGN feedback, the predicted column density distribution to the BH is consistent with observations. Absent AGN feedback, the BH is isotropically obscured and there are not enough optically-thin sightlines to explain Type-I AGN. A 'torus-like' geometry arises self-consistently as AGN feedback evacuates gas in polar regions.

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arXiv2016

Evolution of Intrinsic Scatter in the SFR-Stellar Mass Correlation at 0.5<z<3

We present estimates of intrinsic scatter in the Star Formation Rate (SFR) - Stellar Mass (M*) correlation in the redshift range 0.5 < z < 3.0 and in the mass range 10^7 < M* < 10^11 Msun. We utilize photometry in the Hubble Ultradeep Field (HUDF12), Ultraviolet Ultra Deep Field (UVUDF) campaigns and CANDELS/GOODS-S. We estimate SFR, M* from broadband Spectral Energy Distributions (SEDs) and the best available redshifts. The maximum depth of the HUDF photometry (F160W 29.9 AB, 5 sigma depth) probes the SFR-M* correlation down to M* ~ 10 ^7 Msun, a factor of 10-100X lower in M* than previous studies, and comparable to dwarf galaxies in the local universe. We find the slope of the SFR-M* relationship to be near unity at all redshifts and the normalization to decrease with cosmic time. We find a moderate increase in intrinsic scatter with cosmic time from 0.2 to 0.4 dex across the epoch of peak cosmic star formation. None of our redshift bins show a statistically significant increase in intrinsic scatter at low mass. However, it remains possible that intrinsic scatter increases at low mass on timescales shorter than ~ 100 Myr. Our results are consistent with a picture of gradual and self-similar assembly of galaxies across more than three orders of magnitude in stellar mass from as low as 10^7 Msun.

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arXiv2016

An instability of feedback regulated star formation in galactic nuclei

We examine the stability of feedback-regulated star formation (SF) in galactic nuclei and contrast it to SF in extended discs. In galactic nuclei the dynamical time becomes shorter than the time over which feedback from young stars evolves. We argue analytically that the balance between stellar feedback and gravity is unstable in this regime. We study this using numerical simulations with pc-scale resolution and explicit stellar feedback taken from stellar evolution models. The nuclear gas mass, young stellar mass, and SFR within the central ~100 pc (the short-timescale regime) never reach steady-state, but instead go through dramatic, oscillatory cycles. Stars form until a critical surface density of young stars is present (such that feedback overwhelms gravity), at which point they begin to expel gas from the nucleus. Since the dynamical times are shorter than the stellar evolution times, the stars do not die as the gas is expelled, but continue to push, triggering a runaway quenching of star formation in the nucleus. However the expelled gas is largely not unbound from the galaxy, but goes into a galactic fountain which re-fills the nuclear region after the massive stars from the previous burst cycle have died off (~50 Myr timescale). On large scales (>1 kpc), the galaxy-scale gas content and SFR is more stable. We examine the consequences of this episodic nuclear star formation for the Kennicutt-Schmidt (KS) relation: while a tight KS relation exists on ~1 kpc scales in good agreement with observations, the scatter increases dramatically in smaller apertures centered on galactic nuclei.

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arXiv2016

The Necessity of Feedback Physics in Setting the Peak of the Initial Mass Function

A popular theory of star formation is gravito-turbulent fragmentation, in which self-gravitating structures are created by turbulence-driven density fluctuations. Simple theories of isothermal fragmentation successfully reproduce the core mass function (CMF) which has a very similar shape to the initial mass function (IMF) of stars. However, numerical simulations of isothermal turbulent fragmentation thus far have not succeeded in identifying a fragment mass scale that is independent of the simulation resolution. Moreover, the fluid equations for magnetized, self-gravitating, isothermal turbulence are scale-free, and do not predict any characteristic mass. In this paper we show that, although an isothermal self-gravitating flow does produce a CMF with a mass scale imposed by the initial conditions, this scale changes as the parent cloud evolves. In addition, the cores that form undergo further fragmentation and after sufficient time forget about their initial conditions, yielding a scale-free pure power-law distribution $\mathrm{d} N/\mathrm{d} M\propto M^{-2}$ for the stellar IMF. We show that this problem can be alleviated by introducing additional physics that provides a termination scale for the cascade. Our candidate for such physics is a simple model for stellar radiation feedback. Radiative heating, powered by accretion onto forming stars, arrests the fragmentation cascade and imposes a characteristic mass scale that is nearly independent of the time-evolution or initial conditions in the star-forming cloud, and that agrees well with the peak of the observed IMF. In contrast, models that introduce a stiff equation of state for denser clouds but that do not explicitly include the effects of feedback do not yield an invariant IMF.

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arXiv2016

The formation of massive, quiescent galaxies at cosmic noon

The cosmic noon (z~1.5-3) marked a period of vigorous star formation for most galaxies. However, about a third of the more massive galaxies at those times were quiescent in the sense that their observed stellar populations are inconsistent with rapid star formation. The reduced star formation activity is often attributed to gaseous outflows driven by feedback from supermassive black holes, but the impact of black hole feedback on galaxies in the young Universe is not yet definitively established. We analyze the origin of quiescent galaxies with the help of ultra-high resolution, cosmological simulations that include feedback from stars but do not model the uncertain consequences of black hole feedback. We show that dark matter halos with specific accretion rates below ~0.25-0.4 per Gyr preferentially host galaxies with reduced star formation rates and red broad-band colors. The fraction of such halos in large dark matter only simulations matches the observed fraction of massive quiescent galaxies (~10^10-10^11 Msun). This strongly suggests that halo accretion rate is the key parameter determining which massive galaxies at z~1.5-3 become quiescent. Empirical models that connect galaxy and halo evolution, such as halo occupation distribution or abundance matching models, assume a tight link between galaxy properties and the masses of their parent halos. These models will benefit from adding the specific accretion rate of halos as a second model parameter.

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arXiv2015

Do We Expect Most AGN to Live in Disks?

Recent observations have indicated that a large fraction of the low to intermediate luminosity AGN population lives in disk-dominated hosts, while the more luminous quasars live in bulge-dominated hosts, in conflict with some previous model predictions. We therefore build and compare a semi-empirical model for AGN fueling which accounts for both merger and non-merger 'triggering.' In particular, we show that the 'stochastic accretion' model - in which fueling in disk galaxies is essentially a random process arising whenever dense gas clouds reach the nucleus - provides a good match to the present observations at low/intermediate luminosities. However it falls short of the high-luminosity population. We combine this with models for major merger-induced AGN fueling, which lead to rarer but more luminous events, and predict the resulting abundance of disk-dominated and bulge-dominated AGN host galaxies as a function of luminosity and redshift. We compile and compare observational constraints from z~0-2. The models and observations generically show a transition from disk to bulge dominance in hosts near the Seyfert-quasar transition, at all redshifts. 'Stochastic' fueling dominates AGN by number (dominant at low luminosity), and dominates BH growth below the knee in the present-day BH mass function (<10^7 M_sun). However it accounts for just ~10% of BH mass growth at masses >10^8 M_sun. In total, fueling in disky hosts accounts for ~30% of the total AGN luminosity density/BH mass density. The combined model also accurately predicts the AGN luminosity function and clustering/bias as a function of luminosity and redshift; however, we argue that these are not sensitive probes of BH fueling mechanisms.

astro-ph.CO↗

arXiv2015

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.

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arXiv2015

Accurate, Meshless Methods for Magneto-Hydrodynamics

Recently, we developed a pair of meshless finite-volume Lagrangian methods for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite volume' (MFV) methods. These capture advantages of both smoothed-particle hydrodynamics (SPH) and adaptive mesh-refinement (AMR) schemes. Here, we extend these to include ideal magneto-hydrodynamics (MHD). The MHD equations are second-order consistent and conservative. We augment these with a divergence-cleaning scheme, which maintains div*B~0 to high accuracy. We implement these in the code GIZMO, together with a state-of-the-art implementation of SPH MHD. In every one of a large suite of test problems, the new methods are competitive with moving-mesh and AMR schemes using constrained transport (CT) to ensure div*B=0. They are able to correctly capture the growth and structure of the magneto-rotational instability (MRI), MHD turbulence, and the launching of magnetic jets, in some cases converging more rapidly than AMR codes. Compared to SPH, the MFM/MFV methods exhibit proper convergence at fixed neighbor number, sharper shock capturing, and dramatically reduced noise, div*B errors, and diffusion. Still, 'modern' SPH is able to handle most of our tests, at the cost of much larger kernels and 'by hand' adjustment of artificial diffusion parameters. Compared to AMR, the new meshless methods exhibit enhanced 'grid noise' but reduced advection errors and numerical diffusion, velocity-independent errors, and superior angular momentum conservation and coupling to N-body gravity solvers. As a result they converge more slowly on some problems (involving smooth, slowly-moving flows) but more rapidly on others (involving advection or rotation). In all cases, divergence-control beyond the popular Powell 8-wave approach is necessary, or else all methods we consider will systematically converge to unphysical solutions.

astro-ph.IM↗

arXiv2015

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.

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arXiv2015

The Fundamentally Different Dynamics of Dust and Gas in Molecular Clouds

We study the behavior of large dust grains in turbulent molecular clouds (MCs). In primarily neutral regions, dust grains move as aerodynamic particles, not necessarily with the gas. We therefore directly simulate, for the first time, the behavior of aerodynamic grains in highly supersonic, magnetohydrodynamic turbulence typical of MCs. We show that, under these conditions, grains with sizes a >0.01 micron exhibit dramatic (exceeding factor ~1000) fluctuations in the local dust-to-gas ratio (implying large small-scale variations in abundances, dust cooling rates, and dynamics). The dust can form highly filamentary structures (which would be observed in both dust emission and extinction), which can be much thinner than the characteristic width of gas filaments. Sometimes, the dust and gas filaments are not even in the same location. The 'clumping factor' of the dust (critical for dust growth/coagulation/shattering) can reach ~100, for grains in the ideal size range. The dust clustering is maximized around scales ~0.2pc*(a/micron)*(100 cm^-3/n_gas), and is 'averaged out' on larger scales. However, because the density varies widely in supersonic turbulence, the dynamic range of scales (and interesting grain sizes) for these fluctuations is much broader than in the subsonic case. Our results are applicable to MCs of essentially all sizes and densities, but we note how Lorentz forces and other physics (neglected here) may change them in some regimes. We discuss the potentially dramatic consequences for star formation, dust growth and destruction, and dust-based observations of MCs.

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arXiv2015

Jumping the Gap: The Formation Conditions and Mass Function of Pebble-Pile Planetesimals

In a turbulent proto-planetary disk, dust grains undergo large density fluctuations and under the right circumstances, these grain overdensities can overcome shear, turbulent, and gas pressure support to collapse under self-gravity (forming a "pebble pile" planetesimal). Using a simple analytic model for the fluctuations predicted in simulations, we estimate the rate-of-formation and mass function of self-gravitating, rapidly-collapsing planetesimal-mass bodies formed by this mechanism. The statistics of this process depend sensitively on the size/stopping time of the grains, disk surface density, and turbulent Mach numbers. However, when it occurs, we predict that the resulting planetesimal mass function is broad and quasi-universal, with a slope dN/dM~1/M^(1-2), spanning a size/mass range ~10-1e4 km (~1e-9-5.0 M_Earth). Collapse to planetesimal through super-Earth masses is possible. The key condition is that grain density fluctuations reach large amplitudes on large scales, where gravitational instability proceeds most easily (collapse of small grains is strongly suppressed by turbulent vorticity). We show this leads to a new criterion for 'pebble-pile' formation in terms of the dimensionless particle stopping time (tau_stop > f(Q,Z,alpha)). In a MMSN, this requires grains larger than a=(50,1,0.1)cm at r=(1,30,100)au. At small radii, it would depend on the existence of large boulders. However, because density fluctuations depend super-exponentially on tau_stop (inversely proportional to disk surface density), lower-density disks are more unstable. In fact, we predict that cm-sized grains at ~1au will form pebble piles in a disk with ~10% the MMSN density, so planet formation at ~au may generically occur late, as disks are evaporating. We also predict that conditions become progressively more favorable for pebble-pile formation around lower-mass, cooler stars.

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