arXiv subjects

Jacob B. Simon

Publications and source records attributed to Jacob B. Simon.

At least 55 records · Page 3Linked to original sources

arXiv2018

Origin of Weak Turbulence in the Outer Regions of Protoplanetary Disks

The mechanism behind angular momentum transport in protoplanetary disks, and whether this transport is turbulent in nature, is a fundamental issue in planet formation studies. Recent ALMA observations have suggested that turbulent velocities in the outer regions of these disks are less than ~5-10% of the sound speed, contradicting theoretical predictions of turbulence driven by the magnetorotational instability (MRI). These observations have generally been interpreted to be consistent with a large-scale laminar magnetic wind driving accretion. Here, we carry out local, shearing box simulations with varying ionization levels and background magnetic field strengths in order to determine which parameters produce results consistent with observations. We find that even when the background magnetic field launches a strong largely laminar wind, significant turbulence persists and is driven by localized regions of vertical magnetic field (the result of zonal flows) that are unstable to the MRI. The only conditions for which we find turbulent velocities below the observational limits are weak background magnetic fields and ionization levels well below that usually assumed in theoretical studies. We interpret these findings within the context of a preliminary model in which a large scale magnetic field, confined to the inner disk, hinders ionizing sources from reaching large radial distances, e.g., through a sufficiently dense wind. Thus, in addition to such a wind, this model predicts that for disks with weakly turbulent outer regions, the outer disk will have significantly reduced ionization levels compared to standard models and will harbor only a weak vertical magnetic field.

astro-ph.SR↗

arXiv2018

On the Numerical Robustness of the Streaming Instability: Particle Concentration and Gas Dynamics in Protoplanetary Disks

The Streaming Instability (SI) is a mechanism to concentrate solids in protoplanetary disks. Nonlinear particle clumping from the SI can trigger gravitational collapse into planetesimals. To better understand the numerical robustness of the SI, we perform a suite of vertically-stratified 3D simulations with fixed physical parameters known to produce strong clumping. We vary the numerical implementation, namely the computational domain size and the vertical boundary conditions (vBCs), comparing newly-implemented outflow vBCs to the previously-used periodic and reflecting vBCs. We find strong particle clumping by the SI is mostly independent of the vBCs. However, peak particle densities are higher in larger simulation domains due to a larger particle mass reservoir. We report SI-triggered zonal flows, i.e., azimuthally-banded radial variations of gas pressure. These structures have low amplitudes, insufficient to halt particle radial drift, confirming that particle trapping in gas pressure maxima is not the mechanism of the SI. We find that outflow vBCs produce artificially large gas outflow rates at vertical boundaries. However, the outflow vBCs reduce artificial reflections at vertical boundaries, allowing more particle sedimentation, and showing less temporal variation and better convergence with box size. The radial spacing of dense particle filaments is $\sim0.15$ gas scale heights ($H$) for all vBCs, which sets the feeding zone for planetesimal growth in self-gravitating simulations. Our results validate the use of the outflow vBCs in SI simulations, even with vertical boundaries close ($\leq 0.4H$) to the disk midplane. Overall, our study demonstrates the numerical robustness of nonlinear particle clumping by the SI.

astro-ph.EP↗

arXiv2018

Turbulence in the TW Hya Disk

Turbulence is a fundamental parameter in models of grain growth during the early stages of planet formation. As such, observational constraints on its magnitude are crucial. Here we self-consistently analyze ALMA CO(2-1), SMA CO(3-2), and SMA CO(6-5) observations of the disk around TW Hya and find an upper limit on the turbulent broadening of $<$0.08c$_s$ ($α<$0.007 for $α$ defined only within 2-3 pressure scale heights above the midplane), lower than the tentative detection previously found from an analysis of the CO(2-1) data. We examine in detail the challenges of image plane fitting vs directly fitting the visibilities, while also considering the role of the vertical temperature gradient, systematic uncertainty in the amplitude calibration, and assumptions about the CO abundance, as potential sources of the discrepancy in the turbulence measurements. These tests result in variations of the turbulence limit between $<$0.04c$_s$ and $<$0.13c$_s$, consistently lower than the 0.2-0.4c$_s$ found previously. Having ruled out numerous factors, we restrict the source of the discrepancy to our assumed coupling between temperature and density through hydrostatic equilibrium in the presence of a vertical temperature gradient and/or the confinement of CO to a thin molecular layer above the midplane, although further work is needed to quantify the influence of these prescriptions. Assumptions about hydrostatic equilibrium and the CO distribution are physically motivated, and may have a small influence on measuring the kinematics of the gas, but they become important when constraining small effects such as the strength of the turbulence within a protoplanetary disk.

astro-ph.EP↗

arXiv2017

Evidence for universality in the initial planetesimal mass function

Planetesimals may form from the gravitational collapse of dense particle clumps initiated by the streaming instability. We use simulations of aerodynamically coupled gas-particle mixtures to investigate whether the properties of planetesimals formed in this way depend upon the sizes of the particles that participate in the instability. Based on three high resolution simulations that span a range of dimensionless stopping time $6 \times 10^{-3} \leq τ\leq 2$ no statistically significant differences in the initial planetesimal mass function are found. The mass functions are fit by a power-law, ${\rm d}N / {\rm d}M_p \propto M_p^{-p}$, with $p=1.5-1.7$ and errors of $Δp \approx 0.1$. Comparing the particle density fields prior to collapse, we find that the high wavenumber power spectra are similarly indistinguishable, though the large-scale geometry of structures induced via the streaming instability is significantly different between all three cases. We interpret the results as evidence for a near-universal slope to the mass function, arising from the small-scale structure of streaming-induced turbulence.

astro-ph.EP↗

arXiv2017

A Three-Dimensional View of Turbulence: Constraints on Turbulent Motions in the HD 163296 Protoplanetary Disk using DCO$^+$

Gas kinematics are an important part of the planet formation process. Turbulence influences planetesimal growth and migration from the scale of sub-micron dust grains through gas-giant planets. Radio observations of resolved molecular line emission can directly measure this non-thermal motion and, taking advantage of the layered chemical structure of disks, different molecular lines can be combined to map the turbulence throughout the vertical extent of a protoplanetary disk. Here we present ALMA observations of three molecules (DCO$^+$(3-2), C$^{18}$O(2-1) and CO(2-1)) from the disk around HD 163296. We are able to place stringent upper limits ($v_{\rm turb}<$0.06c$_s$, $<$0.05c$_s$ and $<$0.04c$_s$ for CO(2-1), C$^{18}$O(2-1) and DCO$^+$(3-2) respectively), corresponding to $α\lesssim$3$\times$10$^{-3}$, similar to our prior limit derived from CO(3-2). This indicates that there is little turbulence throughout the vertical extent of the disk, contrary to theoretical predictions based on the magneto-rotational instability and gravito-turbulence. In modeling the DCO$^+$ emission we also find that it is confined to three concentric rings at 65.7$\pm$0.9 au, 149.9$^{+0.5}_{-0.7}$ au and 259$\pm$1 au, indicative of a complex chemical environment.

astro-ph.EP↗

arXiv2016

Prompt planetesimal formation beyond the snow line

We develop a simple model to predict the radial distribution of planetesimal formation. The model is based on the observed growth of dust to mm-sized particles, which drift radially, pile-up, and form planetesimals where the stopping time and dust-to-gas ratio intersect the allowed region for streaming instability-induced gravitational collapse. Using an approximate analytic treatment, we first show that drifting particles define a track in metallicity--stopping time space whose only substantial dependence is on the disk's angular momentum transport efficiency. Prompt planetesimal formation is feasible for high particle accretion rates (relative to the gas, $\dot{M}_p / \dot{M} > 3 \times 10^{-2}$ for $α= 10^{-2}$), that could only be sustained for a limited period of time. If it is possible, it would lead to the deposition of a broad and massive belt of planetesimals with a sharp outer edge. Including turbulent diffusion and vapor condensation processes numerically, we find that a modest enhancement of solids near the snow line occurs for cm-sized particles, but that this is largely immaterial for planetesimal formation. We note that radial drift couples planetesimal formation across radii in the disk, and suggest that considerations of planetesimal formation favor a model in which the initial deposition of material for giant planet cores occurs well beyond the snow line.

astro-ph.EP↗

arXiv2016

The Influence of Magnetic Field Geometry on the Formation of Close-in Exoplanets

Approximately half of Sun-like stars harbor exoplanets packed within a radius of ~0.3 AU, but the formation of these planets and why they form in only half of known systems are still not well understood. We employ a one-dimensional steady state model to gain physical insight into the origin of these close-in exoplanets. We use Shakura & Sunyaev alpha values extracted from recent numerical simulations of protoplanetary disk accretion processes in which the magnitude of alpha, and thus the steady-state gas surface density, depends on the orientation of large scale magnetic fields with respect to the disk's rotation axis. Solving for the metallicity as a function of radius, we find that for fields anti-aligned with the rotation axis, the inner regions of our model disk often falls within a region of parameter space not suitable for planetesimal formation, whereas in the aligned case, the inner disk regions are likely to produce planetesimals through some combination of streaming instability and gravitational collapse, though the degree to which this is true depends on the assumed parameters of our model. More robustly, the aligned field case always produces higher concentrations of solids at small radii compared to the anti-aligned case. In the in situ formation model, this bimodal distribution of solid enhancement leads directly to the observed dichotomy in exoplanet orbital distances.

astro-ph.EP↗

arXiv2016

Turbulence, Transport and Waves in Ohmic Dead Zones

We use local numerical simulations to study a vertically stratified accretion disk with a resistive mid-plane that damps magnetohydrodynamic (MHD) turbulence. This is an idealized model for the dead zones that may be present at some radii in protoplanetary and dwarf novae disks. We vary the relative thickness of the dead and active zones to quantify how forced fluid motions in the dead zone change. We find that the residual Reynolds stress near the mid-plane decreases with increasing dead zone thickness, becoming negligible in cases where the active to dead mass ratio is less than a few percent. This implies that purely Ohmic dead zones would be vulnerable to episodic accretion outbursts via the mechanism of Martin & Lubow (2011). We show that even thick dead zones support a large amount of kinetic energy, but this energy is largely in fluid motions that are inefficient at angular momentum transport. Confirming results from Oishi & Mac Low (2009), the perturbed velocity field in the dead zone is dominated by an oscillatory, vertically extended circulation pattern with a low frequency compared to the orbital frequency. This disturbance has the properties predicted for the lowest order r mode in a hydrodynamic disk. We suggest that in a global disk similar excitations would lead to propagating waves, whose properties would vary with the thickness of the dead zone and the nature of the perturbations (isothermal or adiabatic). Flows with similar amplitudes would buckle settled particle layers and could reduce the efficiency of pebble accretion.

astro-ph.SR↗

arXiv2016

Strongly magnetized accretion discs require poloidal flux

Motivated by indirect observational evidence for strongly magnetized accretion discs around black holes, and the novel theoretical properties of such solutions, we investigate how a strong magnetization state can develop and persist. To this end, we perform local simulations of accretion discs with an initially purely toroidal magnetic field of equipartition strength. We demonstrate that discs with zero net vertical magnetic flux and realistic boundary conditions cannot sustain a strong toroidal field. However, a magnetic pressure-dominated disc can form from an initial configuration with a sufficient amount of net vertical flux and realistic boundary conditions. Our results suggest that poloidal flux is a necessary prerequisite for the sustainability of strongly magnetized accretion discs.

astro-ph.HE↗

arXiv2016

The Mass and Size Distribution of Planetesimals Formed by the Streaming Instability. I. The Role of Self-Gravity

We study the formation of planetesimals in protoplanetary disks from the gravitational collapse of solid over-densities generated via the streaming instability. To carry out these studies, we implement and test a particle-mesh self-gravity module for the Athena code that enables the simulation of aerodynamically coupled systems of gas and collisionless self-gravitating solid particles. Upon employment of our algorithm to planetesimal formation simulations, we find that (when a direct comparison is possible) the Athena simulations yield predicted planetesimal properties that agree well with those found in prior work using different numerical techniques. In particular, the gravitational collapse of streaming-initiated clumps leads to an initial planetesimal mass function that is well-represented by a power-law, dN/dM ~ M^{-p}, with p = 1.6 +/- 0.1, which equates to a differential size distribution dN/dR ~ R^{-q}, with q = 2.8 +/- 0.1. We find no significant trends with resolution from a convergence study of up to 512^3 grid zones and Npar = 1.5x10^8 particles. Likewise, the power-law slope appears indifferent to changes in the relative strength of self-gravity and tidal shear, and to the time when (for reasons of numerical economy) self-gravity is turned on, though the strength of these claims is limited by small number statistics. For a typically assumed radial distribution of minimum mass solar nebula solids (assumed here to have dimensionless stopping time τ= 0.3), our results support the hypothesis that bodies on the scale of large asteroids or Kuiper Belt Objects could have formed as the high-mass tail of a primordial planetesimal population.

astro-ph.SR↗

arXiv2016

Accretion disc dynamo activity in local simulations spanning weak-to-strong net vertical magnetic flux regimes

Strongly magnetized accretion discs around black holes have attractive features that may explain enigmatic aspects of X-ray binary behaviour. The structure and evolution of these discs are governed by a dynamo-like mechanism, which channels part of the accretion power liberated by the magnetorotational instability (MRI) into an ordered toroidal magnetic field. To study dynamo activity, we performed three-dimensional, stratified, isothermal, ideal magnetohydrodynamic shearing box simulations. The strength of the self-sustained toroidal magnetic field depends on the net vertical magnetic flux, which we vary across almost the entire range over which the MRI is linearly unstable. We quantify disc structure and dynamo properties as a function of the initial ratio of mid-plane gas pressure to vertical magnetic field pressure, $β_0^{\rm mid} = p_{\rm gas} / p_B$. For $10^5 \geq β_0^{\rm mid} \geq 10$ the effective $α$-viscosity parameter scales as a power-law. Dynamo activity persists up to and including $β_0^{\rm mid} = 10^2$, at which point the entire vertical column of the disc is magnetic pressure-dominated. Still stronger fields result in a highly inhomogeneous disc structure, with large density fluctuations. We show that the turbulent steady state $β^{\rm mid}$ in our simulations is well-matched by the analytic model of Begelman et al. (2015) describing the creation and buoyant escape of toroidal field, while the vertical structure of the disc can be broadly reproduced using this model. Finally, we discuss the implications of our results for observed properties of X-ray binaries.

astro-ph.HE↗

arXiv2015

Weak Turbulence in the HD 163296 Protoplanetary Disk Revealed by ALMA CO Observations

Turbulence can transport angular momentum in protoplanetary disks and influence the growth and evolution of planets. With spatially and spectrally resolved molecular emission line measurements provided by (sub)millimeter interferometric observations, it is possible to directly measure non-thermal motions in the disk gas that can be attributed to this turbulence. We report a new constraint on the turbulence in the disk around HD 163296, a nearby young A star, determined from ALMA Science Verification observations of four CO emission lines (the CO(3-2), CO(2-1), 13CO(2-1), and C18O(2-1) transitions). The different optical depths for these lines permit probes of non-thermal line-widths at a range of physical conditions (temperature and density) and depths into the disk interior. We derive stringent limits on the non-thermal motions in the upper layers of the outer disk such that any contribution to the line-widths from turbulence is <3% of the local sound speed. These limits are approximately an order of magnitude lower than theoretical predictions for full-blown MHD turbulence driven by the magneto-rotational instability, potentially suggesting that this mechanism is less efficient in the outer (R>30AU) disk than has been previously considered.

astro-ph.SR↗

arXiv2015

Magnetically driven accretion in protoplanetary discs

We characterize magnetically driven accretion at radii between 1 au and 100 au in protoplanetary discs, using a series of local non-ideal magnetohydrodynamic (MHD) simulations. The simulations assume a Minimum Mass Solar Nebula (MMSN) disc that is threaded by a net vertical magnetic field of specified strength. Confirming previous results, we find that the Hall effect has only a modest impact on accretion at 30 au, and essentially none at 100 au. At 1-10 au the Hall effect introduces a pronounced bi-modality in the accretion process, with vertical magnetic fields aligned to the disc rotation supporting a strong laminar Maxwell stress that is absent if the field is anti-aligned. In the anti-aligned case, we instead find evidence for bursts of turbulent stress at 5-10 au, which we tentatively identify with the non-axisymmetric Hall-shear instability. The presence or absence of these bursts depends upon the details of the adopted chemical model, which suggests that appreciable regions of actual protoplanetary discs might lie close to the borderline between laminar and turbulent behaviour. Given the number of important control parameters that have already been identified in MHD models, quantitative predictions for disc structure in terms of only radius and accretion rate appear to be difficult. Instead, we identify robust qualitative tests of magnetically driven accretion. These include the presence of turbulence in the outer disc, independent of the orientation of the vertical magnetic fields, and a Hall-mediated bi-modality in turbulent properties extending from the region of thermal ionization to 10 au.

astro-ph.SR↗

arXiv2015

Signatures of MRI-Driven Turbulence in Protoplanetary Disks: Predictions for ALMA Observations

Spatially resolved observations of molecular line emission have the potential to yield unique constraints on the nature of turbulence within protoplanetary disks. Using a combination of local non-ideal magnetohydrodynamic simulations and radiative transfer calculations, tailored to properties of the disk around HD 163296, we assess the ability of ALMA to detect turbulence driven by the magnetorotational instability (MRI). Our local simulations show that the MRI produces small-scale turbulent velocity fluctuations that increase in strength with height above the mid-plane. For a set of simulations at different disk radii, we fit a Maxell-Boltzmann distribution to the turbulent velocity and construct a turbulent broadening parameter as a function of radius and height. We input this broadening into radiative transfer calculations to quantify observational signatures of MRI-driven disk turbulence. We find that the ratio of the peak line flux to the flux at line center is a robust diagnostic of turbulence that is only mildly degenerate with systematic uncertainties in disk temperature. For the CO(3-2) line, which we expect to probe the most magnetically active slice of the disk column, variations in the predicted peak-to-trough ratio between our most and least turbulent models span a range of approximately 15%. Additional independent constraints can be derived from the morphology of spatially resolved line profiles, and we estimate the resolution required to detect turbulence on different spatial scales. We discuss the role of lower optical depth molecular tracers, which trace regions closer to the disk mid-plane where velocities in MRI-driven models are systematically lower.

astro-ph.SR↗

arXiv2014

Efficiency of Particle Trapping in the Outer Regions of Protoplanetary Disks

We investigate the strength of axisymmetric local pressure maxima (zonal flows) in the outer regions of protoplanetary disks, where ambipolar diffusion reduces turbulent stresses driven by the magnetorotational instability. Using local numerical simulations we show that in the absence of net vertical magnetic fields, the strength of turbulence in the ambipolar dominated region of the disk is low and any zonal flows that are present are weak. For net fields strong enough to yield observed protostellar accretion rates, however, zonal flows with a density amplitude of 10-20% are formed. These strengths are comparable to those seen in simulations of ideal MHD disk turbulence. We investigate whether these zonal flows are able to reverse the inward radial drift of solids, leading to prolonged and enhanced concentration as a prelude to planetesimal formation. For commonly assumed mean surface density profiles (surface density proportional to radius to the -1/2 power or steeper) we find that the predicted perturbations to the background disk profile do not correspond to local pressure maxima. This is a consequence of radial width of the simulated zonal flows, which is larger than was assumed in prior analytic models of particle trapping. These larger scale flows would only trap particles for higher amplitude fluctuations than observed. We conclude that zonal flows are likely to be present in the outer regions of protoplanetary disks and are potentially large enough to be observable, but are unlikely to lead to strong particle trapping.

astro-ph.SR↗

arXiv2013

Quantifying energetics and dissipation in magnetohydrodynamic turbulence

We perform a suite of two- and three-dimensional magnetohydrodynamic (MHD) simulations with the Athena code of the non-driven Kelvin-Helmholtz instability in the subsonic, weak magnetic field limit. Focusing the analysis on the non-linear turbulent regime, we quantify energy transfer on a scale-by-scale basis and identify the physical mechanisms responsible for energy exchange by developing the diagnostic known as spectral energy transfer function analysis. At late times when the fluid is in a state of MHD turbulence, magnetic tension mediates the dominant mode of energy injection into the magnetic reservoir, whereby turbulent fluid motions twist and stretch the magnetic field lines. This generated magnetic energy turbulently cascades to smaller scales, while being exchanged backwards and forwards with the kinetic energy reservoir, until finally being dissipated. Incorporating explicit dissipation pushes the dissipation scale to larger scales than if the dissipation were entirely numerical. For scales larger than the dissipation scale, we show that the physics of energy transfer in decaying MHD turbulence is robust to numerical effects.

astro-ph.HE↗

arXiv2013

Two timescale dispersal of magnetized protoplanetary disks

Protoplanetary disks are likely to be threaded by a weak net flux of vertical magnetic field that is a remnant of the much larger fluxes present in molecular cloud cores. If this flux is approximately conserved its dynamical importance will increase as mass is accreted, initially by stimulating magnetorotational disk turbulence and subsequently by enabling wind angular momentum loss. We use fits to numerical simulations of ambipolar dominated disk turbulence to construct simplified one dimensional evolution models for weakly magnetized protoplanetary disks. We show that the late onset of significant angular momentum loss in a wind can give rise to "two timescale" disk evolution in which a long phase of viscous evolution precedes rapid dispersal as the wind becomes dominant. The wide dispersion in disk lifetimes could therefore be due to varying initial levels of net flux. Magnetohydrodynamic (MHD) wind triggered dispersal differs from photoevaporative dispersal in predicting mass loss from small (less that 1 AU) scales, where thermal winds are suppressed. Our specific models are based on a limited set of simulations that remain uncertain, but qualitatively similar evolution appears likely if mass is lost from disks more quickly than flux, and if MHD winds become important as the plasma beta decreases.

astro-ph.EP↗

arXiv2013

Turbulence In the Outer Regions of Protoplanetary Disks. II. Strong Accretion Driven by a Vertical Magnetic Field

We carry out a series of local, vertically stratified shearing box simulations of protoplanetary disks that include ambipolar diffusion and a net vertical magnetic field. The ambipolar diffusion profiles we employ correspond to 30AU and 100AU in a minimum mass solar nebula (MMSN) disk model, which consists of a far-UV-ionized surface layer and low-ionization disk interior. These simulations serve as a follow up to Simon et al. (2013), in which we found that without a net vertical field, the turbulent stresses that result from the magnetorotational instability (MRI) are too weak to account for observed accretion rates. The simulations in this work show a very strong dependence of the accretion stresses on the strength of the background vertical field; as the field strength increases, the stress amplitude increases. For gas to magnetic pressure ratios of 1e4 and 1e5, we find accretion rates between 1e-8 and 1e-7 solar masses per year. These accretion rates agree with observational constraints, suggesting a vertical magnetic field strength between 60 and 200 microgauss at 30AU and 10 and 30 microgauss at 100AU in a MMSN disk. Furthermore, the stress has a non-negligible component due to a magnetic wind. For sufficiently strong vertical field strengths, MRI turbulence is quenched, and the flow becomes largely laminar, with accretion proceeding through large scale correlations in the radial and toroidal field components as well as through the magnetic wind. In all simulations, the presence of a low ionization region near the disk mid-plane, which we call the ambipolar damping zone, results in reduced stresses there.

astro-ph.SR↗