arXiv subjects

Jacob B. Simon

Publications and source records attributed to Jacob B. Simon.

65 records · Page 4Linked to original sources

arXiv2013

Turbulence In the Outer Regions of Protoplanetary Disks. I. Weak Accretion with No Vertical Magnetic Flux

We use local numerical simulations to investigate the strength and nature of magnetohydrodynamic (MHD) turbulence in the outer regions of protoplanetary disks, where ambipolar diffusion is the dominant non-ideal MHD effect. The simulations include vertical stratification and assume zero net vertical magnetic flux. We employ a super time-stepping technique to ameliorate the Courant restriction on the diffusive time step. We find that in idealized stratified simulations, with a spatially constant ambipolar Elsasser number Am, turbulence driven by the magnetorotational instability (MRI) behaves in a similar manner as in prior unstratified calculations. Turbulence dies away for Am < 1, and becomes progressively more vigorous as ambipolar diffusion is decreased. Near-ideal MHD behavior is recovered for Am > 1000. In the intermediate regime (10 < Am < 1000) ambipolar diffusion leads to substantial increases in both the period of the MRI dynamo cycle and the characteristic scales of magnetic field structures. To quantify the impact of ambipolar physics on disk accretion, we run simulations at 30 AU and 100 AU that include a vertical Am profile based upon far ultraviolet (FUV) ionized disk models. These models develop a vertically layered structure analogous to the Ohmic dead zone that is present at smaller radii. We find that, although the levels of surface turbulence can be strong (and consistent with constraints on turbulent line widths at these radii), the inferred accretion rates are at least an order of magnitude smaller than those observed in T Tauri stars. This discrepancy is very likely due to the assumption of zero vertical magnetic field in our simulations and suggests that vertical magnetic fields are essential for MRI-driven accretion in the outer regions of protoplanetary disks.

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arXiv2012

Turbulent Linewidths as a Diagnostic of Self-Gravity in Protostellar Discs

We use smoothed particle hydrodynamics simulations of massive protostellar discs to investigate the predicted broadening of molecular lines from discs in which self-gravity is the dominant source of angular momentum transport. The simulations include radiative transfer, and span a range of disc-to-star mass ratios between 0.25 and 1.5. Subtracting off the mean azimuthal flow velocity, we compute the distribution of the in-plane and perpendicular peculiar velocity due to large scale structure and turbulence induced by self-gravity. For the lower mass discs, we show that the characteristic peculiar velocities scale with the square root of the effective turbulent viscosity parameter, as expected from local turbulent-disc theory. The derived velocities are anisotropic, with substantially larger in-plane than perpendicular values. As the disc mass is increased, the validity of the locally determined turbulence approximation breaks down, and this is accompanied by anomalously large in-plane broadening. There is also a high variance due to the importance of low-m spiral modes. For low-mass discs, the magnitude of in-plane broadening is, to leading order, equal to the predictions from local disc theory and cannot constrain the source of turbulence. However, combining our results with prior evaluations of turbulent broadening expected in discs where the magnetorotational instability (MRI) is active, we argue that self-gravity may be distinguishable from the MRI in these systems if it is possible to measure the anisotropy of the peculiar velocity field with disc inclination. Furthermore, for large mass discs, the dominant contribution of large-scale modes is a distinguishing characteristic of self-gravitating turbulence versus MRI driven turbulence.

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arXiv2012

Emergent Mesoscale Phenomena in Magnetized Accretion Disc Turbulence

We study how the structure and variability of magnetohydrodynamic (MHD) turbulence in accretion discs converge with domain size. Our results are based on a series of vertically stratified local simulations, computed using the Athena code, that have fixed spatial resolution, but varying radial and azimuthal extent (from ΔR = 0.5H to 16H, where H is the vertical scale height). We show that elementary local diagnostics of the turbulence, including the Shakura-Sunyaev α parameter, the ratio of Maxwell stress to magnetic energy, and the ratio of magnetic to fluid stresses, converge to within the precision of our measurements for spatial domains of radial size Lx \geq 2H. We obtain α = 0.02-0.03, consistent with recent results. Very small domains (Lx = 0.5H) return anomalous results, independent of spatial resolution. The convergence with domain size is only valid for a limited set of diagnostics: larger spatial domains admit the emergence of dynamically important mesoscale structures. In our largest simulations, the Maxwell stress shows a significant large scale non-local component, while the density develops long-lived axisymmetric perturbations (zonal flows) at the 20% level. Most strikingly, the variability of the disc in fixed-sized patches decreases strongly as the simulation volume increases. We find generally good agreement between our largest local simulations and global simulations with comparable spatial resolution. There is no direct evidence that the presence of curvature terms or radial gradients in global calculations materially affect the turbulence, except to perhaps introduce an outer radial scale for mesoscale structures. The demonstrated importance of mean magnetic fields, seen in both large local and global simulations implies that the growth and saturation of these fields is likely of critical importance for the evolution of accretion discs. (abridged)

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arXiv2011

Turbulent Linewidths in Protoplanetary Disks: Predictions from Numerical Simulations

Sub-mm observations of protoplanetary disks now approach the acuity needed to measure the turbulent broadening of molecular lines. These measurements constrain disk angular momentum transport, and furnish evidence of the turbulent environment within which planetesimal formation takes place. We use local magnetohydrodynamic (MHD) simulations of the magnetorotational instability (MRI) to predict the distribution of turbulent velocities in low mass protoplanetary disks, as a function of radius and height above the mid-plane. We model both ideal MHD disks, and disks in which Ohmic dissipation results in a dead zone of suppressed turbulence near the mid-plane. Under ideal conditions, the disk mid-plane is characterized by a velocity distribution that peaks near v \simeq 0.1cs (where cs is the local sound speed), while supersonic velocities are reached at z > 3H (where H is the pressure scale height). Residual velocities of v \approx 0.01cs persist near the mid-plane in dead zones, while the surface layers remain active. Anisotropic variation of the linewidth with disk inclination is modest. We compare our MHD results to hydrodynamic simulations in which large-scale forcing is used to initiate similar turbulent velocities. We show that the qualitative trend of increasing v with height, seen in the MHD case, persists for forced turbulence and is likely a generic property of disk turbulence. Percent level determinations of v at different heights within the disk, or spatially resolved observations that probe the inner disk containing the dead zone region, are therefore needed to test whether the MRI is responsible for protoplanetary disk turbulence.

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arXiv2011

Turbulence in Global Simulations of Magnetized Thin Accretion Disks

We use a global magnetohydrodynamic simulation of a geometrically thin accretion disk to investigate the locality and detailed structure of turbulence driven by the magnetorotational instability (MRI). The model disk has an aspect ratio $H / R \simeq 0.07$, and is computed using a higher-order Godunov MHD scheme with accurate fluxes. We focus the analysis on late times after the system has lost direct memory of its initial magnetic flux state. The disk enters a saturated turbulent state in which the fastest growing modes of the MRI are well-resolved, with a relatively high efficiency of angular momentum transport $< < α> > \approx 2.5 \times 10^{-2}$. The accretion stress peaks at the disk midplane, above and below which exists a moderately magnetized corona with patches of superthermal field. By analyzing the spatial and temporal correlations of the turbulent fields, we find that the spatial structure of the magnetic and kinetic energy is moderately well-localized (with correlation lengths along the major axis of $2.5H$ and $1.5H$ respectively), and generally consistent with that expected from homogenous incompressible turbulence. The density field, conversely, exhibits both a longer correlation length and a long correlation time, results which we ascribe to the importance of spiral density waves within the flow. Consistent with prior results, we show that the mean local stress displays a well-defined correlation with the local vertical flux, and that this relation is apparently causal (in the sense of the flux stimulating the stress) during portions of a global dynamo cycle. We argue that the observed flux-stress relation supports dynamo models in which the structure of coronal magnetic fields plays a central role in determining the dynamics of thin-disk accretion.

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arXiv2011

Resistivity-driven State Changes in Vertically Stratified Accretion Disks

We investigate the effect of shear viscosity and Ohmic resistivity on the magnetorotational instability (MRI) in vertically stratified accretion disks through a series of local simulations with the Athena code. First, we use a series of unstratified simulations to calibrate physical dissipation as a function of resolution and background field strength; the effect of the magnetic Prandtl number, Pm = viscosity/resistivity, on the turbulence is captured by ~32 grid zones per disk scale height, H. In agreement with previous results, our stratified disk calculations are characterized by a subthermal, predominately toroidal magnetic field that produces MRI-driven turbulence for |z| < 2 H. Above |z| = 2 H, magnetic pressure dominates and the field is buoyantly unstable. Large scale radial and toroidal fields are also generated near the mid-plane and subsequently rise through the disk. The polarity of this mean field switches on a roughly 10 orbit period in a process that is well-modeled by an alpha-omega dynamo. Turbulent stress increases with Pm but with a shallower dependence compared to unstratified simulations. For sufficiently large resistivity, on the order of cs H/1000, where cs is the sound speed, MRI turbulence within 2 H of the mid-plane undergoes periods of resistive decay followed by regrowth. This regrowth is caused by amplification of toroidal field via the dynamo. This process results in large amplitude variability in the stress on 10 to 100 orbital timescales, which may have relevance for partially ionized disks that are observed to have high and low accretion states.

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arXiv2010

Long-term Evolution of Protostellar and Protoplanetary Disks. I. Outbursts

As an initial investigation into the long-term evolution of protostellar disks, we explore the conditions required to explain the large outbursts of disk accretion seen in some young stellar objects. We use one-dimensional time-dependent disk models with a phenomenological treatment of the magnetorotational instability (MRI) and gravitational torques to follow disk evolution over long timescales. Comparison with our previous two-dimensional disk model calculations (Zhu et al. 2009b, Z2009b) indicates that the neglect of radial effects and two-dimensional disk structure in the one-dimensional case makes only modest differences in the results; this allows us to use the simpler models to explore parameter space efficiently. We find that the mass infall rates typically estimated for low-mass protostars generally result in AU-scale disk accretion outbursts, as predicted by our previous analysis (Zhu et al. 2009a,Z2009a). We also confirm quasi-steady accretion behavior for high mass infall rates if the values of $α$-parameter for the magnetorotational instability is small, while at this high accretion rate convection from the thermal instability may lead to some variations. We further constrain the combinations of the $α$-parameter and the MRI critical temperature, which can reproduce observed outburst behavior. Our results suggest that dust sublimation may be connected with full activation of the MRI. This is consistent with the idea that small dust captures ions and electrons to suppress the MRI. In a later paper we will explore both long-term outburst and disk evolution with this model, allowing for infall from protostellar envelopes with differing angular momenta.

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arXiv2009

Viscous and Resistive Effects on the MRI with a Net Toroidal Field

Resistivity and viscosity have a significant role in establishing the energy levels in turbulence driven by the magnetorotational instability (MRI) in local astrophysical disk models. This study uses the Athena code to characterize the effects of a constant shear viscosity νand Ohmic resistivity ηin unstratified shearing box simulations with a net toroidal magnetic flux. A previous study of shearing boxes with zero net magnetic field performed with the ZEUS code found that turbulence dies out for values of the magnetic Prandtl number, P_m = ν/η, below P_m \sim 1; for P_m \gtrsim 1, time- and volume-averaged stress levels increase with P_m. We repeat these experiments with Athena and obtain consistent results. Next, the influence of viscosity and resistivity on the toroidal field MRI is investigated both for linear growth and for fully-developed turbulence. In the linear regime, a sufficiently large νor ηcan prevent MRI growth; P_m itself has little direct influence on growth from linear perturbations. By applying a range of values for νand ηto an initial state consisting of fully developed turbulence in the presence of a background toroidal field, we investigate their effects in the fully nonlinear system. Here, increased viscosity enhances the turbulence, and the turbulence decays only if the resistivity is above a critical value; turbulence can be sustained even when P_m < 1, in contrast to the zero net field model. While we find preliminary evidence that the stress converges to a small range of values when νand ηbecome small enough, the influence of dissipation terms on MRI-driven turbulence for relatively large ηand νis significant, independent of field geometry.

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arXiv2009

Locality of MHD Turbulence in Isothermal Disks

We numerically evolve turbulence driven by the magnetorotational instability (MRI) in a 3D, unstratified shearing box and study its structure using two-point correlation functions. We confirm Fromang and Papaloizou's result that shearing box models with zero net magnetic flux are not converged; the dimensionless shear stress $α$ is proportional to the grid scale. We find that the two-point correlation of the magnetic field shows that it is composed of narrow filaments that are swept back by differential rotation into a trailing spiral. The correlation lengths along each of the correlation function principal axes decrease monotonically with the grid scale. For mean azimuthal field models, which we argue are more relevant to astrophysical disks than the zero net field models, we find that: $α$ increases weakly with increasing resolution at fixed box size; $α$ increases slightly as the box size is increased; $α$ increases linearly with net field strength, confirming earlier results; the two-point correlation function of the magnetic field is resolved and converged, and is composed of narrow filaments swept back by the shear; the major axis of the two-point increases slightly as the box size is increased; these results are code independent, based on a comparison of ATHENA and ZEUS runs. The velocity, density, and magnetic fields decorrelate over scales larger than $\sim H$, as do the dynamical terms in the magnetic energy evolution equations. We conclude that MHD turbulence in disks is localized, subject to the limitations imposed by the absence of vertical stratification, the use of an isothermal equation of state, finite box size, finite run time, and finite resolution

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arXiv2008

Simulations of Magnetorotational Turbulence with a Higher-Order Godunov Scheme

(abridged) We apply a second-order Godunov code, Athena, to studies of the magnetorotational instability using unstratified shearing box simulations with a uniform net vertical field and a sinusoidally varying zero net vertical field. The Athena results agree well with similar studies that used different numerical algorithms. We conduct analyses to study the flow of energy from differential rotation to turbulent fluctuations to thermalization. A study of the temporal correlation between the time derivatives of volume-averaged energy components shows that energy injected into turbulent fluctuations dissipates on a timescale of $Ω^{-1}$, where $Ω$ is the orbital frequency of the local domain. Magnetic dissipation dominates over kinetic dissipation, although not by as great a factor as the ratio of magnetic to kinetic energy. We Fourier-transform the magnetic and kinetic energy evolution equations and, using the assumption that the time-averaged energies are constant, determine the level of numerical dissipation as a function of length scale and resolution. By modeling numerical dissipation as if it were physical in origin, we characterize numerical resistivity and viscosity in terms of effective Reynolds and Prandtl numbers. The resulting effective magnetic Prandtl number is $\sim 2$, independent of resolution or initial field geometry. MRI simulations with effective Reynolds and Prandtl numbers determined by numerical dissipation are not equivalent to those where these numbers are set by physical resistivity and viscosity. These results serve, then, as a baseline for future shearing box studies where dissipation is controlled by the inclusion of explicit viscosity and resistivity.

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arXiv2008

Athena: A New Code for Astrophysical MHD

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher-order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume-averages for mass, momentum, and energy, and face-centered area-averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally-split time advance, and (3) the extension to MHD of two different dimensionally-unsplit integration methods. Implementation of the algorithm in both C and Fortran95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.

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