arXiv subjects

James M. Stone

Publications and source records attributed to James M. Stone.

At least 127 records · Page 7Linked to original sources

arXiv2011

Density Waves Excited by Low-Mass Planets in Protoplanetary Disks I: Linear Regime

Density waves excited by planets embedded in protoplanetary disks play a central role in planetary migration and gap opening processes. We carry out 2D shearing sheet simulations to study the linear regime of wave evolution with the grid-based code Athena, and provide detailed comparisons with the theoretical predictions. Low mass planets (down to ~0.03 Earth mass at 1 AU) and high spatial resolution (256 grid points per scale height) are chosen to mitigate the effects of wave nonlinearity. To complement the existing numerical studies, we focus on the primary physical variables such as the spatial profile of the wave, torque density, and the angular momentum flux carried by the wave, instead of secondary quantities such as the planetary migration rate. Our results show percent level agreement with theory in both physical and Fourier space. New phenomena such as the change of the toque density sign far from the planet are discovered and discussed. Also, we explore the effect of the numerical algorithms, and find that a high order of accuracy, high resolution, and an accurate planetary potential are crucial to achieve good agreement with the theory. We find that the use of a too large time-step without properly resolving the dynamical time scale around the planet produces incorrect results, and may lead to spurious gap opening. Global simulations of planet migration and gap opening violating this requirement may be affected by spurious effects resulting in e.g. the incorrect planetary migration rate and gap opening mass.

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arXiv2011

Density Waves Excited by Low-Mass Planets in Protoplanetary Disks II: High-Resolution Simulations of the Nonlinear Regime

We investigate numerically the propagation of density waves excited by a low-mass planet in a protoplanetary disk in the nonlinear regime, using 2D local shearing box simulations with the grid-based code Athena at high spatial resolution (256 grid points per scale height h). The nonlinear evolution results in the wave steepening into a shock, causing damping and angular momentum transfer to the disk. On long timescales this leads to spatial redistribution of the disk density, causing migration feedback and potentially resulting in gap opening. Previous numerical studies concentrated on exploring these secondary phenomena as probes of the nonlinear wave evolution. Here we focus on exploring the evolution of the basic wave properties, such as its density profile evolution, shock formation, post-shock wave behavior, and provide comparison with analytical theory. The generation of potential vorticity at the shock is computed analytically and is subsequently verified by simulations and used to pinpoint the shock location. We confirm the theoretical relation between the shocking length and the planet mass (including the effect of the equation of state), and the post-shock decay of the angular momentum flux carried by the wave. The post-shock evolution of the wave profile is explored, and we quantitatively confirm its convergence to the theoretically expected N-wave shape. The accuracy of various numerical algorithms used to compute the nonlinear wave evolution is also investigated: we find that higher order spatial reconstruction and high resolution are crucial for capturing the shock formation correctly.

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arXiv2011

Global Simulations of Accretion Disks I: Convergence and Comparisons with Local Models

Grid-based magnetohydrodynamic (MHD) simulations have proven invaluable for the study of astrophysical accretion disks. However, the fact that angular momentum transport in disks is mediated by MHD turbulence (with structure down to very small scales) raises the concern that the properties of the modeled accretion disks are affected by the finite numerical resolution of the simulation. By implementing an orbital advection algorithm into the Athena code in cylindrical geometry, we have performed a set of global (but unstratified) Newtonian disk simulations extending up to resolutions previously unattained. We study the convergence of these models as a function of spatial resolution and initial magnetic field geometry. The usual viscosity parameter ($α$) or the ratio of thermal-to-magnetic pressure ($β$) are found to be poor diagnostics of convergence, whereas the average tilt angle of the magnetic field in the $(r,ϕ)$-plane is a very good diagnostic of convergence. We suggest that this is related to the saturation of the MHD turbulence via parasitic modes of the magnetorotational instability. Even in the case of zero-net magnetic flux, we conclude that our highest resolution simulations (with 32-zones and 64-zones per vertical scale height) have achieved convergence. Our global simulations reach resolutions comparable to those used in local, shearing box models of MHD disk turbulence. We find that the saturation predictors derived from local simulations correspond well to the instantaneous correlations between local flux and stress found in our global simulations. However, the conservation of magnetic flux implicit in local models is not realized in our global disks. Thus, the magnetic connectivity of an accretion disk represents physics that is truly global and cannot be captured in any ab-initio local model.

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arXiv2011

Effect of Ambipolar Diffusion on the Non-linear Evolution of Magnetorotational Instability in Weakly Ionized Disks

We study the role of ambipolar diffusion (AD) on the non-linear evolution of the MRI in protoplanetary disks using the strong coupling limit, which applies when the electron recombination time is much shorter than the orbital time. The effect of AD in this limit is characterized by the dimensionless number Am, the frequency of which neutral particles collide with ions normalized to the orbital frequency. We perform three-dimensional unstratified shearing-box simulations of the MRI over a wide range of Am as well as different magnetic field strengths and geometries. The saturation level of the MRI turbulence depends on the magnetic geometry and increases with the net magnetic flux. There is an upper limit to the net flux for sustained turbulence, corresponding to the requirement that the most unstable vertical wavelength be less than the disk scale height. Correspondingly, at a given Am, there exists a maximum value of the turbulent stress alpha_max. For Am<1, the largest stress is associated with a field geometry that has both net vertical and toroidal flux. In this case, we confirm the results of linear analyses that show the fastest growing mode has a non-zero radial wave number with growth rate exceeding the pure vertical field case. We find there is a very tight correlation between the turbulent stress (alpha) and the plasma beta=P_gas/P_mag~1/(2alpha) at the saturated state of the MRI turbulence regardless of field geometry, and alpha_max rapidly decreases with decreasing Am. In particular, we quote alpha_max~0.007 for Am=1 and alpha_max~0.0006 for Am=0.1.

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arXiv2011

A Second Order Godunov Method for Multidimensional Relativistic Magnetohydrodynamics

We describe a new Godunov algorithm for relativistic magnetohydrodynamics (RMHD) that combines a simple, unsplit second order accurate integrator with the constrained transport (CT) method for enforcing the solenoidal constraint on the magnetic field. A variety of approximate Riemann solvers are implemented to compute the fluxes of the conserved variables. The methods are tested with a comprehensive suite of multidimensional problems. These tests have helped us develop a hierarchy of correction steps that are applied when the integration algorithm predicts unphysical states due to errors in the fluxes, or errors in the inversion between conserved and primitive variables. Although used exceedingly rarely, these corrections dramatically improve the stability of the algorithm. We present preliminary results from the application of these algorithms to two problems in RMHD: the propagation of supersonic magnetized jets, and the amplification of magnetic field by turbulence driven by the relativistic Kelvin-Helmholtz instability (KHI). Both of these applications reveal important differences between the results computed with Riemann solvers that adopt different approximations for the fluxes. For example, we show that use of Riemann solvers which include both contact and rotational discontinuities can increase the strength of the magnetic field within the cocoon by a factor of ten in simulations of RMHD jets, and can increase the spectral resolution of three-dimensional RMHD turbulence driven by the KHI by a factor of 2. This increase in accuracy far outweighs the associated increase in computational cost. Our RMHD scheme is publicly available as part of the Athena code.

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arXiv2010

Dynamics of Solids in the Midplane of Protoplanetary Disks: Implications for Planetesimal Formation

(Abridged) We present local 2D and 3D hybrid numerical simulations of particles and gas in the midplane of protoplanetary disks (PPDs) using the Athena code. The particles are coupled to gas aerodynamically, with particle-to-gas feedback included. Magnetorotational turbulence is ignored as an approximation for the dead zone of PPDs, and we ignore particle self-gravity to study the precursor of planetesimal formation. Our simulations include a wide size distribution of particles, ranging from strongly coupled particles with dimensionless stopping time tau_s=Omega t_stop=1e-4 to marginally coupled ones with tau_s=1 (where Omega is the orbital frequency, t_stop is the particle friction time), and a wide range of solid abundances. Our main results are: 1. Particles with tau_s>=0.01 actively participate in the streaming instability, generate turbulence and maintain the height of the particle layer before Kelvin-Helmholtz instability is triggered. 2. Strong particle clumping as a consequence of the streaming instability occurs when a substantial fraction of the solids are large (tau_s>=0.01) and when height-integrated solid to gas mass ratio Z is super-solar. 3. The radial drift velocity is reduced relative to the conventional Nakagawa-Sekiya-Hayashi (NSH) model, especially at high Z. We derive a generalized NSH equilibrium solution for multiple particle species which fits our results very well. 4. Collision velocity between particles with tau_s>=0.01 is dominated by differential radial drift, and is strongly reduced at larger Z. 5. There exist two positive feedback loops with respect to the enrichment of local disk solid abundance and grain growth. All these effects promote planetesimal formation.

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arXiv2010

Particle-Gas Dynamics with Athena: Method and Convergence

The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybrid scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force, it preserves the geometric properties of a particle orbit. We also present a fully-implicit integrator that is unconditionally stable for all regimes of particle-gas coupling. Using our hybrid code, we study the numerical convergence of the non-linear saturated state of the streaming instability. We find that gas flow properties are well converged with modest grid resolution (128 cells per pressure length ηr for dimensionless stopping time tau_s=0.1), and equal number of particles and grid cells. On the other hand, particle clumping properties converge only at higher resolutions, and finer resolution leads to stronger clumping before convergence is reached. Finally, we find that measurement of particle transport properties resulted from the streaming instability may be subject to error of about 20%.

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arXiv2010

Implementation of the Shearing Box Approximation in Athena

We describe the implementation of the shearing box approximation for the study of the dynamics of accretion disks in the Athena magnetohydrodynamics (MHD) code. Second-order Crank-Nicholson time differencing is used for the Coriolis and tidal gravity source terms that appear in the momentum equation for accuracy and stability. We show this approach conserves energy for epicyclic oscillations in hydrodynamic flows to round-off error. In the energy equation, the tidal gravity source terms are differenced as the gradient of an effective potential in a way which guarantees that total energy (including the gravitational potential energy) is also conserved to round-off error. We introduce an orbital advection algorithm for MHD based on constrained transport to preserve the divergence-free constraint on the magnetic field. This algorithm removes the orbital velocity from the time step constraint, and makes the truncation error more uniform in radial position. Modifications to the shearing box boundary conditions applied at the radial boundaries are necessary to conserve the total vertical magnetic flux. In principle similar corrections are also required to conserve mass, momentum and energy, however in practice we find the orbital advection method conserves these quantities to better than 0.03% over hundreds of orbits. The algorithms have been applied to studies of the nonlinear regime of the MRI in very wide (up to 32 scale heights) horizontal domains.

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arXiv2009

Buoyant Bubbles in Intracluster Gas: Effects of Magnetic Fields and Anisotropic Viscosity

Recent observations by Chandra and XMM-Newton indicate there are complex structures at the cores of galaxy clusters, such as cavities and filaments. One plausible model for the formation of such structures is the interaction of radio jets with the intracluster medium (ICM). To investigate this idea, we use three-dimensional magnetohydrodynamic simulations including anisotropic (Braginskii) viscosity to study the effect of magnetic fields on the evolution and morphology of buoyant bubbles in the ICM. We investigate a range of different initial magnetic field geometries and strengths, and study the resulting x-ray surface brightness distribution for comparison to observed clusters. Magnetic tension forces and viscous transport along field lines tend to suppress instabilities parallel, but not perpendicular, to field lines. Thus, the evolution of the bubble depends strongly on the initial field geometry. We find toroidal field loops initially confined to the interior of the bubble are best able reproduce the observed cavity structures.

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arXiv2009

Turbulent resistivity driven by the magnetorotational instability

We measure the turbulent resistivity in the nonlinear regime of the MRI, and evaluate the turbulent magnetic Prandtl number. We perform a set of numerical simulations with the Eulerian finite volume codes Athena and Ramses in the framework of the shearing box model. We consider models including explicit dissipation coefficients and magnetic field topologies such that the net magnetic flux threading the box in both the vertical and azimuthal directions vanishes. We first demonstrate good agreement between the two codes by comparing the properties of the turbulent states in simulations having identical microscopic diffusion coefficients (viscosity and resistivity). We find the properties of the turbulence do not change when the box size is increased in the radial direction, provided it is elongated in the azimuthal direction. To measure the turbulent resistivity in the disk, we impose a fixed electromotive force on the flow and measure the amplitude of the saturated magnetic field that results. We obtain a turbulent resistivity that is in rough agreement with mean field theories like the Second Order Smoothing Approximation. The numerical value translates into a turbulent magnetic Prandtl number Pm_t of order unity. Pm_t appears to be an increasing function of the forcing we impose. It also becomes smaller as the box size is increased in the radial direction, in good agreement with previous results obtained in very large boxes. Our results are in general agreement with other recently published papers studying the same problem but using different methodology. Thus, our conclusion that Pm_t is of order unity appears robust.

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arXiv2008

Anisotropic winds from close-in extra-solar planets

We present two-dimensional hydrodynamic models of thermally driven winds from highly irradiated, close-in extra-solar planets. We adopt a very simple treatment of the radiative heating processes at the base of the wind, and instead focus on the differences between the properties of outflows in multidimensions in comparison to spherically symmetric models computed with the same methods. For hot (T > 2 x 10^{4} K) or highly ionized gas, we find strong (supersonic) polar flows are formed above the planet surface which produce weak shocks and outflow on the night-side. In comparison to a spherically symmetric wind with the same parameters, the sonic surface on the day-side is much closer to the planet surface in multidimensions, and the total mass loss rate is reduced by almost a factor of four. We also compute the steady-state structure of interacting planetary and stellar winds. Both winds end in a termination shock, with a parabolic contact discontinuity which is draped over the planet separating the two shocked winds. The planetary wind termination shock and the sonic surface in the wind are well separated, so that the mass loss rate from the planet is essentially unaffected. However, the confinement of the planetary wind to the small volume bounded by the contact discontinuity greatly enhances the column density close to the planet, which might be important for the interpretation of observations of absorption lines formed by gas surrounding transiting planets.

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arXiv2008

Density Probability Distribution Functions in Supersonic Hydrodynamic and MHD Turbulence

We study the probability distribution function (PDF) of the mass density in simulations of supersonic turbulence with properties appropriate for molecular clouds. For this study we use Athena, a new higher-order Godunov code. We find there are surprisingly similar relationships between the mean of the time-averaged PDF and the turbulent Mach number for driven hydrodynamic and strong-field MHD turbulence. There is, however, a large scatter about these relations, indicating a high level of temporal and spatial variability in the PDF. Thus, the PDF of the mass density is unlikely to be a good measure of magnetic field strength. We also find the PDF of decaying MHD turbulence deviates from the mean-Mach relation found in the driven case. This implies that the instantaneous Mach number alone is not enough to determine the statistical properties of turbulence that is out of equilibrium. The scatter about the mean-Mach relation for driven turbulence, along with the large departure of decaying turbulence PDFs from those of driven turbulence, may illuminate one factor contributing to the large observed cloud-to-cloud variation in the star formation rate per solar mass.

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arXiv2008

Dissipation and Heating in Supersonic Hydrodynamic and MHD Turbulence

We study energy dissipation and heating by supersonic MHD turbulence in molecular clouds using Athena, a new higher-order Godunov code. We analyze the dependence of the saturation amplitude, energy dissipation characteristics, power spectra, sonic scaling, and indicators of intermittency in the turbulence on factors such as the magnetic field strength, driving scale, energy injection rate, and numerical resolution. While convergence in the energies is reached at moderate resolutions, we find that the power spectra require much higher resolutions that are difficult to obtain. In a 1024^3 hydro run, we find a power law relationship between the velocity dispersion and the spatial scale on which it is measured, while for an MHD run at the same resolution we find no such power law. The time-variability and temperature intermittency in the turbulence both show a dependence on the driving scale, indicating that numerically driving turbulence by an arbitrary mechanism may not allow a realistic representation of these properties. We also note similar features in the power spectrum of the compressive component of velocity for supersonic MHD turbulence as in the velocity spectrum of an initially-spherical MHD blast wave, implying that the power law form does not rule out shocks, rather than a turbulent cascade, playing a significant role in the regulation of energy transfer between spatial scales.

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arXiv2008

Spherical Accretion with Anisotropic Thermal Conduction

We study the effects of anisotropic thermal conduction on magnetized spherical accretion flows using global axisymmetric MHD simulations. In low collisionality plasmas, the Bondi spherical accretion solution is unstable to the magnetothermal instability (MTI). The MTI grows rapidly at large radii where the inflow is subsonic. For a weak initial field, the MTI saturates by creating a primarily radial magnetic field, i.e., by aligning the field lines with the background temperature gradient. The saturation is quasilinear in the sense that the magnetic field is amplified by a factor of $\sim 10-30$ independent of the initial field strength (for weak fields). In the saturated state, the conductive heat flux is much larger than the convective heat flux, and is comparable to the field-free (Spitzer) value (since the field lines are largely radial). The MTI by itself does not appreciably change the accretion rate $\dot M$ relative to the Bondi rate $\dot M_B$. However, the radial field lines created by the MTI are amplified by flux freezing as the plasma flows in to small radii. Oppositely directed field lines are brought together by the converging inflow, leading to significant resistive heating. When the magnetic energy density is comparable to the gravitational potential energy density, the plasma is heated to roughly the virial temperature; the mean inflow is highly subsonic; most of the energy released by accretion is transported to large radii by thermal conduction; and the accretion rate $\dot M \ll \dot M_B$. The predominantly radial magnetic field created by the MTI at large radii in spherical accretion flows may account for the stable Faraday rotation measure towards Sgr A* in the Galactic Center.

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arXiv2008

The Magnetothermal Instability in the Intracluster Medium

The electron mean free path in the intracluster medium (ICM) of galaxy clusters is much larger than the gyroradius; thus, heat is transported anisotropically along magnetic field lines. We show that the intracluster medium is unstable to the magnetothermal instability (MTI) using MHD simulations with anisotropic thermal conduction. As a result of the MTI, we find that the temperature profile of the ICM can be substantially modified on timescales of several billion years while the magnetic field is amplified by dynamo action up to more than fifty times the original energy. We also show that the instability drives field lines to become preferentially radial leading to conduction that is a highly efficient fraction of the Spitzer conductivity. As such, we present the first self-consistent calculation of the effective thermal conductivity in the ICM.

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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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arXiv2008

The Magnetohydrodynamics of Shock-Cloud Interaction in Three Dimensions

The magnetohydrodynamic evolution of a dense spherical cloud as it interacts with a strong planar shock is studied, as a model for shock interactions with density inhomogeneities in the interstellar medium. The cloud is assumed to be small enough that radiative cooling, thermal conduction, and self-gravity can be ignored. A variety of initial orientations (including parallel, perpendicular, and oblique to the incident shock normal) and strengths for the magnetic field are investigated. During the early stages of the interaction (less than twice the time taken for the transmitted shock to cross the interior of the cloud) the structure and dynamics of the shocked cloud is fairly insensitive to the magnetic field strength and orientation. However, at late times strong fields substantially alter the dynamics of the cloud, suppressing fragmentation and mixing by stabilizing the interface at the cloud surface. Even weak magnetic fields can drastically alter the evolution of the cloud compared to the hydrodynamic case. Weak fields of different geometries result in different distributions and amplifications of the magnetic energy density, which may affect the thermal and non-thermal x-ray emission expected from shocked clouds associated with, for example, supernovae remnants.

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arXiv2008

Kinematics of solid particles in a turbulent protoplanetary disc

We perform numerical simulations of solid particle motion in a shearing box model of a protoplanetary disc. The accretion flow is turbulent due to the action of the magnetorotational instability. Aerodynamic drag on the particles is modelled using the Epstein law with the gas velocity interpolated to the particle position. The effect of the magnetohydrodynamic turbulence on particle velocity dispersions is quantified for solids of different stopping times t_s, or equivalently, different sizes. The anisotropy of the turbulence is reflected upon the dispersions of the particle velocity components, with the radial component larger than both the azimuthal and vertical components for particles larger than ~ 10 cm (assuming minimum-mass solar nebula conditions at 5 AU). The dispersion of the particle velocity magnitude, as well as that of the radial and azimuthal components, as functions of stopping time, agree with previous analytical results for isotropic turbulence. The relative speed between pairs of particles with the same value of t_s decays faster with decreasing separation than in the case of solids with different stopping time. Correlations in the particle number density introduce a non-uniform spatial distribution of solids in the 10 to 100 cm size range. Any clump of particles is disrupted by the turbulence in less than one tenth on an orbital period, and the maximally concentrated clumps are stable against self-gravitational collapse.

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