arXiv subjects

Charles F. Gammie

Publications and source records attributed to Charles F. Gammie.

At least 91 records · Page 5Linked to original sources

arXiv2011

Challenges in Forming Planets by Gravitational Instability: Disk Irradiation and Clump Migration, Accretion & Tidal Destructio

We present two-dimensional hydrodynamic simulations of self-gravitating protostellar disks subject to axisymmetric infall from envelopes and irradiation from the central star, to explore disk fragmentation due to gravitational instability (GI), and the fragmented clump evolution. We assume that the disk is built gradually and smoothly by the infall, resulting in good numerical convergence. We confirm that for disks around solar-mass stars, infall at high rates at radii beyond ~50 AU leads to disk fragmentation. At lower infall rates <1e-5 Msun/yr, however, irradiation suppresses fragmentation. We find that, once formed, the fragments or clumps migrate inward on typical type-I time scales of ~2e3 yr initially, but later migration deviates from the type-I time scale when the clump becomes more massive than the local disk mass, and/or when they starts to open gaps. As they migrate, the clumps accrete from the disk at a rate 1e-3 to 1e-1 MJupiter/yr, consistent with analytic estimates that assume a 1-2 Hill radii cross section. Most clumps can grow to their isolation masses >0.1 Msun quickly. The eventual fates of these clumps, however, diverges depending on the migration speed: 3 out of 13 clumps become massive enough (brown dwarf mass) to open gaps in the disk and essentially stop migrating; 4 are tidally destroyed during inward migration; 6 migrate across the inner simulated disk boundary. A simple analytic model for clump evolution is derived to explain these different fates. Overall, our results indicate that fast migration, accretion, and tidal destruction of the clumps pose challenges to the scenario of giant planet formation by GI in situ, but may provide a formation mechanism for close binary systems.

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arXiv2011

Global GRMHD Simulations of Black Hole Accretion Flows: a Convergence Study

Global, general relativistic magnetohydrodynamic (GRMHD) simulations of nonradiative, magnetized disks are widely used to model accreting black holes. We have performed a convergence study of GRMHD models computed with HARM3D. The models span a factor of 4 in linear resolution, from 96x96x64 to 384x384x256. We consider three diagnostics of convergence: (1) dimensionless shell-averaged quantities such as plasma β; (2) the azimuthal correlation length of fluid variables; and (3) synthetic spectra of the source including synchrotron emission, absorption, and Compton scattering. Shell-averaged temperature is, except for the lowest resolution run, nearly independent of resolution; shell-averaged plasma β decreases steadily with resolution but shows signs of convergence. The azimuthal correlation lengths of density, internal energy, and temperature decrease steadily with resolution but show signs of convergence. In contrast, the azimuthal correlation length of magnetic field decreases nearly linearly with grid size. We argue by analogy with local models, however, that convergence should be achieved with another factor of 2 in resolution. Synthetic spectra are, except for the lowest resolution run, nearly independent of resolution. The convergence behavior is consistent with that of higher physical resolution local model (shearing box) calculations and with the recent nonrelativistic global convergence studies of Hawley et al. (2011).

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arXiv2011

Pair Production in Low Luminosity Galactic Nuclei

Electron-positron pairs may be produced near accreting black holes by a variety of physical processes, and the resulting pair plasma may be accelerated and collimated into a relativistic jet. Here we use a self-consistent dynamical and radiative model to investigate pair production by γγcollisions in weakly radiative accretion flows around a black hole of mass M and accretion rate \dot{M}. Our flow model is drawn from general relativistic magnetohydrodynamic simulations, and our radiation field is computed by a Monte Carlo transport scheme assuming the electron distribution function is thermal. We argue that the pair production rate scales as r^{-6} M^{-1} \dot{M}^{6}. We confirm this numerically and calibrate the scaling relation. This relation is self-consistent in a wedge in M, \dot{M} parameter space. If \dot{M} is too low the implied pair density over the poles of the black hole is below the Goldreich-Julian density and γγpair production is relatively unimportant; if \dot{M} is too high the models are radiatively efficient. We also argue that for a power-law spectrum the pair production rate should scale with the observables L_X \equiv X-ray luminosity and M as L_X^2 M^{-4}. We confirm this numerically and argue that this relation likely holds even for radiatively efficient flows. The pair production rates are sensitive to black hole spin and to the ion-electron temperature ratio which are fixed in this exploratory calculation. We finish with a brief discussion of the implications for Sgr A* and M87.

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arXiv2010

Radially Extended, Stratified, Local Models of Isothermal Disks

We consider local, stratified, numerical models of isothermal accretion disks. The novel feature of our treatment is that radial extent L_x and azimuthal extent L_y satisfy H << L_x, L_y << R, where H is the scale height and R is the local radius. This enables us to probe mesoscale structure in stratified thin disks. We evolve the model at several resolutions, sizes, and initial magnetic field strengths. Consistent with earlier work, we find that the saturated, turbulent state consists of a weakly magnetized disk midplane coupled to a strongly magnetized corona, with a transition at |z| ~ 2H. The saturated α~ 0.01 - 0.02. A two-point correlation function analysis reveals that the central 4H of the disk is dominated by small scale turbulence that is statistically similar to unstratified disk models, while the coronal magnetic fields are correlated on scales ~ 10 H. Nevertheless angular momentum transport through the corona is small. A study of magnetic field loops in the corona reveals few open field lines and predominantly toroidal loops with a characteristic distance between footpoints that is ~ H. Finally we find quasi-periodic oscillations with characteristic timescale ~ 30 Ω^{-1} in the magnetic field energy density. These oscillations are correlated with oscillations in the mean azimuthal field; we present a phenomenological, alpha-dynamo model that captures most aspects of the oscillations.

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arXiv2010

The Jet in the Galactic Center: An Ideal Laboratory for Magnetohydrodynamics and General Relativity

In this paper we review and discuss some of the intriguing properties of the Galactic Center supermassive black hole candidate Sgr A*. Of all possible black hole sources, the event horizon of Sgr A*, subtends the largest angular scale on the sky. It is therefore a prime candidate to study and image plasma processes in strong gravity and it even allows imaging of the shadow cast by the event horizon. Recent mm-wave VLBI and radio timing observations as well as numerical GRMHD simulations now have provided several breakthroughs that put Sgr A* back into the focus. Firstly, VLBI observations have now measured the intrinsic size of Sgr A* at multiple frequencies, where the highest frequency measurements have approached the scale of the black hole shadow. Moreover, measurements of the radio variability show a clear time lag between 22 GHz and 43 GHz. The combination of size and timing measurements, allows one to actually measure the flow speed and direction of magnetized plasma at some tens of Schwarzschild radii. This data strongly support a moderately relativistic outflow, consistent with an accelerating jet model. This is compared to recent GRMHD simulation that show the presence of a moderately relativistic outflow coupled to an accretion flow Sgr A*. Further VLBI and timing observations coupled to simulations have the potential to map out the velocity profile from 5-40 Schwarzschild radii and to provide a first glimpse at the appearance of a jet-disk system near the event horizon. Future submm-VLBI experiments would even be able to directly image those processes in strong gravity and directly confirm the presence of an event horizon.

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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

Radiative Models of Sgr A* from GRMHD Simulations

Using flow models based on axisymmetric general relativistic magnetohydrodynamics (GRMHD) simulations, we construct radiative models for sgr A*. Spectral energy distributions that include the effects of thermal synchrotron emission and absorption, and Compton scattering, are calculated using a Monte Carlo technique. Images are calculated using a ray-tracing scheme. All models are scaled so that the 230 GHz flux density is 3.4 Jy. The key model parameters are the dimensionless black hole spin a*, the inclination i, and the ion-to-electron temperature ratio Ti/Te. We find that: (1) models with Ti/Te=1 are inconsistent with the observed submillimeter spectral slope; (2) the X-ray flux is a strongly increasing function of a*; (3) the X-ray flux is a strongly increasing function of i; (4) 230 GHz image size is a complicated function of i, a*, and Ti/Te, but the Ti/Te = 10 models are generally large and at most marginally consistent with the 230 GHz VLBI data; (5) for models with Ti/Te=10 and i=85 deg the event horizon is cloaked behind a synchrotron photosphere at 230 GHz and will not be seen by VLBI, but these models overproduce NIR and X-ray flux; (6) in all models whose SEDs are consistent with observations the event horizon is uncloaked at 230 GHz; (7) the models that are most consistent with the observations have a* \sim 0.9. We finish with a discussion of the limitations of our model and prospects for future improvements.

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arXiv2009

grmonty: a Monte Carlo Code for Relativistic Radiative Transport

We describe a Monte Carlo radiative transport code intended for calculating spectra of hot, optically thin plasmas in full general relativity. The version we describe here is designed to model hot accretion flows in the Kerr metric and therefore incorporates synchrotron emission and absorption, and Compton scattering. The code can be readily generalized, however, to account for other radiative processes and an arbitrary spacetime. We describe a suite of test problems, and demonstrate the expected $N^{-1/2}$ convergence rate, where $N$ is the number of Monte Carlo samples. Finally we illustrate the capabilities of the code with a model calculation, a spectrum of the slowly accreting black hole Sgr A* based on data provided by a numerical general relativistic MHD model of the accreting plasma.

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arXiv2009

The Turbulent Magnetic Prandtl Number of MHD Turbulence in Disks

The magnetic Prandtl number Pr_M is the ratio of viscosity to resistivity. In astrophysical disks the diffusion of angular momentum (viscosity) and magnetic fields (resistivity) are controlled by turbulence. Phenomenological models of the evolution of large scale poloidal magnetic fields in disks suggest that the turbulent magnetic Prandtl number Pr_{M,T} controls the rate of escape of vertical field from the disk; for Pr_{M,T} leq R/H vertical field diffuses outward before it can be advected inward by accretion. Here we measure field diffusion and angular momentum transport due to MHD turbulence in a shearing box, and thus Pr_{M,T}, by studying the evolution of a sinusoidal perturbation in the magnetic field that is injected into a turbulent background. We show that the perturbation is always stable, decays approximately exponentially, has decay rate proportional to k^2, and that the implied Pr_{M,T} ~ 1.

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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

Three-Dimensional Simulations of Magnetized Thin Accretion Disks around Black Holes: Stress in the Plunging Region

We describe three-dimensional general relativistic magnetohydrodynamic simulations of a geometrically thin accretion disk around a non-spinning black hole. The disk has a thickness $h/r\sim0.05-0.1$ over the radial range $(2-20)GM/c^2$. In steady state, the specific angular momentum profile of the inflowing magnetized gas deviates by less than 2% from that of the standard thin disk model of Novikov & Thorne (1973). Also, the magnetic torque at the radius of the innermost stable circular orbit (ISCO) is only $\sim2%$ of the inward flux of angular momentum at this radius. Both results indicate that magnetic coupling across the ISCO is relatively unimportant for geometrically thin disks.

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arXiv2008

Orbital Advection by Interpolation: A Fast and Accurate Numerical Scheme for Super-Fast MHD Flows

In numerical models of thin astrophysical disks that use an Eulerian scheme, gas orbits supersonically through a fixed grid. As a result the time step is sharply limited by the Courant condition. Also, because the mean flow speed with respect to the grid varies with position, the truncation error varies systematically with position. For hydrodynamic (unmagnetized) disks an algorithm called FARGO has been developed that advects the gas along its mean orbit using a separate interpolation substep. This relaxes the constraint imposed by the Courant condition, which now depends only on the peculiar velocity of the gas, and results in a truncation error that is more nearly independent of position. This paper describes a FARGO-like algorithm suitable for evolving magnetized disks. Our method is second order accurate on a smooth flow and preserves the divergence-free constraint to machine precision. The main restriction is that the magnetic field must be discretized on a staggered mesh. We give a detailed description of an implementation of the code and demonstrate that it produces the expected results on linear and nonlinear problems. We also point out how the scheme might be generalized to make the integration of other supersonic/super-fast flows more efficient. Although our scheme reduces the variation of truncation error with position, it does not eliminate it. We show that the residual position dependence leads to characteristic radial variations in the density over long integrations.

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arXiv2007

Simulating the Emission and Outflows from Accretion Disks

The radio source Sagittarius A* (Sgr A*) is believed to be a hot, inhomogeneous, magnetized plasma flowing near the event horizon of the 3 million solar mass black hole at the galactic center. At a distance of 8000 parsecs the black hole would be among the largest black holes as judged by angular size. Recent observations are consistent with the idea that the millimeter and sub-millimeter photons are dominated by optically thin, thermal synchrotron emission. Anticipating future Very Long Baseline Interferometry (VLBI) observations of Sgr A* at these wavelengths, we present here the first dynamically self-consistent models of millimeter and sub-millimeter emission from Sgr A* based on general relativistic numerical simulations of the accretion flow. Angle-dependent spectra are calculated assuming a thermal distribution of electrons at the baryonic temperature dictated by the simulation and the accretion rate, which acts as a free parameter in our model. The effects of varying model parameters (black hole spin and inclination of the spin to the line of sight) and source variability on the spectrum are shown. We find that the accretion rate value needed to match our calculated millimeter flux to the observed flux is consistent with constraints on the accretion rate inferred from detections of the rotation measure. We also describe the relativistic jet that is launched along the black hole spin axis by the accretion disk and evolves to scales of 1000 gravitational radii.

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arXiv2006

Vortices in Thin, Compressible, Unmagnetized Disks

We consider the formation and evolution of vortices in a hydrodynamic shearing-sheet model. The evolution is done numerically using a version of the ZEUS code. Consistent with earlier results, an injected vorticity field evolves into a set of long-lived vortices, each of which has a radial extent comparable to the local scale height. But we also find that the resulting velocity field has a positive shear stress, . This effect appears only at high resolution. The transport, which decays with time as t^-1/2, arises primarily because the vortices drive compressive motions. This result suggests a possible mechanism for angular momentum transport in low-ionization disks, with two important caveats: a mechanism must be found to inject vorticity into the disk, and the vortices must not decay rapidly due to three-dimensional instabilities.

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arXiv2005

Nonlinear Criterion for the Stability of Molecular Clouds

Dynamically significant magnetic fields are routinely observed in molecular clouds, with mass-to-flux ratio lambda = (2 pi sqrt{G}) (Sigma/B) ~ 1 (here Sigma is the total column density and B is the field strength). It is widely believed that ``subcritical'' clouds with lambda < 1 cannot collapse, based on virial arguments by Mestel and Spitzer and a linear stability analysis by Nakano and Nakamura. Here we confirm, using high resolution numerical models that begin with a strongly supersonic velocity dispersion, that this criterion is a fully nonlinear stability condition. All the high-resolution models with lambda <= 0.95 form ``Spitzer sheets'' but collapse no further. All models with lambda >= 1.02 collapse to the maximum numerically resolvable density. We also investigate other factors determining the collapse time for supercritical models. We show that there is a strong stochastic element in the collapse time: models that differ only in details of their initial conditions can have collapse times that vary by as much as a factor of 3. The collapse time cannot be determined from just the velocity dispersion; it depends also on its distribution. Finally, we discuss the astrophysical implications of our results.

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arXiv2005

Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics

Conservative numerical schemes for general relativistic magnetohydrodynamics (GRMHD) require a method for transforming between ``conserved'' variables such as momentum and energy density and ``primitive'' variables such as rest-mass density, internal energy, and components of the four-velocity. The forward transformation (primitive to conserved) has a closed-form solution, but the inverse transformation (conserved to primitive) requires the solution of a set of five nonlinear equations. Here we discuss the mathematical properties of the inverse transformation and present six numerical methods for performing the inversion. The first method solves the full set of five nonlinear equations directly using a Newton-Raphson scheme and a guess from the previous timestep. The other methods reduce the five nonlinear equations to either one or two nonlinear equations that are solved numerically. Comparisons between the methods are made using a survey over phase space, a two-dimensional explosion problem, and a general relativistic MHD accretion disk simulation. The run-time of the methods is also examined. Code implementing the schemes is available for download on the web.

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arXiv2005

Nonlinear Stability of Thin, Radially-Stratified Disks

We perform local numerical experiments to investigate the nonlinear stability of thin, radially-stratified disks. We demonstrate the presence of radial convective instability when the disk is nearly in uniform rotation, and show that the net angular momentum transport is slightly inwards, consistent with previous investigations of vertical convection. We then show that a convectively-unstable equilibrium is stabilized by differential rotation. Convective instability is determined by the Richardson number Ri = N_r^2/(qΩ)^2, where N_r is the radial Brunt-Vaisala frequency and qΩis the shear rate. Classical convective instability in a nonshearing medium (Ri -> -infinity) is suppressed when Ri > -1, i.e. when the shear rate becomes greater than the growth rate. Disks with a nearly-Keplerian rotation profile and radial gradients on the order of the disk radius have Ri > -0.01 and are therefore stable to local nonaxisymmetric disturbances. One implication of our results is that the ``baroclinic'' instability recently claimed by Klahr & Bodenheimer is either global or nonexistent. We estimate that our simulations would detect any genuine growth rate > 0.0025Ω.

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arXiv2005

Linear Theory of Thin, Radially-Stratified Disks

We consider the nonaxisymmetric linear theory of radially-stratified disks. We work in a shearing-sheet-like approximation, where the vertical structure of the disk is neglected, and develop equations for the evolution of a plane-wave perturbation comoving with the shear flow (a shearing wave, or ``shwave''). We calculate a complete solution set for compressive and incompressive short-wavelength perturbations in both the stratified and unstratified shearing-sheet models. We develop expressions for the late-time asymptotic evolution of an individual shwave as well as for the expectation value of the energy for an ensemble of shwaves that are initially distributed isotropically in k-space. We find that: (i) incompressive, short-wavelength perturbations in the unstratified shearing sheet exhibit transient growth and asymptotic decay, but the energy of an ensemble of such shwaves is constant with time (consistent with Afshordi, Mukhopadhyay & Narayan 2004); (ii) short-wavelength compressive shwaves grow asymptotically in the unstratified shearing sheet, as does the energy of an ensemble of such shwaves; (iii) incompressive shwaves in the stratified shearing sheet have density and azimuthal velocity perturbations δΣ,δv_y ~ t^{-Ri} (for |Ri| << 1), where Ri = N_x^2/(q Ω)^2 is the Richardson number, N_x^2 is the square of the radial Brunt-Vaisala frequency and qΩis the effective shear rate; (iv) the energy of an ensemble of incompressive shwaves in the stratified shearing sheet behaves asymptotically as Ri t^{1-4Ri} for |Ri| << 1. For Keplerian disks with modest radial gradients, |Ri| is expected to be << 1, and there will therefore be weak growth in a single shwave for Ri < 0 and near-linear growth in the energy of an ensemble of shwaves, independent of the sign of Ri.

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