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Register a new userVertical Structure and Coronal Power of Accretion Disks Powered by MRI Turbulence
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Dmitri A. Uzdensky
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In this paper we consider two outstanding intertwined problems in modern high-energy astrophysics: (1) the vertical thermal structure of an optically thick accretion disk heated by the dissipation of magnetohydrodynamic (MHD) turbulence driven by the magneto-rotational instability (MRI), and (2) determining the fraction of the accretion power released in the corona above the disk. For simplicity, we consider a gas-pressure-dominated disk and assume a constant opacity. We argue that the local turbulent dissipation rate due to the disruption of MRI channel flows by secondary parasitic instabilities should be uniform across most of the disk, almost up to the disk photosphere. We then obtain a self-consistent analytical solution for the vertical thermal structure of the disk, governed by the balance between the heating by MRI turbulence and the cooling by radiative diffusion. Next, we argue that the coronal power fraction is determined by the competition between the Parker instability, viewed as a parasitic instability feeding off of MRI channel flows, and other parasitic instabilities. We show that the Parker instability inevitably becomes important near the disk surface, leading to a certain lower limit on the coronal power. While most of the analysis in this paper focuses on the case of a disk threaded by an externally imposed vertical magnetic field, we also discuss the zero-net-flux case, in which the magnetic field is produced by the MRI dynamo itself, and show that most of our arguments and conclusions should be valid in this case as well.
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Global three dimensional magnetohydrodynamic (MHD) simulations of turbulent accretion disks are presented which start from fully equilibrium initial conditions in which the magnetic forces are accounted for and the induction equation is satisfied. The local linear theory of the magnetorotational instability (MRI) is used as a predictor of the growth of magnetic field perturbations in the global simulations. The linear growth estimates and global simulations diverge when non-linear motions - perhaps triggered by the onset of turbulence - upset the velocity perturbations used to excite the MRI. The saturated state is found to be independent of the initially excited MRI mode, showing that once the disk has expelled the initially net flux field and settled into quasi-periodic oscillations in the toroidal magnetic flux, the dynamo cycle regulates the global saturation stress level. Furthermore, time-averaged measures of converged turbulence, such as the ratio of magnetic energies, are found to be in agreement with previous works. In particular, the globally averaged stress normalized to the gas pressure, <alpha_{rm P}> = 0.034, with notably higher values achieved for simulations with higher azimuthal resolution. Supplementary tests are performed using different numerical algorithms and resolutions. Convergence with resolution during the initial linear MRI growth phase is found for 23-35 cells per scaleheight (in the vertical direction).
We model the vertical structure of magnetized accretion disks subject to viscous and resistive heating, and irradiation by the central star. We apply our formalism to the radial structure of magnetized accretion disks threaded by a poloidal magnetic field dragged during the process of star formation developed by Shu and coworkers. We consider disks around low mass protostars, T Tauri, and FU Orionis stars. We consider two levels of disk magnetization, $lambda_{sys} = 4$ (strongly magnetized disks), and $lambda_{sys} = 12$ (weakly magnetized disks). The rotation rates of strongly magnetized disks have large deviations from Keplerian rotation. In these models, resistive heating dominates the thermal structure for the FU Ori disk. The T Tauri disk is very thin and cold because it is strongly compressed by magnetic pressure; it may be too thin compared with observations. Instead, in the weakly magnetized disks, rotation velocities are close to Keplerian, and resistive heating is always less than 7% of the viscous heating. In these models, the T Tauri disk has a larger aspect ratio, consistent with that inferred from observations. All the disks have spatially extended hot atmospheres where the irradiation flux is absorbed, although most of the mass ($sim 90-95$ %) is in the disk midplane. With the advent of ALMA one expects direct measurements of magnetic fields and their morphology at disk scales. It will then be possible to determine the mass-to-flux ratio of magnetized accretion disks around young stars, an essential parameter for their structure and evolution. Our models contribute to the understanding of the vertical structure and emission of these disks.
We studied dynamical balances in magnetorotational instability (MRI) turbulence with a net vertical field in the shearing box model of disks. Analyzing the turbulence dynamics in Fourier (${bf k}$-)space, we identified three types of active modes that define turbulence characteristics. These modes have lengths similar to the box size, i.e., lie in the small wavenumber region in Fourier space labeled the vital area and are: (i) the channel mode - uniform in the disk plane with the smallest vertical wavenumber,(ii) the zonal flow mode - azimuthally and vertically uniform with the smallest radial wavenumber and (iii) the rest modes. The rest modes comprise those harmonics in the vital area whose energies reach more than $50 %$ of the maximum spectral energy. The rest modes individually are not so significant compared to the channel and zonal flow modes, however, the combined action of their multitude is dominant over these two modes. These three mode types are governed by interplay of the linear and nonlinear processes, leading to their interdependent dynamics. The linear processes consist in disk flow nonmodality-modified classical MRI with a net vertical field. The main nonlinear process is transfer of modes over wavevector angles in Fourier space - the transverse cascade. The channel mode exhibits episodic bursts supplied by linear MRI growth, while the nonlinear processes mostly oppose this, draining the channel energy and redistributing it to the rest modes. As for the zonal flow, it does not have a linear source and is fed by nonlinear interactions of the rest modes.
We discuss the properties of an accretion disk around a star with parameters typical of classical T Tauri stars (CTTS), and with the average accretion rate for these disks. The disk is assumed steady and geometrically thin. The turbulent viscosity coefficient is expressed using the alpha prescription and the main heating mechanisms considered are viscous dissipation and irradiation by the central star. The energy is transported by radiation, turbulent conduction and convection. We find that irradiation from the central star is the main heating agent of the disk, except in the innermost regions, R less than 2 AU. The irradiation increases the temperature of the outer disk relative to the purely viscous case. As a consequence, the outer disk (R larger than 5 AU) becomes less dense, optically thin and almost vertically isothermal, with a temperature distribution T proportional to R^{-1/2}. The decrease in surface density at the outer disk, decreases the disk mass by a factor of 4 respect to a purely viscous case. In addition, irradiation tends to make the outer disk regions stable against gravitational instabilities.
We use global magnetohydrodynamic simulations to study the influence of net vertical magnetic fields on the structure of geometrically thin ($H/r approx 0.05$) accretion disks in the Newtonian limit. We consider initial mid-plane gas to magnetic pressure ratios $beta_0 = 1000,, 300$ and $100$, spanning the transition between weakly and strongly magnetized accretion regimes. We find that magnetic pressure is important for the disks vertical structure in all three cases, with accretion occurring at $z/Rapprox 0.2$ in the two most strongly magnetized models. The disk midplane shows outflow rather than accretion. Accretion through the surface layers is driven mainly by stress due to coherent large scale magnetic field rather than by turbulent stress. Equivalent viscosity parameters measured from our simulations show similar dependencies on initial $beta_0$ to those seen in shearing box simulations, though the disk midplane is not magnetic pressure dominated even for the strongest magnetic field case. Winds are present but are not the dominant driver of disk evolution. Over the (limited) duration of our simulations, we find evidence that the net flux attains a quasi-steady state at levels that can stably maintain a strongly magnetized disk. We suggest that geometrically thin accretion disks in observed systems may commonly exist in a magnetically elevated state, characterized by non-zero but modest vertical magnetic fluxes, with potentially important implications for disk phenomenology in X-ray binaries (XRBs) and active galactic nuclei (AGN).
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