Martin E. Pessah

SUSTAINED MAGNETOROTATIONAL TURBULENCE IN LOCAL SIMULATIONS OF STRATIFIED DISKS WITH ZERO NET MAGNETIC FLUX

We examine the effects of density stratification on magnetohydrodynamic turbulence driven by the magnetorotational instability in local simulations that adopt the shearing box approximation. Our primary result is that, even in the absence of explicit dissipation, the addition of vertical gravity leads to convergence in the turbulent energy densities and stresses as the resolution increases, contrary to results for zero net flux, unstratified boxes. The ratio of total stress to midplane pressure has a mean of ~0.01, although there can be significant fluctuations on long (50?orbits) timescales. We find that the time-averaged stresses are largely insensitive to both the radial and the vertical aspect ratios of our simulation domain. For simulations with explicit dissipation, we find that stratification extends the range of Reynolds and magnetic Prandtl numbers for which turbulence is sustained, but the behavior of such simulations on long timescales is highly variable. Confirming the results of previous studies, we find oscillations in the large-scale toroidal field with periods of ~10?orbits and describe the dynamo process that underlies these cycles. We discuss possible origins for the different convergence properties of the stratified and unstratified domains and identify open questions that remain to be answered.

ANGULAR MOMENTUM TRANSPORT IN ACCRETION DISKS: SCALING LAWS IN MRI-DRIVEN TURBULENCE

We present a scaling law that predicts the values of the stresses obtained in numerical simulations of saturated MRI-driven turbulence in nonstratified shearing boxes. It relates the turbulent stresses to the strength of the vertical magnetic field, the sound speed, the vertical size of the box, and the numerical resolution and predicts accurately the results of 35 numerical simulations performed for a wide variety of physical conditions. We use our result to show that the saturated stresses in simulations with zero net magnetic flux depend linearly on the numerical resolution and would become negligible if the resolution were set equal to the natural dissipation scale in astrophysical disks. We conclude that in order for MRI-driven turbulent angular momentum transport to be able to account for the large value of the effective alpha viscosity inferred observationally, the disk must be threaded by a significant vertical magnetic field and the turbulent magnetic energy must be in near equipartition with the thermal energy. This result has important implications for the spectra of accretion disks and their stability.

The Stability of Magnetized Rotating Plasmas with Superthermal Fields

During the last decade it has become evident that the magnetorotational instability is at the heart of the enhanced angular momentum transport in weakly magnetized accretion disks around neutron stars and black holes. In this paper we investigate the local linear stability of differentially rotating, magnetized flows and the evolution of the magnetorotational instability beyond the weak-field limit. We show that, when superthermal toroidal fields are considered, the effects of both compressibility and magnetic tension forces, which are related to the curvature of toroidal field lines, should be taken fully into account. We demonstrate that the presence of a strong toroidal component in the magnetic field plays a nontrivial role. When strong fields are considered, the strength of the toroidal magnetic field not only modifies the growth rates of the unstable modes but also determines which modes are subject to instabilities. We find that, for rotating configurations with Keplerian laws, the magnetorotational instability is stabilized at low wavenumbers for toroidal Alfven speeds exceeding the geometric mean of the sound speed and the rotational speed. For a broad range of magnetic field strengths, we also find that two additional distinct instabilities are present; they both appear as the result of coupling between the modes that become the Alfven and the slow modes in the limit of no rotation. We discuss the significance of our findings for the stability of cold, magnetically dominated, rotating fluids and argue that, for these systems, the curvature of toroidal field lines cannot be neglected even when short-wavelength perturbations are considered. We also comment on the implications of our results for the validity of shearing box simulations in which superthermal toroidal fields are generated.

The signature of the magnetorotational instability in the Reynolds and Maxwell stress tensors in accretion discs

The magnetorotational instability is thought to be responsible for the generation of magnetohydrodynamic turbulence that leads to enhanced outward angular momentum transport in accretion discs. Here, we present the first formal analytical proof showing that, during the exponential growth of the instability, the mean (averaged over the disc scaleheight) Reynolds stress is always positive, the mean Maxwell stress is always negative, and hence the mean total stress is positive and leads to a net outward flux of angular momentum. More importantly, we show that the ratio of the Maxwell to the Reynolds stresses during the late times of the exponential growth of the instability is determined only by the local shear and does not depend on the initial spectrum of perturbations or the strength of the seed magnetic field. Even though we derived this property of the stress tensors for the exponential growth of the instability in incompressible flows, numerical simulations of shearing boxes show that this characteristic is qualitatively preserved under more general conditions, even during the saturated turbulent state generated by the instability.

The fundamental difference between shear alpha viscosity and turbulent magnetorotational stresses

Numerical simulations of turbulent, magnetized, differentially rotating flows driven by the magnetorotational instability (MRI) are often used to calculate the effective values of alpha viscosity that is invoked in analytical models of accretion discs. In this paper, we use various dynamical models of turbulent magnetohydrodynamic stresses, as well as numerical simulations of shearing boxes, to show that angular momentum transport in MRI-driven accretion discs cannot be described by the standard model for shear viscosity. In particular, we demonstrate that turbulent magnetorotational stresses are not linearly proportional to the local shear and vanish identically for angular velocity profiles that increase outwards.

Local model for angular-momentum transport in accretion disks driven by the magnetorotational instability

We develop a local model for the exponential growth and saturation of the Reynolds and Maxwell stresses in turbulent flows driven by the magnetorotational instability. We first derive equations that describe the effects of the instability on the growth and pumping of the stresses. We highlight the relevance of a new type of correlations that couples the dynamical evolution of the Reynolds and Maxwell stresses and plays a key role in developing and sustaining the magnetorotational turbulence. We then supplement these equations with a phenomenological description of the triple correlations that lead to a saturated turbulent state. We show that the steady-state limit of the model describes successfully the correlations among stresses found in numerical simulations of shearing boxes.

Characterizing the mean-field dynamo in turbulent accretion disks

The formation and evolution of a wide class of astrophysical objects is governed by turbulent, magnetized accretion disks. Understanding their secular dynamics is of primary importance. Apart from enabling mass accretion via the transport of angular momentum, the turbulence affects the long-term evolution of the embedded magnetic flux, which in turn regulates the efficiency of the transport. In this paper, we take a comprehensive next step towards an effective mean-field model for turbulent astrophysical disks by systematically studying the key properties of magnetorotational turbulence in vertically-stratified, isothermal shearing boxes. This allows us to infer emergent properties of the ensuing chaotic flow as a function of the shear parameter as well as the amount of net-vertical flux. Using the test-field method, we furthermore characterize the mean-field dynamo coefficients that describe the long-term evolution of large-scale fields. We simultaneously infer the vertical shape and the spectral scale dependence of these closure coefficients, with the latter describing non-local contributions to the turbulent electromotive force. Based on this, we infer a scale-separation ratio of about ten for the large-scale dynamo. We finally determine scaling properties of the mean-field dynamo coefficients. The relevant component of the dynamo {alpha} effect is found to scale linearly with the shear rate, as is the corresponding turbulent diffusion, {eta}. Together, these scalings allow us to predict, in a quantitative manner, the cycle period of the well-known butterfly diagram. This lends new support to the importance of the {alpha}{Omega} mechanism in determining the evolution of large-scale magnetic fields in turbulent accretion disks.

Gravitational microlensing of γ-ray blazars

We present a detailed study of the effects of gravitational microlensing on compact and distant γ-ray blazars. These objects have γ-ray-emitting regions that are small enough to be affected by microlensing effects produced by stars lying in intermediate galaxies. We compute the gravitational magnification taking into account effects of the lensing and show that, whereas the innermost γ-ray spheres can be significantly magnified, there is little magnification either for very high γ-ray energies or for lower (radio) frequencies (because these wavelengths are emitted from larger regions). We analyse the temporal evolution of the gamma-ray magnification for sources moving in a caustic pattern field, where the combined effects of thousands of stars are taken into account using a numerical technique. We propose that some of the unidentified γ-ray sources (particularly some of those lying at high galactic latitude with gamma-ray statistical properties that are very similar to detected γ-ray blazars) are indeed the result of gravitational lensing magnification of background undetected active galactic nuclei (AGN). This is partly supported from a statistical point of view: we show herein as well, using the latest information from the third EGRET catalogue, that high-latitude γ-ray sources have similar averaged properties to already detected γ-ray AGN. Some differences between both samples, regarding the mean flux level, could also be understood within the lensing model. With an adequate selection of lensing parameters, it is possible to explain a variety of γ-ray light curves with different time-scales, including non-variable sources. The absence of strong radio counterparts could be naturally explained by differential magnification in the extended source formalism.

PLASMA INSTABILITIES IN THE CONTEXT OF CURRENT HELIUM SEDIMENTATION MODELS: DYNAMICAL IMPLICATIONS FOR THE ICM IN GALAXY CLUSTERS

Understanding whether Helium can sediment to the core of galaxy clusters is important for a number of problems in cosmology and astrophysics. All current models addressing this question are one-dimensional and do not account for the fact that magnetic fields can effectively channel ions and electrons, leading to anisotropic transport of momentum, heat, and particle diffusion in the weakly collisional intracluster medium (ICM). This anisotropy can lead to a wide variety of instabilities, which could be relevant for understanding the dynamics of heterogeneous media. In this paper, we consider the radial temperature and composition profiles as obtained from a state-of-the-art Helium sedimentation model and analyze its stability properties. We find that the associated radial profiles are unstable, to different kinds of instabilities depending on the magnetic field orientation, at all radii. The fastest growing modes are usually related to generalizations of the Magnetothermal Instability (MTI) and the Heat-flux-driven Buoyancy Instability (HBI) which operate in heterogeneous media. We find that the effect of sedimentation is to increase (decrease) the predicted growth rates in the inner (outer) cluster region. The unstable modes grow fast compared to the sedimentation timescale. This suggests that the composition gradients as inferred from sedimentation models, which do not fully account for the anisotropic character of the weakly collisional environment, might not be very robust. Our results emphasize the subtleties involved in understanding the gas dynamics of the ICM and argue for the need of a comprehensive approach to address the issue of Helium sedimentation beyond current models.

ON VERTICALLY GLOBAL, HORIZONTALLY LOCAL MODELS FOR ASTROPHYSICAL DISKS

Disks with a barotropic equilibrium structure, for which the pressure is only a function of the density, rotate on cylinders in the presence of a gravitational potential, so that the angular frequency of such a disk is independent of height. Such disks with barotropic equilibria can be approximately modeled using the shearing box framework, representing a small disk volume with height-independent angular frequency. If the disk is in baroclinic equilibrium, the angular frequency does generally depend on height, and it is thus necessary to go beyond the standard shearing box approach. In this paper, we show that given a global disk model, it is possible to develop approximate models that are local in horizontal planes without an expansion in height with shearing-periodic boundary conditions. We refer to the resulting framework as the vertically global shearing box (VGSB). These models can be non-axisymmetric for globally barotropic equilibria but should be axisymmetric for globally baroclinic equilibria. We provide explicit equations for this VGSB which can be implemented in standard magnetohydrodynamic codes by generalizing the shearing-periodic boundary conditions to allow for a height-dependent angular frequency and shear rate. We also discuss the limitations that result from the radial approximations that are needed in order to impose height-dependent shearing periodic boundary conditions. We illustrate the potential of this framework by studying a vertical shear instability and examining the modes associated with the magnetorotational instability.