How strong are the Rossby vortices?

The Rossby wave instability, associated with density bumps in differentially rotating discs, may arise in several different astrophysical contexts, such as galactic or protoplanetary discs. While the linear phase of the instability has been well studied, the nonlinear evolution and especially the saturation phase remain poorly understood. In this paper, we test the non-linear saturation mechanism analogous to that derived for wave-particle interaction in plasma physics. To this end we perform global numerical simulations of the evolution of the instability in a two-dimensional disc. We confirm the physical mechanism for the instability saturation and show that the maximum amplitude of vorticity can be estimated as twice the linear growth rate of the instability. We provide an empirical fitting formula for this growth rate for various parameters of the density bump. We also investigate the effects of the azimuthal mode number of the instability and the energy leakage in the spiral density waves. Finally, we show that our results can be extrapolated to 3D discs.Comment: Accepted for publication in MNRA

Vertical Structure of Stationary Accretion Disks with a Large-Scale Magnetic Field

In earlier works we pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because the hydrodynamic and/or magnetorotational (MRI) instabilities are suppressed high in the disk where the magnetic and radiation pressures are larger than the plasma thermal pressure. Here, we calculate the vertical profiles of the {\it stationary} accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity and the fact that the turbulence vanishes at the surface of the disk. Also, here we require that the radial accretion speed be zero at the disk's surface and we assume that the ratio of the turbulent viscosity to the turbulent magnetic diffusivity is of order unity. Thus at the disk's surface there are three boundary conditions. As a result, for a fixed dimensionless viscosity $\alpha$-value, we find that there is a definite relation between the ratio ${\cal R}$ of the accretion power going into magnetic disk winds to the viscous power dissipation and the midplane plasma-$\beta$, which is the ratio of the plasma to magnetic pressure in the disk. For a specific disk model with ${\cal R}$ of order unity we find that the critical value required for a stationary solution is $\beta_c \approx 2.4r/(\alpha h)$, where $h$ the disk's half thickness. For weaker magnetic fields, $\beta > \beta_c$, we argue that the poloidal field will advect outward while for $\beta< \beta_c$ it will advect inward. Alternatively, if the disk wind is negligible (${\cal R} \ll 1$), there are stationary solutions with $\beta \gg \beta_c$.Comment: 5 pages, 3 figure

Transmission Line Analogy for Relativistic Poynting-Flux Jets

Radio emission, polarization, and Faraday rotation maps of the radio jet of the galaxy 3C 303 have shown that one knot of this jet carries a {\it galactic}-scale electric current and that it is magnetically dominated. We develop the theory of magnetically dominated or Poynting-flux jets by making an analogy of a Poynting jet with a transmission line or waveguide carrying a net current and having a potential drop across it (from the jet's axis to its radius) and a definite impedance which we derive. Time-dependent but not necessarily small perturbations of a Poynting-flux jet are described by the "telegrapher's equations." These predict the propagation speed of disturbances and the effective wave impedance for forward and backward propagating wave components. A localized disturbance of a Poynting jet gives rise to localized dissipation in the jet which may explain the enhanced synchrotron radiation in the knots of the 3C 303 jet, and also in the apparently stationary knot HST-1 in the jet near the nucleus of the nearby galaxy M87. For a relativistic Poynting jet on parsec scales, the reflected voltage wave from an inductive termination or load can lead to a backward propagating wave which breaks down the magnetic insulation of the jet giving $|{\bf E}| /|{\bf B}|\geq 1$. At the threshold for breakdown, $|{\bf E}|/|{\bf B}|=1$, positive and negative particles are directly accelerated in the ${\bf E \times B}$ direction which is approximately along the jet axis. Acceleration can occur up to Lorentz factors $\sim 10^7$. This particle acceleration mechanism is distinct from that in shock waves and that in magnetic field reconnection.Comment: 8 pages, 6 figure

Boundary Between Stable and Unstable Regimes of Accretion

We investigated the boundary between stable and unstable regimes of accretion and its dependence on different parameters. Simulations were performed using a "cubed sphere" code with high grid resolution (244 grid points in the azimuthal direction), which is twice as high as that used in our earlier studies. We chose a very low viscosity value, with alpha-parameter alpha=0.02. We observed from the simulations that the boundary strongly depends on the ratio between magnetospheric radius r_m (where the magnetic stress in the magnetosphere matches the matter stress in the disk) and corotation radius r_cor (where the Keplerian velocity in the disk is equal to the angular velocity of the star). For a small misalignment angle of the dipole field, Theta=5 degrees, accretion is unstable if r_cor/r_m>1.35, and is stable otherwise. In cases of a larger misalignment angle of the dipole, Theta=20 degrees, instability occurs at slightly larger values, r_cor/r_m>1.41.Comment: 4 pages, 4 figures, conference proceedings: "Physics at the Magnetospheric Boundary", Geneva, Switzerland, 25-28 June, 201

AGN Obscuring Tori Supported by Infrared Radiation Pressure

Explicit 2-d axisymmetric solutions are found to the hydrostatic equilibrium, energy balance, and photon diffusion equations within obscuring tori around active galactic nuclei. These solutions demonstrate that infrared radiation pressure can support geometrically thick structures in AGN environments subject to certain constraints: the bolometric luminosity must be roughly 0.03--1 times the Eddington luminosity; and the Compton optical depth of matter in the equatorial plane should be order unity, with a tolerance of about an order of magnitude up or down. Both of these constraints are at least roughly consistent with observations. In addition, angular momentum must be redistributed so that the fractional rotational support against gravity rises from the inner edge of the torus to the outer in a manner specific to the detailed shape of the gravitational potential. This model also predicts that the column densities observed in obscured AGN should range from about 10^{22} to about 10^{24} cm^{-2}.Comment: ApJ, in pres