Toy model for a two-dimensional accretion disk dominated by Poynting flux

We discuss the effect of the Poynting flow on the magnetically dominated thin accretion disk, which is simplified to a two-dimensional disk on the equatorial plane. It is shown in the relativistic formulation that the Poynting flux by the rotating magnetic field with Keplerian angular velocity can balance the energy and angular momentum conservation of a steady accretion flow.Comment: 17 pages, no figure

Warp propagation in astrophysical discs

Astrophysical discs are often warped, that is, their orbital planes change with radius. This occurs whenever there is a non-axisymmetric force acting on the disc, for example the Lense-Thirring precession induced by a misaligned spinning black hole, or the gravitational pull of a misaligned companion. Such misalignments appear to be generic in astrophysics. The wide range of systems that can harbour warped discs - protostars, X-ray binaries, tidal disruption events, quasars and others - allows for a rich variety in the disc's response. Here we review the basic physics of warped discs and its implications.Comment: To be published in Astrophysical Black Holes by Haardt et al., Lecture Notes in Physics, Springer 2015. 19 pages, 2 figure

General Relativistic MHD Jets

Magnetic fields connecting the immediate environs of rotating black holes to large distances appear to be the most promising mechanism for launching relativistic jets, an idea first developed by Blandford and Znajek in the mid-1970s. To enable an understanding of this process, we provide a brief introduction to dynamics and electromagnetism in the spacetime near black holes. We then present a brief summary of the classical Blandford-Znajek mechanism and its conceptual foundations. Recently, it has become possible to study these effects in much greater detail using numerical simulation. After discussing which aspects of the problem can be handled well by numerical means and which aspects remain beyond the grasp of such methods, we summarize their results so far. Simulations have confirmed that processes akin to the classical Blandford-Znajek mechanism can launch powerful electromagnetically-dominated jets, and have shown how the jet luminosity can be related to black hole spin and concurrent accretion rate. However, they have also shown that the luminosity and variability of jets can depend strongly on magnetic field geometry. We close with a discussion of several important open questions.Comment: 21 pages, 2 figures, To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009

Formation of Small-Scale Condensations in the Molecular Clouds via Thermal Instability

A systematic study of the linear thermal instability of a self-gravitating magnetic molecular cloud is carried out for the case when the unperturbed background is subject to local expansion or contraction. We consider the ambipolar diffusion, or ion-neutral friction on the perturbed states. In this way, we obtain a non-dimensional characteristic equation that reduces to the prior characteristic equation in the non-gravitating stationary background. By parametric manipulation of this characteristic equation, we conclude that there are, not only oblate condensation forming solutions, but also prolate solutions according to local expansion or contraction of the background. We obtain the conditions for existence of the Field lengths that thermal instability in the molecular clouds can occur. If these conditions establish, small-scale condensations in the form of spherical, oblate, or prolate may be produced via thermal instability.Comment: 16 page, accepted by Ap&S

The influence of cosmic-rays on the magnetorotational instability

We present a linear perturbation analysis of the magnetorotational instability in the presence of the cosmic rays. Dynamical effects of the cosmic rays are considered by a fluid description and the diffusion of cosmic rays is only along the magnetic field lines. We show an enhancement in the growth rate of the unstable mode because of the existence of cosmic rays. But as the diffusion of cosmic rays increases, we see that the growth rate decreases. Thus, cosmic rays have a destabilizing role in the magnetorotational instability of the accretion discs.Comment: Accepted for publication in Astrophysics & Space Scienc

The Formation of Fragments at Corotation in Isothermal Protoplanetary Disks

Numerical hydrodynamics simulations have established that disks which are evolved under the condition of local isothermality will fragment into small dense clumps due to gravitational instabilities when the Toomre stability parameter $Q$ is sufficiently low. Because fragmentation through disk instability has been suggested as a gas giant planet formation mechanism, it is important to understand the physics underlying this process as thoroughly as possible. In this paper, we offer analytic arguments for why, at low $Q$, fragments are most likely to form first at the corotation radii of growing spiral modes, and we support these arguments with results from 3D hydrodynamics simulations.Comment: 21 pages, 1 figur

Magnetic fields in protoplanetary disks

Magnetic fields likely play a key role in the dynamics and evolution of protoplanetary discs. They have the potential to efficiently transport angular momentum by MHD turbulence or via the magnetocentrifugal acceleration of outflows from the disk surface, and magnetically-driven mixing has implications for disk chemistry and evolution of the grain population. However, the weak ionisation of protoplanetary discs means that magnetic fields may not be able to effectively couple to the matter. I present calculations of the ionisation equilibrium and magnetic diffusivity as a function of height from the disk midplane at radii of 1 and 5 AU. Dust grains tend to suppress magnetic coupling by soaking up electrons and ions from the gas phase and reducing the conductivity of the gas by many orders of magnitude. However, once grains have grown to a few microns in size their effect starts to wane and magnetic fields can begin to couple to the gas even at the disk midplane. Because ions are generally decoupled from the magnetic field by neutral collisions while electrons are not, the Hall effect tends to dominate the diffusion of the magnetic field when it is able to partially couple to the gas. For a standard population of 0.1 micron grains the active surface layers have a combined column of about 2 g/cm^2 at 1 AU; by the time grains have aggregated to 3 microns the active surface density is 80 g/cm^2. In the absence of grains, x-rays maintain magnetic coupling to 10% of the disk material at 1 AU (150 g/cm^2). At 5 AU the entire disk thickness becomes active once grains have aggregated to 1 micron in size.Comment: 11 pages, 11 figs, aastex.cls. Accepted for publication in Astrophysics & Space Science. v3 corrects bibliograph

Interactions between brown-dwarf binaries and Sun-like stars

Several mechanisms have been proposed for the formation of brown dwarfs, but there is as yet no consensus as to which -- if any -- are operative in nature. Any theory of brown dwarf formation must explain the observed statistics of brown dwarfs. These statistics are limited by selection effects, but they are becoming increasingly discriminating. In particular, it appears (a) that brown dwarfs that are secondaries to Sun-like stars tend to be on wide orbits, a\ga 100\,{\rm AU} (the Brown Dwarf Desert), and (b) that these brown dwarfs have a significantly higher chance of being in a close (a\la 10\,{\rm AU}) binary system with another brown dwarf than do brown dwarfs in the field. This then raises the issue of whether these brown dwarfs have formed {\it in situ}, i.e. by fragmentation of a circumstellar disc; or have formed elsewhere and subsequently been captured. We present numerical simulations of the purely gravitational interaction between a close brown-dwarf binary and a Sun-like star. These simulations demonstrate that such interactions have a negligible chance ($<0.001$) of leading to the close brown-dwarf binary being captured by the Sun-like star. Making the interactions dissipative by invoking the hydrodynamic effects of attendant discs might alter this conclusion. However, in order to explain the above statistics, this dissipation would have to favour the capture of brown-dwarf binaries over single brown-dwarfs, and we present arguments why this is unlikely. The simplest inference is that most brown-dwarf binaries -- and therefore possibly also most single brown dwarfs -- form by fragmentation of circumstellar discs around Sun-like protostars, with some of them subsequently being ejected into the field.Comment: 10 pages, 8 figures, Accepted for publication in Astrophysics and Space Scienc