The role of Hall diffusion in the magnetically threaded thin accretion discs

We study role of the Hall diffusion in the magnetic star-disc interaction. In a simplified steady state configuration, the total torque is calculated in terms of the fastness parameter and a new term because of the Hall diffusion. We show the total torque reduces as the Hall term becomes more significant. Also, the critical fastness parameter (at which the total torque is zero) reduces because of the Hall diffusion.     

On disk accretion

A simple but sufficiently accurate method for calculating an accretion disk structure is developed. The detailed analysis of the accretion disk is fulfilled by using this method. The effect of turbulent heat transfer on the disk structure is taken into account along with the effect of radiative transfer. The turbulent heat transfer is shown to play an important role, and may be even predominant in the inner disk region. The dependence of temperatureT and density on thez-coordinate is found. Simple analytic expressions are proposed for the run of the density in all the disk zones. It is shown that the inner disk region is convectively stable. The main parameters of all the zones are derived. The geometry of regular motions is studied; the regular hydrodynamical flows are found to appear directed both toward and outside the central object. A detailed comparison is made with the results of other authors.     

On the computation of accretion disk spectra

Spectra of accretion disks in dwarf novae and some novalike stars have been computed. Many simplifications to the general model of the nature of a cataclysmic variable are needed to make the system numerically tractable. The necessity, justification, and implications of such simplifications are discussed together with the influences of some system parameters on the disk radiation.Paper presented at the IAU Colloquium No. 93 on Cataclysmic Variables. Recent Multi-Frequency Observations and Theoretical Developments, held at Dr. Remeis-Sternwarte Bamberg, F.R.G., 16–19 June, 1986.     

Stability of accretion discs threaded by a strong magnetic field

We study the stability of poloidal magnetic fields anchored in a thin accretion disc. The two-dimensional hydrodynamics in the disc plane is followed by a grid-based numerical simulation including the vertically integrated magnetic forces. The three-dimensional magnetic field outside the disc is calculated in a potential field approximation from the magnetic flux density distribution in the disc. For uniformly rotating discs we confirm numerically the existence of the interchange instability as predicted by Spruit, Stehle & Papaloizou . In agreement with predictions from the shearing sheet model, discs with Keplerian rotation are found to be stabilized by the shear, as long as the contribution of magnetic forces to support against gravity is small. When this support becomes significant, we find a global instability which transports angular momentum outwardly and allows mass to accrete inwardly. The instability takes the form of a m =1 rotating 'crescent', reminiscent of the purely hydrodynamic non-linear instability previously found in pressure-supported discs. A model where the initial surface mass density Σ( r ) and B _z ( r ) decrease with radius as power laws shows transient mass accretion during about six orbital periods, and settles into a state with surface density and field strength decreasing approximately exponentially with radius. We argue that this instability is likely to be the main angular momentum transport mechanism in discs with a poloidal magnetic field sufficiently strong to suppress magnetic turbulence. It may be especially relevant in jet-producing discs.     

Mass accretion by the nuclei of disk galaxies,II

Repeated explosions in the nuclei of galaxies are now accepted as observationally established phenomena. Each explosion leads to the ejection of gas from the central region of a galaxy with velocities depending on the strength of the explosive event. In the process the nucleus temporarily becomes gas-deficient. It is suggested that the mass los is replenished by the accretion of the mass which is shed by those evolved stars in the galactic bulge that possess relatively low rotational velocities. The gas to be accreted is assumed to be magnetized. In the present model, the accretion rate has been assumed to be a function of both radial distance and time. The cross-radial equation of motion has been solved to derive the expression for the rotational velocity which is found to bealmost linear with the radial distance from the centre. The radial equation has been solved to calculate the time-scale over which the nucleus accumulates sufficient mass to undergo instability and suffer explosion. The calculated time-scale range from few multiples of 10⁷ to a few multiples of 10⁸ yr. This range agrees very well with that as has been suggested on the basis of observation in the case of our own Galaxy.     

Mass accretion by the nuclei of disk galaxies

In this work a model has been proposed to explain how the nucleus of a Galaxy can accumulate mass and becomes supermassive — ultimately giving way to gravitational instability leading to an explosion in the nucleus. The process may be repeated many times during the life-span of a Galaxy. The mass shed by the evolved stars populating the central region of the Galaxy can be attracted toward the nuclear core by gravitational pull. Since the incident gas possesses rotational velocity, the centrifugal repulsion of the gas may balance the gravitational pull of the nucleus; thus infall of mass into the nucleus will ordinarily be inhibited. But dissipative agents — such as the prevailing magnetic field and the viscosity of gas — may be sufficient to destroy the rotational velocity of the incident gas and keep the accretion process efficient. The correlation between rotational velocity of gas and its distance from the centre of the Galaxy has been deduced. The radial equation of motion has been solved and the time-scale during which the nucleus accumulates mass sufficient for explosion, has been estimated.     

Alignment and precession of a black hole with a warped accretion disc

We consider the shape of an accretion disc whose outer regions are misaligned with the spin axis of a central black hole and calculate the steady state form of the warped disc in the case where the viscosity and surface densities are power laws in the distance from the central black hole. We discuss the shape of the resulting disc in both the frame of the black hole and that of the outer disc. We note that some parts of the disc and also any companion star maybe shadowed from the central regions by the warp. We compute the torque on the black hole caused by the Lense–Thirring precession, and hence compute the alignment and precession time-scales. We generalize the case with viscosity and hence surface density independent of radius to more realistic density distributions for which the surface density is a decreasing function of radius. We find that the alignment time-scale does not change greatly but the precession time-scale is more sensitive. We also determine the effect on this time-scale if we truncate the disc. For a given truncation radius, the time-scales are less affected for more sharply falling density distributions.     

Formation of astrophysical jets by a contracting magnetic accretion disk

In the present paper, we discuss an MHD model for the formation of astrophysical jets, in which the directed flows are ejected along the rotation axis of an accretion disk formed from a cloud having a large scale magnetic field parallel to the angular momentum axis of the disk. The acceleration of jets is due to thej×B force in the relaxing magnetic twist which is produced by the rotation of the disk. The characteristic features of the jets, predicted by our mechanism and hopefully to be proven by observations, are the helical velocity and the hollow cylindrical shape of the jet, with a diameter of roughly the size of the region from which the acceretion disk collected its mass. Justification for the assumption of the perpendicular orientation of the disk, or the parallelism of the jets, to the external magnetic field may be provided by the fact that the component of rotation whose axis is perpendicular to the field may have been damped in the earlier phase of the cloud contraction.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 Septemper–6 October, 1984.     

Formation of the prelunar accretion disk

According to the single-impact hypothesis for forming the Moon, the angular momentum needed for the present Earth-Moon system can be imparted to the proto-Earth by a collision with a body having one-tenth of the mass or more. The collision must vaporize a large amount of rock which must stay in the form of vapor after expanding in density by a factor of several, so that pressure gradients can accelerate significant amounts of the matter into orbital motion about the proto-Earth. A successful theory must put considerably more than a lunar mass into orbit, having considerably more angular momentum than is needed to assemble a lunar mass in orbit at 3 Earth radii. Such a collision has been simulated by a particular form of a particle-in-cell representation of hydrodynamics and 78 cases have been run representing variations in a variety of parameters. A significant fraction of the cases were successful in creating a satisfactory prelunar accretion disk. A fairly common characteristic of these cases was the presence of an excess velocity in the collision (above that of a parabolic orbit), implying that the projectile involved in the collision existed in an Earth-crossing orbit of significant ellipticity. A majority of the mass of the prelunar accretion disk is contributed by the projectile.     

Wavelength dependence of the polarization of radiation from an accretion disk: Testing accretion disk models

We show that a fundamental choice between various models of an accretion disk around a black hole can be made based on the spectral wavelength distribution of the polarization. This conclusion is based on the possibility of comparing the observed spectral distribution of the polarization with its theoretical values obtained in various accretion disk models. The expected power-law wavelength (frequency) dependences of the polarization for various accretion disk models known in the literature are presented in the table.     

Physics of the primitive solar accretion disk

The theory of viscous accretion disks developed by Lynden-Bell and Pringle has been applied to the evolution of the primitive solar nebula. The additional physical input needed to determine the structure of the disk is described. A series of calculations was carried out using a steady flow approximation to explore the effects on the disk properties of variations in such parameters as the angular momentum and accretion rate of the infalling material from a collapsing interstellar cloud fragment. The more detailed evolutionary calculations involved five cases with various combinations of parameters. It was concluded that the late stages of evolution of the disks would be dominated by the effects of mass loss from the expansion of a hot disk corona into space, and the effects of this were included in the evolutionary calculations. A new theory of comet formation is formulated upon these results. The most important result is the conclusion, which appears to be inescapable, that the primitive solar accretion disk was repeatedly unstable against axisymmetric perturbations, in which rings would form and collapse upon themselves, with the subsequent formation of giant gaseous protoplanets.     

On the pulsational-radial oscillations instability of isothermal magnetized accretion disk with self-gravity

This is the first paper to consider the effects of both magnetic field and self-gravity on the pulsational instability. Our main new results are that the self-gravity enhances the instability of the magneto-acoustic mode in the outer disk strongly, and also affects the instability in the inner disk, but stabilized the viscous mode. The effect of self-gravity is much greater than that of magnetic field in the outer disk, while the effect of magnetic field on the instability is weaker than that in the previous work's (Wuet al., 1995; Yanget al., 1995), in which the self-gravity has not been considered. Finally, we discuss our results.     

Mass and spin co-evolution during the alignment of a black hole in a warped accretion disc

In this paper, we explore the gravitomagnetic interaction of a black hole (BH) with a misaligned accretion disc to study BH spin precession and alignment jointly with BH mass M _BH and spin parameter a evolution, under the assumption that the disc is continually fed, in its outer region, by matter with angular momentum fixed on a given direction     . We develop an iterative scheme based on the adiabatic approximation to study the BH–disc co-evolution: in this approach, the accretion disc transits through a sequence of quasi-steady warped states (Bardeen–Petterson effect) and interacts with the BH until the spin   J _BH  aligns with     . For a BH aligning with a corotating disc, the fractional increase in mass is typically less than a few per cent, while the spin modulus can increase up to a few tens of per cent. The alignment time-scale     is of  ∼10⁵–10⁶ yr  for a maximally rotating BH accreting at the Eddington rate. BH–disc alignment from an initially counter-rotating disc tends to be more efficient compared to the specular corotating case due to the asymmetry seeded in the Kerr metric: counter-rotating matter carries a larger and opposite angular momentum when crossing the innermost stable orbit, so that the spin modulus decreases faster and so the relative inclination angle.     

Energy accumulating accretion disk orbiting a Kerr black hole

A geometrically thin, energy accumulating $aL-disk is suggested which orbits a Kerr black hole. With increasing internal forces, the “standard” disks develop into energy accumulating disks. These accumulating disks are geometrically thin as long as their internal forces remain below a certain bound, allowing nearly geodesic orbits.     

Simulations of jet formation from a magnetized accretion disk

Axisymmetric magnetohydrodynamic (MHD) simulations have been made of the formation of jets from a Keplerian disk threaded by a magnetic field. The disk is treated as a boundary condition, where matter with high specific entropy is ejected with a Keplerian azimuthal speed and a poloidal speed less than the slow magnetosonic velocity, and where boundary conditions on the magnetic fields correspond to a highly conducting disk. Initially, the space above the disk, the corona, is filled with high specific entropy plasma in the thermal equilibrium in the gravitational field of the central object. The initial magnetic field is poloidal and is represented by the superposition of the fields of monopoles located below the plane of the disk.The rotation of the disk twists the initial poloidal magnetic field lines, and this twist propagates into the corona pushing matter into jet-like outflow in a cylindrical region. After the first switch-on wave, which originates during the first rotation period of the inner radius of the disk, the matter outflowing from the disk starts to flow and accelerate in thez-direction owing to both the magnetic and pressure gradient forces. The flow accelerates through the slow magnetosonic and Alfvén surfaces and at larger distances through the fast magnetosonic surface. The flow velocity of the jet is approximately parallel to thez-axis, with the collimation mainly a result of the pinching force of the toroidal magnetic field. The energy flux of the flow increases with increasing magnetic field strength on the disk. Some of the cases studied have been run for long times, 60 rotation periods of the inner radius of the disk, and show indications of approaching a stationary state.     

Forced oscillations in a hydrodynamical accretion disk and QPOs

This is the second of a series of papers aimed to look for an explanation on the generation of high frequency quasi-periodic oscillations (QPOs) in accretion disks around neutron star, black hole, and white dwarf binaries. The model is inspired by the general idea of a resonance mechanism in the accretion disk oscillations as was already pointed out by Abramowicz and Klu’zniak (2001). In a first paper (P'etri, 2005a, paper I), we showed that a rotating misaligned magnetic field of a neutron star gives rise to some resonances close to the inner edge of the accretion disk. In this second paper, we suggest that this process does also exist for an asymmetry in the gravitational potential of the compact object. We prove that the same physics applies, at least in the linear stage of the response to the disturbance in the system. This kind of asymmetry is well suited for neutron stars or white dwarfs possessing an inhomogeneous interior allowing for a deviation from a perfectly spherically symmetric gravitational field. After a discussion on the magnitude of this deformation applied to neutron stars, we show by a linear analysis that the disk initially in a cylindrically symmetric stationary state is subject to {three kinds of resonances: a corotation resonance, a Lindblad resonance due to a driven force and a parametric resonance}. In a second part, we focus on the linear response of a thin accretion disk in the 2D limit. {Waves are launched at the aforementioned resonance positions and propagate in some permitted regions inside the disk, according to the dispersion relation obtained by a WKB analysis}. In a last part, these results are confirmed and extended via non linear hydrodynamical numerical simulations performed with a pseudo-spectral code solving Euler's equations in a 2D cylindrical coordinate frame. {We found that for a weak potential perturbation, the Lindblad resonance is the only effective mechanism producing a significant density fluctuation}. In a last step, we replaced the Newtonian potential by the so called logarithmically modified pseudo-Newtonian potential in order to take into account some general-relativistic effects like the innermost stable circular orbit (ISCO). The latter potential is better suited to describe the close vicinity of a neutron star or a black hole. However, from a qualitative point of view, the resonance conditions remain the same. The highest kHz QPOs are then interpreted as the orbital frequency of the disk at locations where the response to the resonances are maximal. It is also found that strong gravity is not required to excite the resonances.     

Structure of the satellitary accretion disk of Saturn

A detailed computation on the equilibrium structure of an accretion disk around Saturn from which the regular satellites presumably originated is reported. Such a disk is the predecessor of the self-dissipating disk that is formed when the mass infall stops (Cassen and Moosman, 1981, Icarus48, 353–376). When determining the disk structure local energy balance was assumed. Convention was taken into account by introducing local energy dissipation and, in an approximate manner, sonic convection. Changes in the disk structure were investigated by varying the free parameters, i.e., the external flux from both the protosun and the protoplanet, the abundance of dust and the strength of turbulence. It has been verified that the external energy flux does not play an important role in the evolution of the disk structure. Models characterized by either longer times (?3 10³ year) or a noticeable depletion of condensable elements (10^?2 times less than the solar value) have a total mass of the order of 0.34?0.1 times the mass of the regular satellites increased by the mass of the light elements. Low turbulence models (Reynolds critical number $\text{Re}{}^1\text{= 150}$) are characterized approximately by a total mass twice as large the mass of the regular satellites. All the studied models present a temperature distribution that allows the condensation of iron, silicate, and, in the outer regions, ice grains. All models but the one with 10^?2 of the solar value of condensable elements are characterized by a wide convective region that contains the formation zone of the regular satellites.     

Secular ring instability in the protoplanetary accretion disk

The basic parameters describing the angular momentum distribution within the Uranus system and of its tidal evolution have been estimated. The nine satellites orbiting under the synchronous zone of Uranus is the maximum number in the solar system and it makes the Uranus system different compared with any other in the Solar system, however the satellites in question are relatively small and their contribution of the tidal dynamics of the system is small compared with that due to UI and UV. The time for existence of the nine satellites as integrated bodies can be estimated as 1.4 × 10⁹ y (UVI) and more. The total tidal decrease in the Uranus angular velocity of rotation is estimated as 7 × 10^–9s^–1.     

MHD simulations of the long-term evolution of a dipolar magnetosphere surrounded by an accretion disk

The evolution of a stellar, initially dipole type magnetosphere interacting with an accretion disk is investigated using numerical ideal MHD simulations. The simulations follow several 1000 Keplerian periods of the inner disk (for animated movies see http://www.aip.de～cfendt).Our model prescribes a Keplerian disk around a rotating star as a fixed boundary condition. The initial magnetic field distribution remains frozen into the star and the disk. The mass flow rate into the corona is fixed for both components. The initial dipole type magnetic field develops into a spherically radial outflow pattern with two main components – a disk wind and a stellar wind – both evolving into a quasi-stationary final state. A neutral field line divides both components, along which small plasmoids are ejected in irregular time intervals. The half opening angle of the stellar wind cone varies from 30° to55° depending on the ratio of the mass flow rates of disk wind and stellar wind. The maximum speed of the outflow is about the Keplerian speed at the inner disk radius. An axial jet forms during the first decades of rotations. However, this feature does not survive on the very long time scale and a pressure driven low velocity flow along the axis evolves. Within a cone of 15° along the axis the formation of knots may be observed if the stellar wind is weak. With the chosen mass flow rates and field strength we see almost no indication for a flow self-collimation. This is due to the weak net poloidal electric current in the magnetosphere which is in difference to typical jet models.