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1.
We present a linear analysis of the vertical structure and growth of the magnetorotational instability in weakly ionised, stratified accretion discs. The method includes the effects of the magnetic coupling, the conductivity regime of the fluid and the strength of the magnetic field, which is initially vertical. The conductivity is treated as a tensor and assumed constant with height. The Hall effect causes the perturbations to grow faster and act over a much more extended section of the disc, when the magnetic coupling is low. As a result, significant accretion can occur closer to the midplane, despite the weak magnetic coupling, because of the high column density of the fluid. This is an interesting alternative to the commonly held view that accretion is relevant mainly in the surface regions of discs, which have a better coupling, but a much lower fluid density. 相似文献
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Mark Wardle 《Monthly notices of the Royal Astronomical Society》1999,307(4):849-856
MHD in protostellar discs is modified by the Hall current when the ambipolar diffusion approximation breaks down. Here I examine the Balbus–Hawley (magnetorotational) instability of a weak, vertical magnetic field within a weakly ionized disc. Vertical stratification is neglected, and a linear analysis is undertaken for the case in which the wavevector of the perturbation is parallel to the magnetic field.
The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel case if the Hall current is dominated by negative (positive) species. The less-unstable orientation is stable for χ ≲0.5, where χ is the ratio of a generalized neutral–ion collision frequency to the Keplerian frequency. The other orientation has a formal growth rate of the order of the Keplerian angular frequency even in the limit χ →0! In this limit the wavelength of the fastest-growing mode tends to infinity, so the minimum level of ionization for instability is determined by the requirement that a wavelength fit within a disc scaleheight. In the ambipolar diffusion case, this requires χ > vA c s ; in the Hall case this imposes a potentially much weaker limit, 相似文献
The growth rate depends on whether the initial magnetic field is parallel or antiparallel to the angular momentum of the disc. The parallel case is less (more) unstable than the antiparallel case if the Hall current is dominated by negative (positive) species. The less-unstable orientation is stable for χ ≲0.5, where χ is the ratio of a generalized neutral–ion collision frequency to the Keplerian frequency. The other orientation has a formal growth rate of the order of the Keplerian angular frequency even in the limit χ →0! In this limit the wavelength of the fastest-growing mode tends to infinity, so the minimum level of ionization for instability is determined by the requirement that a wavelength fit within a disc scaleheight. In the ambipolar diffusion case, this requires χ > v
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The stability properties of magnetized discs rotating with angular velocity Ω = Ω( s , z ), dependent on both the radial and the vertical coordinates s and z , are considered. Such a rotation law is adequate for many astrophysical discs (e.g., galactic and protoplanetary discs, as well as accretion discs in binaries). In general, the angular velocity depends on height, even in thin accretion discs. A linear stability analysis is performed in the Boussinesq approximation, and the dispersion relation is obtained for short-wavelength perturbations. Any dependence of Ω on z can destabilize the flow. This concerns primarily small-scale perturbations for which the stabilizing effect of buoyancy is strongly suppressed due to the energy exchange with the surrounding plasma. For a weak magnetic field, instability of discs is mainly associated with vertical shear, whilst for an intermediate magnetic field the magnetic shear instability, first considered by Chandrasekhar and Velikhov, is more efficient. This instability is caused by the radial shear which is typically much stronger than the vertical shear. Therefore the growth time for the magnetic shear instability is much shorter than for the vertical shear instability. A relatively strong magnetic field can suppress both these instabilities. The vertical shear instability could be the source of turbulence in protoplanetary discs, where the conductivity is low. 相似文献
6.
R. Salmeron 《Astrophysics and Space Science》2011,335(2):353-371
Star formation is thought to be triggered by gravitational collapse of the dense cores of molecular clouds. Angular momentum
conservation during the collapse results in the progressive increase of the centrifugal force, which eventually halts the
inflow of material and leads to the development of a central mass surrounded by a disc. In the presence of an angular momentum
transport mechanism, mass accretion onto the central object proceeds through this disc, and it is believed that this is how
stars typically gain most of their mass. However, the mechanisms responsible for this transport of angular momentum are not
well understood. Although the gravitational field of a companion star or even gravitational instabilities (particularly in
massive discs) may play a role, the most general mechanisms are turbulence viscosity driven by the magnetorotational instability (MRI), and outflows accelerated centrifugally from the surfaces of the disc. Both processes are powered by the action of magnetic fields and
are, in turn, likely to strongly affect the structure, dynamics, evolutionary path and planet-forming capabilities of their
host discs. The weak ionisation of protostellar discs, however, may prevent the magnetic field from effectively coupling to
the gas and shear and driving these processes. Here I examine the viability and properties of these magnetically-driven processes
in protostellar discs. The results indicate that, despite the weak ionisation, the magnetic field is able to couple to the
gas and shear for fluid conditions thought to be satisfied over a wide range of radii in these discs. 相似文献
7.
V. V. Prudskikh 《Astronomy Letters》2013,39(3):192-200
A criterion for the magnetorotational instability of a protostellar disk in which the dust particles are assumed to be well mixed with the gas over the entire disk volume has been obtained within the framework of Hall magnetohydrodynamics. It is shown that the dusty plasma component affects significantly the Hall current and, under certain conditions, can cause its direction to be reversed compared to the case of a weakly ionized electron-ion plasma. A significant expansion of the range of wave numbers for unstable magnetic fluctuations is a consequence of the Hall current reversal. The spatial localization of the regions of protostellar disks in which not only the long-wavelength Alfvén disturbances but also the short-wavelength ones are subject to the magnetorotational instability is investigated. Possible physical consequences of the presence of anomalously active zones in cold disks for their structure and evolution are pointed out. 相似文献
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M. Flaig R. Kissmann W. Kley 《Monthly notices of the Royal Astronomical Society》2009,394(4):1887-1896
In this paper, we investigate the influence of radiative transport on the growth of the magnetorotational instability (MRI) in accretion discs. The analysis is performed by the use of analytical and numerical means. We provide a general dispersion relation together with the corresponding eigenfunctions describing the growth rates of small disturbances on a homogeneous background shear flow. The dispersion relation includes compressibility and radiative effects in the flux-limited diffusion approximation. By introducing an effective speed of sound, all the effects of radiation transport can be subsumed into one single parameter. It can be shown that the growth rates of the vertical modes – which are the fastest growing ones – are reduced by radiative transport. For the case of non-vertical modes, the growth rates may instead be enhanced. We quantify the effects of compressibility and radiative diffusion on the growth rates for the gas-pressure dominated case. The analytical discussion is supplemented by numerical simulations, which are also used for a first investigation of the non-linear stage of the MRI in gas-pressure dominated accretion discs with radiation transport included. 相似文献
9.
Henrik N. Latter Gordon I. Ogilvie 《Monthly notices of the Royal Astronomical Society》2006,372(4):1829-1839
We investigate the growth or decay rate of the fundamental mode of even symmetry in a viscous accretion disc. This mode occurs in eccentric discs and is known to be potentially overstable. We determine the vertical structure of the disc and its modes, treating radiative energy transport in the diffusion approximation. In the limit of very long radial wavelength, an analytical criterion for viscous overstability is obtained, which involves the effective shear and bulk viscosity, the adiabatic exponent, and the opacity law of the disc. This differs from the prediction of a two-dimensional model. On shorter wavelengths (a few times the disc thickness), the criterion for overstability is more difficult to satisfy because of the different vertical structure of the mode. In a low-viscosity disc a third regime of intermediate wavelengths appears, in which the overstability is suppressed as the horizontal velocity perturbations develop significant vertical shear. We suggest that this effect determines the damping rate of eccentricity in protoplanetary discs, for which the long-wavelength analysis is inapplicable and overstability is unlikely to occur on any scale. In thinner accretion discs and in decretion discs around Be stars overstability may occur only on the longest wavelengths, leading to the preferential excitation of global eccentric modes. 相似文献
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Charles F. Gammie 《Monthly notices of the Royal Astronomical Society》1998,297(3):929-935
We show that radiation-dominated accretion discs are likely to suffer from a 'photon bubble' instability similar to that described by Arons in the context of accretion on to neutron star polar caps. The instability requires a magnetic field for its existence. In an asymptotic regime appropriate to accretion discs, we find that the overstable modes obey the remarkably simple dispersion relation
ο2 =−i gkF ( B , k ).
Here g is the vertical gravitational acceleration, B is the magnetic field, and F is a geometric factor of order unity that depends on the relative orientation of the magnetic field and the wavevector. In the non-linear outcome it seems likely that the instability will enhance vertical energy transport and thereby change the structure of the innermost parts of relativistic accretion discs. 相似文献
ο
Here g is the vertical gravitational acceleration, B is the magnetic field, and F is a geometric factor of order unity that depends on the relative orientation of the magnetic field and the wavevector. In the non-linear outcome it seems likely that the instability will enhance vertical energy transport and thereby change the structure of the innermost parts of relativistic accretion discs. 相似文献
13.
Stephen O'Sullivan Turlough P. Downes 《Monthly notices of the Royal Astronomical Society》2007,376(4):1648-1658
Astrophysical fluids under the influence of magnetic fields are often subjected to single- or two-fluid approximations. In the case of weakly ionized plasmas, however, this can be inappropriate due to distinct responses from the multiple constituent species to both collisional and non-collisional forces. As a result, in dense molecular clouds and protostellar accretion discs, for instance, the conductivity of the plasma may be highly anisotropic leading to phenomena such as Hall and ambipolar diffusion strongly influencing the dynamics.
Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper, which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little-known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component. 相似文献
Diffusive processes are known to restrict the stability of conventional numerical schemes which are not implicit in nature. Furthermore, recent work establishes that a large Hall term can impose an additional severe stability limit on standard explicit schemes. Following a previous paper, which presented the one-dimensional case, we describe a fully three-dimensional method which relaxes the normal restrictions on explicit schemes for multifluid processes. This is achieved by applying the little-known Super TimeStepping technique to the symmetric (ambipolar) component of the evolution operator for the magnetic field in the local plasma rest frame, and the new Hall Diffusion Scheme to the skew-symmetric (Hall) component. 相似文献
14.
Ogilvie 《Monthly notices of the Royal Astronomical Society》1998,297(1):291-314
The theory of waves and instabilities in a differentially rotating disc containing a poloidal magnetic field is developed within the framework of ideal magnetohydrodynamics. A continuous spectrum, for which the eigenfunctions are localized on individual magnetic surfaces, is identified but is found not to contain any instabilities associated with differential rotation. The normal modes of a weakly magnetized thin disc are studied by extending the asymptotic methods used previously to describe the equilibria. Waves propagate radially in the disc according to a dispersion relation which is determined by solving an eigenvalue problem at each radius. The dispersion relation for a hydrodynamic disc is re-examined and the modes are classified according to their behaviour in the limit of large wavenumber. The addition of a magnetic field introduces new, potentially unstable, modes and also breaks up the dispersion diagram by causing avoided crossings. The stability boundary to the magnetorotational instability in the parameter space of polytropic equilibria is located by solving directly for marginally stable equilibria. For a given vertical magnetic field in the disc, bending of the field lines has a stabilizing effect and it is shown that stable equilibria exist which are capable of launching a predominantly centrifugally driven wind. 相似文献
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M. Reyes-Ruiz 《Monthly notices of the Royal Astronomical Society》2000,319(4):1039-1046
In the light of recent results from numerical simulations of accretion disc MHD turbulence, we revisit the problem of the configuration of large-scale magnetic fields resulting from an α Ω dynamo operating in a thin accretion disc. In particular, we analyse the consequences of the peculiar sign of the α -effect suggested by numerical simulations . We determine the symmetry of the fastest-growing modes in the kinematic dynamo approximation and, in the framework of an ' α -quenched' dynamo model, study the evolution of the magnetic field. We find that the resulting field for this negative polarity of the α -effect generally has dipole symmetry with respect to the disc midplane, although the existence of an equilibrium configuration depends on the properties of the turbulence. The role of magnetic field dragging is discussed and, finally, the presence of an external uniform magnetic field is included to address the issue of magneto centrifugal wind launching from accretion discs. 相似文献
17.
Cool weakly ionized gaseous rotating disk form the basis for many models in astrophysics objects. Instabilities against perturbations in such disks play an important role in the theory of the formation of stars and planets. Traditionally, axisymmetric magnetohydrodynamic (MHD) and recently Hall‐MHD instabilities have been thoroughly studied as providers of an efficient mechanism for radial transfer of angular momentum, and of density radial stratification. In the current work, the Hall instability against axisymmetric perturbations in incompressible rotating fluid in external poloidal and toroidal magnetic field is considered. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Stability of thin hot Keplerian discs is investigated asymptotically in small disc's aspect ratio, ε. The study is carried out in the local approximation for short vertical waves in the disc‐thickness scale. Besides the radial rotation shear and the vertical magnetic field, the background configuration is characterized by a vertically near‐constant temperature profile with a small vertical gradient. The temperature‐gradient term in Ohm's law, which characterizes the thermomagnetic transport is found to be of the order of ε. The effect of the thermomagnetic transport slightly modifies the conventional magnetorotational instability (MRI), while a new thermomagnetic instability (TMI) emerges in regions of the wavenumber space where MRI is absent. Explicit solutions are obtained for a wide range of values of plasma beta, β, and thermomagnetic transport coefficient, λ. In particular, it is shown for λ ≪ 1 that the MRI dominates in weak magnetic fields, β ≫ 1, while the TMI is exhibited in strong magnetic fields, β ∼ 1, also with the growth rate of the order of inverse rotation period (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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C. G. Campbell 《Monthly notices of the Royal Astronomical Society》2009,392(1):271-280
A model is presented for an accretion disc in which the inflow is driven purely by the angular momentum removed in a centrifugally accelerated magnetic wind. Turbulent discs around compact stars are considered, with the required magnetic field being generated in the disc by a simple dynamo. The turbulent magnetic Prandtl number, N p , measures the ratio of turbulent viscosity to turbulent magnetic diffusivity. Formally, the hypothetical limit N p → 0 corresponds to the magnetic wind torque dominating the viscous torque, but in practice the inflow is magnetically controlled for N p ≲ 0.1 .
The suggestion by previous authors that purely magnetic wind-driven discs may be unstable is investigated. A detailed steady solution is found which allows perturbations to the thermal balance and vertical equilibrium to be calculated, and hence the effect of perturbations to the magnetic diffusivity, η, to be assessed. For a standard parametrized form of η, the wind-driven angular momentum balance is found to be linearly unstable. An increase in the inflow rate leads to increased bending of the poloidal magnetic field and an enhanced wind mass loss rate. This increases the angular momentum loss rate which drives further inflow. There is a resultant increase in η, due to the temperature perturbation, but this does not relieve field bending sufficiently to prevent the instability. 相似文献
The suggestion by previous authors that purely magnetic wind-driven discs may be unstable is investigated. A detailed steady solution is found which allows perturbations to the thermal balance and vertical equilibrium to be calculated, and hence the effect of perturbations to the magnetic diffusivity, η, to be assessed. For a standard parametrized form of η, the wind-driven angular momentum balance is found to be linearly unstable. An increase in the inflow rate leads to increased bending of the poloidal magnetic field and an enhanced wind mass loss rate. This increases the angular momentum loss rate which drives further inflow. There is a resultant increase in η, due to the temperature perturbation, but this does not relieve field bending sufficiently to prevent the instability. 相似文献
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C. G. Campbell 《Monthly notices of the Royal Astronomical Society》1998,301(3):754-758
An analytic model is presented for the inner structure of an accretion disc in the presence of a strong stellar magnetic field. The model is valid inside the radius at which the electron scattering opacity starts to exceed the Kramers opacity. It illustrates how the increasing stellar poloidal field leads to an elevated disc temperature, ultimately causing a breakdown in the vertical equilibrium owing to rapidly increasing radiation pressure which cannot be balanced by the vertical stellar gravity. Viscous instability also occurs. The solution gives an accurate representation of numerical results, and enables useful expressions to be derived for the radius at which the disc is marginally thin and the radius at which viscous instability occurs. The disruption mechanism appears to have general validity for accretion discs around strongly magnetic stars. 相似文献