A comparison of DA white dwarf temperatures and gravities from Lyman and Balmer line studies

The stability of turbulent accretion discs is considered, in which a magnetically influenced wind plays a major role in driving the inflow. The magnetic field is generated by a dynamo operating in the disc, involving radial shear and turbulence. The steady angular momentum balance is found to be linearly stable for a range of radial boundary conditions, and an expression is derived for the adjustment time-scale as a function of the equilibrium ratio of the magnetic and viscous disc torques.     

Mass loss from the inner regions of accretion discs due to centrifugally driven magnetic wind flows

Wind flows and collimated jets are believed to be a feature of a range of disc accreting systems. These include active galactic nuclei, T Tauri stars, X-ray binaries and cataclysmic variables. The observed collimation implies large-scale magnetic fields and it is known that dipole-symmetry fields of sufficient strength can channel wind flows emanating from the surfaces of a disc. The disc inflow leads to the bending of the poloidal magnetic field lines, and centrifugally driven magnetic winds can be launched when the bending exceeds a critical value. Such winds can result in angular momentum transport at least as effective as turbulent viscosity, and hence they can play a major part in driving the disc inflow.
It is shown here that if the standard boundary condition of vanishing viscous stress close to the stellar surface is applied, together with the standard connection between viscosity and magnetic diffusivity, then poloidal magnetic field bending increases as the star is approached with a corresponding increase in the wind mass loss rate. A significant amount of material can be lost from the system via the enhanced wind from a narrow region close to the stellar surface. This occurs for a Keplerian angular velocity distribution and for a modified form of angular velocity, which allows for matching of the disc and stellar rotation rates through a boundary layer above the stellar surface. The enhanced mass loss is significantly affected by the behaviour of the disc angular velocity as the stellar surface is approached, and hence by the stellar rotation rate. Such a mechanism may be related to the production of jets from the inner regions of disc accreting systems.     

A semi-analytic solution for the radial and vertical structure of accretion discs with a magnetic wind

A semi-analytic method is presented for solving for the radial and vertical structures of an accretion disc, with a magnetically channelled wind flowing from its surfaces. Both magnetic and turbulent viscous effects are taken into account, and the essential wind properties are related to the disc structure. The angular momentum removed by the wind plays a major part in driving the inflow through the disc, with photospheric temperatures being sufficient to generate the required wind mass flux. The magnetic field is generated by an αω-dynamo, but the method of solution should have application with other magnetic field sources. Self-consistent disc-wind solutions result, with rms turbulent Mach numbers which are in good agreement with those found in simulations of turbulence generated from magnetic shearing instabilities.     

Wave excitation in three-dimensional discs by external potential

We study the excitation of density and bending waves and the associated angular momentum transfer in gaseous discs with finite thickness by a rotating external potential. The disc is assumed to be isothermal in the vertical direction and has no self-gravity. The disc perturbations are decomposed into different modes, each characterized by the azimuthal index m and the vertical index n , which specifies the nodal number of the density perturbation along the disc normal direction. The   n = 0  modes correspond to the two-dimensional density waves previously studied by Goldreich & Tremaine and others. In a three-dimensional disc, waves can be excited at both Lindblad resonances (LRs; for modes with   n = 0, 1, 2, …  ) and vertical resonances (VRs; for the   n ≥ 1  modes only). The torque on the disc is positive for waves excited at outer Lindblad/vertical resonances and negative at inner Lindblad/vertical resonances. While the   n = 0  modes are evanescent around corotation, the   n ≥ 1  modes can propagate into the corotation region where they are damped and deposit their angular momenta. We have derived analytical expressions for the amplitudes of different wave modes excited at LRs and/or VRs and the resulting torques on the disc. It is found that for   n ≥ 1  , angular momentum transfer through VRs is much more efficient than LRs. This implies that in some situations (e.g. a circumstellar disc perturbed by a planet in an inclined orbit), VRs may be an important channel of angular momentum transfer between the disc and the external potential. We have also derived new formulae for the angular momentum deposition at corotation and studied wave excitations at disc boundaries.     

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.     

The radial disc structure around a magnetic neutron star: analytic and semi-analytic solutions

The radial structure of a thin accretion disc is calculated in the presence of a central dipole magnetic field aligned with the rotation axis. The problem is treated using a modified expression for the turbulent magnetic diffusion, which allows the angular momentum equation to be integrated analytically. The governing algebraic equations are solved iteratively between 1 and 10⁴ stellar radii. An analytic approximation is provided that is valid near the disruption radius at about 100 stellar radii. At that point, which is approximately 60 per cent of the Alfvén radius and typically about 30 per cent of the corotation radius, the disc becomes viscously unstable. This instability results from the fact that both radiation pressure and opacity caused by electron scattering become important. This in turn is a consequence of the magnetic field which leads to an enhanced temperature in the inner parts. This is because the magnetic field gives rise to a strongly enhanced vertically integrated viscosity, so that the viscous torque can balance the magnetic torque.     

Numerical simulations of astrophysical jets from Keplerian discs – III. The effects of mass loading

We present 2.5D time-dependent simulations of the non-linear evolution of non-relativistic outflows from the surface of Keplerian accretion discs. The gas is accelerated from the surface of the disc (which is a fixed platform in these simulations) into a cold corona in stable hydrostatic equilibrium. We explore the dependence of the resulting jet characteristics upon the mass loading of the winds. Two initial configurations of the threading disc magnetic field are studied: a potential field and a uniform vertical field configuration.
We show that the nature of the resulting highly collimated, jet-like outflows (steady or episodic) is determined by the mass load of the disc wind. The mass load controls the interplay between the collimating effects of the toroidal field and the kinetic energy density in the outflow. In this regard, we demonstrate that the onset of episodic behaviour of jets appears to be determined by the quantity     which compares the speed for a toroidal Alfvén wave to cross the diameter of the jet, with the flow speed v _p along the jet. This quantity decreases with increasing load. For sufficiently large N (small mass loads), disturbances appear to grow leading to instabilities and shocks. Knots are then generated and the outflow becomes episodic. These effects are qualitatively independent of the initial magnetic configuration that we employed and are probably generic to a wide variety of magnetized accretion disc models.     

Negative Reynolds stress generation by accretion disc convection

The phenomenon of negative viscosity-alpha in convectively unstable Keplerian accretion discs is discussed. The convection is considered as a random flow with an axisymmetric mesoscale pattern. Its correlation tensor is computed with a time-averaging procedure using Kley's 2D hydrocode. There is a distinct anisotropy between the turbulence intensities in the radial and azimuthal directions, i.e. the radial velocity rms dominates the azimuthal one. As a consequence, an extra term in the expression for the turbulent transport of angular momentum appears which does not vanish for rigid rotation ('Λ-effect'). It is negative ('inwards transport') and even seems to dominate the positive contribution of the eddy viscosity representing outwards transport of angular momentum. For a turbulence model close to that of the mixing-length theory, the rotational influence on the anisotropy of the turbulence intensities,     , and the covariance  〈 u ' _R u ' _φ 〉  – representing the angular momentum transport – is computed and compared with the accretion disc simulations. Indeed, the negative angular momentum transport can be explained with the observed dominance of the radial turbulence intensity. If, on the other hand, in turbulence fields the azimuthal intensity would dominate or the turbulence is even isotropic, then we always find a positive transport of the angular momentum.     

The Balbus–Hawley instability in weakly ionized discs

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 > v _A c _s; in the Hall case this imposes a potentially much weaker limit,         

Numerical simulations of type I planetary migration in non-turbulent magnetized discs

Using 2D magnetohydrodynamic (MHD) numerical simulations performed with two different finite-difference Eulerian codes, we analyse the effect that a toroidal magnetic field has on low-mass planet migration in non-turbulent protoplanetary discs. The presence of the magnetic field modifies the waves that can propagate in the disc. In agreement with a recent linear analysis, we find that two magnetic resonances develop on both sides of the planet orbit, which contribute to a significant global torque. In order to measure the torque exerted by the disc on the planet, we perform simulations in which the latter is either fixed on a circular orbit or allowed to migrate. For a     planet, when the ratio β between the square of the sound speed and that of the Alfven speed at the location of the planet is equal to 2, we find inward migration when the magnetic field   B _φ  is uniform in the disc, reduced migration when   B _φ  decreases as   r ⁻¹  and outward migration when   B _φ  decreases as   r ⁻²  . These results are in agreement with predictions from the linear analysis. Taken as a whole, our results confirm that even a subthermal stable field can stop inward migration of an earth-like planet.     

Magnetic field bending in accretion discs with dynamos

We consider the problem of poloidal magnetic field advection and bending of an initially vertical field owing to radial inflow in thin accretion discs. For a ratio of kinematic viscosity to magnetic diffusivity of order unity, significant bending of an externally applied vertical field cannot occur in a disc with no internal dynamo. However, we show that if poloidal field is generated by a dynamo operating near its critical state, then significant field bending may be possible. Our results are of particular relevance to wind launching from accretion discs.     

Launching of accretion disc winds along dynamo-generated magnetic fields

The problem of magnetic field generation and advection in accretion discs is considered, in the context of wind launching and angular momentum extraction. A dipole-symmetry solution of the dynamo equations is found, with force-free boundary conditions appropriate for matching to a wind solution. Consideration of the curved field geometry and diffusive nature of the disc enables the position of the sonic point to be calculated and related to the field inclination at the disc surface. A critical inclination of 20° to the horizontal results, for which the sonic point lies in the disc surface and there is no potential barrier to wind launching. Hence the wind mass-loss rate will only become excessive, leading to disc disruption, for large field bending. The compressional effect of the horizontal magnetic field enhances the wind mass flux.     

Magnetic shear-flow instability in thin accretion discs

The possibility that the magnetic shear-flow instability (also known as the 'Balbus–Hawley' instability) might give rise to turbulence in a thin accretion disc is investigated through numerical simulations. The study is linear and the fluid disc is supposed to be incompressible and differentially rotating with a simple velocity profile with Ω∝ R ^{− q} . The simplicity of the model is counterbalanced by the fact that the study is fully global in all three spatial directions with boundaries on each side; finite diffusivities are also allowed. The investigation is also carried out for several values of the azimuthal wavenumber of the perturbations in order to analyse whether non-axisymmetric modes might be preferred, which may produce, in a non-linear extension of the study, a self-sustained magnetic field.
  We find the final pattern steady, with similar kinetic and magnetic energies and the angular momentum always transported outwards. Despite the differential rotation, there are only small differences for the eigenvalues for various non-axisymmetric eigensolutions. Axisymmetric instabilities are by no means preferred; in fact for Prandtl numbers between 0.1 and 1, the azimuthal wavenumbers m =0,1,2(10¹⁶ g s^-1). All three quantities appear to be equally readily excited. The equatorial symmetry is quadrupolar for the magnetic field and dipolar for the flow field system. The maximal magnetic field strength required to cause the instability is almost independent of the magnetic Prandtl number. With typical white dwarf values, a magnetic amplitude of 10⁵ G is estimated.     

Episodic accretion in magnetically layered protoplanetary discs

We study protoplanetary disc evolution assuming that angular momentum transport is driven by gravitational instability at large radii, and magnetohydrodynamic (MHD) turbulence in the hot inner regions. At radii of the order of 1 au such discs develop a magnetically layered structure, with accretion occurring in an ionized surface layer overlying quiescent gas that is too cool to sustain MHD turbulence. We show that layered discs are subject to a limit cycle instability, in which accretion on to the protostar occurs in ∼10⁴-yr bursts with ̇ ∼10⁻⁵ M_⊙ yr⁻¹, separated by quiescent intervals lasting ∼10⁵ yr where ̇ ≈10⁻⁸ M_⊙ yr⁻¹. Such bursts could lead to repeated episodes of strong mass outflow in young stellar objects. The transition to this episodic mode of accretion occurs at an early epoch ( t ≪1 Myr), and the model therefore predicts that many young pre-main-sequence stars should have low rates of accretion through the inner disc. At ages of a few Myr, the discs are up to an order of magnitude more massive than the minimum-mass solar nebula, with most of the mass locked up in the quiescent layer of the disc at r ∼1 au. The predicted rate of low-mass planetary migration is reduced at the outer edge of the layered disc, which could lead to an enhanced probability of giant planet formation at radii of 1–3 au.     

Dimensionless measures of turbulent magnetohydrodynamic dissipation rates

The magnetic Reynolds number, R _M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R _M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number,   R _M,e  , as the ratio of the advection to microphysical dissipation terms in the total magnetic energy equation, incorporating the full spectrum of scales, arbitrary magnetic Prandtl numbers, and distinct pairs of inner and outer scales for magnetic and kinetic spectra. As expected, for a substantial parameter range   R _M,e∼ O (1) ≪ R _M  . We also distinguish   R _M,e  from     where the latter is an effective magnetic Reynolds number for the mean magnetic field equation when a turbulent diffusivity is explicitly imposed as a closure. That   R _M,e  and     approach unity even if   R _M≫ 1  highlights that, just as in hydrodynamic turbulence, energy dissipation of large-scale structures in turbulent flows via a cascade can be much faster than the dissipation of large-scale structures in laminar flows. This illustrates that the rate of energy dissipation by magnetic reconnection is much faster in turbulent flows, and much less sensitive to microphysical reconnection rates compared to laminar flows.     

Radiatively heated, protoplanetary discs with dead zones – I. Dust settling and thermal structure of discs around M stars

The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between two-dimensional self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they include dust settling with multiple grain sizes  ( N = 15)  , the gravitational force of an embedded planet on the disc and the presence of a dead zone (a region with very low levels of turbulence) within it. We show that dust settling drives the temperature of the mid-plane from an   r ^−3/5  distribution (well mixed dust models) towards an   r ^−3/4  . The dead zone, meanwhile, leaves a dusty wall at its outer edge because dust settling in this region is enhanced compared to the active turbulent disc at larger disc radii. The disc heating produced by this irradiated wall provides a positive gradient region of the temperature in the dead zone in front of the wall. This is crucially important for slowing planetary migration because Lindblad torques are inversely proportional to the disc temperature. Furthermore, we show that low turbulence of the dead zone is self-consistently induced by dust settling, resulting in the Kelvin–Helmholtz instability (KHI). We show that the strength of turbulence arising from the KHI in the dead zone is  α= 10⁻⁵  .     

Radiatively driven mass accretion on to galactic nuclei by circumnuclear starbursts

We examine the physical processes of radiatively driven mass accretion on to galactic nuclei, owing to intensive radiation from circumnuclear starbursts. The radiation from a starburst not only causes the inner gas disc to contract via radition flux force, but also extracts angular momentum owing to relativistic radiation drag, thereby inducing an avalanche of the surface layer of the disc. To analyse such a mechanism, the radiation–hydrodynamical equations are solved, including the effects of the radiation drag force as well as the radiation flux force. As a result, it is found that the mass accretion rate owing to the radiative avalanche is given by M ˙ ( r )= η ( L _*/ c ²)( r / R )² (Δ R / R )(1 −  e ^−τ) at radius r , where the efficiency η ranges from 0.2 up to 1, L _* and R are respectively the bolometric luminosity and the radius of the starburst ring, Δ R is the extent of the emission regions, and τ is the face-on optical depth of the disc. In an optically thick regime, the rate depends upon neither the optical depth nor the surface mass density distribution of the disc. The present radiatively driven mass accretion may provide a physical mechanism which enables mass accretion from 100-pc scales down to ∼ parsec scales, and it may eventually be linked to advection-dominated viscous accretion on to a massive black hole. The radiation–hydrodynamical and self-gravitational instabilities of the disc are briefly discussed. In particular, the radiative acceleration possibly builds up a dusty wall, which 'shades' the nucleus in edge-on views. This provides another version of the model for the formation of an obscuring torus.     

Simulations of the formation of stellar discs in the Galactic Centre via cloud–cloud collisions

Young massive stars in the central parsec of our Galaxy are best explained by star formation within at least one, and possibly two, massive self-gravitating gaseous discs. With help of numerical simulations, we here consider whether the observed population of young stars could have originated from a large angle collision of two massive gaseous clouds at   R ≃ 1 pc  from Sgr A*. In all the simulations performed, the post-collision gas flow forms an inner, nearly circular gaseous disc and one or two eccentric outer filaments, consistent with the observations. Furthermore, the radial stellar mass distribution is always very steep,  Σ_*∝ R ⁻²  , again consistent with the observations. All of our simulations produce discs that are warped by between 30° and 60°, in accordance with the most recent observations. The three-dimensional velocity structure of the stellar distribution is sensitive to initial conditions (e.g. the impact parameter of the clouds) and gas cooling details. For example, the runs in which the inner disc is fed intermittently with material possessing fluctuating angular momentum result in multiple stellar discs with different orbital orientations, contradicting the observed data. In all the cases the amount of gas accreted by our inner boundary condition is large, enough to allow Sgr A* to radiate near its Eddington limit over ∼10⁵ yr. This suggests that a refined model would have physically larger clouds (or a cloud and a disc such as the circumnuclear disc) colliding at a distance of a few parsecs rather than 1 pc as in our simulations.