An unconventional accretion disc dynamo

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.     

Self-similar solutions for the dynamical condensation of a radiative gas layer

A new self-similar solution describing the dynamical condensation of a radiative gas is investigated under a plane-parallel geometry. The dynamical condensation is caused by thermal instability. The solution is applicable to generic flow with a net cooling rate per unit volume and time  ∝ρ² T ^α  , where  ρ,  T   and α are the density, temperature and a free parameter, respectively. Given α, a family of self-similar solutions with one parameter η is found in which the central density and pressure evolve as follows:  ρ( x = 0, t ) ∝ ( t _c− t )^{−η/(2−α)}  and   P ( x = 0, t ) ∝ ( t _c− t )^{(1−η)/(1−α)}  , where t _c is the epoch at which the central density becomes infinite. For  η∼ 0  the solution describes the isochoric mode, whereas for  η∼ 1  the solution describes the isobaric mode. The self-similar solutions exist in the range between the two limits; that is, for  0 < η < 1  . No self-similar solution is found for  α > 1  . We compare the obtained self-similar solutions with the results of one-dimensional hydrodynamical simulations. In a converging flow, the results of the numerical simulations agree well with the self-similar solutions in the high-density limit. Our self-similar solutions are applicable to the formation of interstellar clouds (H  i clouds and molecular clouds) by thermal instability.     

Effects of scattering and dust grain size on the temperature structure of protoplanetary discs: a three-layer approach

The temperature in the optically thick interior of protoplanetary discs is essential for the interpretation of millimetre observations of the discs, for the vertical structure of the discs, for models of the disc evolution and the planet formation, and for the chemistry in the discs. Since large icy grains have a large albedo even in the infrared, the effect of scattering of the diffuse radiation in the discs on the interior temperature should be examined. We have performed a series of numerical radiation transfer simulations, including isotropic scattering by grains with various typical sizes for the diffuse radiation as well as for the incident stellar radiation. We also have developed an analytic model including isotropic scattering to understand the physics concealed in the numerical results. With the analytic model, we have shown that the standard two-layer approach is valid only for grey opacity (i.e. grain size ≳10 μm) even without scattering. A three-layer interpretation is required for grain size ≲10 μm. When the grain size is 0.1–10 μm, the numerical simulations show that the isotropic scattering reduces the temperature of the disc interior. This reduction is nicely explained by the analytic three-layer model as a result of the energy loss by scatterings of the incident stellar radiation and of the warm diffuse radiation in the disc atmosphere. For grain size ≳10 μm (i.e. grey scattering), the numerical simulations show that the isotropic scattering does not affect the interior temperature. This is nicely explained by the analytic two-layer model; the energy loss by scattering in the disc atmosphere is exactly offset by the 'green-house effect' due to the scattering of the cold diffuse radiation in the interior.     

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.     

On the absence of winds in advection-dominated accretion flows

We show that recently published assertions that advection-dominated accretion flows (ADAFs) require the presence of strong winds are unfounded because they assume that low radiative efficiency in flows accreting at low rates on to black holes implies vanishing radial energy and angular momentum fluxes through the flow (which is also formulated in terms of the 'Bernoulli function' being positive). This, however, is a property only of self-similar solutions which are an inadequate representation of global accretion flows. We recall general properties of accretion flows on to black holes and show that such, necessarily transonic, flows may have either d positive or negative Bernoulli function depending on the flow viscosity. Flows with low viscosities ( α ≲0.1 in the α -viscosity model) have a negative Bernoulli function. Without exception, all 2D and 1D numerical models of low-viscosity flows constructed to date experience no significant outflows. At high viscosities the presence of outflows depends on the assumed viscosity, on the equation of state and on the outer boundary condition. The positive sign of the Bernoulli function invoked in this context is irrelevant to the presence of outflows. As an illustration, we recall 2D numerical models with moderate viscosity that have positive values of the Bernoulli function and experience no outflows. ADAFs, therefore, do not differ from this point of view from thin Keplerian discs: they may have, but they do not have to have, strong winds.     

Two- and three-dimensional numerical simulations of accretion discs in a close binary system

We perform 2D and 3D numerical simulations of an accretion disc in a close binary system using the simplified flux vector splitting (SFS) finite volume method. In our calculations, the gas is assumed to be ideal with γ =1.01, 1.05, 1.1 and 1.2 . The mass ratio of the mass-losing star to the mass-accreting star is unity. Our results show that spiral shocks are formed on the accretion disc in all cases. In 2D calculations we find that the smaller γ is, the more tightly the spiral winds. We observe this trend in 3D calculations as well in a somewhat weaker sense. Mach numbers in our discs are less than 10. These values are lower than the values in observed accretion discs in close binary systems.
Recently, Steeghs, Harlaftis & Horne found the first convincing evidence for spiral structure in the accretion disc of the eclipsing dwarf nova binary IP Pegasi, using the technique known as Doppler tomography. Although the Mach numbers in present calculations are rather low, we may claim that the spiral structure that we discovered in earlier numerical simulations is now found observationally.     

Self-similar solution of hot accretion flows with ordered magnetic field and outflow

Observations and numerical magnetohydrodynamic (MHD) simulations indicate the existence of outflows and ordered large-scale magnetic fields in the inner region of hot accretion flows. In this paper, we present the self-similar solutions for advection-dominated accretion flows (ADAFs) with outflows and ordered magnetic fields. Stimulated by numerical simulations, we assume that the magnetic field has a strong toroidal component and a vertical component in addition to a stochastic component. We obtain the self-similar solutions to the equations describing the magnetized ADAFs, taking into account the dynamical effects of the outflow. We compare the results with the canonical ADAFs and find that the dynamical properties of ADAFs such as radial velocity, angular velocity and temperature can be significantly changed in the presence of ordered magnetic fields and outflows. The stronger the magnetic field is, the lower the temperature of the accretion flow will be and the faster the flow rotates. The relevance to observations is briefly discussed.     

Dynamic evolution of a quasi-spherical general polytropic magnetofluid with self-gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter n in the conventional polytropic self-similar transformation from the constraint of n+γ=2 with γ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.     

Exploring spiral galaxy potentials with hydrodynamical simulations

We study how well the complex gas velocity fields induced by massive spiral arms are modelled by the hydrodynamical simulations that we used recently to constrain the dark matter fraction in nearby spiral galaxies. More specifically, we explore the dependence of the positions and amplitudes of features in the gas flow on the temperature of the interstellar medium (assumed to behave as a one-component isothermal fluid), the non-axisymmetric disc contribution to the galactic potential, the pattern speed  Ω_p  , and finally the numerical resolution of the simulation. We argue that, after constraining the pattern speed reasonably well by matching the simulations to the observed spiral arm morphology, the amplitude of the non-axisymmetric perturbation (the disc fraction) is left as the primary parameter determining the gas dynamics. However, owing to the sensitivity of the positions of the shocks to modelling parameters, one has to be cautious when quantitatively comparing the simulations to observations. In particular, we show that a global least-squares analysis is not the optimal method for distinguishing different models, as it tends to slightly favour low disc fraction models. Nevertheless, we conclude that, given observational data of reasonably high spatial resolution and an accurate shock-resolving hydro-code, this method tightly constrains the dark matter content within spiral galaxies. We further argue that, even if the perturbations induced by spiral arms are weaker than those of strong bars, they are better suited for this kind of analysis because the spiral arms extend to larger radii where effects like inflows due to numerical viscosity and morphological dependence on gas sound speed are less of a concern than they are in the centres of discs.     

Phase information and the evolution of cosmological density perturbations

The Fourier transform of cosmological density perturbations can be represented in terms of amplitudes and phases for each Fourier mode. We investigate the phase evolution of these modes using a mixture of analytical and numerical techniques. Using a toy model of one-dimensional perturbations evolving under the Zel'dovich approximation as an initial motivation, we develop a statistic that quantifies the information content of the distribution of phases. Using numerical simulations beginning with more realistic Gaussian random-phase initial conditions, we show that the information content of the phases grows from zero in the initial conditions, first slowly and then rapidly when structures become non-linear. This growth of phase information can be expressed in terms of an effective entropy. Gaussian initial conditions are a maximum entropy realization of the initial power spectrum; gravitational evolution decreases the phase entropy. We show that our definition of phase entropy results in a statistic that explicitly quantifies the information stored in the phases of density perturbations (rather than their amplitudes), and that this statistic displays interesting scaling behaviour for self-similar initial conditions.     

The Effect of Helicity Dissipation on the Critical State of an Avalanche Model for Solar Flares

We perform numerical simulations using an avalanche model for solar flares, in which the effect of avalanche event duration is included and the lateral boundary condition can be either open or periodic. The results from the simulations show that self-organized criticality (SOC) exists under a variety of conditions of helicity dissipation, and they are similar in the sense that the indices of power-law distributions of avalanche sizes are the same, while the duration and waiting time distributions differ little. Of interest are: (1) if there exists helicity dissipation in the course of avalanches, SOC exists only when the amount of helicity dissipation per avalanche is small; (2) sudden reductions in the total helicity of the system do not severely disturb SOC, if the amount reduced is moderate; (3) the distribution of waiting times is shown to be exponential, in consistent with the Poisson statistics other avalanche models have predicted, and the exponent increases as the effect of event duration becomes larger. The self-similar structure of the avalanche time series is also examined. These results imply that, although helicity is dissipated in resistive diffusion of flares, the amount of dissipation should be small and the conservation law of helicity thus holds in an approximate sense. Also, the coronal mass ejections (CMEs), observed to take helicity out of the solar corona in an eruptive way, may disrupt the statistical equilibrium of the corona only temporarily.     

Launching mechanisms of astrophysical jets

The combination of accretion disks and supersonic jets is used to model many active astrophysical objects, viz., young stars, relativistic stars, and active galactic nuclei. However, existing theories on the physical processes by which these structures transfer angular momentum and energy from disks to jets through viscous or magnetic torques are still relatively approximate. Global stationary solutions do not permit understanding the formation and stability of these structures; and global numerical simulations that include both the disk and jet physics are often limited to relatively short time scales and astrophysically out-of-range values of viscosity and resistivity parameters that are instead crucial to defining the coupling of the inflow/outflow dynamics. Along these lines we discuss self-consistent time-dependent simulations of the launching of supersonic jets by magnetized accretion disks, using high resolution numerical techniques. We shall concentrate on the effects of the disk physical parameters, and discuss under which conditions steady state solutions of the type proposed in the self-similar models of Blandford and Payne can be reached and maintained in a self-consistent nonlinear stationary state.     

Numerical simulations of type III planetary migration – II. Inward migration of massive planets

We present a numerical study of rapid, so-called type III migration for Jupiter-sized planets embedded in a protoplanetary disc. We limit ourselves to the case of inward migration, and study in detail its evolution and physics, concentrating on the structure of the corotation and circumplanetary regions, and processes for stopping migration. We also consider the dependence of the migration behaviour on several key parameters. We perform this study using the results of global, two-dimensional hydrodynamical simulations with adaptive mesh refinement. The initial conditions are chosen to satisfy the condition for rapid inward migration. We find that type III migration can be divided into two regimes, fast and slow. The structure of the co-orbital region, mass accumulation rate and migration behaviour differ between these two regimes. All our simulations show a transition from the fast to the slow regime, ending type III migration well before reaching the star. The stopping radius is found to be larger for more massive planets and less massive discs. A sharp density drop is also found to be an efficient stopping mechanism. In the fast migration regime the migration rate and induced eccentricity are lower for less massive discs, but almost do not depend on planet mass. Eccentricity is damped on the migration time-scale.     

From Molecular Cores to Stars and Brown Dwarfs

In this paper, we review the results from numerical simulations that investigate the evolution of molecular cores into stars and brown dwarfs. We begin by discussing the four main processes involved in this evolution, fragmentation, accretion, interactions with discs, and stellar dynamical interactions. We then discuss large-scale calculations in which all of these processes are model simultaneously. Finally, we review results that have been obtained from past magnetohydrodynamical (MHD) calculations of fragmentation and look towards future MHD calculations.     

Forming stars on a viscous time-scale: the key to exponential stellar profiles in disc galaxies?

We argue for implementing star formation on a viscous time-scale in hydrodynamical simulations of disc galaxy formation and evolution. Modelling two-dimensional isolated disc galaxies with the Bhatnagar–Gross–Krook (BGK) hydrocode, we verify the analytic claim of various authors that if the characteristic time-scale for star formation is equal to the viscous time-scale in discs, the resulting stellar profile is exponential on several scalelengths whatever the initial gas and dark matter profile. This casts new light on both numerical and semi-analytical disc formation simulations that either (a) commence star formation in an already exponential gaseous disc, (b) begin a disc simulation with conditions known to lead to an exponential, i.e. the collapse of a spherically symmetric nearly uniform sphere of gas in solid-body rotation under the assumption of specific angular momentum conservation, or (c) in simulations performed in a hierarchical context, tune their feedback processes to delay disc formation until the dark matter haloes are slowly evolving and without much substructure so that the gas has the chance to collapse under conditions known to give exponentials. In such models, star formation follows a Schmidt-like law, which for lack of a suitable time-scale, resorts to an efficiency parameter. With star formation prescribed on a viscous time-scale, however, we find gas and star fractions after ∼12 Gyr that are consistent with observations without having to invoke a 'fudge factor' for star formation. Our results strongly suggest that despite our gap in understanding the exact link between star formation and viscosity, the viscous time-scale is indeed the natural time-scale for star formation.     

Growth of the MRI in accretion discs – the influence of radiation transport

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.     

Dependence of the acceleration of the outer edge of a stellar envelope on supernova explosion energy

Based on numerical simulations of a supernova explosion, we investigate the shock-wave breakout through the stellar surface. The computations have been performed in a wide range of explosion energies and presupernova masses. The results are compared with the classical Gandelman-Frank-Kamenetsky self-similar solution. We have determined the dependence of an arbitrary coefficient in the self-similar solution on the explosion energy and presupernova structure. The derived analytical approximation formula for this coefficient can be used to estimate the supernova explosion energy from such parameters of the ejected envelope determined from astronomical observations as its maximum expansion velocity and the density distribution along its outer edge. The formula may prove to be also useful in studying the X-ray and gamma-ray bursts that accompany the shock-wave breakout through the surface of compact presupernovae.     

Smoothed particle hydrodynamic simulations of viscous accretion discs around black holes

Viscous Keplerian discs become sub-Keplerian close to a black hole since they pass through sonic points before entering into it. We study the time evolution of polytropic viscous accretion discs (both in one- and two-dimensional flows) using smoothed particle hydrodynamics. We discover that for a large region of the parameter space spanned by energy, angular momentum and polytropic index, when the flow viscosity parameter is less than a critical value, standing shock waves are formed. If the viscosity is very high then the shock wave disappears. In the intermediate viscosity, the disc oscillates very significantly in the viscous time-scale. Our simulations indicate that these centrifugally supported high density regions close to a black hole play an active role in the flow dynamics, and consequently, the radiation dynamics.     

Dynamical stability and evolution of the discs of Sc galaxies

We examine the local stability of galactic discs against axisymmetric density perturbations with special attention to the different dynamics of the stellar and gaseous components. In particular, the discs of the Milky Way and of NGC 6946 are studied. The Milky Way is shown to be stable, whereas the inner parts of NGC 6946, a typical Sc galaxy from the Kennicutt sample, are dynamically unstable. The ensuing dynamical evolution of the composite disc is studied by numerical simulations. The evolution is so fierce that the stellar disc heats up dynamically on a short time-scale to such a high degree, which seems to contradict the morphological appearance of the galaxy. The star formation rate required to cool the disc dynamically is estimated. Even if the star formation rate in NGC 6946 is at present high enough to meet this requirement, it is argued that the discs of Sc galaxies cannot sustain such a high star formation rate for extended periods.