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.     

Hydrodynamic simulations of propagating warps and bending waves in accretion discs

We present the results of a study of propagating warp or bending waves in accretion discs. Three-dimensional hydrodynamic simulations were performed using smoothed particle hydrodynamics (SPH), and the results are compared with calculations based on the linear theory of warped discs.
We examine the response of a gaseous disc to an initially imposed warping disturbance under a variety of physical conditions. We consider primarily the physical regime in which the dimensionless viscosity parameter α < H r , where H r is the disc aspect ratio, so that bending waves are expected to propagate. We also performed calculations for disc models in which α > H r , where the warps are expected to evolve diffusively. Small-amplitude (linear) perturbations are studied in both Keplerian and slightly non-Keplerian discs, and we find that the results of the SPH calculations can be reasonably well fitted by those of the linear theory. The main results of these calculations are: (i) the warp in Keplerian discs when α < H r propagates with little dispersion, and damps at a rate expected from estimates of the code viscosity; (ii) warps evolve diffusively when α > H r ; (iii) the slightly non-Keplerian discs lead to a substantially more dispersive behaviour of the warps, which damp at a similar rate to the Keplerian case, when α < H r .
Initially imposed higher amplitude, non-linear warping disturbances were studied in Keplerian discs. The results indicate that non-linear warps can lead to the formation of shocks, and that the evolution of the warp becomes less wave-like and more diffusive in character.
This work is relevant to the study of the warped accretion discs that may occur around Kerr black holes or in misaligned binary systems, and is mainly concerned with discs in which α < H r . The results indicate that SPH can model the hydrodynamics of warped discs, even when using rather modest numbers of particles.     

An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics

An approximate Riemann solver for the equations of relativistic magnetohydrodynamics (RMHD) is derived. The Harten–Lax–van Leer contact wave (HLLC) solver, originally developed by Toro, Spruce and Spears, generalizes the algorithm described in a previous paper to the case where magnetic fields are present. The solution to the Riemann problem is approximated by two constant states bounded by two fast shocks and separated by a tangential wave. The scheme is Jacobian-free, in the sense that it avoids the expensive characteristic decomposition of the RMHD equations and it improves over the HLL scheme by restoring the missing contact wave.
Multidimensional integration proceeds via the single step, corner transport upwind (CTU) method of Colella, combined with the constrained transport (CT) algorithm to preserve divergence-free magnetic fields. The resulting numerical scheme is simple to implement, efficient and suitable for a general equation of state. The robustness of the new algorithm is validated against one- and two-dimensional numerical test problems.     

A five-wave Harten–Lax–van Leer Riemann solver for relativistic magnetohydrodynamics

We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine–Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten–Lax–van Leer solver or the recently proposed HLLC schemes.     

Verification of Reynolds stress parameterizations from simulations

We determine the timescales associated with turbulent decay and isotropization in closure models using anisotropically forced and freely decaying turbulence simulations and study the applicability of these models. We compare the results from anisotropically forced three‐dimensional numerical simulations with the predictions of the closure models and obtain the turbulent timescales mentioned above as functions of the Reynolds number. In a second set of simulations, turning the forcing off enables us to study the validity of the closures in freely decaying turbulence. Both types of experiments suggest that the timescale of turbulent decay converges to a constant value at higher Reynolds numbers. Furthermore, the relative importance of isotropization is found to be about 2.5 times larger at higher Reynolds numbers than in the more viscous regime (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A One-Dimensional Relativistic Shock Model for the Light Curve of Gamma-ray Bursts

We investigate the forming of gamma-ray burst pulses with a simple one-dimensional relativistic shock model. The mechanism is that a "central engine" drives forward the nearby plasma inside the fireball to generate a series of pressure waves. We give a relativistic geometric recurrence formula that connects the time when the pressure waves are produced and the time when the corresponding shocks occurred. This relation enables us to relate the pulse magnitude with the observation time. Our analysis shows that the evolution of the pressure waves leads to a fast rise and an exponential decay pulses. In determining the width of the pulses, the acceleration time is more important than that of the deceleration.     

Self-similar shocked accretion of collisional gas with radiative cooling

We describe similarity solutions that characterize the collapse of collisional gas on to scale-free perturbations in an Einstein–de Sitter universe. We consider the effects of radiative cooling and derive self-similar solutions under the assumption that the cooling function is a power law of density and temperature, Λ( T , ρ )∝ ρ ^3/2 T . We use these results to test the ability of smooth particle hydrodynamics (SPH) techniques to follow the collapse and accretion of shocked, rapidly cooling gas in a cosmological context. Our SPH code reproduces the analytical results very well in cases that include or exclude radiative cooling. No substantial deviations from the predicted central mass accretion rates or from the temperature, density and velocity profiles are observed in well-resolved regions inside the shock radius. This test problem lends support to the reliability of SPH techniques to model the complex process of galaxy formation.     

A numerical simulation of a wind/molecular clump interaction

It has been pointed out in the past that it is impossible to accelerate molecular material to velocities ≥ 25 km s⁻¹ with gasdynamic shocks without dissociating the gas. Because of this, it has been argued that observations of molecular emission with radial velocities ∼ 20–100 km s⁻¹ imply the presence of 'C-shocks' (which have much lower post-shock temperatures, and therefore do not dissociate the gas) and the existence of strong (∼ 10–100 μG) magnetic fields.   In this paper, we discuss an alternative mechanism for accelerating molecular material to high velocities: a high-velocity, low-density wind drives a non-dissociative shock (with shock velocity v _cs ≤ 25 km s⁻¹) into a high-density, molecular clump. Once this shock wave has gone through the clump, the molecular material is moving at a velocity ∼  v _cs and has a gas pressure approximately equal to the ram pressure of the impinging wind. The compressed molecular clump can now be accelerated directly by the ram pressure of the wind (without the passage of further shocks through the molecular material), and will eventually move at the wind velocity.   This mechanism has been previously invoked to explain high-velocity molecular emission. However, numerical simulations have shown that a wind/clump interaction leads to the fragmentation of the clump before it can be accelerated to large velocities. In our numerical simulation (which includes an approximate treatment of the relevant microphysics) we find that the fragments that are produced are still largely molecular, and that they are rapidly accelerated to velocities comparable to the wind velocity. We therefore conclude that a wind/molecular clump interaction is indeed a valid mechanism for producing high-velocity molecular features.     

Three-dimensional hydrodynamical simulations of the large-scale structure of W50−SS433

We present 3D hydrodynamical simulations of a precessing jet propagating inside a supernova remnant (SNR) shell, particularly applied to the W50−SS433 system in a search for the origin of its peculiar elongated morphology. Several runs were carried out with different values for the mass-loss rate of the jet, the initial radius of the SNR, and the opening angle of the precession cone. We found that our models successfully reproduce the scale and morphology of W50 when the opening angle of the jets is set to 10° or if this angle linearly varies with time. For these models, more realistic runs were made considering that the remnant is expanding into an interstellar medium with an exponential density profile (as H  i observations suggest). Taking into account all these ingredients, the large-scale morphology of the W50−SS433 system, including the asymmetry between the lobes (formed by the jet–SNR interaction), is well reproduced.     

On the angular momentum transfer on to compact stars in binary systems

Results of three-dimensional numerical simulations of the gas transfer in close binary systems show that, in addition to the formation of a tidally induced spiral shock wave, it is also possible for accretion streams to be produced, having low specific angular momentum in a region close to the accreting star. These streams are mainly placed above the orbital disc but are also unevenly present in the equatorial plane. The relevance of such flows is related to formation of hot coronae or bulges in regions very close to the accretor centre. The eventual formation of such bulges and shock-heated flows is interesting in the context of advection-dominated solutions and for the explanation of spectral properties of the black hole candidates in binary systems.     

Numerical simulations of downward convective overshooting in giants

An attempt at understanding downward overshooting in the convective envelopes of post-main-sequence stars has been made on the basis of three-dimensional large-eddy simulations, using artificially modified OPAL opacity and taking into account radiation and ionization in the equation of state. Two types of star, an intermediate-mass star and a massive star, were considered. To avoid a long thermal relaxation time of the intermediate-mass star, we increased the stellar energy flux artificially while trying to maintain a structure close to the one given by a 1D stellar model. A parametric study of the flux factor was performed. For the massive star, no such process was necessary. Numerical results were analysed when the system reached the statistical steady state. It was shown that the penetration distance in pressure scaleheights is of the order of unity. The scaling relations between penetration distance, input flux and vertical velocity fluctuations studied by Singh et al. were checked. The anisotropy of the turbulent convection and the diffusion models of the third-order moments representing the non-local transport were also investigated. These models are dramatically affected by the velocity fields and no universal constant parameters seem to exist. The limitations of the numerical results were also discussed.     

Hydrodynamic simulations of rotating molecular jets

Molecular outflows and the jets which may drive them can be expected to display signatures associated with rotation if they are the channels through which angular momentum is extracted from material accreting on to protostars. Here, we determine some basic signatures of rapidly rotating flows through three-dimensional numerical simulations of hydrodynamic jets with molecular cooling and chemistry. We find that these rotating jets generate a broad advancing interface which is unstable and develops into a large swarm of small bow features. In comparison to precessing jets, there is no stagnation point along the axis. The greater the rotation rate, the greater the instability. On the other hand, velocity signatures are only significant close to the jet inlet since jet expansion rapidly reduces the rotation speed. We present predictions for atomic, H₂ and CO submillimetre images and spectroscopy including velocity channel maps and position–velocity diagrams. We also include simulated images corresponding to Spitzer IRAC band images and CO emission, relevant for APEX and eventual ALMA observations. We conclude that protostellar jets often show signs of slow precession but only a few sources display properties which could indicate jet rotation.