The Validity of the Super-Particle Approximation during Planetesimal Formation

The formation mechanism of planetesimals in protoplanetary discs is hotly debated. Currently, the favoured model involves the accumulation of meter-sized objects within a turbulent disc, followed by a phase of gravitational instability. At best one can simulate a few million particles numerically as opposed to the several trillion meter-sized particles expected in a real protoplanetary disc. Therefore, single particles are often used as super-particles to represent a distribution of many smaller particles. It is assumed that small scale phenomena do not play a role and particle collisions are not modeled. The super-particle approximation can only be valid in a collisionless or strongly collisional system, however, in many recent numerical simulations this is not the case. In this work we present new results from numerical simulations of planetesimal formation via gravitational instability. A scaled system is studied that does not require the use of super-particles. We find that the scaled particles can be used to model the initial phases of clumping if the properties of the scaled particles are chosen such that all important timescales in the system are equivalent to what is expected in a real protoplanetary disc. Constraints are given for the number of particles needed in order to achieve numerical convergence. We compare this new method to the standard super-particle approach. We find that the super-particle approach produces unreliable results that depend on artifacts such as the gravitational softening in both the requirement for gravitational collapse and the resulting clump statistics. Our results show that short range interactions (collisions) have to be modelled properly.Comment: 10 pages, 7 figures, accepted for publication in Astronomy and Astrophysic

Angular momentum transport and large eddy simulations in magnetorotational turbulence: the small Pm limit

Angular momentum transport in accretion discs is often believed to be due to magnetohydrodynamic turbulence mediated by the magnetorotational instability. Despite an abundant literature on the MRI, the parameters governing the saturation amplitude of the turbulence are poorly understood and the existence of an asymptotic behavior in the Ohmic diffusion regime is not clearly established. We investigate the properties of the turbulent state in the small magnetic Prandtl number limit. Since this is extremely computationally expensive, we also study the relevance and range of applicability of the most common subgrid scale models for this problem. Unstratified shearing boxes simulations are performed both in the compressible and incompressible limits, with a resolution up to 800 cells per disc scale height. The latter constitutes the largest resolution ever attained for a simulation of MRI turbulence. In the presence of a mean magnetic field threading the domain, angular momentum transport converges to a finite value in the small Pm limit. When the mean vertical field amplitude is such that {\beta}, the ratio between the thermal and magnetic pressure, equals 1000, we find {\alpha}~0.032 when Pm approaches zero. In the case of a mean toroidal field for which {\beta}=100, we find {\alpha}~0.018 in the same limit. Both implicit LES and Chollet-Lesieur closure model reproduces these results for the {\alpha} parameter and the power spectra. A reduction in computational cost of a factor at least 16 (and up to 256) is achieved when using such methods. MRI turbulence operates efficiently in the small Pm limit provided there is a mean magnetic field. Implicit LES offers a practical and efficient mean of investigation of this regime but should be used with care, particularly in the case of a vertical field. Chollet-Lesieur closure model is perfectly suited for simulations done with a spectral code.Comment: Accepted for publication in A&

Spiral-wave-driven accretion in quiescent dwarf nov{\ae}

In dwarf nov{\ae} and low-mass X-ray binaries, the tidal potential excites spiral waves in the accretion disc. Spiral wave driven accretion may be important in quiescent discs, where the angular momentum transport mechanism has yet to be identified. Previous studies were limited to unrealistically high temperatures for numerical studies or to specific regimes for analytical studies. We perform the first numerical simulation of spiral wave driven accretion in the cold temperature regime appropriate to quiescent discs, which have Mach numbers > 100. We use the new GPU-accelerated finite volume code Idefix to produce global hydrodynamics 2D simulations of the accretion discs of dwarf nov{\ae} systems with a fine-enough spatial resolution to capture the short scale-height of cold, quiescent discs with Mach numbers ranging from 80 to 370. Running the simulations on timescales of tens of binary orbits shows transient angular momentum transport that decays as the disc relaxes from its initial conditions. We find the angular momentum parameter {\alpha} drops to values << 0.01 , too weak to drive accretion in quiescence

Non-exponential hydrodynamical growth in density-stratified thin Keplerian discs

The short time evolution of three dimensional small perturbations is studied. Exhibiting spectral asymptotic stability, thin discs are nonetheless shown to host intensive hydrodynamical activity in the shape of non modal growth of initial small perturbations. Two mechanisms that lead to such behavior are identified and studied, namely, non-resonant excitation of vertically confined sound waves by stable planar inertia-coriolis modes that results in linear growth with time, as well as resonant coupling of those two modes that leads to a quadratic growth of the initial perturbations. It is further speculated that the non modal growth can give rise to secondary strato-rotational instabilities and thus lead to a new route to turbulence generation in thin discs

Stability analysis of secondary modes, driven by the phase space island

We present a new theoretical approach, based on the Hamiltonian formalism, to investigate the stability of islands in phase space, generated by trapping of energetic particles (EPs) in plasma waves in a tokamak. This approach is relevant to MHD modes driven by EPs (EP-MHD) such as toroidal Alfvén eigenmodes (TAEs), EP-driven geodesic acoustic modes (EGAMs) or fishbones. A generic problem of a single isolated EP-MHD mode is equivalent to and hence can be replaced by a 2D Hamiltonian dynamics in the vicinity of the phase space island. The conventional Langmuir wave/bump-on-tail problem is then used as a representative reduced model to describe the dynamics of the initial EP-MHD. Solving the Fokker-Planck equation in the presence of pitch angle scattering, velocity space diffusion and drag and retaining plasma drifts in a model, we find a 'perturbed' equilibrium, associated with these phase space islands. Its stability is then explored by addressing the Vlasov/Fokker-Planck-Poisson system. The Lagrangian of this system provides the dispersion relation of the secondary modes and allows an estimate of the mode onset. The secondary instabilities have been confirmed to be possible but under certain conditions on the primary island width and in a certain range of mode numbers. The threshold island width, below which the mode stability is reached, is calculated. The secondary mode growth rate is found to be maximum when the associated resonant velocity approaches the boundary of the primary island. This, in turn, leads to a conclusion that the onset of the secondary mode can be prevented provided the primary wave number is the lowest available

The angular momentum transport by standard MRI in quasi-Kepler cylindric Taylor-Couette flows

The instability of a quasi-Kepler flow in dissipative Taylor-Couette systems under the presence of an homogeneous axial magnetic field is considered with focus to the excitation of nonaxisymmetric modes and the resulting angular momentum transport. The excitation of nonaxisymmetric modes requires higher rotation rates than the excitation of the axisymmetric mode and this the more the higher the azimuthal mode number m. We find that the weak-field branch in the instability map of the nonaxisymmetric modes has always a positive slope (in opposition to the axisymmetric modes) so that for given magnetic field the modes with m>0 always have an upper limit of the supercritical Reynolds number. In order to excite a nonaxisymmetric mode at 1 AU in a Kepler disk a minimum field strength of about 1 Gauss is necessary. For weaker magnetic field the nonaxisymmetric modes decay. The angular momentum transport of the nonaxisymmetric modes is always positive and depends linearly on the Lundquist number of the background field. The molecular viscosity and the basic rotation rate do not influence the related {\alpha}-parameter. We did not find any indication that the MRI decays for small magnetic Prandtl number as found by use of shearing-box codes. At 1 AU in a Kepler disk and a field strength of about 1 Gauss the {\alpha} proves to be (only) of order 0.005

Rossby Wave Instability and three-dimensional vortices in accretion disks

Context. The formation of vortices in accretion disks is of high interest in various astrophysical contexts, in particular for planet formation or in the disks of compact objects. But despite numerous attempts it has thus far not been possible to produce strong vortices in fully three-dimensional simulations of disks. Aims. The aim of this paper is to present the first 3D simulation of a strong vortex, established across the vertically stratified structure of a disk by the Rossby Wave Instability. Methods. Using the Versatile Advection Code (VAC), we set up a fully 3D cylindrical stratified disk potentially prone to the Rossby Wave Instability. Results. The simulation confirms the basic expectations obtained from previous 2D analytic and numerical works. The simulation exhibits a strong vortex that grows rapidly and saturates at a finite amplitude. On the other hand the third dimension shows unexpected additional behaviours that could be of strong importance in the astrophysical roles that such vortices can play.Comment: Accepted by Astronomy and Astrophysic

The plasma-wall transition with collisions and an oblique magnetic field: reversal of potential drops at grazing incidences

International audienceThe plasma-wall transition is studied by using 1d3V particle-in-cell (PIC) simulations in the case of a one dimensional plasma bounded by two absorbing walls separated by 200 Debye lengths (λ d). A constant and oblique magnetic field is applied to the system, with an amplitude such that r < λ d < R, where r and R are the electron and ion Larmor radius respectively. Collisions with neutrals are taken into account and modelled by an energy conservative operator, which randomly reorients ion and electron velocities. The plasma-wall transition (PWT) is shown to depend on both the angle of incidence of the magnetic field with respect to the wall θ, and on the ion mean-free-path to Larmor radius ratio, λ ci /R. In the very low collisionality regime (λ ci R) and for a large angle of incidence, the PWT consists in the classical tri-layer structure (Debye sheath / Chodura sheath / Pre-sheath) from the wall towards the center of the plasma. The drops of potential within the different regions are well consistent with already published models. However, when sin θ ≤ R/λ ci or with the ordering λ ci < R , collisions can not be neglected, leading to the disappearance of the Chodura sheath. In these case, a collisional model yields analytic expressions for the potential drop in the quasi-neutral region, and explains, in qualitative and quantitative agreement with the simulation results, its reversal below a critical angle derived in the paper, a regime possibly met in the SOL of tokamaks. It is further shown that the potential drop in the Debye sheath slightly varies with the collision-ality for λ ci R. However, it tends to decrease with λ ci in the high collisionality regime, until the Debye sheath finally vanishes

Effects of agonists of peroxisome proliferator-activated receptor γ on proteoglycan degradation and matrix metalloproteinase production in rat cartilage in vitro

AbstractObjective To examine the effects of agonists of peroxisome proliferator-activated receptor (PPAR) γ on proteoglycan degradation induced by interleukin (IL)-1β or tumor necrosis factor (TNF)α in cartilage in vitro.Design Proteoglycan degradation was measured as release of radioactivity from rat cartilage explants previously labeled with 35SO2−4. Western blots were used to examine tissue levels of aggrecan neoepitopes NITEGE and VDIPEN, generated by aggrecanases and matrix metalloproteinases (MMP), respectively. Production of MMP-2, -3 and -9 by cultured rat chondrocytes was measured by zymography and by fluorimetric assay.Results IL-1β-induced proteoglycan degradation was likely due to aggrecanase, since it was associated with a strong increase of NITEGE signal. MMP-dependent VDIPEN signal increased only after further incubation with pro-MMP activator APMA. PPAR agonists 15d-PGJ2 and GI262570 (10μM) inhibited IL-1β- and TNFα-induced proteoglycan degradation measured both before and after addition of APMA. The agonists also inhibited cytokine-induced MMP production by isolated chondrocytes.Conclusion This study shows that PPARγ agonists inhibit cytokine-induced proteoglycan degradation mediated by both aggrecanase and MMP. This effect is associated with inhibition of production of MMP-3 and -9. These results support the interest for PPARγ agonists as candidate inhibitors of pathological cartilage degradation. Copyright 2002 OsteoArthritis Research Society International. Published by Elsevier Science Ltd. All rights reserved