Formation and long-term evolution of 3D vortices in protoplanetary discs

In the context of planet formation, anticyclonic vortices have recently received lots of attention for the role they can play in planetesimals formation. Radial migration of intermediate size solids toward the central star may prevent their growth to larger solid grains. On the other hand, vortices can trap the dust and accelerate this growth, counteracting fast radial transport. Multiple effects have been shown to affect this scenario, such as vortex migration or decay. The aim of this paper is to study the formation of vortices by the Rossby wave instability and their long term evolution in a full three dimensional protoplanetary disc. We use a robust numerical scheme combined with adaptive mesh refinement in cylindrical coordinates, allowing to affordably compute long term 3D evolutions. We consider a full disc stratified both radially and vertically that is prone to formation of vortices by the Rossby wave instability. We show that the 3D Rossby vortices grow and survive over hundreds of years without migration. The localized overdensity which initiated the instability and vortex formation survives the growth of the Rossby wave instability for very long times. When the vortices are no longer sustained by the Rossby wave instability, their shape changes toward more elliptical vortices. This allows them to survive shear-driven destruction, but they may be prone to elliptical instability and slow decay. When the conditions for growing Rossby wave-related instabilities are maintained in the disc, large-scale vortices can survive over very long timescales and may be able to concentrate solids.Comment: Accepted for publication in A&

Convective magneto-rotational instabilities in accretion disks

We present a study of instabilities occuring in thick magnetized accretion disks. We calculate the growth rates of these instabilities and characterise precisely the contribution of the magneto-rotational and the convective mechanism. All our calculations are performed in radially stratified disks in the cylindrical limit. The numerical calculations are performed using the appropriate local dispersion equation solver discussed in Blokland et al. (2005). A comparison with recent results by Narayan et al. (2002) shows excellent agreement with their approximate growth rates only if the disks are weakly magnetized. However, for disks close to equipartition, the dispersion equation from Narayan et al. (2002) loses its validity. Our calculations allow for a quantitative determination of the increase of the growth rate due to the magneto-rotational mechanism. We find that the increase of the growth rate for long wavelength convective modes caused by this mechanism is almost neglible. On the other hand, the growth rate of short wavelength instabilities can be significantly increased by this mechanism, reaching values up to 60%.Comment: 10 pages, 9 figures, Accepted for publication in Astronomy & Astrophysic

Toward detailed prominence seismology - II. Charting the continuous magnetohydrodynamic spectrum

Starting from accurate MHD flux rope equilibria containing prominence condensations, we initiate a systematic survey of their linear eigenoscillations. To quantify the full spectrum of linear MHD eigenmodes, we require knowledge of all flux-surface localized modes, charting out the continuous parts of the MHD spectrum. We combine analytical and numerical findings for the continuous spectrum for realistic prominence configurations. The equations governing all eigenmodes for translationally symmetric, gravitating equilibria containing an axial shear flow, are analyzed, along with their flux-surface localized limit. The analysis is valid for general 2.5D equilibria, where either density, entropy, or temperature vary from one flux surface to another. We analyze the mode couplings caused by the poloidal variation in the flux rope equilibria, by performing a small gravity parameter expansion. We contrast the analytical results with continuous spectra obtained numerically. For equilibria where the density is a flux function, we show that continuum modes can be overstable, and we present the stability criterion for these convective continuum instabilities. Furthermore, for all equilibria, a four-mode coupling scheme between an Alfvenic mode of poloidal mode number m and three neighboring (m-1, m, m+1) slow modes is identified, occurring in the vicinity of rational flux surfaces. For realistically prominence equilibria, this coupling is shown to play an important role, from weak to stronger gravity parameter g values. The analytic predictions for small g are compared with numerical spectra, and progressive deviations for larger g are identified. The unstable continuum modes could be relevant for short-lived prominence configurations. The gaps created by poloidal mode coupling in the continuous spectrum need further analysis, as they form preferred frequency ranges for global eigenoscillations.Comment: Accepted by Astronmy & Astrophysics, 21 pages, 15 figure

Unstable magnetohydrodynamical continuous spectrum of accretion disks. A new route to magnetohydrodynamical turbulence in accretion disks

We present a detailed study of localised magnetohydrodynamical (MHD) instabilities occuring in two--dimensional magnetized accretion disks. We model axisymmetric MHD disk tori, and solve the equations governing a two--dimensional magnetized accretion disk equilibrium and linear wave modes about this equilibrium. We show the existence of novel MHD instabilities in these two--dimensional equilibria which do not occur in an accretion disk in the cylindrical limit. The disk equilibria are numerically computed by the FINESSE code. The stability of accretion disks is investigated analytically as well as numerically. We use the PHOENIX code to compute all the waves and instabilities accessible to the computed disk equilibrium. We concentrate on strongly magnetized disks and sub--Keplerian rotation in a large part of the disk. These disk equilibria show that the thermal pressure of the disk can only decrease outwards if there is a strong gravitational potential. Our theoretical stability analysis shows that convective continuum instabilities can only appear if the density contours coincide with the poloidal magnetic flux contours. Our numerical results confirm and complement this theoretical analysis. Furthermore, these results show that the influence of gravity can either be stabilizing or destabilizing on this new kind of MHD instability. In the likely case of a non--constant density, the height of the disk should exceed a threshold before this type of instability can play a role. This localised MHD instability provides an ideal, linear route to MHD turbulence in strongly magnetized accretion disk tori.Comment: 20 pages, 10 figures, accepted for publication in Astronomy & Astrophysic

Wind morphology around cool evolved stars in binaries: the case of slowly accelerating oxygen-rich outflows

The late stellar evolutionary phases of low and intermediate-mass stars are strongly constrained by their mass-loss rates. The wind surrounding cool evolved stars frequently shows non-spherical features, thought to be due to an unseen companion orbiting the donor star. We study the morphology of the circumbinary envelope, in particular around oxygen-rich asymptotic giant branch (AGB) stars. We run a grid of 70 3D hydrodynamics simulations of a progressively accelerating wind propagating in the Roche potential formed by a mass-loosing evolved star in orbit with a main sequence companion. We resolve the flow structure both in the immediate vicinity of the secondary, where bow shocks, outflows and wind-captured disks form, and up to 40 orbital separations, where spiral arms, arcs and equatorial density enhancements develop. When the companion is deeply engulfed in the wind, the lower terminal wind speeds and more progressive wind acceleration around oxygen-rich AGB stars make them more prone than carbon-rich AGB stars to display more disturbed outflows, a disk-like structure around the companion and a wind concentrated in the orbital plane. In these configurations, a large fraction of the wind is captured by the companion which leads to a significant shrinking of the orbit over the mass-loss timescale, if the donor star is at least a few times more massive than its companion. Provided the companion has a mass of at least a tenth of the mass of the donor star, it can compress the wind in the orbital plane up to large distances. Our grid of models covers a wide scope of configurations function of the dust chemical content, the terminal wind speed relative to the orbital speed, the extension of the dust condensation region around the cool evolved star and the mass ratio. It provides a frame of reference to interpret high-resolution maps of the outflows surrounding cool evolved stars

Magneto-rotational overstability in accretion disks

We present analytical and numerical studies of magnetorotational instabilities occuring in magnetized accretion disks. In these studies we make use of the linearised compressible MHD equations. These calculations are performed for general radially stratified disks in the cylindrical limit. In particular, we investigate the influence of nonvanishing toroidal magnetic field component on the growth rate and oscillation frequency of magnetorotational instabilities in Keplerian disks. We find the persistence of these instabilities in accretion disks close to equipartition. Our calculations show that these eigenmodes become overstable (complex eigenvalue), due to the presence of a toroidal magnetic field component, while their growth rate reduces slightly. Furthermore, we demonstrate the presence of magneto-rotational overstabilities in weakly magnetized sub-Keplerian rotating disks. We show that the growth rate scales with the rotation frequency of the disk. These eigenmodes also have a nonzero oscillation frequency, due to the presence of the dominant toroidal magnetic field component. The overstable character of the MRI increases as the rotation frequency of the disk decreases.Comment: 11 pager, 18 Postscript figures, accepted for publication in Astronomy & Astrophysic

Exploring self-consistent 2.5D flare simulations with MPI-AMRVAC

Context. Multidimensional solar flare simulations have not yet included a detailed analysis of the lower atmospheric responses, such as downflowing chromospheric compressions and chromospheric evaporation processes. Aims. We present an analysis of multidimensional flare simulations, including an analysis of chromospheric upflows and downflows that provides important groundwork for comparing 1D and multidimensional models. Methods. We followed the evolution of a magnetohydrodynamic standard solar flare model that includes electron beams and in which localized anomalous resistivity initiates magnetic reconnection. We varied the background magnetic field strength to produce simulations that cover a large span of observationally reported solar flare strengths. Chromospheric energy fluxes and energy density maps were used to analyze the transport of energy from the corona to the lower atmosphere, and the resultant evolution of the flare. Quantities traced along 1D field lines allowed for detailed comparisons with 1D evaporation models. Results. The flares produced by varying the background coronal field strength between 20 G and 65 G have GOES classifications between B1.5 and M2.3. All produce a lobster claw reconnection outflow and a fast shock in the tail of this flow with a similar maximum Alfvén Mach number of ∼10. The impact of the reconnection outflow on the lower atmosphere and the heat conduction are the key agents driving the chromospheric evaporation and “downflowing chromospheric compressions”. The peak electron beam heating flux in the lower atmospheres varies between 1.4 × 109 and 4.7 × 1010 erg cm−2 s−1 across the simulations. The downflowing chromospheric compressions have kinetic energy signatures that reach the photosphere, but at subsonic speeds they would not generate sunquakes. The weakest flare generates a relatively dense flare loop system, despite having a negative net mass flux, through the top of the chromosphere, that is to say, more mass is supplied downward than is evaporated upward. The stronger flares all produce positive mass fluxes. Plasmoids form in the current sheets of the stronger flares due to tearing, and in all experiments the loop tops contain turbulent eddies that ring via a magnetic tuning fork process. Conclusions. The presented flares have chromospheric evaporation driven by thermal conduction and the impact and rebound of the reconnection outflow, in contrast to most 1D models where this process is driven by the beam electrons. Several multidimensional phenomena are critical in determining plasma behavior but are not generally considered in 1D flare simulations. They include loop-top turbulence, reconnection outflow jets, heat diffusion, compressive heating from the multidimensional expansion of the flux tubes due to changing pressures, and the interactions of upward and downward flows from the evaporation meeting the material squeezed downward from the loop tops

Magnetohydrostatic solar prominences in near-potential coronal magnetic fields

We present numerical magnetohydrostatic solutions describing the gravitationally stratified, bulk equilibrium of cool, dense prominence plasma embedded in a near-potential coronal field. These solutions are calculated using the FINESSE magnetohydrodynamics equilibrium solver and describe the morphologies of magnetic field distributions in and around prominences and the cool prominence plasma that these fields support. The equilibrium condition for this class of problem is usually different in distinct subdomains, separated by free boundaries, across which solutions are matched by suitable continuity or jump conditions describing force balance. We employ our precise finite element elliptic solver to calculate solutions not accessible by previous analytical techniques with temperature or entropy prescribed as free functions of the magnetic flux function, including a range of values of the polytropic index, temperature variations mainly across magnetic field lines and photospheric field profiles sheared close to the polarity inversion line. Out of the many examples computed here, perhaps the most noteworthy is one which reproduces precisely the three-part structure often encountered in observations: a cool dense prominence within a cavity/flux rope embedded in a hot corona. The stability properties of these new equilibria, which may be relevant to solar eruptions, can be determined in the form of a full resistive MHD spectrum using a companion hyperbolic stability solver.Comment: To appear in ApJ August 200

Toward detailed prominence seismology - I. Computing accurate 2.5D magnetohydrodynamic equilibria

Context. Prominence seismology exploits our knowledge of the linear eigenoscillations for representative magnetohydro- dynamic models of filaments. To date, highly idealized models for prominences have been used, especially with respect to the overall magnetic configurations. Aims. We initiate a more systematic survey of filament wave modes, where we consider full multi-dimensional models with twisted magnetic fields representative of the surrounding magnetic flux rope. This requires the ability to compute accurate 2.5 dimensional magnetohydrodynamic equilibria that balance Lorentz forces, gravity, and pressure gradients, while containing density enhancements (static or in motion). Methods. The governing extended Grad-Shafranov equation is discussed, along with an analytic prediction for circular flux ropes for the Shafranov shift of the central magnetic axis due to gravity. Numerical equilibria are computed with a finite element-based code, demonstrating fourth order accuracy on an explicitly known, non-trivial test case. Results. The code is then used to construct more realistic prominence equilibria, for all three possible choices of a free flux-function. We quantify the influence of gravity, and generate cool condensations in hot cavities, as well as multi- layered prominences. Conclusions. The internal flux rope equilibria computed here have the prerequisite numerical accuracy to allow a yet more advanced analysis of the complete spectrum of linear magnetohydrodynamic perturbations, as will be demonstrated in the companion paper.Comment: Accepted by Astronomy & Astrophysics, 15 pages, 15 figure