Wladimir Lyra

STEADY STATE DUST DISTRIBUTIONS IN DISK VORTICES: OBSERVATIONAL PREDICTIONS AND APPLICATIONS TO TRANSITIONAL DISKS

The Atacama Large Millimeter Array has returned images of transitional disks in which large asymmetries are seen in the distribution of millimeter sized dust in the outer disk. The explanation in vogue borrows from the vortex literature and suggests that these asymmetries are the result of dust trapping in giant vortices, excited via Rossby wave instabilities at planetary gap edges. Due to the drag force, dust trapped in vortices will accumulate in the center and diffusion is needed to maintain a steady state over the lifetime of the disk. While previous work derived semi-analytical models of the process, in this paper we provide analytical steady-steady solutions. Exact solutions exist for certain vortex models. The solution is determined by the vortex rotation profile, the gas scale height, the vortex aspect ratio, and the ratio of dust diffusion to gas-dust friction. In principle, all of these quantities can be derived from observations, which would validate the model and also provide constrains on the strength of the turbulence inside the vortex core. Based on our solution, we derive quantities such as the gas-dust contrast, the trapped dust mass, and the dust contrast at the same orbital location. We apply our model to the recently imaged Oph IRS 48 system, finding values within the range of the observational uncertainties.

Spiral structure of the Third Galactic Quadrant and the solution to the Canis Major debate

ABSTRACT With the discovery of the Sagittarius dwarf spheroidal (Ibata et al. 1994), a galaxycaught in the process of merging with the Milky Way, the hunt for other such ac-cretion events has become a very active field of astrophysical research. The identifi-cation of a stellar ring-like structure in Monoceros, spanning more than 100 degrees(Newberg et al. 2002), and the detection of an overdensity of stars in the directionof the constellation of Canis Major (CMa; Martin et al. 2004), apparently associatedto the ring, has led to the widespread belief that a second galaxy being cannibalisedby the Milky Way had been found. In this scenario, the overdensity would be theremaining core of the disrupted galaxy and the ring would be the tidal debris leftbehind. However, unlike the Sagittarius dwarf, which is well below the Galactic planeand whose orbit, and thus tidal tail, is nearly perpendicular to the plane of the MilkyWay, the putative CMa galaxy and ring are nearly co-planar with the Galactic disk.This severely complicates the interpretation of observations. In this letter, we showthat our new description of the Milky Way leads to a completely different picture. Weargue that the Norma-Cygnus spiral arm defines a distant stellar ring crossing Mono-ceros and the overdensity is simply a projection effect of looking along the nearbylocal arm. Our perspective sheds new light on a very poorly known region, the thirdGalactic quadrant (3GQ), where CMa is located.Key words: Galaxy: structure — open clusters and associations: general — Galaxy:stellar content — galaxies: dwarf

Formation of sharp eccentric rings in debris disks with gas but without planets

‘Debris disks’ around young stars (analogues of the Kuiper Belt in our Solar System) show a variety of non-trivial structures attributed to planetary perturbations and used to constrain the properties of those planets. However, these analyses have largely ignored the fact that some debris disks are found to contain small quantities of gas, a component that all such disks should contain at some level. Several debris disks have been measured with a dust-to-gas ratio of about unity, at which the effect of hydrodynamics on the structure of the disk cannot be ignored. Here we report linear and nonlinear modelling that shows that dust–gas interactions can produce some of the key patterns attributed to planets. We find a robust clumping instability that organizes the dust into narrow, eccentric rings, similar to the Fomalhaut debris disk. The conclusion that such disks might contain planets is not necessarily required to explain these systems.

A Well-posed Kelvin-Helmholtz Instability Test and Comparison

Recently, there has been a significant level of discussion of the correct treatment of Kelvin-Helmholtz instability (KHI) in the astrophysical community. This discussion relies largely on how the KHI test is posed and analyzed. We pose a stringent test of the initial growth of the instability. The goal is to provide a rigorous methodology for verifying a code on two-dimensional KHI. We ran the problem in the Pencil Code, Athena, Enzo, NDSPMHD, and Phurbas. A strict comparison, judgment, or ranking, between codes is beyond the scope of this work, though this work provides the mathematical framework needed for such a study. Nonetheless, how the test is posed circumvents the issues raised by tests starting from a sharp contact discontinuity yet it still shows the poor performance of smoothed particle hydrodynamics (SPH). We then comment on the connection between this behavior to the underlying lack of zeroth-order consistency in SPH interpolation. We comment on the tendency of some methods, particularly those with very low numerical diffusion, to produce secondary Kelvin-Helmholtz billows on similar tests. Though the lack of a fixed, physical diffusive scale in the Euler equations lies at the root of the issue, we suggest that in some methods an extra diffusion operator should be used to damp the growth of instabilities arising from grid noise. This statement applies particularly to moving-mesh tessellation codes, but also to fixed-grid Godunov schemes.

Embryos grown in the dead zone - Assembling the first protoplanetary cores in low mass self-gravitating circumstellar disks of gas and solids

Context: In the borders of the dead zones of protoplanetary disks, the inflow of gas produces a local density maximum that triggers the Rossby wave instability. The vortices that form are efficient ...

Global magnetohydrodynamical models of turbulence in protoplanetary disks. I. A cylindrical potential on a Cartesian grid and transport of solids

Aims. We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. A second goal is to demonstrate that Cartesian codes are comparable to cylindrical and spherical ones in handling the magnetohydrodynamics of the disk simulations while offering advantages, such as the absence of a grid singularity, for certain applications, e.g., circumbinary disks and disk-jet simulations. Methods. We employ the PENCIL CODE, a 3D high-order finite-difference MHD code using Cartesian coordinates. We solve the equations of ideal MHD with a local isothermal equation of state. Planets and stars are treated as particles evolved with an N-body scheme. Solid boulders are treated as individual superparticles that couple to the gas through a drag force that is linear in the local relative velocity between gas and particle. Results. We find that Cartesian grids are well-suited for accretion disk problems. The disk-in-a-box models based on Cartesian grids presented here develop and sustain MHD turbulence, in good agreement with published results achieved with cylindrical codes. Models without an inner boundary do not show the spurious build-up of magnetic pressure and Reynolds stress seen in the models with boundaries, but the global stresses and alpha viscosities are similar in the two cases. We investigate the dependence of the magnetorotational instability on disk scale height, finding evidence that the turbulence generated by the magnetorotational instability grows with thermal pressure. The turbulent stresses depend on the thermal pressure obeying a power law of 0.24 ± 0.03, compatible with the value of 0.25 found in shearing box calculations. The ratio of Maxwell to Reynolds stresses decreases with increasing temperature, dropping from 5 to 1 when the sound speed was raised by a factor 4, maintaing the same field strength. We also study the dynamics of solid boulders in the hydromagnetic turbulence, by making use of 10 6 Lagrangian particles embedded in the Eulerian grid. The effective diffusion provided by the turbulence prevents settling of the solids in a infinitesimally thin layer, forming instead a layer of solids of finite vertical thickness. The measured scale height of this diffusion-supported layer of solids implies turbulent vertical diffusion coefficients with globally averaged Schmidt numbers of 1.0 ± 0.2 for a model with a ≈ 10 -3 and 0.78 ± 0.06 for a model with a ≈ 10 -1 . That is, the vertical turbulent diffusion acting on the solids phase is comparable to the turbulent viscosity acting on the gas phase. The average bulk density of solids in the turbulent flow is quite low (pp = 6.0 x 10 -11 kg m -3 ), but in the high pressure regions, significant overdensities are observed, where the solid-to-gas ratio reached values as great as 85, corresponding to 4 orders of magnitude higher than the initial interstellar value of 0.01.

CONVECTIVE OVERSTABILITY IN ACCRETION DISKS: THREE-DIMENSIONAL LINEAR ANALYSIS AND NONLINEAR SATURATION

Recently, Klahr & Hubbard claimed that a hydrodynamical linear overstability exists in protoplanetary disks, powered by buoyancy in the presence of thermal relaxation. We analyze this claim, confirming it through rigorous compressible linear analysis. We model the system numerically, reproducing the linear growth rate for all cases studied. We also study the saturated properties of the overstability in the shearing box, finding that the saturated state produces finite amplitude fluctuations strong enough to trigger the subcritical baroclinic instability (SBI). Saturation leads to a fast burst of enstrophy in the box, and a large-scale vortex develops in the course of the next ≈100 orbits. The amount of angular momentum transport achieved is of the order of α ≈10^(–3), as in compressible SBI models. For the first time, a self-sustained three-dimensional vortex is produced from linear amplitude perturbation of a quiescent base state.

A PARAMETER STUDY FOR BAROCLINIC VORTEX AMPLIFICATION

Recent studies have shown that baroclinic vortex amplification is strongly dependent on certain factors, namely, the global entropy gradient, the efficiency of thermal diffusion and/or relaxation as well as numerical resolution. We conduct a comprehensive study of a broad range and combination of various entropy gradients, thermal diffusion and thermal relaxation timescales via local shearing sheet simulations covering the parameter space relevant for protoplanetary disks. We measure the Reynolds stresses as a function of our control parameters and see that there is angular momentum transport even for entropy gradients as low as {beta} = -dln s/dln r = 1/2. Values we expect in protoplanetary disks are between {beta} = 0.5-2.0 The amplification-rate of the perturbations, {Gamma}, appears to be proportional to {beta}{sup 2} and thus proportional to the square of the Brunt-Vaeisaelae frequency ({Gamma}{proportional_to}{beta}{sup 2}{proportional_to}N {sup 2}). The saturation level of Reynolds stresses, on the other hand, seems to be proportional to {beta}{sup 1/2}. This highlights the importance of baroclinic effects even for the low entropy gradients expected in protoplanetary disks.

ORBITAL MIGRATION OF INTERACTING LOW-MASS PLANETS IN EVOLUTIONARY RADIATIVE TURBULENT MODELS

The torques exerted by a locally isothermal disk on an embedded planet lead to rapid inward migration. Recent work has shown that modeling the thermodynamics without the assumption of local isothermality reveals regions where the net torque on an embedded planet is positive, leading to outward migration of the planet. When a region with negative torque lies directly exterior to this, planets in the inner region migrate outward and planets in the outer region migrate inward, converging where the torque is zero. We incorporate the torques from an evolving non-isothermal disk into an N-body simulation to examine the behavior of planets or planetary embryos interacting in the convergence zone. We find that mutual interactions do not eject objects from the convergence zone. Small numbers of objects in a laminar disk settle into near resonant orbits that remain stable over the 10 Myr periods that we examine. However, either or both increasing the number of planets or including a correlated, stochastic force to represent turbulence drives orbit crossings and mergers in the convergence zone. These processes can build gas giant cores with masses of order 10 Earth masses from sub-Earth mass embryos in 2-3 Myr.

PARTICLE TRAPPING AND STREAMING INSTABILITY IN VORTICES IN PROTOPLANETARY DISKS

We analyze the concentration of solid particles in vortices created and sustained by radial buoyancy in protoplanetary disks, e.g., baroclinic vortex growth. Besides the gas drag acting on particles, we also allow for back-reaction from dust onto the gas. This becomes important when the local dust-to-gas ratio approaches unity. In our two-dimensional, local, shearing sheet simulations, we see high concentrations of grains inside the vortices for a broad range of Stokes numbers, St. An initial dust-to-gas ratio of 1:100 can easily be reversed to 100:1 for St = 1.0. The increased dust-to-gas ratio triggers the streaming instability, thus counter-intuitively limiting the maximal achievable overdensities. We find that particle trapping inside vortices opens the possibility for gravity assisted planetesimal formation even for small particles (St = 0.01) and a low initial dust-to-gas ratio of 1:10^4, e.g., much smaller than in the previously studied magnetohydrodynamic zonal flow case.