206 research outputs found
Rossby Wave Instability and Long-Term Evolution of Dead Zones in Protoplanetary Discs
The physical mechanism of angular momentum transport in poorly ionized
regions of protoplanetary discs, the dead zones (DZs), is not understood. The
presence of a DZ naturally leads to conditions susceptible to the Rossby wave
instability (RWI), which produces vortices and spiral density waves that may
revive the DZ and be responsible for observed large-scale disc structures. We
present a series of two-dimensional hydrodynamic simulations to investigate the
role of the RWI in DZs, including its impact on the long-term evolution of the
disc and its morphology. The nonlinear RWI can generate Reynolds stresses
(effective parameter) as large as in the DZ, helping to
sustain quasi-steady accretion throughout the disc. It also produces novel disc
morphologies, including azimuthal asymmetries with , and atypical
vortex shapes. The angular momentum transport strength and morphology are most
sensitive to two parameters: the radial extent of the DZ and the disc
viscosity. The largest Reynolds stresses are produced when the radial extent of
the DZ is less than its distance to the central star. Such narrow DZs lead to a
single vortex or two coherent antipodal vortices in the quasi-steady state. The
edges of wider DZs evolve separately, resulting in two independent vortices and
reduced angular momentum transport efficiency. In either case, we find that,
because of the Reynolds stresses generated by the nonlinear RWI, gravitational
instability is unlikely to play a role in angular momentum transport across the
DZ, unless the accretion rate is sufficiently high.Comment: 15 pages, 15 figures, submitted to MNRA
How strong are the Rossby vortices?
The Rossby wave instability, associated with density bumps in differentially
rotating discs, may arise in several different astrophysical contexts, such as
galactic or protoplanetary discs. While the linear phase of the instability has
been well studied, the nonlinear evolution and especially the saturation phase
remain poorly understood. In this paper, we test the non-linear saturation
mechanism analogous to that derived for wave-particle interaction in plasma
physics. To this end we perform global numerical simulations of the evolution
of the instability in a two-dimensional disc. We confirm the physical mechanism
for the instability saturation and show that the maximum amplitude of vorticity
can be estimated as twice the linear growth rate of the instability. We provide
an empirical fitting formula for this growth rate for various parameters of the
density bump. We also investigate the effects of the azimuthal mode number of
the instability and the energy leakage in the spiral density waves. Finally, we
show that our results can be extrapolated to 3D discs.Comment: Accepted for publication in MNRA
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&
Flux Modulation from the Rossby Wave Instability in microquasars accretion disks: toward a HFQPO model
Context. There have been a long string of efforts to understand the source of
the variability observed in microquasars, especially concerning the elusive
High-Frequency Quasi-Periodic Oscillation. These oscillations are among the
fastest phenomena that affect matter in the vicinity of stellar black holes and
therefore could be used as probes of strong-field general relativity.
Nevertheless, no model has yet gained wide acceptance. Aims. The aim of this
article is to investigate the model derived from the occurrence of the Rossby
wave instability at the inner edge of the accretion disk. In particular, our
goal here is to demonstrate the capacity of this instability to modulate the
observed flux in agreement with the observed results. Methods. We use the
AMRVAC hydrodynamical code to model the instability in a 3D optically thin
disk. The GYOTO ray-tracing code is then used to compute the associated light
curve. Results. We show that the 3D Rossby wave instability is able to modulate
the flux well within the observed limits.We highlight that 2D simulations allow
us to obtain the same general characteristics of the light curve as 3D
calculations. With the time resolution we adopted in this work, three
dimensional simulations do not give rise to any new observable features that
could be detected by current instrumentation or archive data.Comment: 10 pages, 10 figures, accepted by A&
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&
Rossby wave instability in 3D discs
The Rossby wave instability (RWI) is a promising mechanism for producing large-scale vortices in protoplanetary discs. The instability operates around a density bump in the disc, and the resulting vortices may facilitate planetesimal formation and angular momentum transfer in the disc dead zone. Most previous works on the RWI deal with 2D (height-integrated) discs. However, vortices in 3D may have different dynamical behaviours from those in 2D. Recent numerical simulations of the RWI in 3D global discs by Meheut et al. have revealed intriguing vertical structure of the vortices, including appreciable vertical velocities. In this paper we present a linear analysis of the RWI, in 3D global models of isothermal discs. We calculate the growth rates of the Rossby modes (of various azimuthal wave numbers m= 2-6) trapped around the fiducial density bump and carry out 3D numerical simulations to compare with our linear results. We show that the 3D RWI growth rates are only slightly smaller than the 2D growth rates, and the velocity structures seen in the numerical simulations during the linear phase are in agreement with the velocity eigenfunctions obtained in our linear calculations. This numerical benchmark shows that numerical simulations can accurately describe the instability. The angular momentum transfer rate associated with Rossby vortices is also studie
Multiple spiral patterns in the transitional disk of HD 100546
Protoplanetary disks around young stars harbor many structures related to
planetary formation. Of particular interest, spiral patterns were discovered
among several of these disks and are expected to be the sign of gravitational
instabilities leading to giant planets formation or gravitational perturbations
caused by already existing planets. In this context, the star HD100546 presents
some specific characteristics with a complex gas and dusty disk including
spirals as well as a possible planet in formation. The objective of this study
is to analyze high contrast and high angular resolution images of this
emblematic system to shed light on critical steps of the planet formation. We
retrieved archival images obtained at Gemini in the near IR (Ks band) with the
instrument NICI and processed the data using advanced high contrast imaging
technique taking advantage of the angular differential imaging. These new
images reveal the spiral pattern previously identified with HST with an
unprecedented resolution, while the large-scale structure of the disk is mostly
erased by the data processing. The single pattern at the southeast in HST
images is now resolved into a multi-armed spiral pattern. Using two models of a
gravitational perturber orbiting in a gaseous disk we attempted to bring
constraints on the characteristics of this perturber assuming each spiral being
independent and we derived qualitative conclusions. The non-detection of the
northeast spiral pattern observed in HST allows to put a lower limit on the
intensity ratio between the two sides of the disk, which if interpreted as
forward scattering yields a larger anisotropic scattering than derived in the
visible. Also, we found that the spirals are likely spatially resolved with a
thickness of about 5-10AU. Finally, we did not detect the candidate forming
planet recently discovered in the Lp band, with a mass upper limit of 16-18 MJ.Comment: Accepted for publication in Astronomy and Astrophysics, 10 pages, 8
figure
Rossby wave instability in locally isothermal and polytropic disks: three-dimensional linear calculations
Numerical calculations of the linear Rossby wave instability (RWI) in global
three-dimensional (3D) disks are presented. The linearized fluid equations are
solved for vertically stratified, radially structured disks with either a
locally isothermal or polytropic equation of state, by decomposing the vertical
dependence of the perturbed hydrodynamic quantities into Hermite and Gegenbauer
polynomials, respectively. It is confirmed that the RWI operates in 3D. For
perturbations with vertical dependence assumed above, there is little
difference in growth rates between 3D and two-dimensional (2D) calculations.
Comparison between 2D and 3D solutions of this type suggest the RWI is
predominantly a 2D instability and that three-dimensional effects, such as
vertical motion, to be interpreted as a perturbative consequence of the
dominant 2D flow. The vertical flow around co-rotation, where vortex-formation
is expected, is examined. In locally isothermal disks the expected vortex
center remains in approximate vertical hydrostatic equilibrium. For polytropic
disks the vortex center has positive vertical velocity, whose magnitude
increases with decreasing polytropic index .Comment: 17 pages, 21 figures, Accepted by Ap
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