Context. The global size and spatial distribution of dust is an important ingredient in the structure and evolution of protoplanetary disks and in the formation of larger bodies, such as ...planetesimals. Aims. We aim to derive simple equations that explain the global evolution of the dust surface density profile and the upper limit of the grain size distribution and which can readily be used for further modeling or for interpreting of observational data. Methods. We have developed a simple model that follows the upper end of the dust size distribution and the evolution of the dust surface density profile. This model is calibrated with state-of-the-art simulations of dust evolution, which treat dust growth, fragmentation, and transport in viscously evolving gas disks. Results. We find very good agreement between the full dust-evolution code and the toy model presented in this paper. We derive analytical profiles that describe the dust-to-gas ratios and the dust surface density profiles well in protoplanetary disks, as well as the radial flux by solid material “rain out”, which is crucial for triggering any gravity assisted formation of planetesimals. We show that fragmentation is the dominating effect in the inner regions of the disk leading to a dust surface density exponent of -1.5, while the outer regions at later times can become drift-dominated, yielding a dust surface density exponent of −0.75. Our results show that radial drift is not efficient in fragmenting dust grains. This supports the theory that small dust grains are resupplied by fragmentation due to the turbulent state of the disk.
Recent observations by the Atacama Large Millimeter/sub-millimeter Array (ALMA) of disks around young stars revealed distinct asymmetries in the dust continuum emission. In this work we wish to study ...axisymmetric and non-axisymmetric structures that are generated by the magneto-rotational instability in the outer regions of protoplanetary disks. We performed non-ideal global 3D magneto-hydrodynamic (MHD) stratified simulations of the dead-zone outer edge using the FARGO MHD code PLUTO. The stellar and disk parameters were taken from a parameterized disk model applied for fitting high-angular resolution multi-wavelength observations of various circumstellar disks. All models quickly turned into a turbulent state. The fiducial model with a dust-to-gas mass ratio of 10-2 developed a large gap followed by a jump in surface density located at the dead-zone outer edge. The jump in density and pressure was strong enough to stop the radial drift of particles at this location. The RT results and simulated ALMA observations predict that it is feasible to observe these large-scale structures that appear in magnetized disks without planets.
Recent numerical simulations have shown long-lived axisymmetric sub- and super-Keplerian flows in protoplanetary disks. These zonal flows are found in local as well as global simulations of disks ...unstable to the magnetorotational instability. This paper covers our study of the strength and lifetime of zonal flows and the resulting long-lived gas over- and underdensities as functions of the azimuthal and radial size of the local shearing box. We further investigate dust particle concentrations without feedback on the gas and without self-gravity. The strength and lifetime of zonal flows increase with the radial extent of the simulation box, but decrease with the azimuthal box size. Our simulations support earlier results that zonal flows have a natural radial length scale of 5-7 gas pressure scale heights. This is the first study that combines three-dimensional MHD simulations of zonal flows and dust particles feeling the gas pressure. The pressure bumps trap particles with St = 1 very efficiently. We show that St = 0.1 particles (of some centimeters in size if at 5 AU in a minimum mass solar nebula) reach a hundred-fold higher density than initially. This opens the path for particles of St = 0.1 and dust-to-gas ratio of 0.01 or for particles of St > or =, slanted 0.5 and dust-to-gas ratio 10 super(-4) to still reach densities that potentially trigger the streaming instability and thus gravoturbulent formation of planetesimals.
Context. This is the fourth paper in a series showing the results of planet population synthesis calculations. In Paper I, we presented our methods. In Paper II, we compared the synthetic and the ...observed planetary population statistically. Paper III addressed the influences of the stellar mass on the population.Aims. Our goal in this fourth paper is to systematically study the effects of important disk properties, namely disk metallicity, mass, and lifetime on fundamental properties of planets like mass and semimajor axis.Methods. For a large number of protoplanetary disks that have properties following distributions derived from observations, we calculated a population of planets with our formation model. The model is based on the classical core accretion paradigm but self-consistently includes planet migration and disk evolution.Results. We find a very large number of correlations. Regarding the planetary initial mass function, metallicity, Mdisk, and τdisk play different roles. For high metallicities, giant planets are more frequent. For high Mdisk, giant planets are more massive. For long τdisk, giant planets are both more frequent and massive. At low metallicities, very massive giant planets cannot form, but otherwise giant planet mass and metallicity are nearly uncorrelated. In contrast, (maximum) planet masses and disk gas masses are correlated. The formation of giant planets is possible for initial planetesimal surface densities ΣS of at least 6 g/cm2 at 5.2 AU. The best spot for giant planet formation is at ~5 AU. In- and outside this distance, higher ΣS are necessary. Low metallicities can be compensated for by high Mdisk, and vice versa, but not ad infinitum. At low metallicities, giant planets only form outside the ice line, while giant planet formation occurs throughout the disk at high metallicities. The extent of migration increases with Mdisk and τdisk and usually decreases with metallicity. No clear correlation of metallicity and the semimajor axis distribution of giant planets exists because in low-metallicity disks, planets start farther out, but migrate more, while the contrary applies to high metallicities. The final semimajor axis distribution contains an imprint of the ice line. Close-in low mass planets have a lower mean metallicity than hot Jupiters. The frequency of giant planets varies approximately as Mdisk1.2 and τdisk2.Conclusions. The properties of protoplanetary disks – the initial and boundary conditions for planet formation – are decisive for the properties of planets, and leave many imprints on the population.
Aims. Dust grains with sizes around (sub)mm are expected to couple only weakly to the gas motion in regions beyond 10 au of circumstellar disks. In this work, we investigate the influence of the ...spatial distribution of these grains on the (sub)mm appearance of magnetized protoplanetary disks. Methods. We perform non-ideal global 3D magneto-hydrodynamic (MHD) stratified disk simulations, including particles of different sizes (50 μm to 1 cm), using a Lagrangian particle solver. Subsequently, we calculate the spatial dust temperature distribution, including the dynamically coupled submicron-sized dust grains, and derive ideal continuum re-emission maps of the disk through radiative transfer simulations. Finally, we investigate the feasibility of observing specific structures in the thermal re-emission maps with the Atacama Large Millimeter/submillimeter Array (ALMA). Results. Depending on the level of turbulence, the radial pressure gradient of the gas, and the grain size, particles settle to the midplane and/or drift radially inward. The pressure bump close to the outer edge of the dead-zone leads to particle-trapping in ring structures. More specifically, vortices in the disk concentrate the dust and create an inhomogeneous distribution of solid material in the azimuthal direction. The large-scale disk perturbations are preserved in the (sub)mm re-emission maps. The observable structures are very similar to those expected from planet-disk interaction. Additionally, the larger dust particles increase the brightness contrast between the gap and ring structures. We find that rings, gaps, and the dust accumulation in the vortex could be traced with ALMA down to a scale of a few astronomical units in circumstellar disks located in nearby star-forming regions. Finally, we present a brief comparison of these structures with those recently found with ALMA in the young circumstellar disks of HL Tau and Oph IRS 48.
We study the behavior of magnetorotational turbulence in shearing box simulations with a radial and azimuthal extent up to 10 scale heights. Maxwell and Reynolds stresses are found to increase by ...more than a factor of 2 when increasing the box size beyond two scale heights in the radial direction. Further increase of the box size has little or no effect on the statistical properties of the turbulence. An inverse cascade excites magnetic field structures at the largest scales of the box. The corresponding 10% variation in the Maxwell stress launches a zonal flow of alternating sub- and super-Keplerian velocity. This, in turn, generates a banded density structure in geostrophic balance between pressure and Coriolis forces. We present a simplified model for the appearance of zonal flows, in which stochastic forcing by the magnetic tension on short timescales creates zonal flow structures with lifetimes of several tens of orbits. We experiment with various improved shearing box algorithms to reduce the numerical diffusivity introduced by the supersonic shear flow. While a standard finite difference advection scheme shows signs of a suppression of turbulent activity near the edges of the box, this problem is eliminated by a new method where the Keplerian shear advection is advanced in time by interpolation in Fourier space.
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