Formation Of Protoplanetary Disks Research Articles

Redistribution of CO at the location of the CO ice line in evolving gas and dust disks

Context. Ice lines are suggested to play a significant role in grain growth and planetesimal formation in protoplanetary disks. Evaporation fronts directly influence the gas and ice abundances of volatile species in the disk and therefore the coagulation physics and efficiency and the chemical composition of the resulting planetesimals. Aims. In this work we investigate the influence of the existence of the CO ice line on the particle growth and on the distribution of CO in the disk. Methods. We include the possibility of tracking the CO content and/or other volatiles in particles and in the gas in our existing dust coagulation and disk evolution model and developed a method for evaporation and condensation of CO using the Hertz-Knudsen equation. Our model does not include fragmentation, yet, which will be part of further investigations. Results. We find no enhanced grain growth just outside the ice line where the particle size is limited by radial drift. Instead we find a depletion of solid material inside the ice line which is solely due to evaporation of the CO. Such a depression inside the ice line may be observable and may help to quantify the processes described in this work. Furthermore, we find that the viscosity and diffusivity of the gas heavily influence the re-distribution of vaporized CO at the ice line and can lead to an increase in the CO abundance by up to a factors of a few in the region just inside the ice line. Depending on the strength of the gaseous transport mechanisms the position of the ice line in our model can change by up to 10 AU and consequently, the temperature at that location can range from 21 K to 23 K.

Gap formation by inclined massive planets in locally isothermal three-dimensional discs

We study gap formation in gaseous protoplanetary discs by a Jupiter mass planet. The planet's orbit is circular and inclined relative to the midplane of the disc. We use the impulse approximation to estimate the gravitational tidal torque between the planet and the disc, and infer the gap profile. For low-mass discs, we provide a criterion for gap opening when the orbital inclination is $\leq 30^{\circ}$. Using the FARGO3D code, we simulate the disc response to an inclined massive planet. The dependence of the depth and width of the gap obtained in the simulations on the inclination of the planet is broadly consistent with the scaling laws derived in the impulse approximation. Although we mainly focus on planets kept on fixed orbits, the formalism permits to infer the temporal evolution of the gap profile in cases where the inclination of the planet changes with time. This study may be useful to understand the migration of massive planets on inclined orbit, because the strength of the interaction with the disc depends on whether a gap is opened or not.

The Moon Meets All Requirements of the IAU Definition for “Planet”

The Earth-Moon system has often been characterized as having some characteristics of a “double planet” system. It is demonstrated that while the orbital barycenter of the Earth-Moon pair lies inside the radius of the Earth, the Moon does meet all three requirements of the IAU definition for “planet” and therefore the Moon can correctly be identified as the Solar System’s 9th planet. In order to avoid confusion by this development it is necessary to add definitions for “double planet”, “double dwarf planet”, “satellite planet”, and “satellite” to complement the International Astronomical Union definitions for “planet” and “dwarf planet”. The Earth-Moon system meets the requirements of a “double planet” system while the Pluto-Charon system meets the requirements of a “double dwarf planet” system. In order to extrapolate sub-stellar taxonomy to exoplanetary systems, general formation mechanisms (star-like gas collapse in molecular clouds vs. proto-planetary disk formation) should be included in the definitions for the various classes of sub-stellar mass bodies.

AN ORDERED MAGNETIC FIELD IN THE PROTOPLANETARY DISK OF AB Aur REVEALED BY MID-INFRARED POLARIMETRY

ABSTRACT Magnetic fields (B-fields) play a key role in the formation and evolution of protoplanetary disks, but their properties are poorly understood due to the lack of observational constraints. Using CanariCam at the 10.4 m Gran Telescopio Canarias, we have mapped out the mid-infrared polarization of the protoplanetary disk around the Herbig Ae star AB Aur. We detect ∼0.44% polarization at 10.3 μm from AB Aur's inner disk (r < 80 au), rising to ∼1.4% at larger radii. Our simulations imply that the mid-infrared polarization of the inner disk arises from dichroic emission of elongated particles aligned in a disk B-field. The field is well ordered on a spatial scale, commensurate with our resolution (∼50 au), and we infer a poloidal shape tilted from the rotational axis of the disk. The disk of AB Aur is optically thick at 10.3 μm, so polarimetry at this wavelength is probing the B-field near the disk surface. Our observations therefore confirm that this layer, favored by some theoretical studies for developing magneto-rotational instability and its resultant viscosity, is indeed very likely to be magnetized. At radii beyond ∼80 au, the mid-infrared polarization results primarily from scattering by dust grains with sizes up to ∼1 μm, a size indicating both grain growth and, probably, turbulent lofting of the particles from the disk mid-plane.

MAGNETICALLY SELF-REGULATED FORMATION OF EARLY PROTOPLANETARY DISKS

ABSTRACT The formation of protoplanetary disks during the collapse of molecular dense cores is significantly influenced by angular momentum transport, notably by the magnetic torque. In turn, the evolution of the magnetic field is determined by dynamical processes and non-ideal MHD effects such as ambipolar diffusion. Considering simple relations between various timescales characteristic of the magnetized collapse, we derive an expression for the early disk radius, where M is the total disk plus protostar mass, is the ambipolar diffusion coefficient, and B z is the magnetic field in the inner part of the core. This is significantly smaller than the disks that would form if angular momentum was conserved. The analytical predictions are confronted against a large sample of 3D, non-ideal MHD collapse calculations covering variations of a factor 100 in core mass, a factor 10 in the level of turbulence, a factor 5 in rotation, and magnetic mass-to-flux over critical mass-to-flux ratios 2 and 5. The disk radius estimates are found to agree with the numerical simulations within less than a factor 2. A striking prediction of our analysis is the weak dependence of circumstellar disk radii upon the various relevant quantities, suggesting weak variations among class-0 disk sizes. In some cases, we note the onset of large spiral arms beyond this radius.

From birth to death of protoplanetary discs: modelling their formation, evolution and dispersal

Formation, evolution, and dispersal processes of protoplanetary disks are investigated and the disk lifetime is estimated. Gravitational collapse of a pre-stellar core forms both a central star and a protoplanetary disk. The central star grows by accretion from the disk, and irradiation by the central star heats up the disk and generates thermal wind, which results in the disk dispersal. We calculate the evolution of protoplanetary disks from their parent pre-stellar cores to dispersal of the disks. We find that the disk lifetimes of typical pre-stellar cores are around 2--4 million years (Myr). A pre-stellar core with high angular momentum forms a larger disk whose lifetime is long, while a disk around a X-ray luminous star has a short lifetime. Integrating the disk lifetimes under various mass and angular velocity of prestellar cores and X-ray luminosities of young stellar objects, we obtain disk fraction at a given stellar age and mean lifetime of the disks. Our model indicates that the mean lifetime of protoplanetary disks is 3.7 Myr, which is consistent with the observational estimate from young stellar clusters. We also find that the dispersion of X-ray luminosity is needed to reproduce the observed disk fraction.

The role of disk self-gravity on gap formation of the HL Tau proto-planetary disk

We use extensive global hydrodynamic disk gas+dust simulations with embedded planets to model the dust ring and gap structures in the HL Tau protoplanetary disk observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). Since the HL Tau is a relatively massive disk, we find the disk self-gravity (DSG) plays an important role in the gap formation induced by the planets. Our simulation results demonstrate that DSG is necessary in explaining of the dust ring and gap in HL Tau disk. The comparison of simulation results shows that the dust rings and gap structures are more evident when the fully 2D DSG (non-axisymmetric components are included) is used than if 1D axisymmetric DSG (only the axisymetric component is included) is used, or the disk self-gravity is not considered. We also find that the couple dust+gas+planet simulations are required because the gap and ring structure is different between dust and gas surface density.

Vortex formation in protoplanetary discs induced by the vertical shear instability

We present the results of 2D and 3D hydrodynamic simulations of idealized protoplanetary discs that examine the formation and evolution of vortices by the vertical shear instability (VSI). In agreement with recent work, we find that discs with radially decreasing temperature profiles and short thermal relaxation time-scales, are subject to the axisymmetric VSI. In three dimensions, the resulting velocity perturbations give rise to quasi-axisymmetric potential vorticity perturbations that break-up into discrete vortices, in a manner that is reminiscent of the Rossby wave instability. Discs with very short thermal evolution time-scales (i.e. {\tau}<0.1 local orbit periods) develop strong vorticity perturbations that roll up into vortices that have small aspect ratios ({\chi}<2) and short lifetimes (~ a few orbits). Longer thermal time-scales give rise to vortices with larger aspect ratios (6<{\chi}<10), and lifetimes that depend on the entropy gradient. A steeply decreasing entropy profile leads to vortex lifetimes that exceed the simulation run times of hundreds of orbital periods. Vortex lifetimes in discs with positive or weakly decreasing entropy profiles are much shorter, being 10s of orbits at most, suggesting that the subcritical baroclinic instability plays an important role in sustaining vortices against destruction through the elliptical instability. Applied to the outer regions of protoplanetary discs, where the VSI is most likely to occur, our results suggest that vortices formed by the VSI are likely to be short lived structures.

Exact Axisymmetric Solutions of the 2-D Lane-Emden Equations with Rotation

We have derived exact axisymmetric solutions of the two-dimensional Lane-Emden equations with rotation. These solutions are intrinsically favored by the differential equations regardless of any adopted boundary conditions and the physical solutions of the Cauchy problem are bound to oscillate about and remain close to these intrinsic solutions. The isothermal solutions are described by power-law density profiles in the radial direction, whereas the polytropic solutions are described by radial density profiles that are powers of the zeroth-order Bessel function of the first kind. Both families of solutions decay exponentially in the vertical direction and both result in increasing or nearly flat radial rotation curves. The results are applicable to gaseous spiral-galaxy disks that exhibit flat rotation curves and to the early stages of protoplanetary disk formation before the central star is formed.

EXTERNAL PHOTOEVAPORATION OF THE SOLAR NEBULA. II. EFFECTS ON DISK STRUCTURE AND EVOLUTION WITH NON-UNIFORM TURBULENT VISCOSITY DUE TO THE MAGNETOROTATIONAL INSTABILITY

The structure and evolution of protoplanetary disks, especially the radial flows of gas through them, are sensitive to a number of factors. One that has been considered only occasionally in the literature is external photoevaporation by far-ultraviolet (FUV) radiation from nearby, massive stars, despite the fact that nearly half of all disks will experience photoevaporation. Another effect apparently not considered in the literature is a spatially and temporally varying value of $\alpha$ in the disk [where the turbulent viscosity $\nu$ is $\alpha$ times the sound speed C times the disk scale height H]. Here we use the formulation of Bai \& Stone (2011) to relate $\alpha$ to the ionization fraction in the disk, assuming turbulent transport of angular momentum is due to the magnetorotational instability. We find that disk evolution is most sensitive to the surface area of dust. Typically $\alpha \lesssim 10^{-5}$ in the inner disk ($< 2$ AU), rising to $\sim 10^{-1}$ beyond 20 AU. This drastically alters the structure of the disk and the flow of mass through it: while the outer disk rapidly viscously spreads, the inner disk hardly evolves; this leads to a steep surface density profile with a slope < p > $\approx$ 2 - 5 in the 5-30 AU region) that is made steeper by external photoevaporation. We also find that the combination of variable $\alpha$ and external photoevaporation eventually causes gas as close as 3 AU, previously accreting inward, to be drawn outward to the photoevaporated outer edge of the disk. These effects have drastic consequences for planet formation and volatile transport in protoplanetary disks.

Modelling circumbinary protoplanetary disks

The Kepler mission's discovery of a number of circumbinary planets orbiting close (a_p < 1.1 au) to the stellar binary raises questions as to how these planets could have formed given the intense gravitational perturbations the dual stars impart on the disk. The gas component of circumbinary protoplanetary disks is perturbed in a similar manner to the solid, planetesimal dominated counterpart, although the mechanism by which disk eccentricity originates differs. This is the first work of a series that aims to investigate the conditions for planet formation in circumbinary protoplanetary disks. We present a number of hydrodynamical simulations that explore the response of gas disks around two observed binary systems: Kepler-16 and Kepler-34. We probe the importance of disk viscosity, aspect-ratio, inner boundary condition, initial surface density gradient, and self-gravity on the dynamical evolution of the disk, as well as its quasi steady-state profile. We find there is a strong influence of binary type on the mean disk eccentricity, e_d, leading to e_d = 0.02 - 0.08 for Kepler-16 and e_d = 0.10 - 0.15 in Kepler-34. The value of alpha-viscosity has little influence on the disk, but we find a strong increase in mean disk eccentricity with increasing aspect-ratio due to wave propagation effects. The choice of inner boundary condition only has a small effect on the surface density and eccentricity of the disk. Our primary finding is that including disk self-gravity has little impact on the evolution or final state of the disk for disks with masses less than 12.5 times that of the minimum-mass solar nebula. This finding contrasts with the results of self-gravity relevance in circumprimary disks, where its inclusion is found to be an important factor in describing the disk evolution.

SMA and ALMA studies of protoplanetary disk formation around low-mass protostars

AbstractWe report our systematic survey observations of protostellar sources with the SubMillimeter Array (SMA) and Atacama Large Millimeter/submillimeter Array (ALMA). The purpose of our survey is to investigate formation mechanism of protoplanetary disks, precursors of planetary systems, out of ~1000 AU-scale protostellar envelopes surrounding the protostars. We found that in the early protostars (B335, NGC1333 IRAS 4B), the envelopes do not show significant rotating motions but infalling motions toward the central protostars. In more evolved protostars (L1527 IRS, L1448-mm, L1551 IRS 5), the envelopes are infalling and rotating with the conserved specific angular momenta (that is, vrot ∝ r−1). In most evolved sources (L1551 NE, TMC-1A, L1489 IRS) large-scale (≳100 AU) disks in Keplerian rotation or protoplanetary disks are evident. These results demonstrate a systematic evolutionary trend of envelope gas motions toward the disk formation.

Interstellar Methanol from the Lab to Protoplanetary Disks

Interstellar methanol is thought to be the precursor of larger, more complex organic molecules. It holds a central role in many astrochemical models (e.g., Garrod &amp; Herbst 2006). Methanol has also been the focus of several laboratory studies (e.g., Watanabe et al. 2004, Fuchs et al. 2009), in an effort to gain insight into grain-surface chemistry, which potentially builds chemical complexity already in the cold, dark prestellar phase. The case of methanol is a prime example of experimental work having implications on astronomical scales. Drozdovskaya et al. (2014) unified physical and chemical models to simulate infalling material during the birth of a low-mass protostar. An axisymmetric 2D semi-analytic collapse model (Visser et al. 2009), wavelength-dependent radiative transfer calculations with RADMC3D (Dullemond &amp; Dominik 2004) and a comprehensive gas-grain chemical network (Walsh et al. 2014) were used to study two modes of protoplanetary disk formation.

Gap formation and stability in non-isothermal protoplanetary discs

Several observations of transition discs show lopsided dust-distributions. A potential explanation is the formation of a large-scale vortex acting as a dust-trap at the edge of a gap opened by a giant planet. Numerical models of gap-edge vortices have thus far employed locally isothermal discs, but the theory of this vortex-forming or `Rossby wave' instability was originally developed for adiabatic discs. We generalise the study of planetary gap stability to non-isothermal discs using customised numerical simulations of disc-planet systems where the planet opens an unstable gap. We include in the energy equation a simple cooling function with cooling timescale $t_c=\beta\Omega_k^{-1}$, where $\Omega_k$ is the Keplerian frequency, and examine the effect of $\beta$ on the stability of gap edges and vortex lifetimes. We find increasing $\beta$ lowers the growth rate of non-axisymmetric perturbations, and the dominant azimuthal wavenumber $m$ decreases. We find a quasi-steady state consisting of one large-scale, over-dense vortex circulating the outer gap edge, typically lasting $O(10^3)$ orbits. Vortex lifetimes were found to generally increase with cooling times up to an optimal value, beyond which vortex lifetimes decrease. This non-monotonic dependence is qualitatively consistent with recent studies using strictly isothermal discs that vary the disc aspect ratio.

A new and simple approach to determine the abundance of hydrogen molecules on interstellar ice mantles

Water is usually the main component of ice mantles, which cover the cores of dust grains in cold portions of dense interstellar clouds. When molecular hydrogen is adsorbed onto an icy mantle through physisorption, a common assumption in gas-grain rate equation models is to use an adsorption energy for molecular hydrogen on a pure water substrate. However, at high density and low temperature, when H2 is efficiently adsorbed onto the mantle, its surface abundance can be strongly overestimated if this assumption is still used. Unfortunately, the more detailed microscopic Monte Carlo treatment cannot be used to study the abundance of H2 in ice mantles if a full gas-grain network is utilized. We present a numerical method adapted for rate-equation models that takes into account the possibility that an H2 molecule can, while diffusing on the surface, find itself bound to another hydrogen molecule, with a far weaker bond than the H2-water bond, which can lead to more efficient desorption. We label the ensuing desorption "encounter desorption". The method is implemented first in a simple system consisting only of hydrogen molecules at steady state between gas and dust using the rate-equation approach and comparing the results with the results of a microscopic Monte Carlo calculation. We then discuss the use of the rate-equation approach with encounter desorption embedded in a complete gas-grain chemical network. For both systems, the rate-equation model with encounter desorption reproduces the H2 granular coverage computed by the microscopic Monte Carlo model. The method is especially useful for dense and cold environments, and for time-dependent physical conditions, such as occur in the collapse of dense cores and the formation of protoplanetary disks. It is not significantly CPU time consuming, so can be used for example with complex 3D chemical-hydrodynamical simulations.

Low-Mass Star Formation: From Molecular Cloud Cores to Protostars and Protoplanetary Disks

This review describes realistic evolution of magnetic field and rotation of the protostars, dynamics of outflows and jets, and the formation and evolution of protoplanetary disks. Recent advances in the protostellar collapse simulations cover a huge dynamic range from molecular cloud core density to stellar density in a self-consistent manner and account for all the non-ideal magnetohydrodynamical effects, such as Ohmic resistivity, ambipolar diffusion, and Hall current. We explain the emergence of the first core, i.e. , the quasi-hydrostatic object that consists of molecular gas, and the second core, i.e. , the protostar. Ohmic dissipation largely removes the magnetic flux from the center of a collapsing cloud core. A fast well-collimated bipolar jet along the rotation axis of the protostar is driven after the magnetic field is re-coupled with warm gas (∼103 K) around the protostar. The circumstellar disk is born in the “dead zone”, a region that is de-coupled from the magnetic field, and the outer radius of the disk increases with that of the dead zone during the early accretion phase. The rapid increase of the disk size occurs after the depletion of the envelope of molecular cloud core. The effect of Hall current may create two distinct populations of protoplanetary disks.

Disk formation and structure

In this chapter, we cover the formation of protoplanetary disk as a natural byproduct of the gravitational collapse of a slowly rotating, hydrostatic cloud. We also summarise the structure of such a disk as it results from hydrostatic equilibrium and viscous accretion.

Hybrid methods in planetesimal dynamics: formation of protoplanetary systems and the mill condition

The formation and evolution of protoplanetary discs remains a challenge from both a theoretical and numerical standpoint. In this work we first perform a series of tests of our new hybrid algorithm presented in Glaschke, Amaro-Seoane and Spurzem 2011 (henceforth Paper I) that combines the advantages of high accuracy of direct-summation N-body methods with a statistical description for the planetesimal disc based on Fokker-Planck techniques. We then address the formation of planets, with a focus on the formation of protoplanets out of planetesimals. We find that the evolution of the system is driven by encounters as well as direct collisions and requires a careful modelling of the evolution of the velocity dispersion and the size distribution over a large range of sizes. The simulations show no termination of the protoplanetary accretion due to gap formation, since the distribution of the planetesimals is only subjected to small fluctuations. We also show that these features are weakly correlated with the positions of the protoplanets. The exploration of different impact strengths indicates that fragmentation mainly controls the overall mass loss, which is less pronounced during the early runaway growth. We prove that the fragmentation in combination with the effective removal of collisional fragments by gas drag sets an universal upper limit of the protoplanetary mass as a function of the distance to the host star, which we refer to as the mill condition.

A detailed numerical analysis of asymmetrical density distribution in Saturn's F ring during an encounter with Prometheus

Saturn's rings, reminiscent of an early Solar System present a unique opportunity to investigate experimentally some mechanisms thought to be responsible for planet and planetesimal formation in protoplanetary discs. Here we extended the comparison of our numerical models of Prometheus encountering the F ring employing non-interacting and interacting particles. Higher resolution analysis revealed that the density increases known to exist at channel edges is more complex and localised than previously thought. Asymmetry between density increases on channel edges revealed that the channel edge facing way from Prometheus to be the most stable but with lowest maximum increases. However, on the channel edge facing Prometheus the interacting model showed large chaotic fluctuations in the maximum density of some clumps, much larger than those of the other channel. The likely cause of this asymmetry is a variance in localised turbulence introduced into the F ring by Prometheus. High resolution velocity dispersion maps showed that there was a spatial link between the highest densities and the highest velocity dispersions in the interacting model. Thus suggesting that the high velocity dispersion we see is the reason for the observed inhomogeneous distribution of fans (evidence of embedded moonlets) on some of the channel edges facing Prometheus.

SURVIVAL OF INTERSTELLAR MOLECULES TO PRESTELLAR DENSE CORE COLLAPSE AND EARLY PHASES OF DISK FORMATION

An outstanding question of astrobiology is the link between the chemical composition of planets, comets, and other solar system bodies and the molecules formed in the interstellar medium. Understanding the chemical and physical evolution of the matter leading to the formation of protoplanetary disks is an important step for this. We provide some new clues to this long-standing problem using three-dimensional chemical simulations of the early phases of disk formation: we interfaced the full gas-grain chemical model Nautilus with the radiation-magnetohydrodynamic model RAMSES, for different configurations and intensities of the magnetic field. Our results show that the chemical content (gas and ices) is globally conserved during the collapsing process, from the parent molecular cloud to the young disk surrounding the first Larson core. A qualitative comparison with cometary composition suggests that comets are constituted of different phases, some molecules being direct tracers of interstellar chemistry, while others, including complex molecules, seem to have been formed in disks, where higher densities and temperatures allow for an active grain surface chemistry. The latter phase, and its connection with the formation of the first Larson core, remains to be modeled.