Formation Of Protoplanetary Disks Research Articles

Simulated observations of young gravitationally unstable protoplanetary discs

The formation and earliest stages of protoplanetary discs remain poorly constrained by observations. ALMA will soon revolutionise this field. Therefore, it is important to provide predictions which will be valuable for the interpretation of future high sensitivity and high angular resolution observations. Here we present simulated ALMA observations based on radiative transfer modelling of a relatively massive (0.39 M_solar) self-gravitating disc embedded in a 10 M_solar dense core, with structure similar to the pre-stellar core L1544. We focus on simple species and conclude that C17O 3-2, HCO+ 3-2, OCS 26-25 and H2CO 404-303 lines can be used to probe the disc structure and kinematics at all scales.

Zooming in on the Formation of Protoplanetary Disks

AbstractWe use the adaptive mesh refinement code RAMSES to model the formation of protoplanetary disks in realistic star formation environments. The resolution scales over up to 29 powers of two (~ 9 orders of magnitude) covering a range from outer scales of 40 pc to inner scales of 0.015 AU. The accretion rate from a 1.5 solar mass envelope peaks near 10−4 M⊙ about 6 kyr after sink particle formation and then decays approximately exponentially, reaching 10−6 M⊙ in 100 kyr. The models suggest universal scalings of physical properties with radius during the main accretion phase, with kinetic and / or magnetic energy in approximate balance with gravitational energy. Efficient accretion is made possible by the braking action of the magnetic field, which nevertheless allows a near-Keplerian disk to grow to a 100 AU size. The magnetic field strength ranges from more than 10 G at 0.1 AU to less than 1 mG at 100 AU, and drives a time dependent bipolar outflow, with a collimated jet and a broader disk wind.

A SEMI-ANALYTICAL DESCRIPTION FOR THE FORMATION AND GRAVITATIONAL EVOLUTION OF PROTOPLANETARY DISKS

We investigate the formation process of self-gravitating protoplanetary disks in unmagnetized molecular clouds. The angular momentum is redistributed by the action of gravitational torques in the massive disk during its early formation. We develop a simplified one-dimensional accretion disk model that takes into account the infall of gas from the envelope onto the disk and the transfer of angular momentum in the disk with an effective viscosity. First we evaluate the gas accretion rate from the cloud core onto the disk by approximately estimating the effects of gas pressure and gravity acting on the cloud core. We formulate the effective viscosity as a function of the Toomre Q parameter that measures the local gravitational stability of the rotating thin disk. We use a function for viscosity that changes sensitively with Q when the disk is gravitationally unstable. We find a strong self-regulation mechanism in the disk evolution. During the formation stage of protoplanetary disks, the evolution of the surface density does not depend on the other details of the modeling of effective viscosity, such as the prefactor of the viscosity coefficient. Next, to verify our model, we compare the time evolution of the disk calculated with our formulation with that of three-dimensional hydrodynamical simulations. The structures of the resultant disks from the one-dimensional accretion disk model agree well with those of the three-dimensional simulations. Our model is a useful tool for the further modeling of chemistry, radiative transfer, and planet formation in protoplanetary disks.

RAPID COAGULATION OF POROUS DUST AGGREGATES OUTSIDE THE SNOW LINE: A PATHWAY TO SUCCESSFUL ICY PLANETESIMAL FORMATION

Rapid orbital drift of macroscopic dust particles is one of the major obstacles against planetesimal formation in protoplanetary disks. We reexamine this problem by considering porosity evolution of dust aggregates. We apply a porosity model based on recent N-body simulations of aggregate collisions, which allows us to study the porosity change upon collision for a wide range of impact energies. As a first step, we neglect collisional fragmentation and instead focus on dust evolution outside the snow line, where the fragmentation has been suggested to be less significant than inside the snow line because of a high sticking efficiency of icy particles. We show that dust particles can evolve into highly porous aggregates (with internal densities of much less than 0.1 g/cm^3) even if collisional compression is taken into account. We also show that the high porosity triggers significant acceleration in collisional growth. This acceleration is a natural consequence of particles' aerodynamical property at low Knudsen numbers, i.e., at particle radii larger than the mean free path of the gas molecules. Thanks to this rapid growth, the highly porous aggregates are found to overcome the radial drift barrier at orbital radii less than 10 AU (assuming the minimum-mass solar nebula model). This suggests that, if collisional fragmentation is truly insignificant, formation of icy planetesimals is possible via direct collisional growth of submicron-sized icy particles.

Present-day star formation: From molecular cloud cores to protostars and protoplanetary disks

Essential physical processes in the formation of protostars and protoplanetary disks are described. Recent advances in non-ideal magnetohydrodynamics simulations, which cover a huge dynamic range from molecular cloud core density (104/cc) to stellar density (1022/cc) in a self-consistent manner, enable us to study the realistic evolution of the magnetic field and rotation of protostars and the dynamics of outflows and jets. First we emphasize the importance of radiative heating and cooling, and describe thermal evolution in a self-gravitationally collapsing cloud. The increased pressure at the center creates the first hydrostatic core, which consists of molecular gas. After the dissociation of molecular hydrogen triggers the second gravitational collapse at the center of the first core, a protostar is quickly formed and the first core gradually transforms into a circumstellar disk that eventually accretes onto the central protostar. The importance of the short-lived first core formed in the early collapsing phase is emphasized in the contexts of driving magnetohydrodynamical bipolar outflows and self-gravitational fragmentation into binary or multiple stars. When the central density becomes sufficiently high (1012/cc), ohmic dissipation largely removes the magnetic flux from a collapsing cloud core, and the strongly twisted magnetic field lines are straightened. The magnetic field lines are twisted and amplified again for much higher density (1016/cc) where the magnetic field is recoupled with warm gas (∼103 K). Finally, protostars at their formation epoch have magnetic fields of 0.1–1 kG, which is comparable to observed values of pre-main-sequence stars. A substantially reduced magnetic flux at the center results in passively wound-up magnetic field lines just after the formation of a protostar. This is followed by driving of a fast bipolar jet along the rotation axis by the resultant magnetic pressure due to excessive winding. Strong collimation of the jet is due to the hoop stress of piled-up toroidal field lines. The angular momentum in a collapsing cloud is removed by magnetohydrodynamical effects such as magnetic braking and driving of outflows and jets. The rotation velocity of the protostar tends to be on the order of break-up speed at its formation epoch, and thus, a further removal mechanism for the angular momentum, such as through the interactions between the protostar, disk, jets, and winds, should be important in its long-term evolution. The circumstellar disk is born in the “dead zone,” a region that is decoupled from the magnetic field. The outer radius of the disk increases with that of the dead zone during accretion from the envelope of the molecular cloud core. A rapid increase in the disk size occurs after depletion of the envelope. The circumstellar disks remain massive in their formation phase, and are subject to gravitational instability, even at 10 AU from the central stars. The further long-term evolution of massive disks is also described. This may provide an improved description for the realistic initial condition and environments for planet formation in gaseous protoplanetary disks.

Global models of planetary system formation in radiatively-inefficient protoplanetary discs

We present the results of N-body simulations of planetary system formation in radiatively-inefficient disc models, where positive corotation torques may counter the rapid inward migration of low-mass planets driven by Lindblad torques. The aim of this work is to examine the nature of planetary systems that arise from oligarchic growth in such discs. We adapt the commonly used Mercury-6 symplectic integrator by including simple prescriptions for planetary migration (types I and II), planetary atmospheres that enhance the probability of planetesimal accretion by protoplanets, gas accretion on to forming planetary cores, and gas disc dispersal. We perform a suite of simulations for a variety of disc models with power-law surface density and temperature profiles, with a focus on models in which unsaturated corotation torques can drive outward migration of protoplanets. In some models, we account for the quenching of corotation torques which arises when planetary orbits become eccentric. Approximately half of our simulations lead to the successful formation of gas giant planets with a broad range of masses and semimajor-axes. Giant planetary masses range from being approximately equal to that of Saturn up to approximately twice that of Jupiter. The semimajor-axes of these range from being ∼0.2 au up to ∼75 au, with disc models that drive stronger outward migration favouring the formation of longer period giant planets. Out of a total of 20 giant planets being formed in our simulation suite, we obtain three systems that contain two giants. No super-Earth or Neptune-mass planets were present in the final stages of our simulations, in contrast to the large abundance of such objects being discovered in observation surveys. This result arises because of rapid inward migration suffered by massive planetary cores that form early in the disc lifetime (for which the corotation torques saturate), combined with gas accretion on to massive cores which leads them to become gas giants. Numerous low-mass planets are formed and survive in the simulations, with masses ranging from a few tenths of an Earth mass up to ∼3 Earth masses. Simulations in which the quenching of corotation torques for planets on modestly eccentric orbits was included failed to produce any giant planets, apparently because Lindblad torques induce rapid inward migration of planetary cores in these systems. We conclude that convergent migration induced by corotation torques operating during planetary formation can enhance the growth rate of planetary cores, but these often migrate into the central star because corotation torques saturate. Outward migration of planetary cores of modest mass can lead to the formation of gas giant planets at large distances from the central star, similar to those observed recently through direct imaging surveys. The excitation of planetary eccentricities through planet–planet scattering during oligarchic growth may quench the effects of corotation torques, however, such that inward migration is driven by Lindblad torques.

Exoplanets

Exoplanets

High-resolution simulations of planetesimal formation in turbulent protoplanetary discs

We present high-resolution computer simulations of dust dynamics and planetesimal formation in turbulence generated by the magnetorotational instability. We show that the turbulent viscosity associated with magnetorotational turbulence in a non-stratified shearing box increases when going from 256^3 to 512^3 grid points in the presence of a weak imposed magnetic field, yielding a turbulent viscosity of $\alpha\approx0.003$ at high resolution. Particles representing approximately meter-sized boulders concentrate in large-scale high-pressure regions in the simulation box. The appearance of zonal flows and particle concentration in pressure bumps is relatively similar at moderate (256^3) and high (512^3) resolution. In the moderate-resolution simulation we activate particle self-gravity at a time when there is little particle concentration, in contrast with previous simulations where particle self-gravity was activated during a concentration event. We observe that bound clumps form over the next ten orbits, with initial birth masses of a few times the dwarf planet Ceres. At high resolution we activate self-gravity during a particle concentration event, leading to a burst of planetesimal formation, with clump masses ranging from a significant fraction of to several times the mass of Ceres. We present a new domain decomposition algorithm for particle-mesh schemes. Particles are spread evenly among the processors and the local gas velocity field and assigned drag forces are exchanged between a domain-decomposed mesh and discrete blocks of particles. We obtain good load balancing on up to 4096 cores even in simulations where particles sediment to the mid-plane and concentrate in pressure bumps.

ELECTROSTATIC BARRIER AGAINST DUST GROWTH IN PROTOPLANETARY DISKS. I. CLASSIFYING THE EVOLUTION OF SIZE DISTRIBUTION

Collisional growth of submicron-sized dust grains into macroscopic aggregates is the first step of planet formation in protoplanetary disks. These grains are expected to carry nonzero negative charges in the weakly ionized disks, but its effect on their collisional growth has not been fully understood so far. In this paper, we investigate how the charging affects the evolution of the dust size distribution properly taking into account the charging mechanism in a weakly ionized gas as well as porosity evolution through low-energy collisions. To clarify the role of the size distribution, we divide our analysis into two steps. First, we analyze the collisional growth of charged aggregates assuming a monodisperse (i.e., narrow) size distribution. We show that the monodisperse growth stalls due to the electrostatic repulsion when a certain condition is met, as is already expected in the previous work. Second, we numerically simulate dust coagulation using Smoluchowski's method to see how the outcome changes when the size distribution is allowed to freely evolve. We find that, under certain conditions, the dust undergoes bimodal growth where only a limited number of aggregates continue to grow carrying the major part of the dust mass in the system. This occurs because remaining small aggregates efficiently sweep up free electrons to prevent the larger aggregates from being strongly charged. We obtain a set of simple criteria that allows us to predict how the size distribution evolves for a given condition. In Paper II (arXiv:1009.3101), we apply these criteria to dust growth in protoplanetary disks.

High-resolution simulations of planetesimal formation in turbulent protoplanetary discs

AbstractWe present high resolution computer simulations of dust dynamics and planetesimal formation in turbulence triggered by the magnetorotational instability. Particles representing approximately meter-sized boulders clump in large scale overpressure regions in the simulation box. These overdensities readily contract due to the combined gravity of the particles to form gravitationally bound clusters with masses ranging from a few to several ten times the mass of the dwarf planet Ceres. Gravitationally bound clumps are observed to collide and merge at both moderate and high resolution. The collisional products form the top end of a distribution of planetesimal masses ranging from less than one Ceres mass to 35 Ceres masses. It remains uncertain whether collisions are driven by dynamical friction or underresolution of clumps.

Vortices as nurseries for planetesimal formation in protoplanetary discs

Turbulent, two-dimensional, hydrodynamic flows are characterized by the emergence of coherent, long-lived vortices without a need to invoke special initial conditions. Vortices have the ability to sequester particles, with typical radii from about 1 mm to 10 cm, that are slightly decoupled from the gas. A generic feature of discs with surface density and effective temperature profiles that are decreasing, power-law functions of radial distance is that four vortex zones exist for a fixed particle size. In particular, two of the zones form an annulus at intermediate radial distances within which small particles reside. Particle capture by vortices occurs on a dynamical time scale near and at the boundaries of this annulus. As the disc ages and the particles grow via coagulation, the size of the annulus shrinks. Older discs prefer to capture smaller particles because the gas surface density decreases with time, a phenomenon we term "vortex aging". More viscous, more dust-opaque and/or less massive discs can have vortices that age faster and trap a broader range of particle sizes throughout the lifetime of the disc. Thus, how efficiently a disc retains its mass in solids depends on the relative time scales between coagulation and vortex aging. If vortices form in protoplanetary discs, they are important in discs with typical masses and for particles that are likely to condense out of the protostellar nebula. Particle capture also occurs at distances relevant to planet formation. Future infrared, submillimetre and centimetre observations of grain opacity as a function of radial distance will test the hypothesis that vortices serve as nurseries for particle growth in protoplanetary discs.

EMERGENCE OF PROTOPLANETARY DISKS AND SUCCESSIVE FORMATION OF GASEOUS PLANETS BY GRAVITATIONAL INSTABILITY

We use resistive magnetohydrodynamical simulations with the nested grid technique to study the formation of protoplanetary disks around protostars from molecular cloud cores that provide the realistic environments for planet formation. We find that gaseous planetary-mass objects are formed in the early evolutionary phase by gravitational instability in regions that are decoupled from the magnetic field and surrounded by the injection points of the magnetohydrodynamical outflows during the formation phase of protoplanetary disks. Magnetic decoupling enables massive disks to form and these are subject to gravitational instability, even at ~ 10 AU. The frequent formation of planetary-mass objects in the disk suggests the possibility of constructing a hybrid planet formation scenario, where the rocky planets form later under the influence of the giant planets in the protoplanetary disk.

Extreme adaptive optics in the mid-IR: The METIS AO system

METIS, the Mid-infrared ELT Imager and Spectrograph, is currently in its phase A study as one of the candidate first-light instruments for the European Extremely Large Telescope. METIS will feature several observational modes, ranging from diffraction limited imaging in L, M and N-bands to high-resolution Integral Field spectroscopy for the L and M-bands. METIS in its current design gives sensitivities similar to Spitzer in imaging and low-resolution spectroscopy and with its high-resolution spectrograph will provide unprecedented line sensitivity. The design of METIS is optimized for both galactic science cases (e.g. conditions in the early solar system, formation and evolution of proto-planetary disks and properties of exoplanets) and extragalactic science cases (e.g. the growth of Supermassive Black Holes). METIS will require a high-order adaptive optics (AO) system to meet its scientific goals, both to provide correction for atmospheric turbulence as well as reduce the impact of wind shake, leading to a residual image motion of 3 - 5 mas rms. METIS is expected to feature both an internal Single Conjugate AO system as well as an external Laser Tomography AO system. The challenges for the METIS AO system are mainly in the broad correction range, an excellent image stability required for coronagraphy and in providing a high sky coverage to be available for as many science targets as possible. An additional challenge for METIS is the need to compensate for composition turbulence, mainly in the form of fast fluctuations in water vapor concentration. Water vapor fluctuations impact the performance of METIS in several ways: Atmospheric dispersion causes a broadening of the point-spread function, both in the science channel and the wavefront channel, but can be corrected using a Atmospheric Dispersion Corrector. Variations in the water vapor composition cannot be corrected this way and are currently estimated to give a residual image motion of ≤10 mas rms. This effect can, especially for coronagraphy, not be neglected. Chromatic optical path difference errors, caused by changes in the index of refraction along the path through the atmosphere were found to be negligible in the case of METIS due to attenuation by the outer scale (at typical values of 25 m). Chromatic anisoplanatism is the effect that the light at different wavelengths travels through a slightly different light path through the atmosphere and can be–at least partly–corrected. The last effect is composition turbulence, mainly caused by fast (> 1 Hz) fluctuations in the water vapor content. Based on data for ALMA and radiometer probes, this leads to a maximum loss in Strehl ratio between 5 and 10%. This mainly has an impact on coronagraphy and the METIS AO team is actively investigating ways to compensate also water vapor turbulence. The main challenge is currently obtaining reliable data on the distribution and magnitude of precipitable water vapor fluctuations.

PARTICLE CLUMPING AND PLANETESIMAL FORMATION DEPEND STRONGLY ON METALLICITY

We present three-dimensional numerical simulations of particle clumping and planetesimal formation in protoplanetary disks with varying amounts of solid material. As centimeter-size pebbles settle to the mid-plane, turbulence develops through vertical shearing and streaming instabilities. We find that when the pebble-to-gas column density ratio is 0.01, corresponding roughly to solar metallicity, clumping is weak, so the pebble density rarely exceeds the gas density. Doubling the column density ratio leads to a dramatic increase in clumping, with characteristic particle densities more than ten times the gas density and maximum densities reaching several thousand times the gas density. This is consistent with unstratified simulations of the streaming instability that show strong clumping in particle dominated flows. The clumps readily contract gravitationally into interacting planetesimals of order 100 km in radius. Our results suggest that the correlation between host star metallicity and exoplanets may reflect the early stages of planet formation. We further speculate that initially low metallicity disks can be particle enriched during the gas dispersal phase, leading to a late burst of planetesimal formation.

ELECTRIC CHARGING OF DUST AGGREGATES AND ITS EFFECT ON DUST COAGULATION IN PROTOPLANETARY DISKS

ABSTRACT Mutual sticking of dust aggregates is the first step toward planetesimal formation in protoplanetary disks. In spite that the electric charging of dust particles is well recognized in some contexts, it has been largely ignored in the current modeling of dust coagulation. In this study, we present a general analysis of the dust charge state in protoplanetary disks, and then demonstrate how the electric charging could dramatically change the currently accepted scenario of dust coagulation. First, we describe a new semianalytical method to calculate the dust charge state and gas ionization state self-consistently. This method is far more efficient than previous numerical methods, and provides a general and clear description of the charge state of a gas–dust mixture. Second, we apply this analysis to compute the collisional cross section of growing aggregates taking their charging into account. As an illustrative example, we focus on early evolutionary stages where the dust has been thought to grow into fractal (D ∼ 2) aggregates with a quasi-monodisperse (i.e., narrow) size distribution. We find that, for a wide range of model parameters, the fractal growth is strongly inhibited by the electric repulsion between colliding aggregates and eventually “freezes out” on its way to the subsequent growth stage involving collisional compression. Strong disk turbulence would help the aggregates to overcome this growth barrier, but then it would cause catastrophic collisional fragmentation in later growth stages. These facts suggest that the combination of electric repulsion and collisional fragmentation would impose a serious limitation on dust growth in protoplanetary disks. We propose a possible scenario of dust evolution after the freezeout. Finally, we point out that the fractal growth of dust aggregates tends to maintain a low ionization degree and, as a result, a large magnetorotationally stable region in the disk.

Time-dependent CO depletion during the formation of protoplanetary disks

Understanding the gas abundance distribution is essential when tracing star formation using molecular line observations. Changing density and temperature conditions cause gas to freeze-out onto dust grains, and this needs to be taken into account when modeling a collapsing molecular cloud. This study aims to provide a realistic estimate of the CO abundance distribution throughout the collapse of a molecular cloud. We provide abundance profiles and synthetic spectral lines which can be compared to observations. We use a 2D hydrodynamical simulation of a collapsing cloud and subsequent formation of a protoplanetary disk as input for the chemical calculations. From the resulting abundances, synthetic spectra are calculated using a molecular excitation and radiation transfer code. We compare three different methods to calculate the abundance of CO. Our models also consider cosmic ray desorption and the effects of an increased CO binding energy. The resulting abundance profiles are compared to observations from the literature and are found to agree well. The resulting abundance profiles agree well with analytic approximations, and the corresponding line fluxes match observational data. Our developed method to calculate abundances in hydrodynamical simulations should greatly aid in comparing these to observations, and can easily be generalized to include gas-phase reaction networks.

Early phases of planet formation in protoplanetary disks

This paper will review recent advancements in our understanding of protoplanetary disks, the region where we expect planets to form. We include a discussion of transition disks and their relevance for our understanding of planet formation. We summarize observational evidence for grain growth and alteration, and discuss the challenges to understanding planetesimal formation.

Observational signature of planet formation: The ALMA view

Protoplanetary disks are the most probable sites where planet formation takes place. According to theory, planet formation in protoplanetary disks should show remarkable signatures, such as a gap/hole or a spiral structure. In fact, recent high-angular and high-sensitivity observations in millimeter and submillimeter wavelengths, as well as optical/near-IR wavelengths, have shown such structures in protoplanetary disks. Two particular examples of such disks around AB Aurigae and HD 142527 are discussed here, with an emphasis on results obtained using the Submillimeter Array. These disks—and their probable planet formation—will be very important future targets for ALMA to study the physical process of planet formation in detail.

The development of a protoplanetary disk from its natal envelope

Class 0 protostars, the youngest type of young stellar objects, show many signs of rapid development from their initial, spheroidal configurations, and therefore are studied intensively for details of the formation of protoplanetary disks within protostellar envelopes. At millimetre wavelengths, kinematic signatures of collapse have been observed in several such protostars, through observations of molecular lines that probe their outer envelopes. It has been suggested that one or more components of the proto-multiple system NGC 1333-IRAS 4 (refs 1, 2) may display signs of an embedded region that is warmer and denser than the bulk of the envelope. Here we report observations that reveal details of the core on Solar System dimensions. We detect in NGC 1333-IRAS 4B a rich emission spectrum of H2O, at wavelengths 20-37 microm, which indicates an origin in extremely dense, warm gas. We can model the emission as infall from a protostellar envelope onto the surface of a deeply embedded, dense disk, and therefore see the development of a protoplanetary disk. This is the only example of mid-infrared water emission from a sample of 30 class 0 objects, perhaps arising from a favourable orientation; alternatively, this may be an early and short-lived stage in the evolution of a protoplanetary disk.

Gravitational Collapse of Magnetized Clouds. I. Ideal Magnetohydrodynamic Accretion Flow

We study the self-similar collapse of an isothermal magnetized rotating cloud in the ideal magnetohydrodynamic (MHD) regime. In the limit of small distance from the accreting protostar, we find an analytic solution that corresponds to free fall onto a central mass point. The density distribution is not spherically symmetric but depends on the mass loading of magnetic field lines, which can be obtained by matching our inner solution to an outer collapse solution previously computed by Allen et al. The concentration of magnetic field trapped by the central mass point under field freezing, independent on the details of the starting state, creates a split-monopole configuration in which the magnetic field strength increases as the inverse square of the distance from the center. Under such conditions, the inflow eventually becomes sub-Alfvenic and the outward transfer of angular momentum by magnetic braking very efficient, thus preventing the formation of a centrifugally supported disk. Instead, the azimuthal velocity of the infalling gas decreases to zero at the center, and the gas spirals into the star. Therefore, the dissipation of dynamically important levels of magnetic field is a fundamental requisite for the formation of protoplanetary disks around young stars.