Protoplanetary Disks

We present detailed electron microprobe analyses and oxygen three-isotope measurements by high precision secondary ion mass spectrometry on 45 type I (FeO-poor) chondrules/fragments and 3 type II (FeO-rich) chondrule fragments from Meteorite Hills 00426 and Queen Alexandra Range 99177, two of the most primitive CR3 chondrites. Type I chondrules/fragments have Mg#’s (defined as the Mg# of constituent olivine and/or low-Ca pyroxene) ranging from 94.2 to 99.2; type II chondrule fragments have Mg#’s of 53–63. Oxygen three-isotope measurements plot on the slope ∼1 primitive chondrule mineral (PCM) line. Within chondrules, Δ17O (=δ17O–0.52 × δ18O) values of coexisting olivine, pyroxene, and plagioclase are homogeneous, with propagated uncertainties of 0.3‰. This indicates each phase crystallized from the final chondrule melt, and that efficient oxygen isotope exchange occurred between ambient gas and chondrule melt. Among type I chondrules there is a well-defined increase in Δ17O, from –5.9‰ to ∼−1‰, as Mg#’s decrease from 99.2 to ∼96; type II chondrule fragments are comparatively 16O-poor (��17O: ∼0.2–0.6‰). The relationship between Mg# and Δ17O among type I chondrules confirms that addition of a 16O-poor oxidizing agent to the highest Mg# chondrule precursors resulted in forming lower Mg# CR chondrules. Using aspects of existing equilibrium condensation models and a mass balance we estimate that type I CR chondrules formed at dust enrichments of 100–200×, from dusts with 0–0.8 times the atomic abundance of ice, relative to CI dust. The type II chondrule fragments are predicted to have formed at CI dust enrichments near 2500×.

We elaborate the model of accretion disks of
young stars with the fossil large-scale magnetic field in the
frame of Shakura and Sunyaev approximation. Equations of
the MHD model include Shakura and Sunyaev equations,
induction equation and equations of ionization balance.
Magnetic field is determined taking into account ohmic diffusion,
magnetic ambipolar diffusion and buoyancy. Ionization
fraction is calculated considering ionization by cosmic
rays and X-rays, thermal ionization, radiative recombinations
and recombinations on the dust grains.

Analytical solution and numerical investigations show
that the magnetic field is coupled to the gas in the case of
radiative recombinations. Magnetic field is quasi-azimuthal
close to accretion disk inner boundary and quasi-radial in
the outer regions.

Magnetic field is quasi-poloidal in the dusty “dead” zones
with low ionization degree, where ohmic diffusion is efficient.
Magnetic ambipolar diffusion reduces vertical magnetic
field in 10 times comparing to the frozen-in field in this
region. Magnetic field is quasi-azimuthal close to the outer
boundary of accretion disks for standard ionization rates and
dust grain size ad = 0.1 μm. In the case of large dust grains
(ad > 0.1 μm) or enhanced ionization rates, the magnetic
field is quasi-radial in the outer regions.

It is shown that the inner boundary of dusty “dead” zone
is placed at r = (0.1–0.6) AU for accretion disks of stars
with M = (0.5–2)M_sun. Outer boundary of “dead” zone is
placed at r = (3–21) AU and it is determined by magnetic
ambipolar diffusion. Mass of solid material in the “dead”
zone is more than 3M⊕ for stars with M ≥ 1M_sun.

We used the Disk Detective citizen science project and the BANYAN II Bayesian analysis tool to identify a new candidate member of a nearby young association with infrared excess. WISE J080822.18-644357.3, an M5.5-type debris disk system with significant excess at both 12 and 22 µm, is a likely member (∼ 90% BANYAN II probability) of the ∼ 45 Myr-old Carina association. Since this would be the oldest M dwarf debris disk detected in a moving group, this discovery could be an important constraint on our understanding of M dwarf debris disk evolution.

We conduct a linear stability calculation of an ideal Keplerian flow on which a sinusoidal zonal flow is imposed. The analysis uses the shearing sheet model and is carried out both in isothermal and adiabatic conditions, with and without self-gravity (SG). In the non-SG regime a structure in the potential vorticity (PV) leads to a non-axisymmetric Kelvin-Helmholtz (KH) instability; in the short-wavelength limit its growth rate agrees with the incompressible calculation by Lithwick (2007), which only considers perturbations elongated in the streamwise direction. The instability's strength is analysed as a function of the structure's properties, and zonal flows are found to be stable if their wavelength is 8H, where H is the disc's scale height, regardless of the value of the adiabatic index γ. The non-axisymmetric KH instability can operate in Rayleigh-stable conditions, and it therefore represents the limiting factor to the structure's properties. Introducing SG triggers a second non-axisymmetric instability, which is found to be located around a PV maximum, while the KH instability is linked to a PV minimum , as expected. In the adiabatic regime, the same gravitational instability is detected even when the structure is present only in the entropy (not in the PV) and the instability spreads to weaker SG conditions as the entropy structure's amplitude is increased. This eventually yields a non-axisymmetric instability in the non-SG regime, albeit of weak strength, localised around an entropy maximum.

One of the first stages of planet formation is the growth of small planetesimals. This stage occurs much before the dispersal of most of the gas from the protoplanetary disk. For small planetesimals, aerodynamic gas drag keeps their relative velocities low and enhances their growth rate. For large protoplanets, m~0.1MEarth, the net torque due to spiral density waves causes the planet to migrate. There is an additional mass range, m~1021-1025 g of intermediate size planetesimals, where gas dynamical friction (GDF) dominates over aerodynamic gas drag, and the net torque of spiral density waves is negligible. Recently, GDF has been studied in the context of fully evolved planets. However, current studies of gas-planetesimal interaction do not account for planetesimal evolution due to GDF in the range of intermediate mass planetesimals (IMPs). Here, we study the implications of GDF on single IMPs by including GDF into few-body simulations of their evolution. We find that planetesimals with small inclinations dissipate their inclinations and rapidly become co-planar with the disk. Eccentric orbits circularize within a few Myrs, provided the the planetesimal mass is sufficiently large, m>1023 g and that the initial eccentricity is sufficiently low, e<0.1. Planetesimals of higher masses, m~1024-1025 g lose their orbital energy on a time-scale of a few Myrs, leading to an embryonic migration to the inner disk. This may lead to an over-abundance of rocky material (in the form of IMPs) in the inner protoplanetary disk (<1AU). In turn, this may induce rapid planetary growth in these regions, and may help explain the origin of super-Earth planets found close to their host stars. In addition, GDF assists in damping the velocities of IMPs, thereby cooling the planetesimal disk and affecting its collisional evolution through quenching the effects of viscous stirring by the large bodies.

ABSTRACT The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. Numerical approaches provide a method to tackle the weaknesses of current planet formation models and are an important tool to close gaps in poorly constrained areas. We present a global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code ENZO. With this setup, we explore the impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison, and study the effects of varying the disk radius. Adopting a marginally stable disk profile (Q_init=1), we validate the numerical robustness of our model for different spatial extensions, from compact to larger, extended disks (R_disk = 10, 100 and 300 AU, M_disk ~ 0.05 M_Sun, M_star = 0.646 M_Sun). By combining our findings from the resolution and parameter studies we find a lower limit of the resolution to be able to resolve GI induced fragmentation features and distinct, turbulence inducing clumps. Irrespective of the physical extension of the disk, topologically disconnected clump features are only resolved if the fragmentation-active zone of the disk is resolved with at least 100 cells, which holds as a minimum requirement for all global disk setups. Our simulations illustrate the capabilities of AMR-based modeling techniques for planet formation simulations and underline the importance of balanced refinement settings to reproduce fragmenting structures.

According to the planetary origin conceptual model proposed in this paper, the protosun centre of the pre-solar nebula exploded, resulting in a shock wave that passed through it and then returned to the centre, generating a new explosion and shock wave. Recurrent explosions in the nebula resulted in a spherical standing sound wave, whose antinodes concentrated dust into rotating rings that transformed into planets. The extremely small angular momentum of the Sun and the tilt of its equatorial plane were caused by the asymmetry of the first, most powerful explosion. Differences between inner and outer planets are explained by the migration of solid matter, while the Oort cloud is explained by the division of the pre-solar nebula into a spherical internal nebula and an expanding spherical shell of gas. The proposed conceptual model can also explain the origin and evolution of exoplanetary systems and may be of use in searching for new planets.

We investigate the gravitational interaction of a Jovian-mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions are investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Non-linear two-dimensional hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near-circular orbit after a characteristic viscous timescale of 10 4 initial orbital periods. This is found to be independent of whether the protoplanet is allowed to accrete mass or not. Inward migration is helped by the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion on to the central star. Maximally accreting protoplanets reach about 4 Jovian masses on reaching the neighbourhood of the central star. Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is 5 Jupiter masses, if they originate in protoplanetary discs similar to the minimum-mass solar nebula. This is because of the reduced accretion rates obtained for planets of increasing mass. Assuming that some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets as well as their inward orbital migration can be accounted for by consideration of disc–protoplanet interactions during the late stages of giant planet formation.

We undertook spectral analysis of fourteen protoplanetary disks (proplyds) in the Orion Nebula in order to detect the presence of photoevaporation due to the nearby Trapezium stars (Ori A, B, C, and D). The proplyd data was taken using the SpeX spectrograph at the Infrared Telescope Facility (IRTF) on Mauna Kea in Hawaii, which measures in the 0.8 to 5.4 μm range. Using the program SpexTool, we extracted spectra from the images of these proplyds in order to detect molecular hydrogen vibrational emission at wavelengths 2.1218 μm and 2.4066 μm. After subtracting abnormal nebular emissions, we determined the flux of these features using IRAF.  We found that the flux of the hydrogen features in the proplyds exceed those of the nebula, which indicates that photoevaporation is, in fact, taking place in these proplyds.

We have applied a model of planetary system formation in the field of a standing sound wave (the ‘SSW-Model’) to the prediction of planets in 586 multi-planetary exosystems (384 biplanetary, 127 tri-planetary and 75 exosystems with four or more confirmed planets). We have verified our predictions using transit-like events from the NASA Threshold-Crossing Event (TCE) catalogue, finding that more than 80% of these events are included in our list of exoplanet predictions. We describe a method for predicting the periods and semi-major axes of additional planets for exosystems with two or more confirmed planets. Our method can significantly facilitate targeted searches for planets in exosystems, enabling the detection of many new exoplanets, including those located in the habitable zones.

We present a mechanism related to the migration of giant protoplanets embedded in a protoplanetary disc whereby a giant protoplanet is caught up, before having migrated all the way to the central star, by a lighter outer giant protoplanet. This outer protoplanet may get captured into the 2:3 resonance with the more massive one, in which case the gaps that the two planets open in the disc overlap. Two effects arise, namely a squared mass-weighted torque imbalance and an increased mass flow through the overlapping gaps from the outer disc to the inner disc, which both play in favour of an outwards migration. Indeed, under the conditions presented here, which describe the evolution of a pair of protoplanets respectively Jupiter-and Saturn-sized, the migration is reversed, while the semimajor axis ratio of the planets is constant and the eccentricities are confined to small values by the disc material. The long-term behaviour of the system is briefly discussed, and could account for the high eccentricities observed for the extrasolar planets with semimajor axis > 0.2 au

The torque felt by a non-accreting protoplanet on a circular orbit embedded in a uniform surface density protoplanetary disk is analyzed by means of time-dependent numerical simulations. Varying the viscosity enables one to disentangle the Lindblad torque (which is independent of viscosity) from the corotation torque, which saturates at low viscosity and is unsaturated at high viscosity. The dependence of the corotation torque upon the viscosity and upon the width of the librating zone is compared with previous analytical expressions, and shown to be in agreement with those. The effect of the potential smoothing respectively on the Lindblad torque and on the corotation torque is investigated, and the question of whether 3D effects and their impact on the total torque sign and magnitude can be modeled by an adequate smoothing prescription in a 2D simulation is addressed. As a side result, this study shows that the total torque acting on a Neptune-sized protoplanet is positive in a sufficiently thin, viscous disk (H/r > ∼ 4%, α > ∼ 10 −2), but the inward migration time of smaller bodies is still very short, making it unlikely that they reach the torque reversal mass before having migrated all the way to the central object.

We conducted a 12-month monitoring campaign of 33 T Tauri stars (TTS) in Taurus. Our goal was to monitor objects that possess a disk but have a weak Hα line, a common accretion tracer for young stars, to determine whether they host a passive circumstellar disk. We used medium-resolution optical spectroscopy to assess the objects' accretion status and to measure the Hα line. We found no convincing example of passive disks; only transition disk and debris disk systems in our sample are non-accreting. Among accretors, we find no example of flickering accretion, leading to an upper limit of 2.2% on the duty cycle of accretion gaps assuming that all accreting TTS experience such events. Combining literature results with our observations, we find that the reliability of traditional Hα-based criteria to test for accretion is high but imperfect, particularly for low-mass TTS. We find a significant correlation between stellar mass and the full width at 10 per cent of the peak (W 10%) of the Hα line that does not seem to be related to variations in free-fall velocity. Finally, our data reveal a positive correlation between the Hα equivalent width and its W 10% , indicative of a systematic modulation in the line profile whereby the high-velocity wings of the line are proportionally more enhanced than its core when the line luminosity increases. We argue that this supports the hypothesis that the mass accretion rate on the central star is correlated with the Hα W 10% through a common physical mechanism.

We report on the λ = 5 − 36µm Spitzer Infrared Spectrograph spectra of 79 young stellar objects in the very young nearby cluster NGC 1333. NGC 1333's youth enables the study of early protoplanetary disk properties, such as the degree of settling as well as the formation of gaps and clearings. We construct spectral energy distributions (SEDs) using our IRS data as well as published photometry and classify our sample into SED classes. Using " extinction-free " spectral indices, we determine whether the disk, envelope, or photosphere dominates the spectrum. We analyze the dereddened spectra of objects which show disk dominated emission using spectral indices and properties of silicate features in order to study the vertical and radial structure of protoplanetary disks in NGC 1333. At least nine objects in our sample of NGC 1333 show signs of large (several AU) radial gaps or clearings in their inner disk. Disks with radial gaps in NGC 1333 show more-nearly pristine silicate dust than their radially continuous counterparts. We compare properties of disks in NGC 1333 to those in three other well studied regions, Taurus-Auriga, Ophiuchus and Chamaeleon I, and find no difference in their degree of sedimentation and dust processing. Subject headings: accretion disks – circumstellar matter – dust, extinction – infrared: stars – open clusters and associations: individual (NGC 1333, Taurus-Auriga, Ophi-uchus, Chamaeleon I) – planetary systems: formation, protoplanetary disks — stars: formation

We investigate the driving of orbital eccentricity of giant protoplanets and brown dwarfs through disc– companion tidal interactions by means of two dimensional numerical simulations. We consider disc models that are thought to be typical of protostellar discs during the planet forming epoch, with characteristic surface densities similar to standard minimum mass solar nebula models. We consider companions, ranging in mass between 1 and 30 Jupiter masses MJ, that are initially embedded within the discs on circular orbits about a central solar mass. We find that a transition in orbital behaviour occurs at a mass in the range 10–20 MJ. For low mass planetary companions, we find that the orbit remains essentially circular. However, for companion masses > ∼ 20 MJ, we find that non steady behaviour of the orbit occurs, characterised by a growth in eccentricity to values of 0.1 < ∼ e < ∼ 0.25. Analysis of the disc response to the presence of a perturbing companion indicates that for the higher masses, the inner parts of the disc that lie exterior to the companion orbit become eccentric through an instability driven by the coupling of an initially small disc eccentricity to the companion's tidal potential. This coupling leads to the excitation of an m = 2 spiral wave at the 1:3 outer eccentric Lindblad resonance, which transports angular momentum outwards, leading to a growth of the disc eccentricity. The interaction of the companion with this eccentric disc, and the driving produced by direct resonant wave excitation at the 1:3 resonance, can lead to the growth of orbital eccentricity, with the driving provided by the eccentric disc being the stronger. Eccentricity growth occurs when the tidally induced gap width is such that eccentricity damping caused by corotating Lindblad resonances is inoperative. These simulations indicate that for standard disc models, gaps become wide enough for the 1:3 resonance to dominate, such that the transition from circular orbits can occur, only for masses in the brown dwarf range. However, the transition mass might be reduced into the range for extrasolar planets if the disc viscosity is significantly lower enabling wider gaps to occur for these masses. Another possibility is that an eccentric disc is produced by an alternative mechanism, such as viscous overstability resulting in a slowly precessing non axisymmetric mass distribution. A large eccentricity in a planet orbit contained within an inner cavity might then be produced.

The increase of computational resources has recently allowed high-resolution, three-dimensional calculations of planets embedded in gaseous protoplanetary disks. They provide estimates of the planet migration timescale that can be compared to analytical predictions. While these predictions can result in extremely short migration timescales for cores of a few Earth masses, recent numerical calculations have given an unexpected outcome: the torque acting on planets with masses between 5 and 20 M È is considerably smaller than the analytic, linear estimate. These findings motivated the present work, which investigates existence and origin of this discrepancy or ''offset,'' as we shall call it, by means of two-and three-dimensional numerical calculations. We show that the offset is indeed physical and arises from the co-orbital corotation torque, since (1) it scales with the disk vortensity gradient, (2) its asymptotic value depends on the disk viscosity, (3) it is associated to an excess of the horseshoe zone width. We show that the offset corresponds to the onset of nonlinearities of the flow around the planet, which alter the streamline topology as the planet mass increases: at low mass the flow nonlinearities are confined to the planet's Bondi sphere, whereas at larger mass the streamlines display a classical picture reminiscent of the restricted three-body problem, with a prograde circumplanetary disk inside a ''Roche lobe.'' This behavior is of particular importance for the subcritical solid cores (M P 15 M È) in thin (H /r P 0:06) protoplanetary disks. Their migration could be significantly slowed down, or reversed, in disks with shallow surface density profiles.

We evaluate the horseshoe drag exerted on a low-mass planet embedded in a gaseous disk, assuming the disk's flow in the co-orbital region to be adiabatic. We restrict this analysis to the case of a planet on a circular orbit, and we assume a steady flow in the corotating frame. We also assume that the corotational flow upstream of the U-turns is unperturbed, so that we discard saturation effects. In addition to the classical expression for the horseshoe drag in barotropic disks, which features the vortensity gradient across corotation, we find an additional term which scales with the entropy gradient, and whose amplitude depends on the perturbed pressure at the stagnation point of the horseshoe separatrices. This additional torque is exerted by evanescent waves launched at the horseshoe separatrices, as a consequence of an asymmetry of the horseshoe region. It has a steep dependence on the potential's softening length, suggesting that the effect can be extremely strong in the three-dimensional case. We describe the main properties of the co-orbital region (the production of vortensity during the U-turns, the appearance of vorticity sheets at the downstream separatrices, and the pressure response), and we give torque expressions suitable to this regime of migration. Side results include a weak, negative feedback on migration, due to the dependence of the location of the stagnation point on the migration rate, and a mild enhancement of the vortensity-related torque at a large entropy gradient.