Limits on Protoplanet Growth by Accretion of Small Solids
Mohamad Ali-Dib, Christopher Thompson
备注：
41 pages, 17 figures. Accepted for publication in the Astrophysical Journal. Expanded analytic treatment of threshold for refluxing. Corrected treatment of ice sublimation in the envelope. Effect added of heating due to the accretion of a fraction of pebble debris onto the core
发表信息：
The Astrophysical Journal, Volume 900, Number 2 (2020)
This paper identifies constraints on the growth of a small planetary core (0.3 M$_{\oplus}$) that accretes millimeter-sized pebbles from a gaseous disk. We construct time-dependent spherical envelope models that capture physical processes not included in existing global hydrodynamic simulations, including particle size evolution, dust transport, and realistic gas equations of state. We assume a low enough disk density that pebbles are marginally coupled to the gas and are trapped efficiently near the core Bondi radius. Pebbles then drift rapidly enough to experience erosion by sandblasting, mutual collisions, and sublimation of water ice. We find that pebble fragmentation is more efficient than dust re-sticking. Therefore the large pebble accretion rate $\dot{M}_p$ needed to build a core of mass > M$_{\oplus}$ leads to a high envelope metallicity and grain opacity. Above $\dot{M}_p$ $\sim 10^{-7}$ M$_{\oplus}$/yr, and without other luminosity sources, convective motions expand near the Bondi radius. The warm, dusty, and turbulent envelope buffers the inward drift of pebble debris: given a turbulent concentration factor $f_{turb} \geq$ 1 near the lower convective boundary, the core growth rate is limited to $1 \times 10^{-7} f_{turb}$ M$_{\oplus}$/yr and the e-folding time 3$f_{turb}^{-1}$ Myr. The remainder of the solid debris is expelled as highly processed silicates. Pebble ice never reaches the core, and the envelope contains comparable amounts of H2/He and metals. We interpret our results using simpler steady models and semi-analytical estimates. Future global simulations incorporating the processes modelled here are needed to understand the influence of rotation and vertical disk structure.
Chondrules are primitive materials in the Solar System. They are formed in the first about 3 Myr of the Solar System's history. This timescale is longer than that of Mars formation, and it is conceivable that protoplanets, planetesimals and chondrules might have existed simultaneously in the solar nebula. Due to protoplanets perturbation on the planetesimal dynamics and chondrule accretion on them, all the formed chondrules are unlikely to be accreted by planetesimals. We investigate the amount of chondrules accreted by planetesimals in such a condition. We assume that a protoplanet is in olig…
Recent observations of protoplanets embedded in circumstellar disks have shed light on the planet formation process. In particular, detection of hydrogen Balmer-line (Hα) emission gives direct constraints on late-stage accretion onto gas giants. Very recently Haffert et al. (2019) measured the spectral line-widths, in addition to intensities, of Hα emission from the two protoplanets orbiting PDS 70. Here, we study these protoplanets by applying radiation-hydrodynamic models of the shock-heated accretion flow onto protoplanets that Aoyama et al. (2018) has recently developed. As a result, we de…
The formation of planets depends on the underlying protoplanetary disc structure, which influences both the accretion and migration rates of embedded planets. The disc itself evolves on time-scales of several Myr during which both temperature and density profiles change as matter accretes onto the central star. Here we use a detailed model of an evolving disc to determine the growth of planets by pebble accretion and their migration through the disc. Cores that reach their pebble isolation mass accrete gas to finally form giant planets with extensive gas envelopes, while planets that do not re…
Recent observations of protoplanetary disks have revealed ring-like structures that can be associated to pressure maxima. Pressure maxima are known to be dust collectors and planet migration traps. Most of planet formation works are based either on the pebble accretion model or on the planetesimal accretion model. However, recent studies proposed the possible formation of Jupiter by the hybrid accretion of pebbles and planetesimals. We aim to study the full process of planet formation consisting of dust evolution, planetesimal formation and planet growth at a pressure maximum in a protoplaneta…
Most of super-Earths detected by the radial velocity (RV) method have significantly smaller eccentricities than the eccentricities corresponding to velocity dispersion equal to their surface escape velocity ("escape eccentricities"). If orbital instability followed by giant impacts among protoplanets that have migrated from outer region is considered, it is usually considered that eccentricities of the merged bodies become comparable to those of orbital crossing bodies, which are excited up to their escape eccentricities by close scattering. However, the eccentricity evolution in the {\it in s…
The paper investigates the influence of accretion heating and turbulent heat conduction on the equilibrium of protoplanetary disks, extending the 2D axis-symmetric passive disk model of Flock (Flock et al. 2016, ApJ 827, 144). The model includes dust sublimation and radiative transfer with the flux-limited diffusion approximation, and predicts the density and temperature profiles as well as the dust to gas ratio of the disk. It is shown that the accretion heating can have a large impact: For accretion rates above 5*10^(-8) M_solar /yr a zone forms behind the silicate condensation front with su…
Planets grow via the collisional accretion of small bodies in a protoplanetary disk. Such small bodies feel strong gas drag and their orbits are significantly affected by the gas flow and atmospheric structure around the planet. We investigate the gas flow in the protoplanetary disk perturbed by the gravity of the planet by three-dimensional hydrodynamic simulation. We then calculate the orbital evolutions of particles in the gas structure obtained from the hydrodynamic simulation. Based on the orbital calculations, we obtain the collision rate between the planet and centimeter to kilometer si…
Axisymmetric dust rings containing tens to hundreds of Earth masses of solids have been observed in protoplanetary discs with (sub-)millimetre imaging. Here, we investigate the growth of a planetary embryo in a massive (150M$_\oplus$) axisymmetric dust trap through dust and gas hydrodynamics simulations. When accounting for the accretion luminosity of the planetary embryo from pebble accretion, the thermal feedback on the surrounding gas leads to the formation of an anticyclonic vortex. Since the vortex forms at the location of the planet, this has significant consequences for the planet's gro…
It has been realized in recent years that the accretion of pebble-sized dust particles onto planetary cores is an important mode of core growth, which enables the formation of giant planets at large distances and assists planet formation in general. The pebble accretion theory is built upon the orbit theory of dust particles in a laminar protoplanetary disk (PPD). For sufficiently large core mass (in the "Hill regime"), essentially all particles of appropriate sizes entering the Hill sphere can be captured. However, the outer regions of PPDs are expected to be weakly turbulent due to the magne…
The known exoplanet population displays a great diversity of orbital architectures, and explaining the origin of this is a major challenge for planet formation theories. The gravitational interaction between young planets and their protoplanetary disks provides one way in which planetary orbits can be shaped during the formation epoch. Disk-planet interactions are strongly influenced by the structure and physical processes that drive the evolution of the protoplanetary disk. In this review we focus on how disk-planet interactions drive the migration of planets when different assumptions are ma…
Layered accretion is one of the inevitable ingredients in protoplanetary disks when disk turbulence is excited by magnetorotational instabilities (MRIs). In the accretion, disk surfaces where MRIs fully operate have a high value of disk accretion rate ($\dot{M}$), while the disk midplane where MRIs are generally quenched ends up with a low value of $\dot{M}$. Significant progress on understanding MRIs has recently been made by a number of dedicated MHD simulations, which requires improvement of the classical treatment of $α$ in 1D disk models. To this end, we obtain a new expression of $α$ by …
In the classical core-accretion planet formation scenario, rapid inward migration and accretion timescales of kilometer size planetesimals may not favor the formation of massive cores of giant planets before the dissipation of protoplanetary disks. On the other hand, the existence of pressure maxima in the disk could act as migration traps and locations for solid material accumulation, favoring the formation of massive cores. We aim to study the radial drift of pebbles and planetesimals and planet migration at pressure maxima in a protoplanetary disk and their implications for the formation of…
Recent ALMA molecular line observations have revealed 3-D gas velocity structure in protoplanetary disks, shedding light on mechanisms of disk accretion and structure formation. 1) By carrying out viscous simulations, we confirm that the disk's velocity structure differs dramatically using vertical stress profiles from different accretion mechanisms. Thus, kinematic observations tracing flows at different disk heights can potentially distinguish different accretion mechanisms. On the other hand, the disk surface density evolution is mostly determined by the vertically integrated stress. The sh…
The core accretion hypothesis posits that planets with significant gaseous envelopes accreted them from their protoplanetary discs after the formation of rocky/icy cores. Observations indicate that such exoplanets exist at a broad range of orbital radii, but it is not known whether they accreted their envelopes in situ, or originated elsewhere and migrated to their current locations. We consider the evolution of solid cores embedded in evolving viscous discs that undergo gaseous envelope accretion in situ with orbital radii in the range $0.1-10\rm au$. Additionally, we determine the long-term …
Pebble accretion is one of the major theories in planet formation. Aerodynamically small particles, called pebbles, are highly affected by the gas flow. A growing planet embedded in a protoplanetary disk induces three-dimensional (3D) gas flow. In our previous study, Paper I, we focused on the shear regime of pebble accretion, and investigated the influence of planet-induced gas flow on pebble accretion. In Paper I, we found that pebble accretion is inefficient in the planet-induced gas flow compared to that in the unperturbed flow, in particular when ${\rm St}\lesssim10^{-3}$, where St is the…
Recent observations have detected excess H$α$ emission from young stellar systems with an age of several Myr such as PDS 70. One-dimensional radiation-hydrodynamic models of shock-heated flows that we developed previously demonstrate that planetary accretion flows of $>$ a few ten km s$^{-1}$ can produce H$α$ emission. It is, however, a challenge to understand the accretion process of proto-giant planets from observations of such shock-originated emission because of a huge gap in scale between the circumplanetary disk (CPD) and the microscopic accretion shock. To overcome the scale gap problem…
We examine the migration of luminous low-mass cores in laminar protoplanetary discs where accretion occurs mainly because of disc winds and where the planet luminosity is generated by pebble accretion. Using 2D hydrodynamical simulations, we determine the eccentricities induced by thermal forces as a function of gas and pebble accretion rates, and also evaluate the importance of the torque exerted by the solid component relative to the gas torque. For a gas accretion rate $\dot M= 2\times 10^{-8}$ $M_\odot/$yr and pebble flux $\dot M_{peb}=170$ $M_\oplus$/Myr, we find that embryo eccentricitie…
We introduce collisions of solids as a new and efficient ionization mechanism for gas in protoplanetary disks, which especially operates in the dense midplane of protoplanetary disks. This idea is sparked by laboratory experiments where we found that charge, which is exchanged by grains in mutual collision (tribocharging), is not tied to their surfaces alone. As kind of collateral effect, charges also become entrained into the gas phase, i.e. collisions ionize the protoplanetary disk. Therefore, solids are not only sinks of charges in disks but also sources. A first estimate shows that ionizat…
The streaming instability is a promising mechanism to drive the formation of planetesimals in protoplanetary disks. To trigger this process, it has been argued that sedimentation of solids onto the mid-plane needs to be efficient and therefore that a quiescent gaseous environment is required. It is often suggested that dead-zone or disk-wind structure created by non-ideal magnetohydrodynamical (MHD) effects meets this requirement. However, simulations have shown that the midplane of a dead zone is not completely quiescent. In order to examine the concentration of solids in such an environment,…
On the accumulation of planetesimals near disc gaps created by protoplanets
我们已经进行了三维二维流体（气尘）流体动力学模型的拱盘嵌入原行星（3 - 333 M \oplu）和小固体（半径10厘米至10米）。我们发现，大质量行星（\gtrsim土星质量）在气体盘中打开足够深的间隙，使得间隙外缘的密度最大值可以非常有效地捕获米级固体。这允许固体在间隙的外边缘处积聚，因为固体从大半径螺旋向内到捕获区域。对于那些向内螺旋最快的物体，通常是米大小的巨石，这种积累过程发生得最快，而较小和较大的物体在圆盘的寿命内不会足够快地迁移以从该过程中受益。在木星质量的行星周围，我们发现可能会形成与几个地球质量一样大的固体物质的束缚团块，可能会在自引力下坍塌形成行星或微行星。这些结果与Lyra et al.（2009）一致，支持他们的发现，即第二代微行星或类地行星的形成可能是由高质量行星的存在引发的。
Protoplanetary disks are dynamic objects, within which dust grains and gas are expected to be redistributed over large distances. Evidence for this redistribution is seen both in other protoplanetary disks and in our own Solar System, with high-temperature materials thought to originate close to the central star found in the cold, outer regions of the disks. While models have shown this redistribution is possible through a variety of mechanisms, these models have generally ignored the possible growth of solids via grain-grain collisions that would occur during transit. Here we investigate the …
Hydrodynamical instabilities in disks around young stars depend on the thermodynamic stratification of the disk and on the local rate of thermal relaxation. Here, we map the spatial extent of unstable regions for the Vertical Shear Instability (VSI), the Convective OverStability (COS), and the amplification of vortices via the Subcritical Baroclinic Instability (SBI). We use steady state accretion disk models, including stellar irradiation, accretion heating and radiative transfer. We determine the local radial and vertical stratification and thermal relaxation rate in the disk, in dependence …
In models of planetary accretion, pebbles form by dust coagulation and rapidly migrate toward the central star. Planetesimals may continuously form from pebbles over the age of the protoplanetary disk by yet uncertain mechanisms. Meanwhile, large planetary embryos grow efficiently by accumulation of leftover pebbles that are not incorporated in planetesimals. Although this process, called pebble accretion, is offering a new promising pathway for formation of giant planets' cores, architectures of planetary systems formed through the process remain elusive. In the present paper, we perform simu…
The formation of the first planetesimals and the final growth of planetary cores relies on the abundance of small pebbles. The efficiencies of both the streaming instability (SI) process, suggested to catalyze the early growth of planetesimals, and the pebble-accretion process, suggested to accelerate the growth of planetary cores, depend on the sizes of solids residing in the disk. In particular, these processes were found to be sensitive to size distribution of solids, and efficient planetesimal formation and growth through these channels require a limited pebble size distribution. Here we s…
We present a near-infrared direct imaging search for accretion signatures of possible protoplanets around the young stellar object (YSO) TW Hya, a multi-ring disk exhibiting evidence of planet formation. The Pa$β$ line (1.282 $μ$m) is an indication of accretion onto a protoplanet, and its intensity is much higher than that of blackbody radiation from the protoplanet. We focused on the Pa$β$ line and performed Keck/OSIRIS spectroscopic observations. Although spectral differential imaging (SDI) reduction detected no accretion signatures, the results of the present study allowed us to set 5$σ$ de…
Physical processes that redistribute or remove angular momentum from protoplanetary disks can drive mass accretion onto the star and affect the outcome of planet formation. Despite ubiquitous evidence that protoplanetary disks are engaged in accretion, the process(es) responsible remain unclear. Here we present evidence for redshifted molecular absorption in the spectrum of a Class I source that indicates rapid inflow at the disk surface. High resolution mid-infrared spectroscopy of GV Tau N reveals a rich absorption spectrum of individual lines of C2H2, HCN, NH3, and water. From the propertie…
Several planetary systems are known to host multiple giant planets. However, when two giant planets are accreting from the same disk, it is unclear what effect the presence of the second planet has on the gas accretion process of both planets. In this paper we perform long-term 2D isothermal hydrodynamical simulations (over more than 0.5 Myrs) with the FARGO-2D1D code, considering two non-migrating planets accreting from the same gaseous disk. We find that the evolution of the planets' mass ratio depends on gap formation. However, in all cases, when the planets start accreting at the same time…
