The secular behavior of an orbit under the gravitational perturbation due to a two-dimensional uniform disk is studied in this paper, through analytical and numerical approaches. We develop the secular approximation of this problem and obtain the averaged Hamiltonian for this system first. We find that, when the ratio of the semimajor axes of the inner orbit and the disk radius takes very small values ($\ll1$), and if the inclination between the inner orbit and the disk is greater than the critical value of $30^\circ$, the inner orbit will undergo the (classical) Lidov-Kozai resonance in which variations of eccentricity and inclination are usually very large and the system has two equilibrium points at $ω=π/2,3π/2$ ($ω$ is the argument of perihelion). The critical value will slightly drop to about $27^\circ$ as the ratio increases to 0.4. However, the secular resonances will not occur for the outer orbit and the variations of the eccentricity and inclination are small. When the ratio of the orbit and the disk radius is nearly $1$, there are many more complicated Lidov-Kozai resonance types which lead to the orbital behaviors that are different from the classical Lidov-Kozai case. In these resonances, the system has more equilibrium points which could appear at $ω=0,π/2,π,3π/2$, and even other values of $ω$. The variations of eccentricity and inclination become relatively moderate, moreover, in some cases the orbit can be maintained at a highly inclined state. In addition, a analysis shows that a Kuzmin disk can also lead to the (classical) Lidov-Kozai resonance and the critical inclination is also $30^\circ$.
Using two-dimensional simulations, we compute the torque and rate of work (power) on a low-mass gravitational body, with softening length $R_{\rm soft}$, embedded in a gaseous disk when its orbit is eccentric and retrograde with respect to the disk. We explore orbital eccentricities $e$ between $0$ and $0.6$. We find that the power has its maximum at $e\simeq 0.25(h/0.05)^{2/3}$, where $h$ is the aspect ratio of the disk. We show that the power and the torque converge to the values predicted in the local (non-resonant) approximation of the dynamical friction (DF) when $R_{\rm soft}$ tends to z…
We investigate the formation of hot and massive circumplanetary disks (CPDs) and the orbital evolution of satellites formed in these disks. Because of the comparatively small size-scale of the sub-disk, quick magnetic diffusion prevents the magnetorotational instability (MRI) from being well-developed at ionization levels that would allow MRI in the parent protoplanetary disk. In the absence of significant angular momentum transport, continuous mass supply from the parental protoplanetary disk leads to the formation of a massive CPD. We have developed an evolutionary model for this scenario an…
Protoplanets formed in a marginally gravitationally unstable (MGU) disk by either core accretion or disk instability will be subject to dynamical interactions with massive spiral arms, possibly resulting in inward or outward orbital migration, mergers with each other, or even outright ejection from the protoplanetary system. The latter process has been hypothesized as a possible formation scenario for the unexpectedly high frequency of unbound gas giant exoplanets (free floating planets, FFP). Previous calculations with the EDTONS fixed grid three dimensional (3D) hydrodynamics code found that…
I derive a fully analytic expression for the linear corotation torque to first order in eccentricity for planets in non-barotropic protoplanetary disks, taking into account the effect of disk entropy gradients. This torque formula is applicable to both the co-orbital corotation torque and the non co-orbital corotation torques -- for planets in orbits with non-zero eccentricity -- in disks where the thermal diffusivity and viscosity are sufficient to maintain linearity of these interactions. While the co-orbital corotation torque is important for migration of planets in Type I migration, the no…
Core accretion and disk instability require giant protoplanets to form in the presence of disk gas. Protoplanet migration models generally assume disk masses low enough that the disk's self-gravity can be neglected. However, disk instability requires a disk massive enough to be marginally gravitationally unstable (MGU). Even for core accretion, a FU Orionis outburst may require a brief MGU disk phase. We present a new set of three dimensional, gravitational radiation hydrodynamics models of MGU disks with multiple protoplanets, which interact gravitationally with the disk and with each other, …
Sufficiently massive growing giant planets have circumplanetary disks, and the capture of solid bodies by the disks would likely influence the growth of the planets and formation of satellite systems around them. In addition to dust particles that are supplied to the disk with inflowing gas, recent studies suggest the importance of capture of planetesimals whose motion is decoupled from the gas, but orbital evolution of captured bodies in circumplanetary gas disks has not been studied in detail. In the present work, using three-body orbital integration and analytic calculations, we examine orb…
The gravitational instabilities are important to the evolution of the disks and the planet formation in the disks. We calculate the evolution of the disks which form from the collapse of the molecular cloud cores. By changing the properties of the cloud cores and the hydrodynamical viscosity parameters, we explore their effects on the properties of the gravitational instabilities. We find that the disk is unstable when the angular velocity of the molecular cloud core is larger than a critical value. The time duration of the instability increases as the angular velocity of the core increases. T…
Planets close to their stars are thought to form farther out and migrate inward due to angular momentum exchange with gaseous protoplanetary disks. This process can produce systems of planets in co-orbital (Trojan or 1:1) resonance, in which two planets share the same orbit, usually separated by 60 degrees. Co-orbital systems are detectable among the planetary systems found by the Kepler mission either directly or by transit timing variations. However, no co-orbital systems have been found within the thousands of Kepler planets and candidates. Here we study the orbital evolution of co-orbital …
Spin evolution of stellar-mass Black Holes (sBHs) embedded in AGN accretion disks is an important process relevant to production of gravitaional waves from binary Black Hole (BBH) merger events through the AGN channel. Since embedded sBHs are surrounded by circum-stellar disks (CSDs), the rotation of CSD gas flows determine the direction of the angular momentum it accretes. In this Letter, we use global 2D hydrodynamic simulations to show that while a disk-embedded sBH on a circular orbit transforms the initial retrograde Keplerian shear of the background accretion disk into a prograde CSD flo…
Planets are formed from collisional growth of small bodies in a protoplanetary disk. Bodies much larger than approximately $1$\,m are mainly controlled by the gravity of the host star and experience weak gas drag; their orbits are mainly expressed by orbital elements: semimajor axes $a$, eccentricities $e$, and inclinations $i$, which are modulated by gas drag. In a previous study, $\dot a$, $\dot e$, and $\dot i$ were analytically derived for $e \ll 1$ and $i \ll H/a$, where $H$ is the scale height of the disk. Their formulae are valid in the early stage of planet formation. However, once mas…
As planets form and grow within gaseous protoplanetary disks, the mutual gravitational interaction between the disk and planet leads to the exchange of angular momentum, and migration of the planet. We review current understanding of disk-planet interactions, focussing in particular on physical processes that determine the speed and direction of migration. We describe the evolution of low mass planets embedded in protoplanetary disks, and examine the influence of Lindblad and corotation torques as a function of the disk properties. The role of the disk in causing the evolution of eccentricitie…
Recently it is proposed that porous icy dust aggregates are formed by pairwise accretion of dust aggregates beyond the snowline. We calculate the equilibrium random velocity of porous dust aggregates taking into account mutual gravitational scattering, collisions, gas drag, and turbulent stirring and scattering. We find that the disk of porous dust aggregates becomes gravitationally unstable as they evolve through gravitational compression in the minimum-mass solar nebula model for a reasonable range of turbulence strength, which leads to rapid formation of planetesimals.
We consider the dynamics of porous icy dust aggregates in a turbulent gas disk and investigate the stability of the disk. We evaluate the random velocity of porous dust aggregates by considering their self-gravity, collisions, aerodynamic drag, turbulent stirring and scattering due to gas. We extend our previous work by introducing the anisotropic velocity dispersion and the relaxation time of the random velocity. We find the minimum mass solar nebular model to be gravitationally unstable if the turbulent viscosity parameter $α$ is less than about $4 \times 10^{-3}$. The upper limit of $α$ for…
The present investigation relates the orbital radii of regular satellites of Uranus, Jupiter, Neptune, and Saturn to photon energies in the spectra of atomic and molecular hydrogen. To explain these observations a model is developed involving stimulated radiative molecular association (SRMA) reactions among the photons and atoms in the protosatellite disks of the planets. In this model thermal energy is extracted from each disk due to a resonance at radii where there is a match between the temperature in the disk and a photon energy. Matter accumulates at these radii, and satellites and rings …
Gap formation by giant planets in self-gravitating disks may lead to a gravitational edge instability (GEI). We demonstrate this GEI with global 3D and 2D self-gravitating disk-planet simulations using the ZEUS, PLUTO and FARGO hydrodynamic codes. High resolution 2D simulations show that an unstable outer gap edge can lead to outwards orbital migration. Our results have important implications for theories of giant planet formation in massive disks.
Saturn's mid-sized moons (satellites) have a puzzling orbital configuration with trapping in mean-motion resonances with every other pairs (Mimas-Tethys 4:2 and Enceladus-Dione 2:1). To reproduce their current orbital configuration on the basis of Crida & Charnoz's model of satellite formation from a hypothetical ancient massive rings, adjacent pairs must pass 1st-order mean-motion resonances without being trapped. The trapping could be avoided by fast orbital migration and/or excitation of the satellite's eccentricity caused by gravitational interactions between the satellites and the rings (…
Puffed-up Edges of Planet-opened Gaps in Protoplanetary Disks. II. The Role of the Planet's Orbital Eccentricity
Academia Sinica Institute of Astronomy and Astrophysics（中央研究院天文及天文物理研究所）；National Center for Theoretical Sciences（国家理论科学中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学汤川研究所）
When gas giant protoplanets grow sufficiently massive, circumplanetary disks would form. While solid bodies captured by the circumplanetary disks likely contribute to the growth of the planets and regular satellites around them, some of captured bodies would remain in planet-centered orbits after the dispersal of the disk. We examine capture and subsequent orbital evolution of planetesimals in waning circumplanetary gas disks using three-body orbital integration. We find that some of captured planetesimals can survive in the circumplanetary disk for a long period of time under such weak gas dr…
Gravitational lensing events provide unique opportunities to discover and study planetary systems and binaries. Here we build on previous work to explore the role that orbital motion can play in both identifying and learning more about multiple-mass systems that serve as gravitational lenses. We find that a significant fraction of planet-lens and binary-lens light curves are influenced by orbital motion. Furthermore, the effects of orbital motion extend the range of binaries for which lens multiplicity can be discovered and studied. Orbital motion will play an increasingly important role as ob…
Context. A low-mass brown dwarf has been recently imaged around HR 2562 (HD 50571), a star hosting a debris disk resolved in the far infrared. Interestingly, the companion location is compatible with an orbit coplanar with the disk and interior to the debris belt. This feature makes the system a valuable laboratory to analyze the formation of substellar companions in a circumstellar disk and potential disk-companion dynamical interactions. Aims. We aim to further characterize the orbital motion of HR 2562 B and its interactions with the host star debris disk. Methods. We performed a monitoring…
Sub-Jupiter classed circumbinary planets discovered in close-in binary systems have orbits just beyond the dynamically unstable region, which is determined by the eccentricity and mass ratio of the host binary stars. These planets are assumed to have formed beyond the snow line and migrated to the current orbits rather than forming in situ. We propose a scenario in which a planet formed beyond the snow line and migrated to the inner edge of the circumbinary disk, which was within the unstable area, and then moved to the current orbit through outward transportation. This outward transportation …
Recently, gas giant planets in nearly circular orbits with large semimajor axes ($a \sim$ 30--1000AU) have been detected by direct imaging. We have investigated orbital evolution in a formation scenario for such planets, based on core accretion model: i) Icy cores accrete from planetesimals at $\lesssim$ 30AU, ii) they are scattered outward by an emerging nearby gas giant to acquire highly eccentric orbits, and iii) their orbits are circularized through accretion of disk gas in outer regions, where they spend most of time. We analytically derived equations to describe the orbital circularizati…
We study the tidal interaction between a low-mass companion (e.g., a protoplanet or a black hole) in orbit about a central mass, and the accretion disk within which it is submerged. We present results for a companion on a coplanar orbit with eccentricity e between 0.1 and 0.6. For these eccentricities, dynamical friction arguments in its local approximation, that is, ignoring differential rotation and the curvature of the orbit, provide simple analytical expressions for the rates of energy and angular momentum exchange between the disk and the companion. We examine the range of validity of the…
We investigate the chance of detecting proto-planetary or debris disks in stars that induce microlensing events (lenses). The modification of the light curves shapes due to occultation and extinction by the disks as well as the additional gravitational deflection caused by the additional mass is considered. The magnification of gravitational microlensing events is calculated using the ray shooting method. The occultation is taken into account by neglecting or weighting the images on the lens plane according to a transmission map of the corresponding disk for a point source point lens (PSPL) mo…
Stellar flybys in star clusters may perturb the evolution of young planetary systems in terms of disk truncation, planetary migration and planetary mass accretion. We investigate the feedback of a young planetary system during a single close stellar encounter in a typical open young stellar cluster. We consider 5 masses for the stellar perturbers: 0.5, 0.8, 1, 3 and 8 M$_{Sun}$, in coplanar, prograde and retrograde orbits respect to the planetary disk, varying the pertruber-host star orbital periastron from 100 AU to 500 AU. We have made 3D modelizations with the smooth particle hydrodynamics …
We carry out a series of high-resolution (1024 X 1024) hydrodynamic simulations to investigate the orbital evolution of a Saturn-Jupiter pair embedded in a gaseous disk. This work extends the results of our previous work by exploring a different orbital configuration---Jupiter lies outside Saturn (q<1, where q= M_i/M_o is the mass ratio of the inner planet and the outer one). We focus on the effects of different initial separations (d) between the two planets and the various surface density profiles of the disk, where σ\propto r^{-α}. We also compare the results of different orbital configurat…
The HR8799 planetary system with four ~10 mJup planets in wide orbits up to 70 au, and periods up to 500 yr has been detected with the direct imaging. Its intriguing orbital architecture is not fully resolved due to time-limited astrometry covering ~20 years. Earlier, we constructed a heuristic model of the system based on rapid, convergent migration of the planets. We developed a better structured and CPU-efficient variant of this model. We re-analyzed the self-consistent, homogeneous astrometric dataset in Konopacky (2016). The best-fitting configuration agrees with our earlier findings. The…
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 s…
We describe the dynamics of a stream of equally spaced macroscopic particles in orbit around a central body (e.g. a planet or star). A co-orbital configuration of small bodies may be subject to gravitational instability, which takes the system to a spreading, disordered and collisional state. We detail the linear instability's mathematical and physical features using the shearing sheet model and subsequently track its nonlinear evolution with local N-body simulations. This model provides a convenient tool with which to understand the gravitational and collisional dynamics of narrow belts, such…
Gravitational instability is one of considerable mechanisms to explain the formation of giant planets. We study the gravitational stability for the protoplanetary disks around a protostar. The temperature and Toomre's Q-value are calculated by assuming local equilibrium between viscous heating and radiative cooling (local thermal equilibrium). We assume constant $α$ viscosity and use a cooling function with realistic opacity. Then, we derive the critical surface density $Σ_{\rm{c}}$ that is necessary for a disk to become gravitationally unstable as a function of $r$. This critical surface dens…
Structures observed in debris disks may be caused by gravitational interaction with planetary or stellar companions. These perturbed disks are often thought to indicate the presence of planets and offer insights into the properties of both the disk and the perturbing planets. Gaps in debris disks may indicate a planet physically present within the gap, but such gaps can also occur away from the planet's orbit at mean-motion resonances (MMRs), and this is the focus of our interest here. We extend our study of planet-disk interaction through MMRs, presented in an earlier paper, to systems in whi…
Jupiter has four large regular satellites called the Galilean satellites: Io, Europa, Ganymede, and Callisto. The inner three of the Galilean satellites orbit in a 4:2:1 mean motion resonance; therefore their orbital configuration may originate from the stopping of the migration of Io near the bump in the surface density distribution and following resonant trapping of Europa and Ganymede. The formation mechanism of the bump near the orbit of the innermost satellite, Io, is not yet understood, however. Here, we show that photophoresis in the circumjovian disk could be the cause of the bump, usi…
We investigate the formation process of planetesimals from the dust layer by the gravitational instability in the gas disk using local $N$-body simulations. The gas is modeled as a background laminar flow. We study the formation process of planetesimals and its dependence on the strength of the gas drag. Our simulation results show that the formation process is divided into three stages qualitatively: the formation of wake-like density structures, the creation of planetesimal seeds, and their collisional growth. The linear analysis of the dissipative gravitational instability shows that the du…
Observational evidence exists for the formation of gas giant planets on wide orbits around young stars by disk gravitational instability, but the roles of disk instability and core accretion for forming gas giants on shorter period orbits are less clear. The controversy extends to population synthesis models of exoplanet demographics and to hydrodynamical models of the fragmentation process. The latter refers largely to the handling of radiative transfer in three dimensional (3D) hydrodynamical models, which controls heating and cooling processes in gravitationally unstable disks, and hence de…
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 …
The dynamics of solid bodies in protoplanetary disks are subject to the properties of any underlying gas turbulence. Turbulence driven by disk self-gravity shows features distinct from those driven by the magnetorotational instability (MRI). We study the dynamics of solids in gravito-turbulent disks with two-dimensional (in the disk plane), hybrid (particle and gas) simulations. Gravito-turbulent disks can exhibit stronger gravitational stirring than MRI-active disks, resulting in greater radial diffusion and larger eccentricities and relative speeds for large particles (those with dimensionle…
We revisit the problem of secular resonance sweeping during the dissipation of a protoplanetary disk and its possible role in exciting the orbits of primordial asteroids, in the light of recent models of solar system evolution. We develop an integrator that incorporates the gravitational effect of a uniformly (or not) depleting, axisymmetric disk with arbitrary surface density profile; its performance is verified by analytical calculations. The secular response of fictitious asteroids, under perturbations from Jupiter, Saturn and a decaying disk, is thoroughly studied. Note that the existence …
[Abridged] Star and planet formation are the complex outcomes of gravitational collapse and angular momentum transport mediated by protostellar and protoplanetary disks. In this review we focus on the role of gravitational instability in this process. We begin with a brief overview of the observational evidence for massive disks that might be subject to gravitational instability, and then highlight the diverse ways in which the instability manifests itself in protostellar and protoplanetary disks: the generation of spiral arms, small scale turbulence-like density fluctuations, and fragmentatio…
We solve the equations of two-dimensional hydrodynamics describing a circumbinary disk accreting onto an eccentric, equal-mass binary. We compute the time rate of change of the binary semimajor axis $a$ and eccentricity $e$ over a continuous range of eccentricities spanning $e=0$ to $e=0.9$. We find that binaries with initial eccentricities $e_0 \lesssim 0.1$ tend to $e=0$, where the binary semimajor axis expands. All others are attracted to $e \approx 0.4$, where the binary semimajor axis decays. The $e \approx 0.4$ attractor is caused by a rapid change in the disk response from a nearly orig…
We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is much smaller than the wavelength of the wave. Moreover, we also suppose that the wave's frequency is much smaller than the particle's orbital one. We make neither a priori assumptions about the direction of the wavevector nor on the orbital geometry of the planet. We find that, while the semi-major axis is left unaffected, the eccentricity, the inclination,…
Protostellar (class 0/I) disks, having masses comparable to those of their nascent host stars, and fed continuously from their natal infalling envelopes, are prone to gravitational instability (GI). Motivated by advances in near-infrared (NIR) adaptive optics imaging and mm-wave interferometry, we explore the observational signatures of GI in disks, using hydrodynamical and Monte Carlo radiative transfer simulations to synthesize NIR scattered light images and mm dust continuum maps. Spiral arms induced by GI, located at disk radii of hundreds of AUs, are local overdensities and have their pho…
We report the results of our three-dimensional radiation hydrodynamics simulation of collapsing unmagnetized molecular cloud cores. We investigate the formation and evolution of the circumstellar disk and the clumps formed by disk fragmentation. Our simulation shows that disk fragmentation occurs in the early phase of circumstellar disk evolution and many clumps form. The clump can be represented by a polytrope sphere of index $n \sim 3$ and $n \gtrsim 4$ at central temperature $T_c \lesssim100$ K and $T_c \gtrsim 100$ K, respectively. We demonstrate, numerically and theoretically, that the ma…
We study the motion of test particles in the metric of a localized and slowly rotating astronomical source, within the framework of linear gravitoelectromagnetism, grounded on a Post-Minkowskian approximation of general relativity. Special attention is paid to gravitational inductive effects due to time-varying gravitomagnetic fields. We show that, within the limits of the approximation mentioned above, there are cumulative effects on the orbit of the particles either for planetary sources or for binary systems. They turn out to be negligible.
