The secular dynamics of small planetesimals in tight binary systems play a fundamental role in establishing the possibility of accretional collisions in such extreme cases. The most important secular parameters are the forced eccentricity and secular frequency, which depend on the initial conditions of the particles, as well as on the mass and orbital parameters of the secondary star. We construct a second-order theory (with respect to the masses) for the planar secular motion of small planetasimals and deduce new expressions for the forced eccentricity and secular frequency. We also reanalyze the radial velocity data available for Gamma-Cephei and present a series of orbital solutions leading to residuals compatible with the best fits. Finally, we discuss how different orbital configurations for Gamma-Cephei may affect the dynamics of small bodies in circunmstellar motion. For Gamma-Cephei, we find that the classical first-order expressions for the secular frequency and forced eccentricity lead to large inaccuracies around 50 % for semimajor axes larger than one tenth the orbital separation between the stellar components. Low eccentricities and/or masses reduce the importance of the second-order terms. The dynamics of small planetesimals only show a weak dependence with the orbital fits of the stellar components, and the same result is found including the effects of a nonlinear gas drag. Thus, the possibility of planetary formation in this binary system largely appears insensitive to the orbital fits adopted for the stellar components, and any future alterations in the system parameters (due to new observations) should not change this picture. Finally, we show that planetesimals migrating because of gas drag may be trapped in mean-motion resonances with the binary, even though the migration is divergent.
We present an algebraic map (MAMA) for the dynamical and collisional evolution of a planetesimal swarm orbiting the main star of a tight binary system (TBS). The orbital evolution of each planetesimal is dictated by the secular perturbations of the secondary star and gas drag due to interactions with a protoplanetary disk. The gas disk is assumed eccentric with a constant precession rate. Gravitational interactions between the planetesimals are ignored. All bodies are assumed coplanar. A comparison with full N-body simulations shows that the map is of the order of 100 times faster, while prese…
We study the gravitational instability (GI) of small solids in a gas disk as a mechanism to form planetesimals. Dissipation from gas drag introduces secular GI, which proceeds even when standard GI criteria for a critical density or Toomre's $Q$ predict stability. We include the stabilizing effects of turbulent diffusion, which suppresses small scale GI. The radially wide rings that do collapse contain up to $\sim 0.1$ Earth masses of solids. Subsequent fragmentation of the ring (not modeled here) would produce a clan of chemically homogenous planetesimals. Particle radial drift time scales (a…
Extended gaps in the debris disks of both Vega and Fomalhaut have been observed. These structures have been attributed to tidal perturbations by multiple super-Jupiter gas giant planets. Within the current observational limits, however, no such massive planets have been detected. Here we propose a less stringent `lone-planet' scenario to account for the observed structure with a single eccentric gas giant and suggest that clearing of these wide gaps is induced by its sweeping secular resonance. During the depletion of the disk gas, the planet's secular resonance propagates inward and clears a …
Circumbinary planetary systems recently discovered by Kepler represent an important testbed for planet formation theories. Planetesimal growth in disks around binaries has been expected to be inhibited interior to ~10 AU by secular excitation of high relative velocities between planetesimals, leading to their collisional destruction (rather than agglomeration). Here we show that gravity of the gaseous circumbinary disk in which planets form drives fast precession of both the planetesimal and binary orbits, resulting in strong suppression of planetesimal eccentricities beyond 2-3 AU and making …
Planet formation in small-separation (~20 AU) eccentric binaries such as gamma Cephei or alpha Centauri is believed to be adversely affected by the presence of the stellar companion. Strong dynamical excitation of planetesimals by the eccentric companion can result in collisional destruction (rather than growth) of 1-100 km objects, giving rise to the "fragmentation barrier" for planet formation. We revise this issue using a novel description of secular dynamics of planetesimals in binaries, which accounts for the gravity of the eccentric, coplanar protoplanetary disk, as well as gas drag. By …
We estimate minimum dust abundances required for secular gravitational instability (SGI) to operate at the midplane dust layer of protoplanetary disks. For SGI to be a viable process, the growth time of the instability T_grow must be shorter than the radial drift time of the dust T_drift. The growth time depends on the turbulent diffusion parameter alpha, because the modes with short wavelengths are stabilized by turbulent diffusion. Assuming that turbulence is excited via the Kelvin-Helmholtz or streaming instabilities in the dust layer, and that its strength is controlled by the energy suppl…
Chondrules are silicate spheroids found in meteorites, serving as important fossil records of the early solar system. In order to form chondrules, chondrule precursors must be heated to temperatures much higher than the typical conditions in the current asteroid belt. One proposed mechanism for chondrule heating is the passage through bow shocks of highly eccentric planetesimals in the protoplanetary disk in the early solar system. However, it is difficult for planetesimals to gain and maintain such high eccentricities. In this paper, we present a new scenario in which planetesimals in the ast…
The distribution of heavy elements is anomalously low in the asteroid main belt region compared with elsewhere in the solar system. Observational surveys also indicate a deficit in the number of small ($ \le 50$~km size) asteroids that is two orders of magnitude lower than what is expected from the single power-law distribution that results from a collisional coagulation and fragmentation equilibrium. Here, we consider the possibility that a major fraction of the original asteroid population may have been cleared out by Jupiter's secular resonance, as it swept through the main asteroid belt du…
Detectable debris discs are thought to require dynamical excitation (`stirring'), so that planetesimal collisions release large quantities of dust. We investigate the effects of the secular perturbations of a planet, which may lie at a significant distance from the planetesimal disc, to see if these perturbations can stir the disc, and if so over what time-scale. The secular perturbations cause orbits at different semi-major axes to precess at different rates, and after some time t_cross initially non-intersecting orbits begin to cross. We show that t_cross is proportional to a_disc^(9/2)/(m_p…
Episodic planetesimal disruptions triggered by dissipation of gas disk
Nanjing University（南京大学）；Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University（教育部现代天文与天体物理重点实验室，南京大学）；State Key Laboratory of Critical Earth Material Cycling and Mineral Deposits & Lunar and Planetary Science Institute, School of Earth Sciences and Engineering, Nanjing University（南京大学地球科学与工程学院关键地球物质循环与矿床国家重点实验室及月球与行星科学研究所）；CAS Center for Excellence in Comparative Planetology（中国科学院比较行星学卓越创新中心）
The Kepler mission has discovered about a dozen circumbinary planetary systems, all containing planets on ~ 1 AU orbits. We place bounds on the locations in the circumbinary protoplanetary disk, where these planets could have formed through collisional agglomeration starting from small (km-sized or less) planetesimals. We first present a model of secular planetesimal dynamics that accounts for the (1) perturbation due to the eccentric precessing binary, as well as the (2) gravity and (3) gas drag from a precessing eccentric disk. Their simultaneous action leads to rich dynamics, with (multiple…
Planet formation around one component of a tight, eccentric binary system such as $γ$ Cephei (with semimajor axis around 20 AU) is theoretically challenging because of destructive high-velocity collisions between planetesimals. Despite this fragmentation barrier, planets are known to exist in such orbital configurations. Here we present a novel numerical framework for carrying out multi-annulus coagulation-fragmentation calculations of planetesimal growth, which fully accounts for the specifics of planetesimal dynamics in binaries, details of planetesimal collision outcomes, and the radial tra…
It is well known that asteroids and comets fall into the Sun. Metal pollution of white dwarfs and transient spectroscopic signatures of young stars like $β$-Pic provide growing evidence that extra solar planetesimals can attain extreme orbital eccentricities and fall onto their parent stars. We aim to develop a general, practically implementable, semi-analytical theory of secular eccentricity excitation of small bodies in mean motion resonances with an eccentric planet valid for arbitrary values of the eccentricities and including the short-range force due to General Relativity. Our semi-analy…
Secular oscillations in multi-planet systems can drive chaotic evolution of a small inner body through non-linear resonant perturbations. This "secular chaos" readily pushes the inner body to an extreme eccentricity, triggering tidal interactions or collision with the central star. We present a numerical study of secular chaos in systems with two planets and test particles using the ring-averaging method, with emphasis on the relationship between the planets' properties and the time-scale and efficiency of chaotic diffusion. We find that secular chaos can excite extreme eccentricities on time-…
Streaming instability is a privileged channel to bridge the gap between collisional growth of dust grains and planetesimal formation triggered by gravity. This instability is thought to develop through its secular mode, which is long-time growing and may not develop easily in real discs. We address this point by revisiting its perturbation analysis. A third-order expansion with respect to the Stokes number reveals important features over-looked so far. The secular mode can be stable. Epicycles can be unstable, more resistant to viscosity and are identified by Green's function analysis as promi…
Secular gravitational instability (GI) is one of the promising mechanisms for creating annular substructures and planetesimals in protoplanetary disks. We perform numerical simulations of the secular GI in a radially extended disk with inward drifting dust grains. The results show that, even in the presence of the dust diffusion, the dust rings form via the secular GI while the dust grains are moving inward, and the dust surface density increases by a factor of ten. Once the secular GI develops into a nonlinear regime, the total mass of the resultant rings can be a significant fraction of the …
We analyze the dynamics of individual kilometer-size planetesimals in circumstellar orbits of a tight binary system. We include both the gravitational perturbations of the secondary star and a non-linear gas drag stemming from an eccentric gas disk with a finite precession rate. We consider several precession rates and eccentricities for the gas, and compare the results with a static disk in circular orbit. The disk precession introduces three main differences with respect to the classical static case: (i) The equilibrium secular solutions generated by the gas drag are no longer fixed points i…
Planetesimal belts are invoked to explain the prolonged existence of debris disks. Important parameters to model their collisional evolution and to compute the dust production rate are the intrinsic probability of collision $P_i$ and the mean impact velocity $U_c$. If a planet orbits close to the belt, the values of both these parameters are affected by its secular perturbations yielding a strong correlation between eccentricity $e$ and pericentre longitude $\varpi$. We adopt a new algorithm to compute both $P_i$ and $U_c$ in presence of various levels of secular correlation due to different r…
Secular and mean motion resonances (MMR) are effective perturbations for shaping planetary systems. In binary star systems, they play a key role during the early and late phases of planetary formation, as well as for the dynamical stability of a planetary system. In this study, we aim to correlate the presence of orbital resonances with the rate of icy asteroids crossing the habitable zone (HZ), from a circumprimary disk of planetesimals in various binary star systems. We modelled a belt of small bodies in the inner and outer regions, interior and exterior to the orbit of a gas giant planet, r…
Using numerical simulations, we show that smooth migration of the giant planets through a planetesimal disk leads to an orbital architecture that is inconsistent with the current one: the resulting eccentricities and inclinations of their orbits are too small. The crossing of mutual mean motion resonances by the planets would excite their orbital eccentricities but not their orbital inclinations. Moreover, the amplitudes of the eigenmodes characterising the current secular evolution of the eccentricities of Jupiter and Saturn would not be reproduced correctly; only one eigenmode is excited by …
About $20\%$ of exoplanets discovered by radial velocity surveys reside in stellar binaries. To clarify their origin one has to understand the dynamics of planetesimals in protoplanetary disks within binaries. The standard description, accounting for only gas drag and gravity of the companion star has been challenged recently, as the gravity of the protoplanetary disk was shown to play a crucial role in planetesimal dynamics. An added complication is the tendency of protoplanetary disks in binaries to become eccentric, giving rise to additional excitation of planetesimal eccentricity. Here, fo…
Standard models of planet formation explain how planets form in axisymmetric, unperturbed disks in single star systems. However, it is possible that giant planets could have already formed when other planetary embryos start to grow. We investigate the dynamics of planetesimals under the perturbation of a giant planet in a gaseous disk. Our aim is to understand the effect of the planet's perturbation on the formation of giant planet cores outside the orbit of the planet. We calculate the orbital evolution of planetesimals ranging from $10^{13}$ to $10^{20}$g, with a Jupiter-mass planet located …
Existence of planets is binaries with relatively small separations (around 20 AU), such as αCentauri or γCephei poses severe challenges to standard planet formation theories. The problem lies in the vigorous secular excitation of planetesimal eccentricities at separations of several AU, where some of the planets are found, by the massive, eccentric stellar companions. High relative velocities of planetesimals preclude their growth in mutual collisions for a wide range of sizes, from below 1 km up to several hundred km, resulting in fragmentation barrier to planet formation. Here we show that r…
Detections of planets in eccentric, close (separations of ~20 AU) binary systems such as αCen or γCep provide an important test of planet formation theories. Gravitational perturbations from the companion are expected to excite high planetesimal eccentricities resulting in destruction, rather than growth, of objects with sizes of up to several hundred km in collisions of similar-size bodies. It was recently suggested that gravity of a massive axisymmetric gaseous disk in which planetesimals are embedded drives rapid precession of their orbits, suppressing eccentricity excitation. However, disk…
The presence of a planetary system can shield a planetesimal disk from the secular gravitational perturbations due to distant outer massive objects (planets or stellar companions). As the host star evolves off the main sequence to become a white dwarf, these planets can be engulfed, triggering secular instabilities and leading to the tidal disruptions of small rocky bodies. These disrupted bodies can feed the white dwarfs with rocky material and possibly explain the high-metallicity material in their atmospheres. We illustrate how this mechanism can operate when the gravitational perturbations…
So far, more than 130 extrasolar planets have been found in multiple stellar systems. Dynamical simulations show that the outcome of the planetary formation process can lead to different planetary architectures (i.e. location, size, mass, and water content) when the star system is single or double. In the late phase of planetary formation, when embryo-sized objects dominate the inner region of the system, asteroids are also present and can provide additional material for objects inside the habitable zone (HZ). In this study, we make a comparison of several binary star systems and aim to show h…
In the last years several exoplanets have been discovered that orbit one component of a compact binary system (separation < 50 astronomical units), the probably best-known case is gamma-Cephei. So far, all attempts to explain the in-situ formation of these planets has been unsuccessful, in part because of the strong gravitational perturbations of the secondary star on any initial planetesimal swarm. Here we test whether planetary bodies in compact binaries, in particular gamma-Cephei, could have originated from a close encounter with a passing star, assuming initial configurations for the stel…
We analyse the secular dynamics of planets on S-type coplanar orbits in tight binary systems, based on first- and second-order analytical models, and compare their predictions with full N-body simulations. The perturbation parameter adopted for the development of these models depends on the masses of the stars and on the semimajor axis ratio between the planet and the binary. We show that each model has both advantages and limitations. While the first-order analytical model is algebraically simple and easy to implement, it is only applicable in regions of the parameter space where the perturba…
We investigate how the self gravity changes the orbital stability of Twotinos using N-body simulations in which the gravitational interaction between planetesimals are fully calculated. We show the timescale in which the half of Twotinos becomes unstable, t_{half}, obey the formula, t_{half} = 4 \times 106(Mtot0.1M\oplus)-1(mp7.6 \times 1023g)-1(hi2i1/20.002)(years), if we assume the primordial planetesimals disk have the power low surface mass density, Σ= Σ_0 \times r-2/3. Where Mtot, mp, hi2i1/2 are the total mass of large bodies of Twotinos, the maximum mass of planetesimals, and the inclin…
Planetesimal Formation under Realistic Gas Dynamics: Dust Concentration in Turbulent and Windy Protoplanetary Disks
CAS Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese Academy of Sciences（中国科学院行星科学重点实验室、紫金山天文台）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Astronomy, Tsinghua University（清华大学天文学系）
Binary systems are very common among field stars. While this relatively small number of planets in binaries is probably partly due to strong observational biases, there is, however, statistical evidence that planets are indeed less frequent in binaries with separations smaller than 100 au, strongly suggesting that the presence of a close in companion star has an adverse effect on planet formation. It is indeed possible for the gravitational pull of the second star to affect all the different stages of planet formation, from proto-planetary disk formation to dust accumulation into planetesimals…
Dynamics of the TWA 7 planetary system and possibility of an additional planet
Univ. Grenoble Alpes, CNRS, IPAG（格勒诺布尔阿尔卑斯大学）；Department of Astronomy, University of California, Berkeley（加州大学伯克利天文学系）；LIRA, CNRS, Observatoire de Paris, Université PSL（巴黎天文台）
TWA 7行星系统通过结合N体模拟和摄动理论，探讨未检测到的内行星对尘埃盘形态和共轨道动态的影响，揭示系统在参数空间中的窄区域配置。
