山中陽裕「Orbital Evolution of a Circumbinary Planet within Dynamically Unstable Region」(2018年度)

Among 3869 extrasolar planets known today, 21 circumbinary planets (CBPs), which orbit around two stars, have been discovered. Although CBPs take a small proportion of known exoplanets, it is important to study planet formation processes in binary systems because the formation processes of discovered CBPs are unclear and planetary systems around binary stars may have different charaster- istics than those around single stars. Moreover, about a half of solar type stars are considered to be multiple systems, suggesting more undiscovered CBPs may exist. Sub-Jupiter class CBPs discovered in close-in binary systems have orbits just beyond the dynamically unstable region determined by the eccentricity and mass ratio of the host binary stars. Since the planets’ semi-major axes fall within 1 au they are assumed to have formed in the outer area and migrated to the current orbit rather than forming in situ, but previous attempts to reproduce their orbit have not succeeded. We propose a scenario in which a planet formed in the outer region migrates to the inner edge of the circumbinary disk and then moves to the current orbit through outward migration. This migration is driven by the balance of orbital excitation of the central stars inside the gravitationally unstable region and damping by the gas drag force. We developed a N-body calculation code and carried out N-body simulations with a dissipating circumbinary protoplanetary disk for binary systems with different eccentricities and mass ratios. Results show that planets are more likely to achieve a stable orbit just beyond the unstable region in less eccentric binary systems. This result is not as sensitive to mass ratio as it is to eccentricity. These dependencies are consistent with the data from observed binary systems hosting CBPs. We derived rates of planets successfully achieving stable orbits close to the unstable boundary for each set of binary parameters. The planet-surviving parameter range covers most of observed CBP systems, suggesting our results support the idea that circumbinary planets’ orbits close to the unstable boundary result from outward migration from a gravitationally unstable orbit to the present orbit and shows probability of more CBPs discovered near unstable boundary by searching for transit signals with periods close to the predicted boundary for the system. in future observations.


月は地球をはじめとした他の太陽系天体と比較して特有の性質を持つため、どのようにして形成されたかという問題は極めて難しい問題である。現在の月形成は巨大衝突説と呼ばれるシナリオが最も有力である。巨大衝突説では形成初期の地球に火星サイズほどの原始惑星が衝突(Giant impact)し、地球の周りに気液共存状態の原始月円盤を形成すると考えられている。しかし、Giant impactからの円盤形成、そしてその円盤が十分にcoolingした後における月の形成については先行研究の数値計算により具体的なタイムスケールが算出されているが、その間の円盤のcoolingの状態は不明瞭な点が多く、様々な円盤モデルが乱立し、考えられるタイムスケールも幅広い値を取っている。また、このcoolingの過程が月形成の律速段階と考えられるので、月物質の化学進化にも大きく影響を与える。本研究ではcoolingのタイムスケールを評価するために、coolingについての先行研究の仮定について検証した。すなわち原始月円盤中の液滴にRayleigh-Taylor不安定性を考慮することで、Machida & Abe (2004)が提唱した原始月円盤モデル:Stratify modelとは異なるモデルを考えた。この場合、円盤進化の過程として2つのシナリオが考えられるが、そのどちらも拡散のタイムスケールは~10^2 yrになることが分かった。また、Sharnoz&Michaut(2015)が用いた3D-modeの分散関係の仮定である非圧縮性がStratify modelの液体層へ適用可能な条件について調べた。その結果、液体層のgasmassfractionと温度が液体層の非圧縮性を決定する重要なファクターであることを明らかにした。今後は、本研究で明らかになった原始月円盤中の液滴へのRayleigh-Taylor不安定性の影響と、Stratify modelの液体層の非圧縮性条件を考慮した上で、原始月円盤の粘性進化を考察していくことが重要である。

石澤祐弥「In-situ formation of the Uranian satellites from debris disk formed by giant impact」(2017年度)

Uranus has a 98◦ tilt of the rotational axis with respect to the plane of Solar System, whereas the regular satellites of Uranus orbit in the plane of its equatorial plane. Several scenarios have been proposed so far to explain the large tilt and the origin of the satellites respectively (e.g., Slattery et al., 1992; Canup and Ward, 2006; Crida and Charnoz, 2012). In this study, I adopted the so-called giant impact scenario, which could explain both the large tilt of Uranus and the formation of the regular satellites simultaneously. The hydrodynamic simulations of the giant impact have been carried out using the smoothed particle hydrodynamics (SPH) method (Slattery et al, 1992; Ueta et al., in prep.). They suggested that the giant impact of an Earth-sized protoplanet with proto-Uranus could tilt the rotational axis, and a circum-planetary debris disk would be produced throughout the current Uranian satellites orbits by the impact. However, it is still unknown whether the Uranian satellites can be actually formed from such a wide disk. Here I modeled a wide debris disk of solids with several conditions, performed N-body simulations to investigate the in-situ satellite formation from the debris disk and also discussed what kind of debris disks is suitable for the in-situ formation. I used a 4th order Hermite scheme and Leap frog method for the numerical integration, and considered the gravity, collision and merger between each particle (Kokubo et al., 2000). I found that satellites with the similar orbital radii and masses to the current satellite are formed in the outer region from 5RU to 25RU, where RU indicates the Uranian radius. Such satellites are formed under the conditions both when the power-index of the surface density distribution of the disk is larger than or equal to roughly -2 and when the initial disk mass is around 3 × 10^−4MU, which is corresponding to three times of the the satellite system mass, where MU indicates the Uranian mass. However, I also found that in the inner region 2.5RU to 5RU satellites are generally formed with much larger mass compared to the current satellites in the same region. I propose an additional scenario of orbital evolution to explain the inner satellite distribution as the following; After the in-situ formation in a wide circum-planetary disk, the inner satellites migrate inward onto Uranus due to the tidal torque of Uranus and the tidal dissipation inside the satellites, then the satellites falling into the inside of 2.5RU are disrupted by the planetary tides. The disrupted satellites can form rings around Uranus and small satellites are secondarily formed from the rings in the way proposed by Crida and Charnoz (2012). The outer satellites stay almost in their orbits since they are too far from Uranus to migrate. I speculate that thirteen inner satellites and five major satellites of Uranus are formed in different ways. I analytically calculated the orbital evolutions of the five major satellites from the past in several cases and found that the outer three satellites can stay almost in their orbits during 4.5 billion years even if under the situation of extremely strong tides of Uranus. Satellite’s orbit changes also due to the gravitational interaction with the disk in addition to the tides. It would play a key role to explain the satellite distribution and should be investigated in more detail in the future.


月は地球をはじめとした他の太陽系天体と比較して特有の性質を持つため、どのようにして形成されたかという問題は極めて難しい問題である。現在の月形成は巨大衝突説と呼ばれるシナリオが最も有力である。巨大衝突説では形成初期の地球に火星サイズほどの原始惑星が衝突し、その破片が再び自己重力によって集まって形成されて月が形成されたと考えられている。しかし現在でも揮発性元素 (約 1000 K 以下の温度で蒸発する元素) の枯渇などの月の組成の特徴については完全には説明できてはいない。本研究では円盤の鉛直方向の 1 次元モデルを用いて、円盤の光球面の温度を計算した。従来考えられていた温度は太陽系空間での岩石の凝縮温度である 2000 K であったが、今回の研究結果から円盤の光球面の温度は 500 K ほどまで小さくなることが明らかになった。そのため円盤の冷却時間はこれまでよりも十分長くなることが示唆され、最速のシナリオでも約 1 yr、最大のシナリオでは何と約 107 yr もの時間がかかることが分かった。これは円盤形成時間 (1 日) や月集積時間 (1 ヶ月) よりも十分長いため巨大衝突説で月形成のタイ ムスケールは原始月円盤が決定するものと思われる。また円盤中の乱流についても考察した。月の揮発性元素の枯渇の原因は円盤の乱流によって蒸気が地球に粘性降着したものであると想定した。今回求めた円盤の寿命と角運動量輸送時間を比較することで円盤の乱流の大きさに制限を与えた。その結果、円盤内の乱流は非常に穏やかな乱流であることが分かった。今後は、本研究で明らかになった原始月円盤の冷却時間および乱流の大きさを用いて、大規模な月形成の数値計算を行っていくことが重要である。

上田翔士「Development of Numerical Code based on the DISPH Method for Simulation of the Impacts of Small Planetary Bodies」(2013年度)

The evolution of atmosphere and ocean on the Earth is significantly influenced by the impact of small planetary bodies. The modified atmosphere and ocean could change the surface environment, and it may determine the habitability of the planet. While some physical mechanisms causing atmospheric erosion by impact have been investigated, a comprehensive understanding of the impact-induced atmospheric erosion process is lack- ing. The most realistic numerical simulations, Shuvalov (2009) and Shuvalov et al. (2013), assumed only rock material as the target of impacts, and did not consider the oceanic erosion. In this study, we aim to develop an advanced numerical code for simulation of impacts of small bodies, assuming the target as land and/or ocean. We use a new Lagrangian hydrocode in Hosono et al. (2013), Density Independent Smoothed Particles Hydrodynamics (DISPH). In the hydrostatic equilibrium tests, the contact discontinuity with quite large difference of density, such as the boundaries between the atmosphere and ocean/land, can be expressed exactly by using the DISPH method with unequal- mass particles and equal-separation arrangement. A numerical code for simulations of impacts is developed in this work with various impact parameters, such as projectile di- ameter, impact velocity, impact angle, projectile material, and target material. From the preliminary simulations of impacts with the numerical code, we find that the variation of impact parameters makes a large difference to the picture after the collision. We have some problems in employing realistic non-ideal EOS suitable for these simulation and setting the initial conditions. However, we find that we can express exactly the contact discontinuity with quite different values of density by using the DISPH code. This result is of great importance for calculation load as well, and it might also help us solve other unsettled problems in astrophysical and planetary sciences field.