Masahiro Ogihara

N-Body Simulations of Planetary Accretion Around M Dwarf Stars

We have investigated planetary accretion from planetesimals in terrestrial planet regions inside the ice line around M dwarf stars through N-body simulations including tidal interactions with disk gas. Because of low luminosity of M dwarfs, habitable zones (HZs) are located in inner regions (~0.1 AU). In the close-in HZ, type-I migration and the orbital decay induced by eccentricity damping are efficient according to the high disk gas density in the small orbital radii. Since the orbital decay is terminated around the disk inner edge and the disk edge is close to the HZ, the protoplanets accumulated near the disk edge affect formation of planets in the HZ. Ice lines are also in relatively inner regions at ~0.3 AU. Due to the small orbital radii, icy protoplanets accrete rapidly and undergo type-I migration before disk depletion. The rapid orbital decay, the proximity of the disk inner edge, and large amount of inflow of icy protoplanets are characteristic in planetary accretion in terrestrial planet regions around M dwarfs. In the case of full efficiency of type-I migration predicted by the linear theory, we found that protoplanets that migrate to the vicinity of the host star undergo close scatterings and collisions, and four to six planets eventually remain in mutual mean-motion resonances and their orbits have small eccentricities (0.01) and they are stable both before and after disk gas decays. In the case of slow migration, the resonant capture is so efficient that densely packed ~40 small protoplanets remain in mutual mean-motion resonances. In this case, they start orbit crossing, after the disk gas decays and eccentricity damping due to tidal interaction with gas is no more effective. Through merging of the protoplanets, several planets in widely separated non-resonant orbits with relatively large eccentricities (~0.05) are formed. Thus, the final orbital configurations (separations, resonant or non-resonant, eccentricity, and distribution) of the terrestrial planets around M dwarfs sensitively depend on strength of type-I migration. We also found that large amount of water-ice is delivered by type-I migration from outer regions and final planets near the inner disk edge around M dwarfs are generally abundant in water-ice except for the innermost one that is shielded by the outer planets, unless type-I migration speed is reduced by a factor of more than 100 from that predicted by the linear theory.

N-BODY SIMULATIONS OF SATELLITE FORMATION AROUND GIANT PLANETS: ORIGIN OF ORBITAL CONFIGURATION OF THE GALILEAN MOONS

As the number of discovered extrasolar planets has been increasing, diversity of planetary systems requires studies of new formation scenarios. It is important to study satellite formation in circumplanetary disks, which is often viewed as analogous to formation of rocky planets in protoplanetary disks. We investigated satellite formation from satellitesimals around giant planets through N-body simulations that include gravitational interactions with a circumplanetary gas disk. Our main aim is to reproduce the observable properties of the Galilean satellites around Jupiter through numerical simulations, as previous N-body simulations have not explained the origin of the resonant configuration. We performed accretion simulations based on the work of Sasaki et al., in which an inner cavity is added to the model of Canup & Ward. We found that several satellites are formed and captured in mutual mean motion resonances outside the disk inner edge and are stable after rapid disk gas dissipation, which explains the characteristics of the Galilean satellites. In addition, owing to the existence of the disk edge, a radial compositional gradient of the Galilean satellites can also be reproduced. An additional objective of this study is to discuss orbital properties of formed satellites for a wide range of conditions by considering large uncertainties in model parameters. Through numerical experiments and semianalytical arguments, we determined that if the inner edge of a disk is introduced, a Galilean-like configuration in which several satellites are captured into a 2:1 resonance outside the disk inner cavity is almost universal. In fact, such a configuration is produced even for a massive disk 104 g cm–2 and rapid type I migration. This result implies the inevitability of a Galilean satellite formation in addition to providing theoretical predictions for extrasolar satellites. That is, we can predict a substantial number of exomoon systems in the 2:1 mean motion resonance close to their host planets awaiting discovery.

Accretion of terrestrial planets from oligarchs in a turbulent disk

Abstract We have investigated the final accretion stage of terrestrial planets from Mars-mass protoplanets that formed through oligarchic growth in a disk comparable to the minimum mass solar nebula (MMSN), through N-body simulation including random torques exerted by disk turbulence due to Magneto-Rotational Instability. For the torques, we used the semi-analytical formula developed by Laughlin et al. [Laughlin, G., Steinacker, A., Adams, F.C., 2004. Astrophys. J. 608, 489–496]. The damping of orbital eccentricities (in all runs) and type-I migration (in some runs) due to the tidal interactions with disk gas is also included. Without any effect of disk gas, Earth-mass planets are formed in terrestrial planet regions in a disk comparable to MMSN but with too large orbital eccentricities to be consistent with the present eccentricities of Earth and Venus in our Solar System. With the eccentricity damping caused by the tidal interaction with a remnant gas disk, Earth-mass planets with eccentricities consistent with those of Earth and Venus are formed in a limited range of disk gas surface density (∼10−4 times MMSN). However, in this case, on average, too many (≳6) planets remain in terrestrial planet regions, because the damping leads to isolation between the planets. We have carried out a series of N-body simulations including the random torques with different disk surface density and strength of turbulence. We found that the orbital eccentricities pumped up by the turbulent torques and associated random walks in semimajor axes tend to delay isolation of planets, resulting in more coagulation of planets. The eccentricities are still damped after planets become isolated. As a result, the number of final planets decreases with increase in strength of the turbulence, while Earth-mass planets with small eccentricities are still formed. In the case of relatively strong turbulence, the number of final planets are 4–5 at 0.5–2 AU, which is more consistent with Solar System, for relatively wide range of disk gas surface density ( ∼ 10 −4 – 10 −2 times MMSN).

A reassessment of the in situ formation of close-in super-Earths

Context. A large fraction of stars host one or multiple close-in super-Earth planets. There is an active debate about whether these planets formed in situ or at greater distances from the central star and migrated to their current position. It has been shown that part of their observed properties (e.g., eccentricity distribution) can be reproduced by N-body simulations of in situ formation starting with a population of protoplanets of high masses and neglecting the e ects of the disk gas. Aims. We plan to reassess the in situ formation of close-in super-Earths through more complete simulations. Methods. We performed N-body simulations of a population of small planetary embryos and planetesimals that include the e ects of disk-planet interactions (e.g., eccentricity damping, Type I migration). In addition, we also consider the accretion of a primitive atmosphere from a protoplanetary disk. Results. We find that planetary embryos grow very quickly well before the gas dispersal, and thus undergo rapid inward migration, which means that one cannot neglect the e ects of a gas disk when considering the in-situ formation of close-in super-Earths. Owing to their rapid inward migration, super-Earths reach a compact configuration near the disk’s inner edge whose distribution of orbital parameters matches the observed close-in super-Earths population poorly. On the other hand, simulations including eccentricity damping, but no Type I migration, reproduce the observed distributions better. Including the accretion of an atmosphere does not help reproduce the bulk architecture of observations. Interestingly, we find that the massive embryos can migrate inside the disk edge while capturing only a moderately massive hydrogen/helium atmosphere. By this process they avoid becoming giant planets. Conclusions. The bulk of close-in super-Earths cannot form in situ, unless Type I migration is suppressed in the entire disk inside 1 AU.

CONDITION FOR CAPTURE INTO FIRST-ORDER MEAN MOTION RESONANCES AND APPLICATION TO CONSTRAINTS ON THE ORIGIN OF RESONANT SYSTEMS

We investigate the condition for capture into first-order mean motion resonances using numerical simulations with a wide range of various parameters. In particular, we focus on deriving the critical migration timescale for capture into the 2:1 resonance; additional numerical experiments for closely spaced resonances (e.g., 3:2) are also performed. We find that the critical migration timescale is determined by the planet-to-stellar mass ratio, and its dependence exhibits power-law behavior with index ?4/3. This dependence is also supported by simple analytic arguments. We also find that the critical migration timescale for systems with equal-mass bodies is shorter than that in the restricted problem; for instance, for the 2:1 resonance between two equal-mass bodies, the critical timescale decreases by a factor of 10. In addition, using the obtained formula, the origin of observed systems that include first-order commensurabilities is constrained. Assuming that pairs of planets originally form well separated from each other and then undergo convergent migration and are captured in resonances, it is possible that a number of exoplanets experienced rapid orbital migration. For systems in closely spaced resonances, the differential migration timescale between the resonant pair can be constrained well; it is further suggested that several exoplanets underwent migration that can equal or even exceed the type I migration rate predicted by the linear theory. This implies that some of them may have formed in situ. Future observations and the use of our model will allow us to statistically determine the typical migration speed in a protoplanetary disk.

Infrared Doppler instrument for the Subaru Telescope (IRD)

Because of their large numbers, red dwarfs may be the most abundant planet hosts in our Galaxy. In order to detect Earth-like planets around nearby red dwarfs (in particular late-M stars), it is crucial to conduct the precise radial velocity (RV) measurements at near-infrared wavelengths where these stars emit most of light. We report the development of the Infrared Doppler (IRD) spectrometer for the Subaru telescope. IRD is a fiber-fed, high-precision, near infrared spectrometer with a spectral resolution of R~70,000 covering from 0.97 to 1.75 μm. To achieve 1m/s RV measurement precision, we employ our original laser frequency comb of a wide-wavelength coverage as an extremely stable wavelength standard in the near-infrared. The spectrometer optics is composed of a new wide-pitch Echelle-grating and Volume-Phase Holographic gratings. To achieve ultimate thermal stability, very low thermal expansion ceramic is used for most of the optical components including the optical bench. The spectrometer will utilize a 4096×4096-pixel HgCdTe array.

Infrared Doppler instrument (IRD) for the Subaru telescope to search for Earth-like planets around nearby M-dwarfs

We report the current status of the Infrared Doppler (IRD) instrument for the Subaru telescope, which aims at detecting Earth-like planets around nearby M darwfs via the radial velocity (RV) measurements. IRD is a fiber-fed, near infrared spectrometer which enables us to obtain high-resolution spectrum (R~70000) from 0.97 to 1.75 μm. We have been developing new technologies to achieve 1m/s RV measurement precision, including an original laser frequency comb as an extremely stable wavelength standard in the near infrared. To achieve ultimate thermal stability, very low thermal expansion ceramic is used for most of the optical components including the optical bench.

Formation of terrestrial planets in disks evolving via disk winds and implications for the origin of the solar system’s terrestrial planets

Recent three-dimensional magnetohydrodynamical simulations have identified a disk wind by which gas materials are lost from the surface of a protoplanetary disk, which can significantly alter the evolution of the inner disk and the formation of terrestrial planets. A simultaneous description of the realistic evolution of the gaseous and solid components in a disk may provide a clue for solving the problem of the mass concentration of the terrestrial planets in the solar system. We simulate the formation of terrestrial planets from planetary embryos in a disk that evolves via magnetorotational instability and a disk wind. The aim is to examine the effects of a disk wind on the orbital evolution and final configuration of planetary systems. We perform N-body simulations of sixty 0.1 Earth-mass embryos in an evolving disk. The evolution of the gas surface density of the disk is tracked by solving a one-dimensional diffusion equation with a sink term that accounts for the disk wind. We find that even in the case of a weak disk wind, the radial slope of the gas surface density of the inner disk becomes shallower, which slows or halts the type I migration of embryos. If the effect of the disk wind is strong, the disk profile is significantly altered (e.g., positive surface density gradient, inside-out evacuation), leading to outward migration of embryos inside ~ 1 AU. Disk winds play an essential role in terrestrial planet formation inside a few AU by changing the disk profile. In addition, embryos can undergo convergent migration to ~ 1 AU in certainly probable conditions. In such a case, the characteristic features of the solar systems terrestrial planets (e.g., mass concentration around 1 AU, late giant impact) may be reproduced.

Suppression of type I migration by disk winds

Planets less massive than Saturn tend to rapidly migrate inward in protoplanetary disks. This is the so-called type I migration. Simulations attempting to reproduce the observed properties of exoplanets show that type I migration needs to be significantly reduced over a wide region of the disk for a long time. However, the mechanism capable of suppressing type I migration over a wide region has remained elusive. The recently found turbulence-driven disk winds offer new possibilities. We investigate the effects of disk winds on the disk profile and type I migration for a range of parameters that describe the strength of disk winds. We also examine the in situ formation of close-in super-Earths in disks that evolve through disk winds. The disk profile, which is regulated by viscous diffusion and disk winds, was derived by solving the diffusion equation. We carried out a number of simulations and plot here migration maps that indicate the type I migration rate. We also performed N-body simulations of the formation of close-in super-Earths from a population of planetesimals and planetary embryos. We define a key parameter, Kw, which determines the ratio of strengths between the viscous diffusion and disk winds. For a wide range of Kw, the type I migration rate is presented in migration maps. These maps show that type I migration is suppressed over the whole close-in region when the effects of disk winds are relatively strong (Kw < 100). From the results of N-body simulations, we see that type I migration is significantly slowed down assuming Kw = 40. We also show that the results of N-body simulations match statistical orbital distributions of close-in super-Earths.

Crowding-out of Giants by Dwarfs: An Origin for the Lack of Companion Planets in Hot Jupiter Systems

We investigate the formation of close-in terrestrial planets from planetary embryos under the influence of a hot Jupiter (HJ) using gravitational N-body simulations that include gravitational interactions between the gas disk and the terrestrial planet (e.g., type I migration). Our simulations show that several terrestrial planets efficiently form outside the orbit of the HJ, making a chain of planets, and all of them gravitationally interact directly or indirectly with the HJ through resonance, which leads to inward migration of the HJ. We call this mechanism of induced migration of the HJ crowding-out. The HJ is eventually lost through collision with the central star, and only several terrestrial planets remain. We also find that the efficiency of the crowding-out effect depends on the model parameters; for example, the heavier the disk is, the more efficient the crowding-out is. When planet formation occurs in a massive disk, the HJ can be lost to the central star and is never observed. On the other hand, for a less massive disk, the HJ and terrestrial planets can coexist; however, the companion planets may be below the detection limit of current observations. In both cases, systems with a HJ and terrestrial planets have little chance of detection. Therefore, our model naturally explains the lack of companion planets in HJ systems regardless of the disk mass. In effect, our model provides a theoretical prediction for future observations; additional planets can be discovered just outside the HJ, and their masses should generally be small.