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Register a new userFormation of Protoplanets from Massive Planetesimals in Binary Systems
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More than half of stars reside in binary or multiple star systems and many planets have been found in binary systems. From theoretical point of view, however, whether or not the planetary formation proceeds in a binary system is a very complex problem, because secular perturbation from the companion star can easily stir up the eccentricity of the planetesimals and cause high-velocity, destructive collisions between planetesimals. Early stage of planetary formation process in binary systems has been studied by restricted three-body approach with gas drag and it is commonly accepted that accretion of planetesimals can proceed due to orbital phasing by gas drag. However, the gas drag becomes less effective as the planetesimals become massive. Therefore it is still uncertain whether the collision velocity remains small and planetary accretion can proceed, once the planetesimals become massive. We performed {it N}-body simulations of planetary formation in binary systems starting from massive planetesimals whose size is about 100-500 km. We found that the eccentricity vectors of planetesimals quickly converge to the forced eccentricity due to the coupling of the perturbation of the companion and the mutual interaction of planetesimals if the initial disk model is sufficiently wide in radial distribution. This convergence decreases the collision velocity and as a result accretion can proceed much in the same way as in isolated systems. The basic processes of the planetary formation, such as runaway growth and oligarchic growth and final configuration of the protoplanets are essentially the same in binary systems and single star systems, at least in the late stage where the effect of gas drag is small.
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In this paper we extend our numerical method for simulating terrestrial planet formation from Leinhardt and Richardson (2005) to include dynamical friction from the unresolved debris component. In the previous work we implemented a rubble pile planetesimal collision model into direct N-body simulations of terrestrial planet formation. The new collision model treated both accretion and erosion of planetesimals but did not include dynamical friction from debris particles smaller than the resolution limit for the simulation. By extending our numerical model to include dynamical friction from the unresolved debris, we can simulate the dynamical effect of debris produced during collisions and can also investigate the effect of initial debris mass on terrestrial planet formation. We find that significant initial debris mass, 10% or more of the total disk mass, changes the mode of planetesimal growth. Specifically, planetesimals in this situation do not go through a runaway growth phase. Instead they grow concurrently, similar to oligarchic growth. In addition to including the dynamical friction from the unresolved debris, we have implemented particle tracking as a proxy for monitoring compositional mixing. Although there is much less mixing due to collisions and gravitational scattering when dynamical friction of the background debris is included, there is significant inward migration of the largest protoplanets in the most extreme initial conditions.
Many massive objects have been found in the outer region of the Solar system. How they were formed and evolved has not been well understood, although there have been intensive studies on accretion process of terrestrial planets. One of the mysteries is the existence of binary planetesimals with near-equal mass components and highly eccentric orbits. These binary planetesimals are quite different from the satellites observed in the asteroid belt region. The ratio of the Hill radius to the physical radius of the planetesimals is much larger for the outer region of the disk, compared to the inner region of the disk. The Hill radius increases with the semi major axis. Therefore, planetesimals in the outer region can form close and eccentric binaries, while those in the inner region would simply collide. In this paper, we carried out $N$-body simulations in different regions of the disk and studied if binaries form in the outer region of the disk. We found that large planetesimals tend to form binaries. A significant fraction of large planetesimals are components of the binaries. Planetesimals that become the components of binaries eventually collide with a third body, through three-body encounters. Thus, the existence of binaries can enhance the growth rate of planetesimals in the Trans-Neptunian Object (TNO) region.
Context. Abridged. Many stars are members of binary systems. During early phases when the stars are surrounded by discs, the binary orbit and disc midplane may be mutually inclined. The discs around T Tauri stars will become mildly warped and undergo solid body precession around the angular momentum vector of the binary system. It is unclear how planetesimals in such a disc will evolve and affect planet formation. Aims. We investigate the dynamics of planetesimals embedded in discs that are perturbed by a binary companion on a circular, inclined orbit. We examine collisional velocities of the planetesimals to determine when they can grow through accretion. We vary the binary inclination, binary separation, D, disc mass, and planetesimal radius. Our standard model has D=60 AU, inclination=45 deg, and a disc mass equivalent to the MMSN. Methods. We use a 3D hydrodynamics code to model the disc. Planetesimals are test particles which experience gas drag, the gravitational force of the disc, the companion star gravity. Planetesimal orbit crossing events are detected and used to estimate collisional velocities. Results. For binary systems with modest inclination (25 deg), disc gravity prevents planetesimal orbits from undergoing strong differential nodal precession (which occurs in absence of the disc), and forces planetesimals to precess with the disc on average. For bodies of different size the orbit planes become modestly mutually inclined, leading to collisional velocities that inhibit growth. For larger inclinations (45 degrees), the Kozai effect operates, leading to destructively large relative velocities. Conclusions. Planet formation via planetesimal accretion is difficult in an inclined binary system with parameters similar to those considered in this paper. For systems in which the Kozai mechanism operates, the prospects for forming planets are very remote.
We introduce a set of stellar models for massive stars whose evolution has been affected by mass transfer in a binary system, at a range of metallicities. As noted by other authors, the effect of such mass transfer is frequently more than just rejuvenation. We find that, whilst stars with convective cores which have accreted only H-rich matter rejuvenate as expected, those stars which have accreted He-rich matter (for example at the end stages of conservative mass transfer) evolve in a way that is qualitatively similar to rejuvenated stars of much higher metallicity. Thus the effects of non-conservative evolution depend strongly on whether He-rich matter is amongst the portion accreted or ejected. This may lead to a significant divergence in binary evolution paths with only a small difference in initial assumptions. We compare our models to observed systems and find approximate formulae for the effect of mass accretion on the effective age and metallicity of the resulting star.
Aims: We simulate the spectra of massive binaries at different phases of the orbital cycle, accounting for the gravitational influence of the companion star on the shape and physical properties of the stellar surface. Methods: We used the Roche potential modified to account for radiation pressure to compute the stellar surface of close circular systems and we used the TIDES code for surface computation of eccentric systems. In both cases, we accounted for gravity darkening and mutual heating generated by irradiation to compute the surface temperature. We then interpolated NLTE plane-parallel atmosphere model spectra in a grid to obtain the local spectrum at each surface point. We finally summed all contributions, accounting for the Doppler shift, limb-darkening, and visibility to obtain the total synthetic spectrum. We computed different orbital phases and sets of physical and orbital parameters. Results: Our models predict line strength variations through the orbital cycle, but fail to completely reproduce the Struve-Sahade effect. Including radiation pressure allows us to reproduce a surface temperature distribution that is consistent with observations of semi-detached binary systems. Conclusions: Radiation pressure effects on the stellar surface are weak in (over)contact binaries and well-detached systems but can become very significant in semi-detached systems. The classical von Zeipel theorem is sufficient for the spectral computation. Broad-band light curves derived from the spectral computation are different from those computed with a model in which the stellar surfaces are equipotentials of the Roche potential scaled by the instantaneous orbital separation. In many cases, the fit of two Gaussian/Lorentzian profiles fails to properly measure the equivalent width of the lines and leads to apparent variations that could explain some of the effects reported in the literature.
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