Hans Scholl

Planetary formation in the γ Cephei system

Received; accepted Abstract. We numerically investigate under which conditions the planet detected at 2.1 AU of Cephei could form through the core-accretion scenario despite the perturbing presence of the highly eccentric companion star. We first show that the initial stage of runaway accretion of kilometer-sized planetesimals is possible within 2.5 AU from the central star only if large amounts of gas are present. In this case, gaseous friction induces periastron alignment of the orbits which reduces the otherwise high mutual impact velocities due to the companions secular perturbations. The following stage of mutual accretion of large embryos is also modeled. According to our simulations, the giant impacts among the embryos always lead to a core of 10 Mwithin 10 Myr, the average lifetime of gaseous discs. However, the core always ends up within 1.5 AU from the central star. Either the core grows more quickly in the inner region of the disc, or it migrates inside by scattering the residual embryos.

Planet formation in α Centauri A revisited: not so accretion friendly after all

We numerically explore planet formation aroundα Centauri A by focusing on the crucial planetesimals-to-embryos phase. Our approach is significa ntly improved with respect to the earlier work of Marzari & Scholl (2000), since our determini stic N-body code computing the relative velocities between test planetesimals handles bo dies with different size. Due to this step up, we can derive the accretion vs. fragmentation trend of a planetesimal population having any given size distribution. This is a critical aspec t of planet formation in binaries since the pericenter alignment of planetesimal orbits due t o the gravitational perturbations of the companion star and to gas friction strongly depends on size. Contrary to Marzari & Scholl (2000), we find that, for the nominal case of a Minimum Mass Sol ar Nebula gas disc, the region beyond∼ 0.5 AU from the primary is strongly hostile to planetesimal accretion. In this area, impact velocities between different-size bodies are increased, by the differential orbital phasing, to values too high to allow mutual accretion. For any realistic size distribution for the planetesimal population, this accretion-inhibiting effect is the dominant collision outcome and the accretion process is halted. Results are relatively robust with respect to the profile and density of the gas disc. Except for an unrealistic almost gas -free case, the inner ”accretionsafe” area never extends beyond 0.75AU. We conclude that planet formation is very diffi cult in the terrestrial region around α Centauri A, unless it started from fast-formed very large (>30km) planetesimals. Notwithstanding these unlikely initial conditions, the only possible explanation for the presence of planets around 1 AU from the star would be the hypothetical outward migration of planets formed closer to the star or a different orbital configuration in the binary’s early history. Our conclusions di ffer from those of several studies focusing on the later embryos-to-planets stage, confirming that the planet esimals-to-embryos phase is more affected by binary perturbations.

Influence of the circumbinary disk gravity on planetesimal accumulation in the Kepler-16 system

Context. Recent observations from NASA’s Kepler mission detected the first planets in circumbinary orbits. The question we try to answer is where these planets formed in the circumbinary disk and how far inside they migrated to reach their present location. Aims. We investigate the first and most delicate phase of planet formation when planetesimals accumulate to form planetary embryos. Methods. We use the hydrodynamical code FARGO to study the evolution of the disk and of a test population of planetesimals embedded in it. With this hybrid hydrodynamical-N-body code we can properly account for the gas drag force on the planetesimals and for the gravitational force of the disk on them. Results. The numerical simulations show that the gravity of the eccentric disk on the planetesimal swarm excites their eccentricities to much higher values than those induced by the binary perturbations only within 10 AU from the stars. Moreover, the disk gravity prevents a full alignment of the planetesimal pericenters. Both these effects lead to high impact velocities, beyond the critical value for erosion. Conclusions. Planetesimal accumulation in circumbinary disks appears to be prevented close to the stellar pair by the gravitational perturbations of the circumbinary disk. The observed planets possibly formed in the outer regions of the disk and then migrated inside by tidal interaction with the disk.

Terrestrial planet formation in exoplanetary systems with a giant planet on an external orbit

The Epsilon Eridani and 47 UMa extrasolar systems both have moderately massive planets orbiting relatively far away from the central star (at 3.3 and beyond 2.1 AU, respectively). This peculiarity makes them possible candidates for harboring terrestrial planets in their inner regions since the external giant planet might not have inhibited planet growth in the neighborhood of the star. Here we numerically investigate how the accretion of terrestrial planets may have been affected by the presence of the detected giant planets in external orbits. The uncertain timing of the giant planet formation with respect to the planetesimal accumulation process lead us to consider two possible scenarios: 1) the perturbing massive planet was fully formed when the planetesimals in the inner zone were still in their early phases of accumulation, and 2) the giant planet reached its final mass only later on when lunar-sized embryos were already present in the inner disk. In the first case we have used a deterministic numerical algorithm to compute the relative velocity distribution in a swarm of planetesimals affected by the gravitational perturbations of the giant planet and, possibly, by gas drag. The second scenario is explored by using the symplectic algorithm by Chambers (1999) to simulate the late stage of terrestrial planet formation. The Epsilon Eridani system turns out to be a very hostile environment for planetary formation in the terrestrial region when the giant planet formed early. The planets high eccentricity (0.608) induces very large relative velocities between planetesimals in inner orbits and collisions result mostly in disruption rather than accretion. On the other hand, if large embryos had enough time to form before the completion of the giant planet, they can accrete each other in giant impacts and coalesce into a few terrestrial planets within 0.8 AU from the star. For the 47 UMa system the situation is quite similar. The large mass of the inner giant planet excites large eccentricities among the planetesimals in the terrestrial region preventing accumulation. However, the damping effect on the relative velocities caused by gas drag opens a chance for accretion in a small region around the star inside 0.3 AU. The second and more distant planet recently discovered around 47 Uma does not significantly affect the encounter velocity distribution in the inner regions of the system. As for Epsilon Eridani, orderly growth of lunar-sized embryos takes place within 0.8 AU in presence of a late-formed giant planet. In either case, beyond 0.8 AU planetesimals or planetary embryos are rapidly removed by the massive planet perturbations.

Gas drag effects on planetesimals in the 2:1 resonance with proto-Jupiter

Abstract The combined effects are studied of gas drag and gravitational perturbations by a proto-Jupiter on the orbital evolution of a swarm of planetesimals in the primordial asteroid belt in the 2:1 mean motion resonance region. The gas drag in the primordial nebula causes planetesimals to spiral towards the Sun and, therefore, to cross mean motion resonances with proto-Jupiter. The dynamics of planetesimals are numerically investigated while passing through an inner resonance in a planar model. It is found that eccentricities are drastically increased and the maximum value reached by each planetesimal depends only on the resonance argument ψ at the resonance entry. The higher average eccentricity of the swarm within the resonance borders induces a faster spiralling rate of planetesimals and a consequent decrease of their number density, in particular at the 2:1, the most relevant resonance in the asteroid belt. This phenomenon causes the formation of a gap in the swarm at the resonance location. By intergrating a large number of planetesimal orbits, the gap formation process is analysed; it is found that the planetesimal number density near the resonance centre is reduced to 10–40% of its average value, depending on the free eccentricity assumed for the proto-Jupiter. Relative velocities between planetesimals are increased by a factor of four by resonant perturbations, favouring fragmentation at impacts; higher impact velocities and the reduced planetesimal density slow down the planetesimal accretion process and inhibit the formation of big bodies in the resonance region.

Dynamics and Planet Formation in/Around Binaries

The extent to which planetesimal accretion is affected by the perturbing presence of a companion star is an important issue in the formation of planets in and around binary systems. In this chapter, we review this issue by concentrating on one crucial parameter: the distribution of encounter velocities within the planetesimal swarm. The evolution of this parameter is numerically explored accounting for the secular perturbations of the binary and the friction due to the very likely presence of gas in the disk. Maps of the average encounter velocity ⟨Δv⟩ between different size planetesimals are presented for a total of 120 stellar dynamical configurations obtained by different combinations of the binary semimajor axis a b and eccentricity e b . According to the different values of ⟨Δv⟩, 3 different planetesimal accumulation modes are identified: 1) in regions where ⟨Δv⟩ is comparable to that derived for planetesimal swarms around single-stars, “standard” accretion is likely, eventually via runaway growth, 2) in regions where ⟨Δv⟩ is larger than v ero , the threshold velocity above which all impacts are eroding, no accretion is possible and planet growth is stopped, 3) in between these two extremes, there is a large fraction of binary configurations where the increase in ⟨Δv⟩ is still below the erosion threshold. Planetesimal accumulation can still occur but it possibly proceeds at a slower rate than in the single-star case, following the so-called type II runaway growth mode.

FORMATION OF LARGE SCALE STRUCTURES OF THE UNIVERSE ON THE CONNECTION MACHINE-2.

We have developped two new N-body codes on Connection Machine 2. We present preliminary results concerning the formation of large scale structure of the Universe.