Abstract
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.
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Notes
- 1.
Our gas-drag model is a simplified one where the gas disk is assumed to be fully axisymmetric and follows a classical (Hayashi 1981) power law distribution. It is however more than likely that in reality the gas disk should depart from this simplified view because it would also “feel” the companion star’s perturbations. Several numerical studies have investigated the complex behavior of gaseous disks in binary systems. They all show that pronounced spiral structures rapidly form within the disk (e.g., Artymowicz and Lubow 1994; Savonije et al. 1994) and that gas streamlines exhibit radial velocities. To follow the dynamical behavior of planetesimals in such non-axisymmetric gas profiles would require a study of the coupled evolution of both gas and planetesimal populations, which have to rely on hydrodynamic-code modeling of the gas in addition to N-body type simulations for the planetesimals. Such an all-encompassing gas + planetesimals modeling is clearly the next step in binary disk studies and have already been started by several teams. It is interesting to note that preliminary results seem to show that planetesimal behaviors in systems with “realistic” gas disk modeling do not seem to drastically depart from the behavior in the axisymmetric case. There is in particular no phase alignment between eccentric planetesimal orbits and gas streamlines, so that gas friction on planetesimals is still very high (S.J. Paardekooper, private communication).
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S. Kortenkamp acknowledges support from NASA for some of this work under grants NNG04GP56G and NNG04GI14G.
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Marzari, F., Thébault, P., Kortenkamp, S., Scholl, H. (2010). Dynamics and Planet Formation in/Around Binaries. In: Haghighipour, N. (eds) Planets in Binary Star Systems. Astrophysics and Space Science Library, vol 366. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8687-7_7
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