Terrestrial planet growth in binary star systems

More than half of all main sequence stars, and an even larger fraction of pre-main sequence stars, are in binary/multiple star systems (Duquennoy & Mayor 1991; Mathieu et al. 2000). At least 19 of the first 120 extrasolar planets to be detected are on so-called S-type orbits that encircle one component of a main-sequence binary star system (Eggen-berger et al. 2004). The effect of the stellar companion on the formation of these planets, however, remains unclear. As discussed in Section 2, one planet has been confirmed in a P-type orbit which encircles the center of mass of PSR 1620-26, a radio pulsar binary comprised of a neutron star and a white dwarf in a —191-day stellar orbit (Lyne et al.

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Figure 2. The temporal evolution of a circumstellar disk centered around a Centauri A, whose midplane was initially inclined by 15° to the stellar orbit, is shown (simulation Ai15_3 in Quintana et al. 2002). The embryos' and planetesimals' eccentricities are displayed as a function of their semi-major axes, and the radius of each symbol is proportional to the radius of the body that it represents. After 200 Myr, four terrestrial planets had formed within 2 AU, accreting ~88% of the initial disk mass. See Quintana (2004) for analogous diagrams of two additional systems with nearly identical initial conditions.

1988). Two substellar companions have been detected around the G6V star HD 202206, with minimum masses (M sin i) of 17.4 MJ at 0.83 AU and 2.44 MJ at 2.55 AU (Udry et al. 2004). The inner companion is so massive that it is considered to be a brown dwarf, and it is likely that the outer companion formed from within a circumbinary (star-brown dwarf) disk (Correia et al. 2005). Planets have not been detected in P-type orbits around main-sequence binary stars, but short-period binaries are not included in precise Doppler radial-velocity search programs because of their complex and varying spectra.

The vast majority of theoretical effort to understand the formation of planetary systems has concentrated on isolated stars like our Sun. Binary star systems present a much higher dimensional phase space to cover (stellar mass ratio and orbital parameters), and orbital calculations in binary systems are more complicated than in systems that have one dominant mass. Nonetheless, zeroth-order questions about the dynamics of terrestrial planetary growth around single stars are now sufficiently well understood that it is worthwhile to investigate how the process of terrestrial planet growth differs in binary star systems.

The initial stages of terrestrial planet growth have been studied for gas-free circum-primary disks around 1 Mq stars that have binary companions with masses in the range 0.1-1 Mq by Whitmire et al. (1998) and for a gas-rich disk around a Centauri A by Marzari & Scholl (2000). Kortenkamp & Wetherill (2000) investigated this stage in the analogous problem of terrestrial planet growth within a gaseous disk containing preexisting giant planets. Gas drag acts to reduce inclinations and align eccentricities of small solid bodies within binary star systems, thereby facilitating planetesimal formation. Planetesimals that are favorably located to survive this stage are likely to be less e 0.8

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Figure 3. Same as Figure 2, except that the initial position of one of the planetesimals was moved by one meter along the direction of the orbit (simulation A«15_4 in Quintana et al. 2002). The differences between the simulations are produced by deterministic chaos, which implies that results of planetary accretion are extremely sensitive to changes in initial conditions. Thus, results are only valid in a statistical sense, and several simulations with very similar initial conditions must be run in order to adequately sample the distribution of possible outcomes. See Quintana (2004) for analogous diagrams of two additional systems with nearly identical initial conditions.

affected by the binary companion in the runaway and oligarchic growth stages, so they are probably able to grow into planetary embryos.

Quintana et al. (2002) performed dynamical simulations of the growth from planetary embryos into planets around each star within the a Centauri AB binary star system. These simulations begin with an initial disk composed of 140 planetesimals each of mass 0.00933 M® and 14 planetary embryos each of mass 0.0933 M®. The initial masses and orbital parameters of the planetesimals and embryos were virtually identical to those used for the most 'successful' simulations of terrestrial planet growth in our Solar System (Chambers 2001). Planets with orbits similar to the giant planets within our Solar System could not be present in the a Centauri system. Nonetheless, if a planet formed near 1 AU, it could potentially survive for eons. Quintana et al. found that when the disk was inclined to the binary orbit by up to 30° (or when the initial inclination was equal to 180°), three to five terrestrial planets formed, and their configuration resembled that of the planets in our Solar System (Figs. 2 and 3). In contrast, terrestrial planet growth around a star lacking both stellar and giant planet companions is slower and extends to larger semi-major axis for the same initial disk parameters. When the disk was initially inclined to the binary orbit by 45° or 60°, a substantial fraction of the disk particles were lost to the inner star, and typically only one or two planets of significant size remained at the end of the calculation (Fig. 4). Complementary simulations of terrestrial planet growth around a Centauri A by Barbieri et al. (2002), who varied the initial distribution of planetesimals substantially, yielded results that are consistent with those of Quintana et al. A study of terrestrial planet growth around individual components

Figure 4. The temporal evolution of our standard planetesimal disk centered around a Cen A, with its midplane initially inclined at i = 60° to the stellar orbit, is shown here (simulation Ai60l_4 in Quintana et al. 2002). The binary companion's high initial inclination causes large variations in the eccentricity of each planetesimal and embryo, and most of the mass is perturbed into the central star within the first few million years. An evolution plot for a simulation with nearly identical initial conditions that yields a smaller single planet is shown in Figure 6 of Quintana et al., and one for a simulation that ends up with a planet plus two planetesimals is shown by Lissauer et al. (2004).

in wide binary systems with stellar properties different from the a Centauri system is currently in progress; see Lissauer et al. (2004) for some preliminary results.

Quintana & Lissauer (2006) have performed an analogous investigation of the late stages of planetary growth in P-type orbits about close binary stars. Terrestrial planets similar to those formed in simulations of accretion around the Sun with giant planets perturbing the system can form around sufficiently tight binary stars. Increasing the initial binary eccentricity eB yields terrestrial planet systems that tend to be more sparce and have more orbitally diverse orbits. Binary stars with apastron distance QB = aB (1 + eB) ^ 0.2 AU, where aB is the initial binary semi-major axis and the eB is initial binary eccentricity, do not, statistically, have very different effects on the planetary accretion disk under study (Fig. 5). The effect of the stellar perturbations on the planetesimal disk, however, become evident in simulations with aB = 0.2 AU and eB = 0.5, and in systems with aB > 0.2 AU. From 1-2 terrestrial planets (more massive than the planet Mercury) formed in systems with aB > 0.2 AU (Fig. 6), and more than half of the initial planetesimal/embryo disk mass was ejected from these systems.

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