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Fig. 9.14. Interferometric observation of the binary system L1551 (Rodriguez et al., 1998). Two compact sources are evident in the map. The separation of the binary is 45 AU and the disk around each core extends to approximately 10 AU.

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Despite the observational evidence in support of the existence of planet-forming environments in moderately close binary star systems, the perturbative effect of the binary companion may not always favor planet formation. For instance, as shown by Nelson (2000), giant planet formation cannot proceed through the disk instability mechanism (Boss, 2000) around the primary of a binary star system with separation of ~ 50 AU. Also, when forming planetary embryos, as shown by Heppenheimer (1978), Whitmire et al. (1998), and Thebault et al. (2004), the perturbation of the secondary star may increase the relative velocities of planetesimals and cause their collisions to result in breakage and fragmentation (Fig. 9.15). Results of the studies by these authors suggest that planetesimal accretion will be efficient only in binaries with large separation [50 AU as indicated by Heppenheimer (1978), 26 AU as shown by Whitmire et al. (1998), and 100 AU as reported by Mayer et al. (2005)]. Finally, in a binary star system, the stellar companion may create unstable regions where the building blocks of planets will not maintain their orbits and, as a result, planet formation will be inhibited (Whitmire et al., 1998).

Interestingly, despite all these difficulties, numerical simulations have shown that it may indeed be possible to form giant and/or terrestrial planets in and around a dual-star system. Recent simulations by Boss (2006), and Mayer, Boss & Nelson (2007) indicate that Jupiter-like planets can form around the primary of a binary

distance to the Star (A.U.)

Fig. 9.15. Graphs of the evolution of eccentricity (top) and encounter velocities (bottom) for planetesimals at the region between 0.3 and 5 AU from the primary of 7 Cephei (Thebault et al., 2004). The planetesimals disk in the bottom simulation was initially at its truncated radius of 4 AU. As shown here, the perturbative effect of the secondary star increases the eccentricities and relative velocities of these objects.

distance to the Star (A.U.)

Fig. 9.15. Graphs of the evolution of eccentricity (top) and encounter velocities (bottom) for planetesimals at the region between 0.3 and 5 AU from the primary of 7 Cephei (Thebault et al., 2004). The planetesimals disk in the bottom simulation was initially at its truncated radius of 4 AU. As shown here, the perturbative effect of the secondary star increases the eccentricities and relative velocities of these objects.

Fig. 9.16. Giant planet formation via disk instability mechanism in a binary system. The separation of the binary is 120 AU and it was initially on a circular orbit. The mass of each disk is 0.1 solar-masses. The snap shot was taken 160 years after the start of the simulations. Figure courtesy of L. Mayer, A. Boss and A. Nelson.

star system via gravitational instability in a marginally unstable circumprimary disk (Fig. 9.16). On the other hand, as shown by Thebault et al. (2004), the core accretion mechanism may also be able to form giant planets around the primary of a binary star. However, as the results of their simulations for planet formation in the y Cephei system indicate, the semimajor axis of the final gas-giant planet may be smaller than its observed value.

In regard to the formation of terrestrial planets in binary systems, in a series of articles, Quintana and her colleagues integrated the orbits of a few hundred Moon- to Mars-sized objects and showed that terrestrial-class objects can form in and around binaries (Quintana et al., 2002; Lissauer et al., 2004; Quintana & Lissauer, 2006; Quintana et al., 2007). Figure 9.17 shows the results of some of their simulations. As shown here, depending on the mass-ratio of the binary and the initial values of its orbital parameters, in a few hundred million years, terrestrial planets can form around a close (0.01 to 0.1 AU) binary star system.

Quintana and colleagues also studied terrestrial planet formation in binaries with larger separations (Quintana et al., 2007). Figure 9.18 shows the results of their simulations for a binary with a separation of 20 AU. Similar to Fig. 9.17, terrestrial-type objects are formed around the primary of the binary in a few hundred million years. Statistical analysis of their results, as shown in Fig. 9.19, 9.20, and 9.21 indicate that, as expected in binaries with larger perihelia, where disk truncation has been smaller and more planet-forming material is available, terrestrial planet formation is efficient and the number of final terrestrial planets is large. The

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0,5 1.0 1.5 2.0 2.5 0.5 10 15 2.0 2.5 0.5 1.0 1.5 2.0 2.5 a (AU) n (AU) a (AU)

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Fig. 9.17. Terrestrial planet formation around a close binary system (Quintana & Lis-sauer, 2006). The binary is circular and its separation is 0.05 AU. Each star of the binary has a mass of 0.5 solar-masses. A Jupiter-like planet has also been included in the simulation. The circles represent planetary embryos and planetesimals with radii that are proportional to their physical sizes. As shown here, the perturbative effect of the outer giant planet excites the orbits of the bodies at the outer edge of the disk and causes radial mixing as well as truncation. Within the first 100 Myr, several terrestrial-class objects are formed around the binary system.

results of simulations by Quintana et al. (2007) also indicate that in a binary with a periastron distance larger than 10 AU, terrestrial planet formation can proceed efficiently in a region within 2 AU of the primary star. In binaries with periastra smaller than 5 AU, this region may be limited to inside 1 AU (Fig. 9.20).

Despite the destructive role of the binary companion in increasing the relative velocities of planetesimals, which causes their collisions to result in erosion, this efficiency of terrestrial planet formation in binary systems may be attributed to the fact that the effect of the binary companion on increasing the relative velocities of planetesimals can be counterbalanced by dissipative forces such as gas-drag and dynamical friction (Marzari et al., 1997; Marzari & Scholl, 2000). The combination of the drag force of the gas and the gravitational force of the secondary star may result in the alignment of the periastra of planetesimals and increases the efficiency of their accretion by reducing their relative velocities. This is a process that is more effective when the sizes of the two colliding planetesimals are comparable and small. For colliding bodies with different sizes, depending on the size distribution of small

Fig. 9.18. Terrestrial planet formation around the primary of a binary star system (Quintana et al., 2007). The stars of the binary are 0.5 solar-masses with semimajor axis of 20 AU. The eccentricity of the binary is 0.75 (left column), 0.625 (middle column), and 0.5 (right column). As shown here, in each simulation, two terrestrial-type objects are formed after 100 Myr. The last row shows the results of additional simulations of the same systems, with final results showing in black, gray and white, corresponding to different runs. The differences in the final assembly of the planetary system of each simulation are results of the stochasticity of this type of numerical integrations.

Fig. 9.18. Terrestrial planet formation around the primary of a binary star system (Quintana et al., 2007). The stars of the binary are 0.5 solar-masses with semimajor axis of 20 AU. The eccentricity of the binary is 0.75 (left column), 0.625 (middle column), and 0.5 (right column). As shown here, in each simulation, two terrestrial-type objects are formed after 100 Myr. The last row shows the results of additional simulations of the same systems, with final results showing in black, gray and white, corresponding to different runs. The differences in the final assembly of the planetary system of each simulation are results of the stochasticity of this type of numerical integrations.

objects, and the radius of each individual planetesimal, the process of the alignment of periastra may instead increase the relative velocities of the two objects, and cause their collisions to become eroding (Fig. 9.22, also see Thebault et al., 2006).

Simulations of terrestrial planet formation have also been extended to binaries with larger separations (20-40 AU) that also host a giant planet (Haghighipour & Raymond, 2007). As discussed in the next section, by numerically integrating the orbits of the binary, its giant planet, and a few hundred planetary embryos, these authors have shown that it is possible to form Earth-like objects, with considerable amount of water, in the habitable zone of the primary of a moderately close binary-planetary system.

Fig. 9.19. Graphs of the final masses of the terrestrial planets formed in systems of Fig. 9.18. The simulations have been run for three different masses of the binary stars. The red corresponds to simulations in a binary with 0.5 solar-masses stars, the blue represents results in a binary with 1 solar-mass stars, yellow is for a binary with a 1 solar-mass primary and a 0.5 solar-masses secondary, and black represents a binary with a 0.5 solarmasses primary and a 1 solar-mass secondary. These results show that despite the disk truncation in binaries with smaller perihelia, the average masses of the final planets are not significantly altered. (Quintana et al., 2007).

Fig. 9.19. Graphs of the final masses of the terrestrial planets formed in systems of Fig. 9.18. The simulations have been run for three different masses of the binary stars. The red corresponds to simulations in a binary with 0.5 solar-masses stars, the blue represents results in a binary with 1 solar-mass stars, yellow is for a binary with a 1 solar-mass primary and a 0.5 solar-masses secondary, and black represents a binary with a 0.5 solarmasses primary and a 1 solar-mass secondary. These results show that despite the disk truncation in binaries with smaller perihelia, the average masses of the final planets are not significantly altered. (Quintana et al., 2007).

Fig. 9.20. Graphs of the semimajor axis of the outermost planet of the simulations of Fig. 9.18. As shown here, while the outer edge of the disk is affected by the presence of the binary companion, the inner portion of the disk, where terrestrial planets are formed, stays unaffected by this object (Quintana et al., 2007).

Fig. 9.20. Graphs of the semimajor axis of the outermost planet of the simulations of Fig. 9.18. As shown here, while the outer edge of the disk is affected by the presence of the binary companion, the inner portion of the disk, where terrestrial planets are formed, stays unaffected by this object (Quintana et al., 2007).

Pinal Number of Planeta

Fig. 9.21. The number of final terrestrial-type planets formed in the binaries of Fig. 9.18. As expected, for a given binary mass-ratio, the number of terrestrial planets increases in systems with larger perihelia. This number also increases when the mass of the binary companion is smaller. (Quintana et al., 2007).

Pinal Number of Planeta

Fig. 9.21. The number of final terrestrial-type planets formed in the binaries of Fig. 9.18. As expected, for a given binary mass-ratio, the number of terrestrial planets increases in systems with larger perihelia. This number also increases when the mass of the binary companion is smaller. (Quintana et al., 2007).

Fig. 9.22. Encounter velocities of planetesimals with different sizes in a binary system with semimajor axis of 10 AU, eccentricity of 0.3, and mass-ratio of 0.5 (Thebault et al., 2006). The simulations include gas-drag. The vertical line shows the time of orbital crossing. As shown here, gas-drag lowers the encounter velocities of smaller equal-size planetesimals through the periastron alignment process.

Fig. 9.22. Encounter velocities of planetesimals with different sizes in a binary system with semimajor axis of 10 AU, eccentricity of 0.3, and mass-ratio of 0.5 (Thebault et al., 2006). The simulations include gas-drag. The vertical line shows the time of orbital crossing. As shown here, gas-drag lowers the encounter velocities of smaller equal-size planetesimals through the periastron alignment process.

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