Using an updated collision model, we conduct a suite of high resolution N-body integrations to probe the relationship between giant planet mass, and terrestrial planet formation and system architecture. We vary the mass of the planets that reside at Jupiter's and Saturn's orbit and examine the effects on the interior terrestrial system. We find that massive giant planets are more likely to eject material from the outer edge of the terrestrial disk and produce terrestrial planets that are on smaller, more circular orbits. We do not find a strong correlation between exterior giant planet mass and the number of Earth analogues (analogous in mass and semi-major axis) produced in the system. These results allow us to make predictions on the nature of terrestrial planets orbiting distant Sun-like star systems that harbor giant planet companions on long orbits-systems which will be a priority for NASA's upcoming Wide-Field Infrared Survey Telescope (WFIRST) mission.

With n-body simulations, we model terrestrial circumbinary planet (CBP) formation with an initial surface density profile motivated by hydrodynamic circumbinary gas disc simulations. The binary plays an important role in shaping the initial distribution of bodies. After the gas disc has dissipated, the torque from the binary speeds up the planet formation process by promoting body-body interactions but also drives the ejection of planet building material from the system at an early time. Fewer but more massive planets form around a close binary compared to a single star system. A sufficiently wide or eccentric binary can prohibit terrestrial planet formation. Eccentric binaries and exterior giant planets exacerbate these effects as they both reduce the radial range of the stable orbits. However, with a large enough stable region, the planets that do form are more massive, more eccentric and more inclined. The giant planets remain on stable orbits in all our simulations suggesting that giant planets are long-lived in planetary systems once they are formed.

A particle orbiting a misaligned eccentric orbit binary undergoes nodal precession either around the binary angular momentum vector (a circulating orbit) or around a stationary inclination (a librating orbit). In the absence of general relativity (GR), the stationary inclination is inclined by 90° to the binary angular momentum vector (aligned with the binary eccentricity vector) and does not depend on the particle semimajor axis. GR causes apsidal precession of the binary orbit. Close to the binary, the behavior of the particle is not significantly affected, and a librating particle precesses with the binary. However, we find that the stationary inclination and the minimum inclination required for libration both increase with the particle semimajor axis. There is a critical radius beyond which there are no librating orbits, only circulating orbits, and therefore there is a maximum orbital radius for a stationary polar-orbiting body. The critical radius is within planet-forming regions around binaries with a semimajor axis ≲1 au. This has implications for the search for misaligned circumbinary planets and the radial extent of polar circumbinary disks.

All circumbinary planets (CBPs) currently detected are in orbits that are almost coplanar to the binary orbit. While misaligned CBPs are more difficult to detect, observations of polar-aligned circumbinary gas and debris disks around eccentric binaries suggest that polar planet formation may be possible. A polar-aligned planet has a stable orbit that is inclined by 90° to the orbital plane of the binary with an angular momentum vector that is aligned to the binary eccentricity vector. With n-body simulations we model polar terrestrial planet formation using hydrodynamic gas disk simulations to motivate the initial particle distribution. Terrestrial planet formation around an eccentric binary is more likely in a polar alignment than in a coplanar alignment. Similar planetary systems form in a polar alignment around an eccentric binary and a coplanar alignment around a circular binary. The polar planetary systems are stable even with the effects of general relativity. Planetary orbits around an eccentric binary exhibit tilt and eccentricity oscillations at all inclinations; however, the oscillations are larger in the coplanar case than the polar case. We suggest that polar-aligned terrestrial planets will be found in the future.

Exoplanets orbiting in the habitable zone around M dwarf stars have been prime targets in the search for life due to the long lifetimes of the host star, the prominence of such stars in the galaxy, and the apparent excess of terrestrial planets found around M dwarfs. However, the heightened stellar activity of M dwarfs and the often tidally locked planets in these systems have raised questions about the habitability of these planets. In this Letter we examine another significant challenge that may exist: these systems seem to lack the architecture necessary to deliver asteroids to the habitable terrestrial planets, and asteroid impacts may play a crucial role in the origin of life. The most widely accepted mechanism for producing a stable asteroid belt and the late-stage delivery of asteroids after gas disk dissipation requires a giant planet exterior to the snow-line radius. We show that none of the observed systems with planets in the habitable zone of their star also contain a giant planet and therefore are unlikely to have stable asteroid belts. We consider the locations of observed giant planets relative to the snow-line radius as a function of stellar mass and find that there is a population of giant planets outside of the snow-line radius around M dwarfs. Therefore, asteroid belt formation around M dwarfs is generally possible. However, we find that multiplanetary system architectures around M dwarfs can be quite different from those around more massive stars.