The Stability of Planets in the Alpha Centauri System

Abstract

This paper investigates the long-term orbital stability of small bodies near the central binary of the Alpha Centauri system. Test particles on circular orbits are integrated in the field of this binary for 32 000 binary periods or approximately 2.5 Myr. In the region exterior to the binary, particles with semi-major axes less than roughly three times the binary's semi-major axis a b are unstable. Inside the binary, particles are unstable if further than 0.2 a b from the primary, with stablility closer in a strong function of inclination: orbits inclined near 90 • are unstable in as close as 0.01 a b from either star. METHOD AND MODELS

Symplectic Integrator Algorithms for Modeling Planetary Accretion in Binary Star Systems

“…Particles with 3 AU < a < 8 AU survived longer but ultimately became unstable, with the time required to become unstable generally increasing as a decreased. In this simulation, all particles with a 2.76 AU remained stable throughout the integration, which agrees with the result of Wiegert & Holman (1997). This is indicated by the line labeled a crit in the top panel of Figure 3.…”

“…The bottom panel of Figure 3 shows the critical semimajor axis as a function of initial inclination in our integrations and those of Wiegert & Holman (1997). In general the agreement is good, although in some cases particles are found to be unstable in one of the simulations but not the other.…”

“…Test-particle orbits in binary systems can be integrated with the standard symplectic mapping technique using Jacobi coordinates (e.g., Wiegert & Holman 1997;Holman & Wiegert 1999). However, to integrate close encounters, we need to incorporate the special procedures used by Duncan et al (1998) or Chambers (1999.…”

The planet search program at the ESO Coudé Echelle spectrometer

“…In Endl et al (2001a), Paper II of this series, we have combined the CES limits with the results from the dynamical stability study of Wiegert & Holman (1997) which led to strong constraints for the presence of giant planets orbiting α Cen A or B. Upper limits for giant planets around the third member of the α Centauri system, Prox Cen, based on the results of a different RV analysis of the CES data were presented in Kürster et al (1999b).…”

The Texas High-Precision Radial-velocity Programs

“…Orbital stability calculations (Wiegert & Holman 1997) indicate that stable planetary orbits can exist in a wide variety of binary systems. Data on three such systems are shown in Figure 1.…”