Stability of a planet in the HD 41004 binary system
Satyal et al
The Hill stability criterion is applied to analyse the stability of a planet in the binary star system of HD 41004 AB, with the primary and secondary separated by 22 AU, and masses of 0.7 M⊙ and 0.4 M⊙, respectively. The primary hosts one planet in an S-type orbit, and the secondary hosts a brown dwarf (18.64 MJ) on a relatively close orbit, 0.0177 AU, thereby forming another binary pair within this binary system. This star-brown dwarf pair (HD 41004 B+Bb) is considered a single body during our numerical calculations, while the dynamics of the planet around the primary, HD 41004 Ab, is studied in different phase-spaces. HD 41004 Ab is a 2.6 MJ planet orbiting at the distance of 1.7 AU with orbital eccentricity 0.39. For the purpose of this study, the system is reduced to a three-body problem and is solved numerically as the elliptic restricted three-body problem (ERTBP). The Hill stability function is used as a chaos indicator to configure and analyse the orbital stability of the planet, HD 41004 Ab. The indicator has been effective in measuring the planet's orbital perturbation due to the secondary star during its periastron passage. The calculated Hill stability time series of the planet for the coplanar case shows the stable and quasi-periodic orbits for at least ten million years. For the reduced ERTBP the stability of the system is also studied for different values of planet's orbital inclination with the binary plane. Also, by recording the planet's ejection time from the system or collision time with a star during the integration period, stability of the system is analysed in a bigger phase-space of the planet's orbital inclination, ≤ 90°, and its semimajor axis, 1.65–1.75 AU. Based on our analysis it is found that the system can maintain a stable configuration for the planet's orbital inclination as high as 65° relative to the binary plane. The results from the Hill stability criterion and the planet's dynamical lifetime map are found to be consistent with each other.