Formation and evolution of the two 4/3 resonant giants planets in HD 200964

Abstract

Context. It has been suggested that HD 200964 is the first exoplanetary system with two Jovian planets evolving in the 4/3 meanmotion resonance (MMR). Previous scenarios to simulate the formation of two giant planets in the stable 4/3 resonance configuration have failed. Moreover, the orbital parameters available in the literature point out an unstable configuration of the planetary pair. Aims. The purpose of this paper is i) to determine the orbits of the planets from the radial velocity measurements and update the value of the stellar mass (1.57 M ); ii) to analyse the stability of the planetary evolution in the vicinity and inside the 4/3 MMR; and iii) to elaborate a possible scenario for the formation of systems in the 4/3 MMR. Methods. We use a previous model to simulate the formation of the stable planetary pair trapped inside the 4/3 resonance. Our scenario includes an interaction between the type I and type II of migration, planetary growth and stellar evolution from the main sequence to the sub-giant branch. The redetermination of the orbits is done using a biased Monte Carlo procedure, while the planetary dynamics is studied using numerical tools, such as dynamical maps and dynamical power spectra. Results. The results of the formation simulations are able to very closely reproduce the 4/3 resonant dynamics of the best-fit configuration obtained in this paper. Moreover, the confidence interval of the fit matches well with the very narrow stable region of the 4/3 MMR. Conclusions. The formation process of the HD 200964 system is very sensitive to the planetary masses and protoplanetary disk parameters. Only a thin, flat disk allows the embryo-sized planets to reach the 4/3 resonant configuration. The stable evolution of the resonant planets is also sensitive to the mass of the central star, because of overlapping high-order resonances inside the 4/3 resonance. Regardless of the very narrow domain of stable motion, the confidence interval of our fit closely matches the stability area.

Precise radial velocities of giant stars XIII. A second Jupiter orbiting in 4:3 resonance in the 7 CMa system

“…The resonant angle of the first planet circulates from 0 • to 360 • , while σ c is librating around 180 • . The confinement of σ c around 180 • shows that it is the truly resonant librating angle of the 7 CMa system, as shown previously for the HD 200964 system by Tadeu dos Santos et al (2015). Therefore, we can conclude that the two-planet system is effectively trapped in the narrow stable region of the 4:3 mean motion resonance and that the stability analysis reveals the true configuration of the system.…”

“…Rein et al (2012) reached the same conclusions using hydrodynamical simulations of convergent migration and in-situ formation. On the other hand, Tadeu dos Santos et al (2015) were able to reproduce the formation process of HD 200964 using models that contained an interaction between the type I and type II of migration, planetary growth and stellar evolution from the main sequence to the sub-giant branch. However, the authors pointed out that the formation process is very sensitive to the planetary masses and protoplanetary disk parameters, where only a thin, vertically isothermal and laminar disk, with a nearly constant surface density profile allows the embryo-sized planets to reach the 4:3 resonant configuration.…”

Speeding past planets? Asteroids radiatively propelled by giant branch Yarkovsky effects

“…As the value of p increases, and the configuration approaches a co-orbital state, the probability of capture decreases. Nevertheless, Tadeu dos Santos et al (2015) illustrated how planets can bypass -or migrate throughthe 2:1 and 3:2 mean motion resonances to become trapped in the 4:3 mean motion resonance. Similarly, figures 9 and 7 of Papaloizou & Szuszkiewicz (2005) respectively illustrated how entrapment into the 6:5 and 9:8 mean motion resonances may be possible; Quillen, et al (2013)…”

Two Jovian Planets around the Giant Star HD 202696: A Growing Population of Packed Massive Planetary Pairs around Massive Stars?

“…The HD 200964 system is similar to 24 Sex in terms of stellar mass and minimum planetary masses, but it has a much more compact orbital configuration, with periods of P b ≈ 610 and P c ≈ 830 days. The HD 200964 system is only stable if the orbits are in a 4:3 MMR (Wittenmyer et al 2012;Tadeu dos Santos et al 2015).…”