On the effects of secular resonances on the dynamical evolution and orbital architecture of planetary systems in binary stars

It is widely known that the secular resonances of giant planets have played fundamental roles in the formation and dynamical evolution of the inner Solar System. These resonances have shaped the architecture of the asteroid belt [1,2], and have had significant contributions to the final mass, water content, and orbital architecture of terrestrial planets [3,4]. The successful detection of circumstellar planets in moderately close binary stars (i.e., binaries with separations smaller than 40 AU) in the past two decades has raised the question that, how these secular resonances appear and operate when the system is subject to the perturbation of a secondary star. We have launched an expansive project on this topic where in a three-article series [5,6,7], we have demonstrated how secular resonances of giant planets appear in binary star systems, and how they affect the formation and orbital evolution of planets interior to their orbits. Using the concept of generalized disturbing function, we have derived the formula for the locations of secular resonances in binary stars with two giant planets, and have shown that in systems where the perturbation of the secondary star is stronger, the locations of secular resonances are farther way from the primary and closer to the giant planets. The latter indicates that in these systems, the secular resonances have larger areas to migrate, and therefore, affect the dynamics of the system more strongly [6]. The most important result obtained from our study is that the perturbation of the secondary star suppresses the effects of secular resonances.

To investigate the effects of secular resonances on the orbital architecture of the system, we also simulated the late stage of terrestrial planet formation for different types of the secondary, and different orbital elements of the binary and giant planets. Results demonstrate that terrestrial planet formation can indeed proceed constructively in such systems; however, as predicted by the general theory, secular resonances are suppressed and do not contribute to the formation process. It is in fact the mean-motion resonances of the inner giant planet that drive the dynamics of the protoplanetary disk, and the mass and orbital architecture of the final bodies. Simulations also show that in the majority of the cases, the final systems contain only one terrestrial planet with a mass of 0.6 - 1.7 Earth masses. Multiple planets appear in rare occasions in the of form Earth-Mars analogs with the smaller planet in an exterior orbit. When giant planets are in larger orbits, the number of these double-planet systems increases and their planets become more massive. Results also show that when the orbits of the giant planets carry inclinations, while secular resonances are still suppressed, mean-motion resonances are strongly enhanced, drastically reducing the efficacy of the formation process. We present details of our simulations and discuss the implications of their results [7].

[1] Milani, A. & Kneževic, Z. 1992, Icarus, 98, 211

[2] Milani, A. & Kneževic, Z. 1994, Icarus, 107, 219

[3] Levison, H. F. & Agnor, c. 2003, AJ, 125, 2692

[4] Haghighipour, N. & Winter, O. C. 2016, Cel. Mech. Dyn. Ast., 124, 235

[5] Andrews, M. & Haghighipour, N. 2024, Proc. IAUS, 382, 116-122

[6] Haghighipour, N. & Andrews, M. 2025a, ApJ, in press

[7] Haghighipour, N. & Andrews, M. 2025b, ApJ, in press