Secular evolution on hierarchical three body systems

Planets and disks have been observed around binary stars both in circumstellar and in circumbinary configuration. Statistical trends have been stablished for the former case. For example, observations show that the ocurrence rate of planets increases with the binary separation making it indistinguishable from the single-star case for values beyond 200 au. The dynamics of planets in circumstellar and circumbinary configuration is expected to be richer than in the single-star case.

In my masters research project, I studied the secular dynamics of young circumstellar planets in binary systems. To what extent the change in stellar bulk properties (mass, radius, and luminosity) during the pre-main-sequence modifies the secular dynamics of the planet? To answer this question, I derived formulas up to octupolar order for the equations of motion of the hierarchical system including the conservative terms due to gravity, the non-conservative terms due to non-sphericity of the bodies and also due to tides, and a general relativity correction to the argument of the pericenter motion. Those were implemented on C-based modular code (SecDev3B) which integrates the equations of motion updating the stellar bulk parameters at each timestep from the output of stellar evolutionary codes.

I revisited the secular evolution of the highly eccentric planet HD 80606b assuming constant stellar properties and found that the timescale of evolution differs greatly when one includes the octupolar terms because those induce additional modulations on the eccentricity and semi-major axis evolution. Using stellar evolution tracks, I simulated a hypothetical circumstellar planet on a \(0.6 \ M_\odot \ (\times 2)\) binary and found that the stellar contraction decreases by a factor of two the time it would take for the orbit of the planet to decay to a half of its initial value. We conclude that the effect of stellar evolution during the pre-main-sequence has the potential to alter the orbital configuration of planets in binary systems

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