The formation efficiency of close-in planets via Lidov–Kozai migration: analytic calculations

Abstract

Lidov-Kozai oscillations of planets in stellar binaries, combined with tidal dissipation, can lead to the formation of hot Jupiters (HJs) or tidal disruption of planets. Recent population synthesis studies have found that the fraction of systems resulting in HJs (F HJ ) depends strongly on the planet mass, host stellar type and tidal dissipation strength, while the total migration fraction F mig = F HJ + F dis (including both HJ formation and tidal disruption) exhibits much weaker dependence. We present an analytical method for calculating F HJ and F mig in the Lidov-Kozai migration scenario. The key ingredient of our method is to determine the critical initial planet-binary inclination angle that drives the planet to reach sufficiently large eccentricity for efficient tidal dissipation or disruption. This calculation includes the effects of octupole potential and short-range forces on the planet. Our analytical method reproduces the resulting planet migration/disruption fractions from population synthesis, and can be easily implemented for various planet, stellar/companion types, and for different distributions of initial planetary semi-major axes, binary separations and eccentricities. We extend our calculations to planets in the super-Earth mass range and discuss the conditions for such planets to survive Lidov-Kozai migration and form close-in rocky planets.

Chaotic Tides in Migrating Gas Giants: Forming Hot and Transient Warm Jupiters via Lidov-Kozai Migration

“…Fmig = 0.77Nmig/Nrun with Nmig the number of systems that displayed chaotic tidal migration and Nrun the total number of runs. For 1MJ , 1Rp planets, the HJ formation percentage from our population synthesis is larger than the value obtained for standard LK migration by a factor of ∼ 1.6 (3.9 % vs 2.4 %); see(ASL16; Muñoz et al 2016).…”

“…Indeed, several aspects of our results presented in this paper can be applied to other flavours of high-e migration (see Teyssandier et al 2018, which studies dynamical tides in the "secular chaos" scenario). Comparing to our previous study of LK migration with static tides (Anderson et al 2016;Muñoz et al 2016), we show that including chaotic tides leads to a number of "favorable" features for the formation of close-in giant planets: e.g., it naturally produces eccentric WJs on short timescales ( 10 − 100 Myrs) and speeds up the formation of HJs; it generates a wider HJ period distribution; and it prevents some gas giants from undergoing tidal disruption, thereby increase the HJ formation fraction. Overall, chaotic tides make high-e migration a more promising mechanism for producing HJs…”

“…10. In the standard LK migration scenario (with static tides), a large fraction of migrated giant planets are tidally disrupted because r p,dis can be quite close to rp,ST; moreover, Saturn-mass planets can rarely migrate successfully via LK oscillations and static tides because r p,dis rp,ST (ASL16, Muñoz et al 2016). In contrast, with chaotic tides, there is always a region of parameter space where chaotic tidal migration is possible without disruption (rp,crit > r p,dis ; see Fig.…”

“…14 shows that changing the properties of the gas giant has little effect on the parameter space that produces eccentric WJs. Unlike standard LK migration with static tides, where systems with Mp = 0.3MJ produce hot Saturns at a rate of 0.5% (assuming ∆tL = 1 s) after evolving for 5 Gyr (see ASL16, Muñoz et al 2016), chaotic tides allow low-mass planets to survive high-eccentricity migration without suffering tidal disruption, and produce hot Saturns at a rate of about 2.2% after only 1 Gyr.…”

On the formation of hot and warm Jupiters via secular high-eccentricity migration in stellar triples

“…For reference, and in order to investigate the differences, we also carried out simulations of a planet in a stellar binary mimicking previous studies of high-e migration in stellar binaries (Wu & Murray 2003;Fabrycky & Tremaine 2007;Naoz et al 2012;Petrovich 2015a;Anderson et al 2016;Petrovich & Tremaine 2016). With some approximations, high-e migration fractions in stellar binaries can also be calculated analytically (Muñoz et al 2016).…”